TSTP Solution File: ITP106^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP106^2 : TPTP v8.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 22:51:55 EDT 2024
% Result : Theorem 68.49s 10.16s
% Output : Refutation 68.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : ITP106^2 : TPTP v8.2.0. Released v7.5.0.
% 0.06/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n028.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat May 18 15:16:22 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (16501)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.38 % (16504)WARNING: value z3 for option sas not known
% 0.17/0.38 % (16505)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.38 % (16503)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.38 % (16506)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.17/0.38 % (16504)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.17/0.38 % (16507)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.17/0.38 % (16508)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.38 % (16502)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.42 % (16508)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.44 % Exception at run slice level
% 0.17/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.44 % Exception at run slice level
% 0.17/0.44 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.45 % (16510)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.17/0.46 % (16511)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.17/0.46 % Exception at run slice level
% 0.17/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.48 % (16512)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.17/0.50 % (16510)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.51 % (16511)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.17/0.51 % Exception at run slice level
% 0.17/0.51 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.17/0.53 % (16513)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 65.95/9.84 % (16506)First to succeed.
% 68.15/10.15 % (16506)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-16501"
% 68.49/10.16 % (16506)Refutation found. Thanks to Tanya!
% 68.49/10.16 % SZS status Theorem for theBenchmark
% 68.49/10.16 % SZS output start Proof for theBenchmark
% 68.49/10.16 thf(type_def_5, type, partia1265057091ct_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(type_def_6, type, set: $tType > $tType).
% 68.49/10.16 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 68.49/10.16 thf(type_def_8, type, monoid_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(type_def_9, type, product_unit: $tType).
% 68.49/10.16 thf(type_def_10, type, nat: $tType).
% 68.49/10.16 thf(type_def_11, type, product_prod: ($tType * $tType) > $tType).
% 68.49/10.16 thf(type_def_12, type, ring_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(type_def_13, type, a: $tType).
% 68.49/10.16 thf(type_def_14, type, b: $tType).
% 68.49/10.16 thf(type_def_15, type, eq_eq_object_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(type_def_16, type, int: $tType).
% 68.49/10.16 thf(func_def_0, type, partia1265057091ct_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(func_def_1, type, eq_eq_object_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(func_def_2, type, monoid_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(func_def_3, type, ring_ext: ($tType * $tType) > $tType).
% 68.49/10.16 thf(func_def_4, type, product_unit: $tType).
% 68.49/10.16 thf(func_def_5, type, product_prod: ($tType * $tType) > $tType).
% 68.49/10.16 thf(func_def_6, type, set: $tType > $tType).
% 68.49/10.16 thf(func_def_7, type, nat: $tType).
% 68.49/10.16 thf(func_def_8, type, int: $tType).
% 68.49/10.16 thf(func_def_9, type, b: $tType).
% 68.49/10.16 thf(func_def_10, type, a: $tType).
% 68.49/10.16 thf(func_def_11, type, group_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_12, type, semiring_1: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_13, type, ab_group_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_14, type, semiring_char_0: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_15, type, semigroup_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_16, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_17, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_18, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_19, type, cancel1352612707id_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_20, type, cancel146912293up_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_21, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 68.49/10.16 thf(func_def_22, type, partial_carrier: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,X1) > set(X0))).
% 68.49/10.16 thf(func_def_23, type, units: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,X1)) > set(X0))).
% 68.49/10.16 thf(func_def_24, type, comm_group: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,X1)) > $o)).
% 68.49/10.16 thf(func_def_25, type, group: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,X1)) > $o)).
% 68.49/10.16 thf(func_def_26, type, mult: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,X1)) > X0 > X0 > X0)).
% 68.49/10.16 thf(func_def_27, type, one: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,X1)) > X0)).
% 68.49/10.16 thf(func_def_28, type, units_of: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,X1)) > partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)))).
% 68.49/10.16 thf(func_def_29, type, minus_minus: !>[X0: $tType]:(X0 > X0 > X0)).
% 68.49/10.16 thf(func_def_30, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 68.49/10.16 thf(func_def_31, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 68.49/10.16 thf(func_def_32, type, suc: nat > nat).
% 68.49/10.16 thf(func_def_33, type, semiring_1_of_nat: !>[X0: $tType]:(nat > X0)).
% 68.49/10.16 thf(func_def_34, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod(X0,X1))).
% 68.49/10.16 thf(func_def_35, type, product_rec_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod(X0,X1) > X2)).
% 68.49/10.16 thf(func_def_36, type, a_inv: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > X0 > X0)).
% 68.49/10.16 thf(func_def_37, type, a_minus: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > X0 > X0 > X0)).
% 68.49/10.16 thf(func_def_38, type, abelian_group: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > $o)).
% 68.49/10.16 thf(func_def_39, type, add_pow: !>[X0: $tType, X1: $tType, X2: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > X2 > X0 > X0)).
% 68.49/10.16 thf(func_def_40, type, field: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > $o)).
% 68.49/10.16 thf(func_def_41, type, add: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > X0 > X0 > X0)).
% 68.49/10.16 thf(func_def_42, type, more: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > X1)).
% 68.49/10.16 thf(func_def_43, type, zero: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > X0)).
% 68.49/10.16 thf(func_def_44, type, semiring: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))) > $o)).
% 68.49/10.16 thf(func_def_45, type, collect: !>[X0: $tType]:((X0 > $o) > set(X0))).
% 68.49/10.16 thf(func_def_46, type, member: !>[X0: $tType]:(X0 > set(X0) > $o)).
% 68.49/10.16 thf(func_def_47, type, r: partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b)))).
% 68.49/10.16 thf(func_def_48, type, r2: a).
% 68.49/10.16 thf(func_def_49, type, r3: a).
% 68.49/10.16 thf(func_def_50, type, r4: a).
% 68.49/10.16 thf(func_def_51, type, rel: partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit))).
% 68.49/10.16 thf(func_def_52, type, s: a).
% 68.49/10.16 thf(func_def_53, type, s2: a).
% 68.49/10.16 thf(func_def_54, type, s3: a).
% 68.49/10.16 thf(func_def_58, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 68.49/10.16 thf(func_def_59, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 68.49/10.16 thf(func_def_60, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 68.49/10.16 thf(func_def_61, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 68.49/10.16 thf(func_def_62, type, vAND: $o > $o > $o).
% 68.49/10.16 thf(func_def_63, type, sP0: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > $o)).
% 68.49/10.16 thf(func_def_64, type, sP1: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > $o)).
% 68.49/10.16 thf(func_def_65, type, sP2: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > $o)).
% 68.49/10.16 thf(func_def_66, type, sP3: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > $o)).
% 68.49/10.16 thf(func_def_67, type, sP4: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > $o)).
% 68.49/10.16 thf(func_def_68, type, sK5: a).
% 68.49/10.16 thf(func_def_69, type, sK6: a).
% 68.49/10.16 thf(func_def_70, type, sK7: a > a).
% 68.49/10.16 thf(func_def_71, type, sK8: a > a).
% 68.49/10.16 thf(func_def_72, type, sK9: a > a).
% 68.49/10.16 thf(func_def_73, type, sK10: a > a).
% 68.49/10.16 thf(func_def_74, type, sK11: a > a).
% 68.49/10.16 thf(func_def_75, type, sK12: a > a).
% 68.49/10.16 thf(func_def_76, type, sK13: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 68.49/10.16 thf(func_def_77, type, sK14: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_78, type, sK15: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_79, type, sK16: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_80, type, sK17: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_81, type, sK18: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_82, type, sK19: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_83, type, sK20: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_84, type, sK21: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_85, type, sK22: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_86, type, sK23: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_87, type, sK24: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_88, type, sK25: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_89, type, sK26: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_90, type, sK27: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_91, type, sK28: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_92, type, sK29: !>[X0: $tType, X1: $tType]:(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_93, type, sK30: (nat > $o) > nat).
% 68.49/10.16 thf(func_def_94, type, sK31: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X0)).
% 68.49/10.16 thf(func_def_95, type, sK32: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X1)).
% 68.49/10.16 thf(func_def_96, type, sK33: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X0)).
% 68.49/10.16 thf(func_def_97, type, sK34: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > X1)).
% 68.49/10.16 thf(func_def_98, type, sK35: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 68.49/10.16 thf(func_def_99, type, sK36: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X1)).
% 68.49/10.16 thf(func_def_100, type, sK37: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X0)).
% 68.49/10.16 thf(func_def_101, type, sK38: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X1)).
% 68.49/10.16 thf(func_def_102, type, sK39: !>[X0: $tType, X1: $tType]:((product_prod(X1,X0) > $o) > X0)).
% 68.49/10.16 thf(func_def_103, type, sK40: !>[X0: $tType, X1: $tType]:(X1 > partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_104, type, sK41: !>[X0: $tType, X1: $tType]:(X1 > partia1265057091ct_ext(X1,monoid_ext(X1,X0)) > X1)).
% 68.49/10.16 thf(func_def_105, type, sK42: !>[X0: $tType, X1: $tType]:(X1 > partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))) > X1)).
% 68.49/10.16 thf(func_def_106, type, sK43: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,product_prod(X1,X2)) > X0)).
% 68.49/10.16 thf(func_def_107, type, sK44: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,product_prod(X1,X2)) > X1)).
% 68.49/10.16 thf(func_def_108, type, sK45: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,product_prod(X1,X2)) > X2)).
% 68.49/10.16 thf(func_def_109, type, sK46: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,product_prod(X1,X0)) > $o) > X2)).
% 68.49/10.16 thf(func_def_110, type, sK47: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,product_prod(X1,X0)) > $o) > X1)).
% 68.49/10.16 thf(func_def_111, type, sK48: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,product_prod(X1,X0)) > $o) > X0)).
% 68.49/10.16 thf(func_def_112, type, sK49: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0)).
% 68.49/10.16 thf(func_def_113, type, sK50: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1)).
% 68.49/10.16 thf(func_def_114, type, sK51: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2)).
% 68.49/10.16 thf(func_def_115, type, sK52: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3)).
% 68.49/10.16 thf(func_def_116, type, sK53: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X3)).
% 68.49/10.16 thf(func_def_117, type, sK54: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X2)).
% 68.49/10.16 thf(func_def_118, type, sK55: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X1)).
% 68.49/10.16 thf(func_def_119, type, sK56: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType]:((product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o) > X0)).
% 68.49/10.16 thf(func_def_120, type, sK57: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0)).
% 68.49/10.16 thf(func_def_121, type, sK58: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1)).
% 68.49/10.16 thf(func_def_122, type, sK59: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2)).
% 68.49/10.16 thf(func_def_123, type, sK60: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3)).
% 68.49/10.16 thf(func_def_124, type, sK61: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4)).
% 68.49/10.16 thf(func_def_125, type, sK62: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X4)).
% 68.49/10.16 thf(func_def_126, type, sK63: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X3)).
% 68.49/10.16 thf(func_def_127, type, sK64: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X2)).
% 68.49/10.16 thf(func_def_128, type, sK65: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X1)).
% 68.49/10.16 thf(func_def_129, type, sK66: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType]:((product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o) > X0)).
% 68.49/10.16 thf(func_def_130, type, sK67: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0)).
% 68.49/10.16 thf(func_def_131, type, sK68: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1)).
% 68.49/10.16 thf(func_def_132, type, sK69: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2)).
% 68.49/10.16 thf(func_def_133, type, sK70: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3)).
% 68.49/10.16 thf(func_def_134, type, sK71: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4)).
% 68.49/10.16 thf(func_def_135, type, sK72: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5)).
% 68.49/10.16 thf(func_def_136, type, sK73: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X5)).
% 68.49/10.16 thf(func_def_137, type, sK74: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X4)).
% 68.49/10.16 thf(func_def_138, type, sK75: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X3)).
% 68.49/10.16 thf(func_def_139, type, sK76: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X2)).
% 68.49/10.16 thf(func_def_140, type, sK77: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X1)).
% 68.49/10.16 thf(func_def_141, type, sK78: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType]:((product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o) > X0)).
% 68.49/10.16 thf(func_def_142, type, sK79: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X0)).
% 68.49/10.16 thf(func_def_143, type, sK80: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X1)).
% 68.49/10.16 thf(func_def_144, type, sK81: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X2)).
% 68.49/10.16 thf(func_def_145, type, sK82: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X3)).
% 68.49/10.16 thf(func_def_146, type, sK83: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X4)).
% 68.49/10.16 thf(func_def_147, type, sK84: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X5)).
% 68.49/10.16 thf(func_def_148, type, sK85: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))) > X6)).
% 68.49/10.16 thf(func_def_149, type, sK86: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X6)).
% 68.49/10.16 thf(func_def_150, type, sK87: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X5)).
% 68.49/10.16 thf(func_def_151, type, sK88: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X4)).
% 68.49/10.16 thf(func_def_152, type, sK89: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X3)).
% 68.49/10.16 thf(func_def_153, type, sK90: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X2)).
% 68.49/10.16 thf(func_def_154, type, sK91: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X1)).
% 68.49/10.16 thf(func_def_155, type, sK92: !>[X0: $tType, X1: $tType, X2: $tType, X3: $tType, X4: $tType, X5: $tType, X6: $tType]:((product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o) > X0)).
% 68.49/10.16 thf(func_def_157, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 68.49/10.16 thf(func_def_158, type, vOR: $o > $o > $o).
% 68.49/10.16 thf(func_def_159, type, vIMP: $o > $o > $o).
% 68.49/10.16 thf(func_def_160, type, vNOT: $o > $o).
% 68.49/10.16 thf(f52001,plain,(
% 68.49/10.16 $false),
% 68.49/10.16 inference(avatar_sat_refutation,[],[f1730,f1735,f1740,f1745,f1750,f1755,f1760,f1765,f1770,f1775,f1780,f1785,f1790,f1795,f1800,f1805,f1810,f1815,f1820,f1825,f1830,f1834,f1866,f1871,f1876,f1880,f1884,f1888,f1898,f1902,f1906,f1910,f1914,f1918,f1948,f1953,f1958,f1962,f1966,f1970,f1983,f1987,f1991,f1995,f1999,f2025,f2029,f2033,f2046,f2050,f2064,f2068,f2076,f2084,f2098,f2102,f2106,f2110,f2114,f2134,f2139,f2144,f2151,f2155,f2159,f2164,f2177,f2183,f2196,f2241,f2250,f2258,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2298,f2304,f2308,f2312,f2316,f2320,f2324,f2414,f2418,f2422,f2426,f2430,f2434,f2438,f2446,f2482,f2486,f2490,f2494,f2498,f2528,f2549,f2557,f2561,f2565,f2570,f2574,f2578,f2582,f2586,f2590,f2617,f2626,f2631,f2636,f2640,f2645,f2649,f2654,f2659,f2671,f2691,f2695,f2699,f2719,f2733,f2737,f2757,f2761,f2765,f2769,f2793,f2813,f2817,f2833,f2844,f2859,f2863,f2875,f2881,f2887,f2897,f2902,f2906,f2910,f2932,f2936,f2956,f2964,f2968,f2972,f3000,f3004,f3032,f3036,f3058,f3062,f3066,f3098,f3102,f3132,f3141,f3145,f3149,f3195,f3199,f3203,f3238,f3259,f3265,f3269,f3291,f3295,f3307,f3312,f3331,f3359,f3363,f3385,f3390,f3394,f3408,f3412,f3430,f3445,f3457,f3461,f3481,f3485,f3514,f3518,f3530,f3535,f3539,f3559,f3563,f3568,f3588,f3592,f3612,f3624,f3628,f3636,f3640,f3669,f3682,f3691,f3699,f3703,f3707,f3711,f3715,f3750,f3770,f3782,f3786,f3807,f3828,f3833,f3838,f3843,f3865,f3869,f3901,f3905,f3920,f3924,f3946,f3950,f3954,f3958,f3962,f4000,f4005,f4018,f4029,f4033,f4045,f4049,f4053,f4087,f4096,f4114,f4126,f4130,f4152,f4156,f4176,f4198,f4202,f4206,f4229,f4239,f4254,f4258,f4262,f4292,f4297,f4309,f4318,f4328,f4332,f4384,f4407,f4411,f4431,f4446,f4450,f4470,f4488,f4493,f4511,f4536,f4540,f4559,f4565,f4573,f4601,f4620,f4631,f4648,f4659,f4671,f4688,f4696,f4708,f4722,f4729,f4747,f4751,f4777,f4781,f4785,f4789,f4793,f4910,f4914,f4918,f4922,f5002,f5006,f5010,f5022,f5026,f5030,f5034,f5038,f5042,f5059,f5063,f5067,f5071,f5219,f5297,f5301,f5305,f5309,f5313,f5331,f5377,f5381,f5385,f5389,f5393,f5397,f5401,f5751,f5755,f5867,f5871,f5918,f5922,f5927,f5949,f5967,f6325,f6351,f6356,f6361,f6366,f6459,f6636,f6651,f6656,f6768,f6772,f6776,f6780,f6784,f6788,f6792,f6796,f6800,f6804,f6825,f7105,f7110,f7136,f7296,f7356,f7360,f7364,f7368,f7372,f7377,f7410,f7414,f7418,f7481,f7658,f7663,f7668,f7673,f7753,f7757,f7761,f7765,f7769,f7773,f7777,f7781,f7785,f7789,f7793,f7797,f7801,f7805,f7809,f7814,f7818,f8869,f9072,f9185,f9191,f9215,f9221,f9245,f9250,f9255,f9259,f9264,f9337,f9341,f9350,f9931,f9935,f9939,f9943,f9947,f9951,f9955,f9959,f10052,f10056,f10060,f10064,f10068,f10072,f10077,f10083,f10089,f10112,f10117,f10123,f10147,f10153,f11068,f13795,f13799,f13803,f13807,f13811,f13815,f13819,f13828,f13851,f15485,f15513,f15517,f15824,f15828,f15832,f15836,f15840,f15844,f15848,f16006,f16010,f16015,f16020,f16025,f16958,f17253,f17258,f17262,f17266,f17271,f17276,f17463,f17467,f17514,f17520,f17525,f17530,f17568,f17572,f17576,f17580,f17584,f17588,f17592,f17596,f17667,f17671,f17675,f17679,f17683,f19967,f20011,f20246,f20250,f20283,f20289,f20294,f20355,f20380,f20386,f20391,f20397,f20429,f20433,f20437,f20441,f20446,f20451,f22914,f22919,f22924,f22928,f22932,f22936,f22940,f22944,f22948,f22952,f22957,f22964,f22971,f22977,f22983,f22988,f22993,f22998,f23003,f23008,f23013,f23019,f23760,f24346,f24352,f24377,f24383,f24387,f24413,f24419,f24425,f24431,f24457,f24463,f24480,f24485,f24491,f24495,f24499,f24504,f24546,f24552,f24557,f24562,f24567,f24572,f24611,f24616,f24654,f24660,f24667,f24672,f24677,f24705,f24711,f24724,f24730,f24877,f24883,f24888,f25041,f25046,f25075,f25080,f25126,f25133,f25171,f25176,f25210,f25215,f25244,f25250,f25254,f25259,f25264,f25269,f25277,f25282,f25388,f25411,f25423,f25463,f25467,f25471,f25475,f25481,f25516,f25520,f25524,f25672,f25680,f25684,f25689,f25693,f25775,f25866,f25870,f25874,f25881,f25921,f25925,f25930,f25936,f25941,f26352,f26356,f26360,f26365,f26369,f26384,f26389,f26415,f26421,f26426,f26466,f26567,f26571,f26575,f26579,f26583,f26587,f26592,f26816,f26947,f26954,f26960,f26964,f27240,f27244,f27280,f27285,f27308,f27313,f27347,f27353,f27403,f27409,f27459,f27464,f27556,f27561,f27567,f27600,f27606,f27862,f27866,f27994,f28006,f28010,f28014,f28018,f28022,f28027,f28102,f28107,f28112,f28322,f28326,f28330,f28604,f28608,f28612,f28616,f28923,f28928,f28934,f28938,f29188,f29193,f29219,f29223,f29227,f29231,f29238,f29244,f29495,f29499,f29525,f29530,f29536,f29543,f29548,f29552,f29556,f29560,f29564,f29819,f29825,f29930,f29936,f30035,f30041,f30220,f30226,f30340,f30344,f30348,f30352,f30356,f30609,f30614,f30713,f30719,f30753,f30759,f30791,f30796,f30800,f30805,f30821,f30827,f30832,f30836,f30933,f30938,f30953,f30958,f30993,f30999,f31003,f31007,f31011,f31015,f31019,f31025,f31113,f31117,f31121,f31125,f31348,f31353,f31406,f31410,f31414,f31418,f31422,f31426,f31430,f32114,f32118,f32124,f32212,f32219,f32307,f32312,f32334,f32339,f32343,f32372,f32376,f32380,f32663,f32670,f32676,f32680,f32703,f32708,f32713,f32824,f32829,f32942,f32946,f32950,f32954,f33119,f33125,f33131,f33136,f33246,f33250,f33254,f33358,f33364,f33467,f33473,f33596,f33601,f33605,f33609,f33614,f33753,f33758,f33949,f34004,f34008,f34106,f34110,f34117,f34207,f34212,f34216,f34327,f34332,f34467,f34471,f34476,f34591,f34595,f34600,f34715,f34975,f34979,f34983,f34987,f34991,f35263,f35268,f35404,f35409,f35546,f35550,f35554,f35602,f35606,f35611,f35794,f35798,f35802,f35806,f35811,f35863,f35868,f35918,f35922,f36240,f36399,f36403,f36407,f36413,f36420,f36803,f37013,f37020,f37128,f37135,f37254,f37276,f37282,f37286,f37390,f37396,f37502,f37790,f37796,f37915,f37919,f37925,f38017,f38022,f38027,f38032,f38037,f38180,f38185,f38189,f38334,f38338,f38342,f38346,f38351,f38509,f38514,f38518,f38884,f38888,f38892,f39253,f39257,f39261,f39491,f39498,f39505,f39510,f39661,f39666,f39858,f39862,f39866,f39870,f40138,f40218,f40276,f40280,f40284,f40290,f40297,f40304,f40465,f40472,f40509,f40516,f40624,f40631,f40669,f40716,f40847,f40851,f40857,f40974,f40980,f41185,f41189,f41193,f41425,f41431,f41550,f41556,f41689,f41695,f41787,f41793,f41912,f42457,f42504,f42534,f42559,f42615,f42619,f42802,f43018,f43023,f43097,f43128,f43132,f43139,f43232,f43238,f43350,f43356,f43552,f44096,f44191,f44198,f44205,f44209,f44443,f44449,f44606,f44612,f44731,f44737,f44849,f44855,f44967,f45012,f45104,f45111,f45203,f45207,f45359,f45406,f45435,f45442,f45449,f45479,f45486,f45578,f45626,f45718,f45748,f45752,f45756,f45964,f45968,f45972,f45976,f45980,f46538,f46562,f46566,f46622,f47679,f47800,f48128,f48132,f48136,f48203,f48210,f48375,f48382,f48474,f48548,f48554,f48666,f48713,f48829,f48836,f48871,f48878,f48885,f48889,f49445,f49449,f49453,f49457,f49461,f49866,f49870,f49984,f49988,f50228,f50232,f50277,f50307,f50373,f50408,f50503,f50507,f50587,f50646,f50680,f50705,f50739,f50743,f50769,f50827,f50834,f50839,f50851,f50872,f50879,f50884,f50896,f50900,f50904,f50950,f50984,f50988,f50992,f50996,f51000,f51004,f51008,f51858,f51862,f51896,f51943,f51958,f51963,f51967,f51971,f51975,f52000])).
% 68.49/10.16 thf(f52000,plain,(
% 68.49/10.16 ~spl93_182 | ~spl93_223 | ~spl93_592 | ~spl93_1053),
% 68.49/10.16 inference(avatar_contradiction_clause,[],[f51999])).
% 68.49/10.16 thf(f51999,plain,(
% 68.49/10.16 $false | (~spl93_182 | ~spl93_223 | ~spl93_592 | ~spl93_1053)),
% 68.49/10.16 inference(trivial_inequality_removal,[],[f51998])).
% 68.49/10.16 thf(f51998,plain,(
% 68.49/10.16 ($true = $false) | (~spl93_182 | ~spl93_223 | ~spl93_592 | ~spl93_1053)),
% 68.49/10.16 inference(forward_demodulation,[],[f51997,f25671])).
% 68.49/10.16 thf(f25671,plain,(
% 68.49/10.16 ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ~spl93_592),
% 68.49/10.16 inference(avatar_component_clause,[],[f25669])).
% 68.49/10.16 thf(f25669,plain,(
% 68.49/10.16 spl93_592 <=> ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_592])])).
% 68.49/10.16 thf(f51997,plain,(
% 68.49/10.16 ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | (~spl93_182 | ~spl93_223 | ~spl93_1053)),
% 68.49/10.16 inference(forward_demodulation,[],[f51993,f3837])).
% 68.49/10.16 thf(f3837,plain,(
% 68.49/10.16 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))) | ~spl93_223),
% 68.49/10.16 inference(avatar_component_clause,[],[f3835])).
% 68.49/10.16 thf(f3835,plain,(
% 68.49/10.16 spl93_223 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_223])])).
% 68.49/10.16 thf(f51993,plain,(
% 68.49/10.16 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | (~spl93_182 | ~spl93_1053)),
% 68.49/10.16 inference(trivial_inequality_removal,[],[f51985])).
% 68.49/10.16 thf(f51985,plain,(
% 68.49/10.16 ($true != $true) | (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | (~spl93_182 | ~spl93_1053)),
% 68.49/10.16 inference(superposition,[],[f51966,f3384])).
% 68.49/10.16 thf(f3384,plain,(
% 68.49/10.16 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | ~spl93_182),
% 68.49/10.16 inference(avatar_component_clause,[],[f3382])).
% 68.49/10.16 thf(f3382,plain,(
% 68.49/10.16 spl93_182 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_182])])).
% 68.49/10.16 thf(f51966,plain,(
% 68.49/10.16 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | ~spl93_1053),
% 68.49/10.16 inference(avatar_component_clause,[],[f51965])).
% 68.49/10.16 thf(f51965,plain,(
% 68.49/10.16 spl93_1053 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_1053])])).
% 68.49/10.16 thf(f51975,plain,(
% 68.49/10.16 spl93_1055 | ~spl93_216 | ~spl93_819),
% 68.49/10.16 inference(avatar_split_clause,[],[f45583,f35796,f3748,f51973])).
% 68.49/10.16 thf(f51973,plain,(
% 68.49/10.16 spl93_1055 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2) = X2))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_1055])])).
% 68.49/10.16 thf(f3748,plain,(
% 68.49/10.16 spl93_216 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X1) = X0)),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_216])])).
% 68.49/10.16 thf(f35796,plain,(
% 68.49/10.16 spl93_819 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X1))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_819])])).
% 68.49/10.16 thf(f45583,plain,(
% 68.49/10.16 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2) = X2)) ) | (~spl93_216 | ~spl93_819)),
% 68.49/10.16 inference(superposition,[],[f35797,f3749])).
% 68.49/10.16 thf(f3749,plain,(
% 68.49/10.16 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X1) = X0)) ) | ~spl93_216),
% 68.49/10.16 inference(avatar_component_clause,[],[f3748])).
% 68.49/10.16 thf(f35797,plain,(
% 68.49/10.16 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X1)) ) | ~spl93_819),
% 68.49/10.16 inference(avatar_component_clause,[],[f35796])).
% 68.49/10.16 thf(f51971,plain,(
% 68.49/10.16 spl93_1054 | ~spl93_182 | ~spl93_271),
% 68.49/10.16 inference(avatar_split_clause,[],[f4463,f4448,f3382,f51969])).
% 68.49/10.16 thf(f51969,plain,(
% 68.49/10.16 spl93_1054 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_1054])])).
% 68.49/10.16 thf(f4448,plain,(
% 68.49/10.16 spl93_271 <=> ! [X0 : a,X3 : a,X2 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.16 introduced(avatar_definition,[new_symbols(naming,[spl93_271])])).
% 68.49/10.16 thf(f4463,plain,(
% 68.49/10.16 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_182 | ~spl93_271)),
% 68.49/10.16 inference(trivial_inequality_removal,[],[f4456])).
% 68.49/10.16 thf(f4456,plain,(
% 68.49/10.16 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_182 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f3384])).
% 68.49/10.17 thf(f4449,plain,(
% 68.49/10.17 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | ~spl93_271),
% 68.49/10.17 inference(avatar_component_clause,[],[f4448])).
% 68.49/10.17 thf(f51967,plain,(
% 68.49/10.17 spl93_1053 | ~spl93_183 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4462,f4448,f3387,f51965])).
% 68.49/10.17 thf(f3387,plain,(
% 68.49/10.17 spl93_183 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_183])])).
% 68.49/10.17 thf(f4462,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_183 | ~spl93_271)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4457])).
% 68.49/10.17 thf(f4457,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_183 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f3389])).
% 68.49/10.17 thf(f3389,plain,(
% 68.49/10.17 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | ~spl93_183),
% 68.49/10.17 inference(avatar_component_clause,[],[f3387])).
% 68.49/10.17 thf(f51963,plain,(
% 68.49/10.17 ~spl93_1052 | ~spl93_440 | spl93_1047),
% 68.49/10.17 inference(avatar_split_clause,[],[f51945,f51928,f13821,f51960])).
% 68.49/10.17 thf(f51960,plain,(
% 68.49/10.17 spl93_1052 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1052])])).
% 68.49/10.17 thf(f13821,plain,(
% 68.49/10.17 spl93_440 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK6)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_440])])).
% 68.49/10.17 thf(f51928,plain,(
% 68.49/10.17 spl93_1047 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1047])])).
% 68.49/10.17 thf(f51945,plain,(
% 68.49/10.17 (sK6 != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2)))) | (~spl93_440 | spl93_1047)),
% 68.49/10.17 inference(forward_demodulation,[],[f51929,f13823])).
% 68.49/10.17 thf(f13823,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK6) | ~spl93_440),
% 68.49/10.17 inference(avatar_component_clause,[],[f13821])).
% 68.49/10.17 thf(f51929,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2)))) | spl93_1047),
% 68.49/10.17 inference(avatar_component_clause,[],[f51928])).
% 68.49/10.17 thf(f51958,plain,(
% 68.49/10.17 ~spl93_1051 | ~spl93_440 | spl93_1050),
% 68.49/10.17 inference(avatar_split_clause,[],[f51944,f51940,f13821,f51955])).
% 68.49/10.17 thf(f51955,plain,(
% 68.49/10.17 spl93_1051 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) = sK6)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1051])])).
% 68.49/10.17 thf(f51940,plain,(
% 68.49/10.17 spl93_1050 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1050])])).
% 68.49/10.17 thf(f51944,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) != sK6) | (~spl93_440 | spl93_1050)),
% 68.49/10.17 inference(forward_demodulation,[],[f51942,f13823])).
% 68.49/10.17 thf(f51942,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | spl93_1050),
% 68.49/10.17 inference(avatar_component_clause,[],[f51940])).
% 68.49/10.17 thf(f51943,plain,(
% 68.49/10.17 spl93_1047 | ~spl93_1048 | ~spl93_1049 | ~spl93_1050 | ~spl93_210 | ~spl93_224),
% 68.49/10.17 inference(avatar_split_clause,[],[f3856,f3840,f3689,f51940,f51936,f51932,f51928])).
% 68.49/10.17 thf(f51932,plain,(
% 68.49/10.17 spl93_1048 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1048])])).
% 68.49/10.17 thf(f51936,plain,(
% 68.49/10.17 spl93_1049 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),s3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1049])])).
% 68.49/10.17 thf(f3689,plain,(
% 68.49/10.17 spl93_210 <=> ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_210])])).
% 68.49/10.17 thf(f3840,plain,(
% 68.49/10.17 spl93_224 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),s3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_224])])).
% 68.49/10.17 thf(f3856,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),s3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2)))) | (~spl93_210 | ~spl93_224)),
% 68.49/10.17 inference(superposition,[],[f3690,f3842])).
% 68.49/10.17 thf(f3842,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),s3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))) | ~spl93_224),
% 68.49/10.17 inference(avatar_component_clause,[],[f3840])).
% 68.49/10.17 thf(f3690,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) ) | ~spl93_210),
% 68.49/10.17 inference(avatar_component_clause,[],[f3689])).
% 68.49/10.17 thf(f51896,plain,(
% 68.49/10.17 spl93_1046 | ~spl93_221 | ~spl93_819),
% 68.49/10.17 inference(avatar_split_clause,[],[f45582,f35796,f3826,f51894])).
% 68.49/10.17 thf(f51894,plain,(
% 68.49/10.17 spl93_1046 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1046])])).
% 68.49/10.17 thf(f3826,plain,(
% 68.49/10.17 spl93_221 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) = X1)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_221])])).
% 68.49/10.17 thf(f45582,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) = X2)) ) | (~spl93_221 | ~spl93_819)),
% 68.49/10.17 inference(superposition,[],[f35797,f3827])).
% 68.49/10.17 thf(f3827,plain,(
% 68.49/10.17 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) = X1)) ) | ~spl93_221),
% 68.49/10.17 inference(avatar_component_clause,[],[f3826])).
% 68.49/10.17 thf(f51862,plain,(
% 68.49/10.17 spl93_1045 | ~spl93_48 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4478,f4468,f2031,f51860])).
% 68.49/10.17 thf(f51860,plain,(
% 68.49/10.17 spl93_1045 <=> ! [X1 : $tType,X5 : $tType,X6 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X7 : product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(X6,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))))),product_Pair(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X6,sK67(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X3,sK68(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X4,sK69(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X5,sK70(X6,X3,X4,X5,X1,X0),X7)),X2)))) = X7) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X1,sK71(X6,X3,X4,X5,X1,X0),X7)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X0,sK72(X6,X3,X4,X5,X1,X0),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1045])])).
% 68.49/10.17 thf(f2031,plain,(
% 68.49/10.17 spl93_48 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK33(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK34(X0,X1),X2)) = X2)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_48])])).
% 68.49/10.17 thf(f4468,plain,(
% 68.49/10.17 spl93_272 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X0,sK67(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X1,sK68(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X2,sK69(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X3,sK70(X0,X1,X2,X3,X4,X5),X6)),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X4,sK71(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X5,sK72(X0,X1,X2,X3,X4,X5),X6)))))) = X6)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_272])])).
% 68.49/10.17 thf(f4478,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X7 : product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))))] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(X6,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))))),product_Pair(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X6,sK67(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X3,sK68(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X4,sK69(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X5,sK70(X6,X3,X4,X5,X1,X0),X7)),X2)))) = X7) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X1,sK71(X6,X3,X4,X5,X1,X0),X7)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X0,sK72(X6,X3,X4,X5,X1,X0),X7))) ) | (~spl93_48 | ~spl93_272)),
% 68.49/10.17 inference(constrained_superposition,[],[f4469,f2032])).
% 68.49/10.17 thf(f2032,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK33(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK34(X0,X1),X2)) = X2)) ) | ~spl93_48),
% 68.49/10.17 inference(avatar_component_clause,[],[f2031])).
% 68.49/10.17 thf(f4469,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X0,sK67(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X1,sK68(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X2,sK69(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X3,sK70(X0,X1,X2,X3,X4,X5),X6)),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X4,sK71(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X5,sK72(X0,X1,X2,X3,X4,X5),X6)))))) = X6)) ) | ~spl93_272),
% 68.49/10.17 inference(avatar_component_clause,[],[f4468])).
% 68.49/10.17 thf(f51858,plain,(
% 68.49/10.17 spl93_1044 | ~spl93_47 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4477,f4468,f2027,f51856])).
% 68.49/10.17 thf(f51856,plain,(
% 68.49/10.17 spl93_1044 <=> ! [X1 : $tType,X5 : $tType,X6 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X7 : product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(X6,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))))),product_Pair(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X6,sK67(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X3,sK68(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X4,sK69(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X5,sK70(X6,X3,X4,X5,X1,X0),X7)),X2)))) = X7) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X1,sK71(X6,X3,X4,X5,X1,X0),X7)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X0,sK72(X6,X3,X4,X5,X1,X0),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1044])])).
% 68.49/10.17 thf(f2027,plain,(
% 68.49/10.17 spl93_47 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK31(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK32(X0,X1),X2)) = X2)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_47])])).
% 68.49/10.17 thf(f4477,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X7 : product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))))] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(X6,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))))),product_Pair(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X6,sK67(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X3,sK68(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X4,sK69(X6,X3,X4,X5,X1,X0),X7)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X5,sK70(X6,X3,X4,X5,X1,X0),X7)),X2)))) = X7) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X1,sK71(X6,X3,X4,X5,X1,X0),X7)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X6,product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),X0,sK72(X6,X3,X4,X5,X1,X0),X7))) ) | (~spl93_47 | ~spl93_272)),
% 68.49/10.17 inference(constrained_superposition,[],[f4469,f2028])).
% 68.49/10.17 thf(f2028,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK31(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK32(X0,X1),X2)) = X2)) ) | ~spl93_47),
% 68.49/10.17 inference(avatar_component_clause,[],[f2027])).
% 68.49/10.17 thf(f51008,plain,(
% 68.49/10.17 spl93_1043 | ~spl93_22 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4476,f4468,f1832,f51006])).
% 68.49/10.17 thf(f51006,plain,(
% 68.49/10.17 spl93_1043 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X0,sK67(X0,X1,X2,X3,X4,$o),X5)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,$o))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,$o))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X1,sK68(X0,X1,X2,X3,X4,$o),X5)),vAPP(product_prod(X3,product_prod(X4,$o)),product_prod(X2,product_prod(X3,product_prod(X4,$o))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,$o)),product_prod(X2,product_prod(X3,product_prod(X4,$o)))),product_Pair(X2,product_prod(X3,product_prod(X4,$o))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X2,sK69(X0,X1,X2,X3,X4,$o),X5)),vAPP(product_prod(X4,$o),product_prod(X3,product_prod(X4,$o)),vAPP(X3,sTfun(product_prod(X4,$o),product_prod(X3,product_prod(X4,$o))),product_Pair(X3,product_prod(X4,$o)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X3,sK70(X0,X1,X2,X3,X4,$o),X5)),vAPP($o,product_prod(X4,$o),vAPP(X4,sTfun($o,product_prod(X4,$o)),product_Pair(X4,$o),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X4,sK71(X0,X1,X2,X3,X4,$o),X5)),$true))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),$o,sK72(X0,X1,X2,X3,X4,$o),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1043])])).
% 68.49/10.17 thf(f1832,plain,(
% 68.49/10.17 spl93_22 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_22])])).
% 68.49/10.17 thf(f4476,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X0,sK67(X0,X1,X2,X3,X4,$o),X5)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,$o))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,$o))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X1,sK68(X0,X1,X2,X3,X4,$o),X5)),vAPP(product_prod(X3,product_prod(X4,$o)),product_prod(X2,product_prod(X3,product_prod(X4,$o))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,$o)),product_prod(X2,product_prod(X3,product_prod(X4,$o)))),product_Pair(X2,product_prod(X3,product_prod(X4,$o))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X2,sK69(X0,X1,X2,X3,X4,$o),X5)),vAPP(product_prod(X4,$o),product_prod(X3,product_prod(X4,$o)),vAPP(X3,sTfun(product_prod(X4,$o),product_prod(X3,product_prod(X4,$o))),product_Pair(X3,product_prod(X4,$o)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X3,sK70(X0,X1,X2,X3,X4,$o),X5)),vAPP($o,product_prod(X4,$o),vAPP(X4,sTfun($o,product_prod(X4,$o)),product_Pair(X4,$o),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),X4,sK71(X0,X1,X2,X3,X4,$o),X5)),$true))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,$o))))),$o,sK72(X0,X1,X2,X3,X4,$o),X5))) ) | (~spl93_22 | ~spl93_272)),
% 68.49/10.17 inference(superposition,[],[f4469,f1833])).
% 68.49/10.17 thf(f1833,plain,(
% 68.49/10.17 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl93_22),
% 68.49/10.17 inference(avatar_component_clause,[],[f1832])).
% 68.49/10.17 thf(f51004,plain,(
% 68.49/10.17 spl93_1042 | ~spl93_276 | ~spl93_812),
% 68.49/10.17 inference(avatar_split_clause,[],[f45370,f35544,f4534,f51002])).
% 68.49/10.17 thf(f51002,plain,(
% 68.49/10.17 spl93_1042 <=> ! [X2 : int,X0 : int,X1 : int] : ((X0 != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1042])])).
% 68.49/10.17 thf(f4534,plain,(
% 68.49/10.17 spl93_276 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X1)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_276])])).
% 68.49/10.17 thf(f35544,plain,(
% 68.49/10.17 spl93_812 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X0))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_812])])).
% 68.49/10.17 thf(f45370,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X2)) ) | (~spl93_276 | ~spl93_812)),
% 68.49/10.17 inference(superposition,[],[f35545,f4535])).
% 68.49/10.17 thf(f4535,plain,(
% 68.49/10.17 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X1)) ) | ~spl93_276),
% 68.49/10.17 inference(avatar_component_clause,[],[f4534])).
% 68.49/10.17 thf(f35545,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X0)) ) | ~spl93_812),
% 68.49/10.17 inference(avatar_component_clause,[],[f35544])).
% 68.49/10.17 thf(f51000,plain,(
% 68.49/10.17 spl93_1041 | ~spl93_22 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4475,f4468,f1832,f50998])).
% 68.49/10.17 thf(f50998,plain,(
% 68.49/10.17 spl93_1041 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X0,sK67(X0,X1,X2,X3,$o,X4),X5)),vAPP(product_prod(X2,product_prod(X3,product_prod($o,X4))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod($o,X4))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X1,sK68(X0,X1,X2,X3,$o,X4),X5)),vAPP(product_prod(X3,product_prod($o,X4)),product_prod(X2,product_prod(X3,product_prod($o,X4))),vAPP(X2,sTfun(product_prod(X3,product_prod($o,X4)),product_prod(X2,product_prod(X3,product_prod($o,X4)))),product_Pair(X2,product_prod(X3,product_prod($o,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X2,sK69(X0,X1,X2,X3,$o,X4),X5)),vAPP(product_prod($o,X4),product_prod(X3,product_prod($o,X4)),vAPP(X3,sTfun(product_prod($o,X4),product_prod(X3,product_prod($o,X4))),product_Pair(X3,product_prod($o,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X3,sK70(X0,X1,X2,X3,$o,X4),X5)),vAPP(X4,product_prod($o,X4),vAPP($o,sTfun(X4,product_prod($o,X4)),product_Pair($o,X4),$true),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X4,sK72(X0,X1,X2,X3,$o,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),$o,sK71(X0,X1,X2,X3,$o,X4),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1041])])).
% 68.49/10.17 thf(f4475,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X0,sK67(X0,X1,X2,X3,$o,X4),X5)),vAPP(product_prod(X2,product_prod(X3,product_prod($o,X4))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod($o,X4))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod($o,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X1,sK68(X0,X1,X2,X3,$o,X4),X5)),vAPP(product_prod(X3,product_prod($o,X4)),product_prod(X2,product_prod(X3,product_prod($o,X4))),vAPP(X2,sTfun(product_prod(X3,product_prod($o,X4)),product_prod(X2,product_prod(X3,product_prod($o,X4)))),product_Pair(X2,product_prod(X3,product_prod($o,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X2,sK69(X0,X1,X2,X3,$o,X4),X5)),vAPP(product_prod($o,X4),product_prod(X3,product_prod($o,X4)),vAPP(X3,sTfun(product_prod($o,X4),product_prod(X3,product_prod($o,X4))),product_Pair(X3,product_prod($o,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X3,sK70(X0,X1,X2,X3,$o,X4),X5)),vAPP(X4,product_prod($o,X4),vAPP($o,sTfun(X4,product_prod($o,X4)),product_Pair($o,X4),$true),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),X4,sK72(X0,X1,X2,X3,$o,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod($o,X4))))),$o,sK71(X0,X1,X2,X3,$o,X4),X5))) ) | (~spl93_22 | ~spl93_272)),
% 68.49/10.17 inference(superposition,[],[f4469,f1833])).
% 68.49/10.17 thf(f50996,plain,(
% 68.49/10.17 spl93_1040 | ~spl93_22 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4474,f4468,f1832,f50994])).
% 68.49/10.17 thf(f50994,plain,(
% 68.49/10.17 spl93_1040 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X0,sK67(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod(X2,product_prod($o,product_prod(X3,X4))),product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),vAPP(X1,sTfun(product_prod(X2,product_prod($o,product_prod(X3,X4))),product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),product_Pair(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X1,sK68(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod($o,product_prod(X3,X4)),product_prod(X2,product_prod($o,product_prod(X3,X4))),vAPP(X2,sTfun(product_prod($o,product_prod(X3,X4)),product_prod(X2,product_prod($o,product_prod(X3,X4)))),product_Pair(X2,product_prod($o,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X2,sK69(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod($o,product_prod(X3,X4)),vAPP($o,sTfun(product_prod(X3,X4),product_prod($o,product_prod(X3,X4))),product_Pair($o,product_prod(X3,X4)),$true),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X3,sK71(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X4,sK72(X0,X1,X2,$o,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),$o,sK70(X0,X1,X2,$o,X3,X4),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1040])])).
% 68.49/10.17 thf(f4474,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X0,sK67(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod(X2,product_prod($o,product_prod(X3,X4))),product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),vAPP(X1,sTfun(product_prod(X2,product_prod($o,product_prod(X3,X4))),product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),product_Pair(X1,product_prod(X2,product_prod($o,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X1,sK68(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod($o,product_prod(X3,X4)),product_prod(X2,product_prod($o,product_prod(X3,X4))),vAPP(X2,sTfun(product_prod($o,product_prod(X3,X4)),product_prod(X2,product_prod($o,product_prod(X3,X4)))),product_Pair(X2,product_prod($o,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X2,sK69(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod($o,product_prod(X3,X4)),vAPP($o,sTfun(product_prod(X3,X4),product_prod($o,product_prod(X3,X4))),product_Pair($o,product_prod(X3,X4)),$true),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X3,sK71(X0,X1,X2,$o,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),X4,sK72(X0,X1,X2,$o,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,product_prod(X3,X4))))),$o,sK70(X0,X1,X2,$o,X3,X4),X5))) ) | (~spl93_22 | ~spl93_272)),
% 68.49/10.17 inference(superposition,[],[f4469,f1833])).
% 68.49/10.17 thf(f50992,plain,(
% 68.49/10.17 spl93_1039 | ~spl93_22 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4473,f4468,f1832,f50990])).
% 68.49/10.17 thf(f50990,plain,(
% 68.49/10.17 spl93_1039 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))))] : ((vAPP(product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))))),product_Pair(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X0,sK67(X0,X1,$o,X2,X3,X4),X5)),vAPP(product_prod($o,product_prod(X2,product_prod(X3,X4))),product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),vAPP(X1,sTfun(product_prod($o,product_prod(X2,product_prod(X3,X4))),product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),product_Pair(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X1,sK68(X0,X1,$o,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod($o,product_prod(X2,product_prod(X3,X4))),vAPP($o,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod($o,product_prod(X2,product_prod(X3,X4)))),product_Pair($o,product_prod(X2,product_prod(X3,X4))),$true),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X0,X1,$o,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X0,X1,$o,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X0,X1,$o,X2,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),$o,sK69(X0,X1,$o,X2,X3,X4),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1039])])).
% 68.49/10.17 thf(f4473,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))))] : ((vAPP(product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))))),product_Pair(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X0,sK67(X0,X1,$o,X2,X3,X4),X5)),vAPP(product_prod($o,product_prod(X2,product_prod(X3,X4))),product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),vAPP(X1,sTfun(product_prod($o,product_prod(X2,product_prod(X3,X4))),product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),product_Pair(X1,product_prod($o,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X1,sK68(X0,X1,$o,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod($o,product_prod(X2,product_prod(X3,X4))),vAPP($o,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod($o,product_prod(X2,product_prod(X3,X4)))),product_Pair($o,product_prod(X2,product_prod(X3,X4))),$true),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X0,X1,$o,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X0,X1,$o,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X0,X1,$o,X2,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,product_prod(X3,X4))))),$o,sK69(X0,X1,$o,X2,X3,X4),X5))) ) | (~spl93_22 | ~spl93_272)),
% 68.49/10.17 inference(superposition,[],[f4469,f1833])).
% 68.49/10.17 thf(f50988,plain,(
% 68.49/10.17 spl93_1038 | ~spl93_22 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4472,f4468,f1832,f50986])).
% 68.49/10.17 thf(f50986,plain,(
% 68.49/10.17 spl93_1038 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))] : ((vAPP(product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))),product_Pair(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK67(X0,$o,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP($o,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$true),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X0,$o,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X0,$o,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X0,$o,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X0,$o,X1,X2,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,sK68(X0,$o,X1,X2,X3,X4),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1038])])).
% 68.49/10.17 thf(f4472,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))] : ((vAPP(product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))),product_Pair(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK67(X0,$o,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP($o,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair($o,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$true),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X0,$o,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X0,$o,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X0,$o,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X0,$o,X1,X2,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,sK68(X0,$o,X1,X2,X3,X4),X5))) ) | (~spl93_22 | ~spl93_272)),
% 68.49/10.17 inference(superposition,[],[f4469,f1833])).
% 68.49/10.17 thf(f50984,plain,(
% 68.49/10.17 spl93_1037 | ~spl93_22 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4471,f4468,f1832,f50982])).
% 68.49/10.17 thf(f50982,plain,(
% 68.49/10.17 spl93_1037 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))] : ((vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))),product_Pair($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$true),vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68($o,X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69($o,X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70($o,X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71($o,X0,X1,X2,X3,X4),X5)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72($o,X0,X1,X2,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,sK67($o,X0,X1,X2,X3,X4),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1037])])).
% 68.49/10.17 thf(f4471,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))] : ((vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))),product_Pair($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$true),vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68($o,X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69($o,X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70($o,X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71($o,X0,X1,X2,X3,X4),X5)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72($o,X0,X1,X2,X3,X4),X5)))))) = X5) | ($false = vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,sK67($o,X0,X1,X2,X3,X4),X5))) ) | (~spl93_22 | ~spl93_272)),
% 68.49/10.17 inference(superposition,[],[f4469,f1833])).
% 68.49/10.17 thf(f50950,plain,(
% 68.49/10.17 spl93_1036 | ~spl93_139 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4479,f4468,f2831,f50948])).
% 68.49/10.17 thf(f50948,plain,(
% 68.49/10.17 spl93_1036 <=> ! [X1 : $tType,X5 : $tType,X0 : $tType,X4 : $tType,X6 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X7 : product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))))] : ((vAPP(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),vAPP(X6,sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))))),product_Pair(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X6,sK67(X6,X4,X5,X2,X0,X1),X7)),vAPP(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(X4,sTfun(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),product_Pair(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X4,sK68(X6,X4,X5,X2,X0,X1),X7)),vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1))),vAPP(X5,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_Pair(X5,product_prod(X2,product_prod(X0,X1))),vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X5,sK69(X6,X4,X5,X2,X0,X1),X7)),X3))) = X7) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X1,sK72(X6,X4,X5,X2,X0,X1),X7)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X0,sK71(X6,X4,X5,X2,X0,X1),X7)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X2,sK70(X6,X4,X5,X2,X0,X1),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1036])])).
% 68.49/10.17 thf(f2831,plain,(
% 68.49/10.17 spl93_139 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK43(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK44(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK45(X0,X1,X2),X3))) = X3)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_139])])).
% 68.49/10.17 thf(f4479,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X7 : product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))))] : ((vAPP(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),vAPP(X6,sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))))),product_Pair(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X6,sK67(X6,X4,X5,X2,X0,X1),X7)),vAPP(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(X4,sTfun(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),product_Pair(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X4,sK68(X6,X4,X5,X2,X0,X1),X7)),vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1))),vAPP(X5,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_Pair(X5,product_prod(X2,product_prod(X0,X1))),vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X5,sK69(X6,X4,X5,X2,X0,X1),X7)),X3))) = X7) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X1,sK72(X6,X4,X5,X2,X0,X1),X7)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X0,sK71(X6,X4,X5,X2,X0,X1),X7)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X6,product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),X2,sK70(X6,X4,X5,X2,X0,X1),X7))) ) | (~spl93_139 | ~spl93_272)),
% 68.49/10.17 inference(constrained_superposition,[],[f4469,f2832])).
% 68.49/10.17 thf(f2832,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ((vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK43(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK44(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK45(X0,X1,X2),X3))) = X3)) ) | ~spl93_139),
% 68.49/10.17 inference(avatar_component_clause,[],[f2831])).
% 68.49/10.17 thf(f50904,plain,(
% 68.49/10.17 spl93_1035 | ~spl93_48 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4452,f4448,f2031,f50902])).
% 68.49/10.17 thf(f50902,plain,(
% 68.49/10.17 spl93_1035 <=> ! [X2 : a,X0 : product_prod(a,a),X1 : a] : (($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),X0),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(product_prod(a,a),a,sK34(a,a),X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK33(a,a),X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK34(a,a),X0)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X1),X2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1035])])).
% 68.49/10.17 thf(f4452,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : product_prod(a,a),X1 : a] : (($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),X0),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(product_prod(a,a),a,sK34(a,a),X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK33(a,a),X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK34(a,a),X0)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X1),X2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_48 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f2032])).
% 68.49/10.17 thf(f50900,plain,(
% 68.49/10.17 spl93_1034 | ~spl93_216 | ~spl93_812),
% 68.49/10.17 inference(avatar_split_clause,[],[f45363,f35544,f3748,f50898])).
% 68.49/10.17 thf(f50898,plain,(
% 68.49/10.17 spl93_1034 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1) = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1034])])).
% 68.49/10.17 thf(f45363,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1) = X2)) ) | (~spl93_216 | ~spl93_812)),
% 68.49/10.17 inference(superposition,[],[f35545,f3749])).
% 68.49/10.17 thf(f50896,plain,(
% 68.49/10.17 spl93_1033 | ~spl93_47 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4451,f4448,f2027,f50894])).
% 68.49/10.17 thf(f50894,plain,(
% 68.49/10.17 spl93_1033 <=> ! [X2 : a,X0 : product_prod(a,a),X1 : a] : (($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),X0),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(product_prod(a,a),a,sK32(a,a),X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK31(a,a),X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK32(a,a),X0)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X1),X2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1033])])).
% 68.49/10.17 thf(f4451,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : product_prod(a,a),X1 : a] : (($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),X0),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(product_prod(a,a),a,sK32(a,a),X0)),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK31(a,a),X0)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(product_prod(a,a),a,sK32(a,a),X0)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X1),X2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_47 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f2028])).
% 68.49/10.17 thf(f50884,plain,(
% 68.49/10.17 ~spl93_1032 | ~spl93_345 | spl93_1027),
% 68.49/10.17 inference(avatar_split_clause,[],[f50874,f50857,f6456,f50881])).
% 68.49/10.17 thf(f50881,plain,(
% 68.49/10.17 spl93_1032 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1032])])).
% 68.49/10.17 thf(f6456,plain,(
% 68.49/10.17 spl93_345 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_345])])).
% 68.49/10.17 thf(f50857,plain,(
% 68.49/10.17 spl93_1027 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1027])])).
% 68.49/10.17 thf(f50874,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | spl93_1027)),
% 68.49/10.17 inference(forward_demodulation,[],[f50859,f6458])).
% 68.49/10.17 thf(f6458,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) | ~spl93_345),
% 68.49/10.17 inference(avatar_component_clause,[],[f6456])).
% 68.49/10.17 thf(f50859,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | spl93_1027),
% 68.49/10.17 inference(avatar_component_clause,[],[f50857])).
% 68.49/10.17 thf(f50879,plain,(
% 68.49/10.17 ~spl93_1031 | ~spl93_345 | spl93_1028),
% 68.49/10.17 inference(avatar_split_clause,[],[f50873,f50861,f6456,f50876])).
% 68.49/10.17 thf(f50876,plain,(
% 68.49/10.17 spl93_1031 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1031])])).
% 68.49/10.17 thf(f50861,plain,(
% 68.49/10.17 spl93_1028 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1028])])).
% 68.49/10.17 thf(f50873,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | spl93_1028)),
% 68.49/10.17 inference(forward_demodulation,[],[f50863,f6458])).
% 68.49/10.17 thf(f50863,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | spl93_1028),
% 68.49/10.17 inference(avatar_component_clause,[],[f50861])).
% 68.49/10.17 thf(f50872,plain,(
% 68.49/10.17 spl93_1026 | ~spl93_1027 | ~spl93_1028 | spl93_1029 | ~spl93_1030 | ~spl93_69 | ~spl93_213 | ~spl93_223),
% 68.49/10.17 inference(avatar_split_clause,[],[f3854,f3835,f3705,f2174,f50869,f50865,f50861,f50857,f50853])).
% 68.49/10.17 thf(f50853,plain,(
% 68.49/10.17 spl93_1026 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1026])])).
% 68.49/10.17 thf(f50865,plain,(
% 68.49/10.17 spl93_1029 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1029])])).
% 68.49/10.17 thf(f50869,plain,(
% 68.49/10.17 spl93_1030 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1030])])).
% 68.49/10.17 thf(f2174,plain,(
% 68.49/10.17 spl93_69 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_69])])).
% 68.49/10.17 thf(f3705,plain,(
% 68.49/10.17 spl93_213 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_213])])).
% 68.49/10.17 thf(f3854,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (~spl93_69 | ~spl93_213 | ~spl93_223)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3853])).
% 68.49/10.17 thf(f3853,plain,(
% 68.49/10.17 ($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (~spl93_69 | ~spl93_213 | ~spl93_223)),
% 68.49/10.17 inference(forward_demodulation,[],[f3851,f2176])).
% 68.49/10.17 thf(f2176,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true) | ~spl93_69),
% 68.49/10.17 inference(avatar_component_clause,[],[f2174])).
% 68.49/10.17 thf(f3851,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) != $true) | (~spl93_213 | ~spl93_223)),
% 68.49/10.17 inference(superposition,[],[f3706,f3837])).
% 68.49/10.17 thf(f3706,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2))) ) | ~spl93_213),
% 68.49/10.17 inference(avatar_component_clause,[],[f3705])).
% 68.49/10.17 thf(f50851,plain,(
% 68.49/10.17 spl93_1025 | ~spl93_221 | ~spl93_812),
% 68.49/10.17 inference(avatar_split_clause,[],[f45362,f35544,f3826,f50849])).
% 68.49/10.17 thf(f50849,plain,(
% 68.49/10.17 spl93_1025 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1025])])).
% 68.49/10.17 thf(f45362,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) = X2)) ) | (~spl93_221 | ~spl93_812)),
% 68.49/10.17 inference(superposition,[],[f35545,f3827])).
% 68.49/10.17 thf(f50839,plain,(
% 68.49/10.17 ~spl93_1024 | ~spl93_345 | spl93_1019),
% 68.49/10.17 inference(avatar_split_clause,[],[f50829,f50812,f6456,f50836])).
% 68.49/10.17 thf(f50836,plain,(
% 68.49/10.17 spl93_1024 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1024])])).
% 68.49/10.17 thf(f50812,plain,(
% 68.49/10.17 spl93_1019 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1019])])).
% 68.49/10.17 thf(f50829,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | spl93_1019)),
% 68.49/10.17 inference(forward_demodulation,[],[f50814,f6458])).
% 68.49/10.17 thf(f50814,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | spl93_1019),
% 68.49/10.17 inference(avatar_component_clause,[],[f50812])).
% 68.49/10.17 thf(f50834,plain,(
% 68.49/10.17 ~spl93_1023 | ~spl93_345 | spl93_1020),
% 68.49/10.17 inference(avatar_split_clause,[],[f50828,f50816,f6456,f50831])).
% 68.49/10.17 thf(f50831,plain,(
% 68.49/10.17 spl93_1023 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1023])])).
% 68.49/10.17 thf(f50816,plain,(
% 68.49/10.17 spl93_1020 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1020])])).
% 68.49/10.17 thf(f50828,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | spl93_1020)),
% 68.49/10.17 inference(forward_demodulation,[],[f50818,f6458])).
% 68.49/10.17 thf(f50818,plain,(
% 68.49/10.17 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | spl93_1020),
% 68.49/10.17 inference(avatar_component_clause,[],[f50816])).
% 68.49/10.17 thf(f50827,plain,(
% 68.49/10.17 spl93_1018 | ~spl93_1019 | ~spl93_1020 | spl93_1021 | ~spl93_1022 | ~spl93_69 | ~spl93_213 | ~spl93_222),
% 68.49/10.17 inference(avatar_split_clause,[],[f3848,f3830,f3705,f2174,f50824,f50820,f50816,f50812,f50808])).
% 68.49/10.17 thf(f50808,plain,(
% 68.49/10.17 spl93_1018 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1018])])).
% 68.49/10.17 thf(f50820,plain,(
% 68.49/10.17 spl93_1021 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1021])])).
% 68.49/10.17 thf(f50824,plain,(
% 68.49/10.17 spl93_1022 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1022])])).
% 68.49/10.17 thf(f3830,plain,(
% 68.49/10.17 spl93_222 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_222])])).
% 68.49/10.17 thf(f3848,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (~spl93_69 | ~spl93_213 | ~spl93_222)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3847])).
% 68.49/10.17 thf(f3847,plain,(
% 68.49/10.17 ($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (~spl93_69 | ~spl93_213 | ~spl93_222)),
% 68.49/10.17 inference(forward_demodulation,[],[f3845,f2176])).
% 68.49/10.17 thf(f3845,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) != $true) | (~spl93_213 | ~spl93_222)),
% 68.49/10.17 inference(superposition,[],[f3706,f3832])).
% 68.49/10.17 thf(f3832,plain,(
% 68.49/10.17 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))) | ~spl93_222),
% 68.49/10.17 inference(avatar_component_clause,[],[f3830])).
% 68.49/10.17 thf(f50769,plain,(
% 68.49/10.17 spl93_1017 | ~spl93_46 | ~spl93_72 | ~spl93_240),
% 68.49/10.17 inference(avatar_split_clause,[],[f4040,f4031,f2239,f2023,f50767])).
% 68.49/10.17 thf(f50767,plain,(
% 68.49/10.17 spl93_1017 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1017])])).
% 68.49/10.17 thf(f2023,plain,(
% 68.49/10.17 spl93_46 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),X1,one(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_46])])).
% 68.49/10.17 thf(f2239,plain,(
% 68.49/10.17 spl93_72 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),sTfun(X1,sTfun(X1,X1)),mult(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_72])])).
% 68.49/10.17 thf(f4031,plain,(
% 68.49/10.17 spl93_240 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_240])])).
% 68.49/10.17 thf(f4040,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_72 | ~spl93_240)),
% 68.49/10.17 inference(forward_demodulation,[],[f4039,f2024])).
% 68.49/10.17 thf(f2024,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),X1,one(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))) ) | ~spl93_46),
% 68.49/10.17 inference(avatar_component_clause,[],[f2023])).
% 68.49/10.17 thf(f4039,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X3 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_72 | ~spl93_240)),
% 68.49/10.17 inference(forward_demodulation,[],[f4034,f2024])).
% 68.49/10.17 thf(f4034,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X3 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_72 | ~spl93_240)),
% 68.49/10.17 inference(superposition,[],[f4032,f2240])).
% 68.49/10.17 thf(f2240,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),sTfun(X1,sTfun(X1,X1)),mult(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))) ) | ~spl93_72),
% 68.49/10.17 inference(avatar_component_clause,[],[f2239])).
% 68.49/10.17 thf(f4032,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) ) | ~spl93_240),
% 68.49/10.17 inference(avatar_component_clause,[],[f4031])).
% 68.49/10.17 thf(f50743,plain,(
% 68.49/10.17 spl93_1016 | ~spl93_21 | ~spl93_301 | ~spl93_327 | ~spl93_722),
% 68.49/10.17 inference(avatar_split_clause,[],[f40206,f31001,f5387,f4916,f1827,f50741])).
% 68.49/10.17 thf(f50741,plain,(
% 68.49/10.17 spl93_1016 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X1) = X2) | (X1 != X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1016])])).
% 68.49/10.17 thf(f1827,plain,(
% 68.49/10.17 spl93_21 <=> (group_add(int) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_21])])).
% 68.49/10.17 thf(f4916,plain,(
% 68.49/10.17 spl93_301 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_301])])).
% 68.49/10.17 thf(f5387,plain,(
% 68.49/10.17 spl93_327 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) = $false))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_327])])).
% 68.49/10.17 thf(f31001,plain,(
% 68.49/10.17 spl93_722 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X2) != X1) | (X1 = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_722])])).
% 68.49/10.17 thf(f40206,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X1) = X2) | (X1 != X2)) ) | (~spl93_21 | ~spl93_301 | ~spl93_327 | ~spl93_722)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f40205])).
% 68.49/10.17 thf(f40205,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : (($true = $false) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X1) = X2) | (X1 != X2)) ) | (~spl93_21 | ~spl93_301 | ~spl93_327 | ~spl93_722)),
% 68.49/10.17 inference(forward_demodulation,[],[f40204,f1829])).
% 68.49/10.17 thf(f1829,plain,(
% 68.49/10.17 (group_add(int) = $true) | ~spl93_21),
% 68.49/10.17 inference(avatar_component_clause,[],[f1827])).
% 68.49/10.17 thf(f40204,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X1) = X2) | (X1 != X2) | (group_add(int) = $false)) ) | (~spl93_301 | ~spl93_327 | ~spl93_722)),
% 68.49/10.17 inference(forward_demodulation,[],[f40172,f4917])).
% 68.49/10.17 thf(f4917,plain,(
% 68.49/10.17 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)))) ) | ~spl93_301),
% 68.49/10.17 inference(avatar_component_clause,[],[f4916])).
% 68.49/10.17 thf(f40172,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))),X1) = X2) | (group_add(int) = $false)) ) | (~spl93_327 | ~spl93_722)),
% 68.49/10.17 inference(superposition,[],[f31002,f5388])).
% 68.49/10.17 thf(f5388,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) = $false)) ) | ~spl93_327),
% 68.49/10.17 inference(avatar_component_clause,[],[f5387])).
% 68.49/10.17 thf(f31002,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X2) != X1) | (X1 = X2)) ) | ~spl93_722),
% 68.49/10.17 inference(avatar_component_clause,[],[f31001])).
% 68.49/10.17 thf(f50739,plain,(
% 68.49/10.17 spl93_1015 | ~spl93_272 | ~spl93_275),
% 68.49/10.17 inference(avatar_split_clause,[],[f4527,f4509,f4468,f50737])).
% 68.49/10.17 thf(f50737,plain,(
% 68.49/10.17 spl93_1015 <=> ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X8 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X6 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X7 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))) > $o] : (($true != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,X7,X6)) | ($true = vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,X7,X8)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X4,sK78(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X3,sK77(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X2,sK76(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X1,sK75(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X0,sK74(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X5,sK67(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X5,sK73(X4,X3,X2,X1,X0,X5),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1015])])).
% 68.49/10.17 thf(f4509,plain,(
% 68.49/10.17 spl93_275 <=> ! [X1 : $tType,X5 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7)) | ($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X5,sK73(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X4,sK74(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X3,sK75(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X2,sK76(X0,X1,X2,X3,X4,X5),X6)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X1,sK77(X0,X1,X2,X3,X4,X5),X6)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X0,sK78(X0,X1,X2,X3,X4,X5),X6)))))))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_275])])).
% 68.49/10.17 thf(f4527,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X8 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X6 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X7 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))) > $o] : (($true != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,X7,X6)) | ($true = vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o,X7,X8)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X4,sK78(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X3,sK77(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X2,sK76(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X1,sK75(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X0,sK74(X4,X3,X2,X1,X0,X5),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X5,sK67(X5,X0,X1,X2,X3,X4),X6) != vAPP(sTfun(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),$o),X5,sK73(X4,X3,X2,X1,X0,X5),X7))) ) | (~spl93_272 | ~spl93_275)),
% 68.49/10.17 inference(constrained_superposition,[],[f4510,f4469])).
% 68.49/10.17 thf(f4510,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X5,sK73(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X4,sK74(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X3,sK75(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X2,sK76(X0,X1,X2,X3,X4,X5),X6)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X1,sK77(X0,X1,X2,X3,X4,X5),X6)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X0,sK78(X0,X1,X2,X3,X4,X5),X6)))))))) | ($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7))) ) | ~spl93_275),
% 68.49/10.17 inference(avatar_component_clause,[],[f4509])).
% 68.49/10.17 thf(f50705,plain,(
% 68.49/10.17 spl93_1014 | ~spl93_206 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4480,f4468,f3634,f50703])).
% 68.49/10.17 thf(f50703,plain,(
% 68.49/10.17 spl93_1014 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X6 : $tType,X5 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X7 : product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))))] : ((vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))))),product_Pair(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X6,sK67(X6,X5,X3,X0,X1,X2),X7)),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),product_Pair(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X5,sK68(X6,X5,X3,X0,X1,X2),X7)),X4)) = X7) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X2,sK72(X6,X5,X3,X0,X1,X2),X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X1,sK71(X6,X5,X3,X0,X1,X2),X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X0,sK70(X6,X5,X3,X0,X1,X2),X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X3,sK69(X6,X5,X3,X0,X1,X2),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1014])])).
% 68.49/10.17 thf(f3634,plain,(
% 68.49/10.17 spl93_206 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK49(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK50(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK51(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK52(X0,X1,X2,X3),X4)))) = X4)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_206])])).
% 68.49/10.17 thf(f4480,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X7 : product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2)))] : ((vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))))),product_Pair(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X6,sK67(X6,X5,X3,X0,X1,X2),X7)),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),product_Pair(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X5,sK68(X6,X5,X3,X0,X1,X2),X7)),X4)) = X7) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X2,sK72(X6,X5,X3,X0,X1,X2),X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X1,sK71(X6,X5,X3,X0,X1,X2),X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X0,sK70(X6,X5,X3,X0,X1,X2),X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(product_prod(X6,product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),X3,sK69(X6,X5,X3,X0,X1,X2),X7))) ) | (~spl93_206 | ~spl93_272)),
% 68.49/10.17 inference(constrained_superposition,[],[f4469,f3635])).
% 68.49/10.17 thf(f3635,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ((vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK49(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK50(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK51(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK52(X0,X1,X2,X3),X4)))) = X4)) ) | ~spl93_206),
% 68.49/10.17 inference(avatar_component_clause,[],[f3634])).
% 68.49/10.17 thf(f50680,plain,(
% 68.49/10.17 spl93_1013 | ~spl93_22 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4460,f4448,f1832,f50678])).
% 68.49/10.17 thf(f50678,plain,(
% 68.49/10.17 spl93_1013 <=> ! [X0 : a,X3 : a,X2 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X1))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1013])])).
% 68.49/10.17 thf(f4460,plain,(
% 68.49/10.17 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X1))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_22 | ~spl93_271)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4459])).
% 68.49/10.17 thf(f4459,plain,(
% 68.49/10.17 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X1))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_22 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f1833])).
% 68.49/10.17 thf(f50646,plain,(
% 68.49/10.17 spl93_1012 | ~spl93_256 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4481,f4468,f4237,f50644])).
% 68.49/10.17 thf(f50644,plain,(
% 68.49/10.17 spl93_1012 <=> ! [X1 : $tType,X2 : $tType,X6 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X7 : product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),vAPP(X6,sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))))),product_Pair(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X6,sK67(X6,X4,X0,X1,X2,X3),X7)),X5) = X7) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X3,sK72(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X2,sK71(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X1,sK70(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X0,sK69(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X4,sK68(X6,X4,X0,X1,X2,X3),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1012])])).
% 68.49/10.17 thf(f4237,plain,(
% 68.49/10.17 spl93_256 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X0,sK57(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X1,sK58(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X2,sK59(X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X3,sK60(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X4,sK61(X0,X1,X2,X3,X4),X5))))) = X5)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_256])])).
% 68.49/10.17 thf(f4481,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X7 : product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),vAPP(X6,sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))))),product_Pair(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X6,sK67(X6,X4,X0,X1,X2,X3),X7)),X5) = X7) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X3,sK72(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X2,sK71(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X1,sK70(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X0,sK69(X6,X4,X0,X1,X2,X3),X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X6,product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),X4,sK68(X6,X4,X0,X1,X2,X3),X7))) ) | (~spl93_256 | ~spl93_272)),
% 68.49/10.17 inference(constrained_superposition,[],[f4469,f4238])).
% 68.49/10.17 thf(f4238,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X0,sK57(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X1,sK58(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X2,sK59(X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X3,sK60(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X4,sK61(X0,X1,X2,X3,X4),X5))))) = X5)) ) | ~spl93_256),
% 68.49/10.17 inference(avatar_component_clause,[],[f4237])).
% 68.49/10.17 thf(f50587,plain,(
% 68.49/10.17 spl93_1011 | ~spl93_46 | ~spl93_72 | ~spl93_228),
% 68.49/10.17 inference(avatar_split_clause,[],[f3914,f3903,f2239,f2023,f50585])).
% 68.49/10.17 thf(f50585,plain,(
% 68.49/10.17 spl93_1011 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1011])])).
% 68.49/10.17 thf(f3903,plain,(
% 68.49/10.17 spl93_228 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_228])])).
% 68.49/10.17 thf(f3914,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_72 | ~spl93_228)),
% 68.49/10.17 inference(forward_demodulation,[],[f3913,f2024])).
% 68.49/10.17 thf(f3913,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_72 | ~spl93_228)),
% 68.49/10.17 inference(forward_demodulation,[],[f3906,f2024])).
% 68.49/10.17 thf(f3906,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_72 | ~spl93_228)),
% 68.49/10.17 inference(superposition,[],[f3904,f2240])).
% 68.49/10.17 thf(f3904,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) ) | ~spl93_228),
% 68.49/10.17 inference(avatar_component_clause,[],[f3903])).
% 68.49/10.17 thf(f50507,plain,(
% 68.49/10.17 spl93_1010 | ~spl93_20 | ~spl93_417 | ~spl93_722),
% 68.49/10.17 inference(avatar_split_clause,[],[f40203,f31001,f9957,f1822,f50505])).
% 68.49/10.17 thf(f50505,plain,(
% 68.49/10.17 spl93_1010 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) != X2) | (X1 = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1010])])).
% 68.49/10.17 thf(f1822,plain,(
% 68.49/10.17 spl93_20 <=> (ab_group_add(int) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_20])])).
% 68.49/10.17 thf(f9957,plain,(
% 68.49/10.17 spl93_417 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (ab_group_add(X0) = $false))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_417])])).
% 68.49/10.17 thf(f40203,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) != X2) | (X1 = X2)) ) | (~spl93_20 | ~spl93_417 | ~spl93_722)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f40202])).
% 68.49/10.17 thf(f40202,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : (($true = $false) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) != X2) | (X1 = X2)) ) | (~spl93_20 | ~spl93_417 | ~spl93_722)),
% 68.49/10.17 inference(forward_demodulation,[],[f40171,f1824])).
% 68.49/10.17 thf(f1824,plain,(
% 68.49/10.17 (ab_group_add(int) = $true) | ~spl93_20),
% 68.49/10.17 inference(avatar_component_clause,[],[f1822])).
% 68.49/10.17 thf(f40171,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) != X2) | (X1 = X2) | (ab_group_add(int) = $false)) ) | (~spl93_417 | ~spl93_722)),
% 68.49/10.17 inference(superposition,[],[f31002,f9958])).
% 68.49/10.17 thf(f9958,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (ab_group_add(X0) = $false)) ) | ~spl93_417),
% 68.49/10.17 inference(avatar_component_clause,[],[f9957])).
% 68.49/10.17 thf(f50503,plain,(
% 68.49/10.17 spl93_1009 | ~spl93_75 | ~spl93_220),
% 68.49/10.17 inference(avatar_split_clause,[],[f3821,f3805,f2256,f50501])).
% 68.49/10.17 thf(f50501,plain,(
% 68.49/10.17 spl93_1009 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3))),X4 : X0 > product_prod(X1,product_prod(X2,X3)) > $o] : (($true != vAPP(product_prod(X1,product_prod(X2,X3)),$o,vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o),X4,vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4))),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4))),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4),X5)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1009])])).
% 68.49/10.17 thf(f2256,plain,(
% 68.49/10.17 spl93_75 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : (vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_75])])).
% 68.49/10.17 thf(f3805,plain,(
% 68.49/10.17 spl93_220 <=> ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5)) | ($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X2,X3),X4)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X2,sK54(X0,X1,X2,X3),X4)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X2,X3),X4)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X2,X3),X4)))))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_220])])).
% 68.49/10.17 thf(f3821,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : X0 > product_prod(X1,product_prod(X2,X3)) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (($true != vAPP(product_prod(X1,product_prod(X2,X3)),$o,vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o),X4,vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4))),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4))),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,vAPP(sTfun(X0,sTfun(product_prod(X1,product_prod(X2,X3)),$o)),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),product_rec_prod(X0,product_prod(X1,product_prod(X2,X3)),$o),X4),X5))) ) | (~spl93_75 | ~spl93_220)),
% 68.49/10.17 inference(superposition,[],[f3806,f2257])).
% 68.49/10.17 thf(f2257,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : ((vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))) ) | ~spl93_75),
% 68.49/10.17 inference(avatar_component_clause,[],[f2256])).
% 68.49/10.17 thf(f3806,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X2,X3),X4)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X2,sK54(X0,X1,X2,X3),X4)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X2,X3),X4)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X2,X3),X4)))))) | ($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5))) ) | ~spl93_220),
% 68.49/10.17 inference(avatar_component_clause,[],[f3805])).
% 68.49/10.17 thf(f50408,plain,(
% 68.49/10.17 spl93_1008 | ~spl93_170),
% 68.49/10.17 inference(avatar_split_clause,[],[f3220,f3201,f50406])).
% 68.49/10.17 thf(f50406,plain,(
% 68.49/10.17 spl93_1008 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(X2,product_prod(X0,X1))] : (vAPP(product_prod(X0,X1),product_prod(X2,product_prod(X0,X1)),vAPP(X2,sTfun(product_prod(X0,X1),product_prod(X2,product_prod(X0,X1))),product_Pair(X2,product_prod(X0,X1)),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X2,sK46(X1,X0,X2),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o)),bCOMB,vNOT),vAPP(product_prod(X2,product_prod(X0,X1)),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vEQ(product_prod(X2,product_prod(X0,X1))),X3)))),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X0,sK47(X1,X0,X2),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o)),bCOMB,vNOT),vAPP(product_prod(X2,product_prod(X0,X1)),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vEQ(product_prod(X2,product_prod(X0,X1))),X3)))),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X1,sK48(X1,X0,X2),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o)),bCOMB,vNOT),vAPP(product_prod(X2,product_prod(X0,X1)),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vEQ(product_prod(X2,product_prod(X0,X1))),X3))))) = X3)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1008])])).
% 68.49/10.17 thf(f3201,plain,(
% 68.49/10.17 spl93_170 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X2,product_prod(X1,X0)),X3 : product_prod(X2,product_prod(X1,X0)) > $o] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK46(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X2),X3))))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_170])])).
% 68.49/10.17 thf(f3220,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1))] : ((vAPP(product_prod(X0,X1),product_prod(X2,product_prod(X0,X1)),vAPP(X2,sTfun(product_prod(X0,X1),product_prod(X2,product_prod(X0,X1))),product_Pair(X2,product_prod(X0,X1)),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X2,sK46(X1,X0,X2),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o)),bCOMB,vNOT),vAPP(product_prod(X2,product_prod(X0,X1)),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vEQ(product_prod(X2,product_prod(X0,X1))),X3)))),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X0,sK47(X1,X0,X2),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o)),bCOMB,vNOT),vAPP(product_prod(X2,product_prod(X0,X1)),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vEQ(product_prod(X2,product_prod(X0,X1))),X3)))),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X1,sK48(X1,X0,X2),vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X2,product_prod(X0,X1)),$o),sTfun(product_prod(X2,product_prod(X0,X1)),$o)),bCOMB,vNOT),vAPP(product_prod(X2,product_prod(X0,X1)),sTfun(product_prod(X2,product_prod(X0,X1)),$o),vEQ(product_prod(X2,product_prod(X0,X1))),X3))))) = X3)) ) | ~spl93_170),
% 68.49/10.17 inference(leibniz_equality_elimination,[],[f3202])).
% 68.49/10.17 thf(f3202,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK46(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X2),X3))))) | ($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4))) ) | ~spl93_170),
% 68.49/10.17 inference(avatar_component_clause,[],[f3201])).
% 68.49/10.17 thf(f50373,plain,(
% 68.49/10.17 spl93_1007 | ~spl93_272),
% 68.49/10.17 inference(avatar_split_clause,[],[f4482,f4468,f50371])).
% 68.49/10.17 thf(f50371,plain,(
% 68.49/10.17 spl93_1007 <=> ! [X1 : $tType,X3 : $tType,X5 : $tType,X0 : $tType,X4 : $tType,X2 : $tType,X7 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X6 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))] : ((X6 = X7) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X5,sK67(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X5,sK67(X5,X0,X1,X2,X3,X4),X7)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1007])])).
% 68.49/10.17 thf(f4482,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X7 : product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))))] : ((X6 = X7) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X4,sK72(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X3,sK71(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X2,sK70(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X1,sK69(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X0,sK68(X5,X0,X1,X2,X3,X4),X7)) | (vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X5,sK67(X5,X0,X1,X2,X3,X4),X6) != vAPP(product_prod(X5,product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),X5,sK67(X5,X0,X1,X2,X3,X4),X7))) ) | ~spl93_272),
% 68.49/10.17 inference(constrained_superposition,[],[f4469,f4469])).
% 68.49/10.17 thf(f50307,plain,(
% 68.49/10.17 spl93_1006 | ~spl93_72 | ~spl93_225),
% 68.49/10.17 inference(avatar_split_clause,[],[f3870,f3863,f2239,f50305])).
% 68.49/10.17 thf(f50305,plain,(
% 68.49/10.17 spl93_1006 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK16(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK17(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK18(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK16(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK17(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK18(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1006])])).
% 68.49/10.17 thf(f3863,plain,(
% 68.49/10.17 spl93_225 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_225])])).
% 68.49/10.17 thf(f3870,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK16(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK17(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK18(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK16(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK17(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK18(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_72 | ~spl93_225)),
% 68.49/10.17 inference(superposition,[],[f3864,f2240])).
% 68.49/10.17 thf(f3864,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0))) ) | ~spl93_225),
% 68.49/10.17 inference(avatar_component_clause,[],[f3863])).
% 68.49/10.17 thf(f50277,plain,(
% 68.49/10.17 spl93_1005 | ~spl93_46 | ~spl93_217),
% 68.49/10.17 inference(avatar_split_clause,[],[f3771,f3768,f2023,f50275])).
% 68.49/10.17 thf(f50275,plain,(
% 68.49/10.17 spl93_1005 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1005])])).
% 68.49/10.17 thf(f3768,plain,(
% 68.49/10.17 spl93_217 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_217])])).
% 68.49/10.17 thf(f3771,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK19(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK20(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP0(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_217)),
% 68.49/10.17 inference(superposition,[],[f3769,f2024])).
% 68.49/10.17 thf(f3769,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) ) | ~spl93_217),
% 68.49/10.17 inference(avatar_component_clause,[],[f3768])).
% 68.49/10.17 thf(f50232,plain,(
% 68.49/10.17 spl93_1004 | ~spl93_395 | ~spl93_722),
% 68.49/10.17 inference(avatar_split_clause,[],[f40161,f31001,f8867,f50230])).
% 68.49/10.17 thf(f50230,plain,(
% 68.49/10.17 spl93_1004 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) != X2) | (X1 = X2))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1004])])).
% 68.49/10.17 thf(f8867,plain,(
% 68.49/10.17 spl93_395 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_395])])).
% 68.49/10.17 thf(f40161,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) != X2) | (X1 = X2)) ) | (~spl93_395 | ~spl93_722)),
% 68.49/10.17 inference(superposition,[],[f31002,f8868])).
% 68.49/10.17 thf(f8868,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))) ) | ~spl93_395),
% 68.49/10.17 inference(avatar_component_clause,[],[f8867])).
% 68.49/10.17 thf(f50228,plain,(
% 68.49/10.17 spl93_1003 | ~spl93_220),
% 68.49/10.17 inference(avatar_split_clause,[],[f3824,f3805,f50226])).
% 68.49/10.17 thf(f50226,plain,(
% 68.49/10.17 spl93_1003 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3))),X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ((vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))))) != X4) | (X4 = X5))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1003])])).
% 68.49/10.17 thf(f3824,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3))),X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ((vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))))) != X4) | (X4 = X5)) ) | ~spl93_220),
% 68.49/10.17 inference(equality_proxy_clausification,[],[f3823])).
% 68.49/10.17 thf(f3823,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3))),X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ((vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))))) != X4) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4),X5))) ) | ~spl93_220),
% 68.49/10.17 inference(equality_proxy_clausification,[],[f3811])).
% 68.49/10.17 thf(f3811,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3))),X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4))))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),vEQ(product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4),X5))) ) | ~spl93_220),
% 68.49/10.17 inference(primitive_instantiation,[],[f3806])).
% 68.49/10.17 thf(f49988,plain,(
% 68.49/10.17 spl93_1002 | ~spl93_48 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4395,f4382,f2031,f49986])).
% 68.49/10.17 thf(f49986,plain,(
% 68.49/10.17 spl93_1002 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : $tType,X7 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),X6 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X3,sK62(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X4,sK63(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X5,sK64(X0,X1,X5,X4,X3),X6)),X2))))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,X7)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X5,X4,X3),X6)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X5,X4,X3),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1002])])).
% 68.49/10.17 thf(f4382,plain,(
% 68.49/10.17 spl93_266 <=> ! [X1 : $tType,X4 : $tType,X0 : $tType,X2 : $tType,X3 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] : (($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6)) | ($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X4,sK62(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X3,sK63(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X2,sK64(X0,X1,X2,X3,X4),X5)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X2,X3,X4),X5)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X2,X3,X4),X5))))))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_266])])).
% 68.49/10.17 thf(f4395,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X6 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))) > $o,X7 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X3,sK62(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X4,sK63(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X5,sK64(X0,X1,X5,X4,X3),X6)),X2))))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,X7)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X5,X4,X3),X6)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X5,X4,X3),X6))) ) | (~spl93_48 | ~spl93_266)),
% 68.49/10.17 inference(constrained_superposition,[],[f4383,f2032])).
% 68.49/10.17 thf(f4383,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o] : (($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X4,sK62(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X3,sK63(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X2,sK64(X0,X1,X2,X3,X4),X5)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X2,X3,X4),X5)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X2,X3,X4),X5))))))) | ($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6))) ) | ~spl93_266),
% 68.49/10.17 inference(avatar_component_clause,[],[f4382])).
% 68.49/10.17 thf(f49984,plain,(
% 68.49/10.17 spl93_1001 | ~spl93_47 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4394,f4382,f2027,f49982])).
% 68.49/10.17 thf(f49982,plain,(
% 68.49/10.17 spl93_1001 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : $tType,X7 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),X6 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X3,sK62(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X4,sK63(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X5,sK64(X0,X1,X5,X4,X3),X6)),X2))))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,X7)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X5,X4,X3),X6)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X5,X4,X3),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1001])])).
% 68.49/10.17 thf(f4394,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X6 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))) > $o,X7 : product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,vAPP(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,product_prod(X1,X0))),product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0))))),product_Pair(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X3,sK62(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X5,product_prod(X1,X0)),product_prod(X4,product_prod(X5,product_prod(X1,X0)))),product_Pair(X4,product_prod(X5,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X4,sK63(X0,X1,X5,X4,X3),X6)),vAPP(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0)),vAPP(X5,sTfun(product_prod(X1,X0),product_prod(X5,product_prod(X1,X0))),product_Pair(X5,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X5,sK64(X0,X1,X5,X4,X3),X6)),X2))))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o,X6,X7)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X5,X4,X3),X6)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X5,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X5,X4,X3),X6))) ) | (~spl93_47 | ~spl93_266)),
% 68.49/10.17 inference(constrained_superposition,[],[f4383,f2028])).
% 68.49/10.17 thf(f49870,plain,(
% 68.49/10.17 spl93_1000 | ~spl93_22 | ~spl93_268),
% 68.49/10.17 inference(avatar_split_clause,[],[f4424,f4409,f1832,f49868])).
% 68.49/10.17 thf(f49868,plain,(
% 68.49/10.17 spl93_1000 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X4 : X0,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_1000])])).
% 68.49/10.17 thf(f4409,plain,(
% 68.49/10.17 spl93_268 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_268])])).
% 68.49/10.17 thf(f4424,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_268)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4423])).
% 68.49/10.17 thf(f4423,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_268)),
% 68.49/10.17 inference(superposition,[],[f4410,f1833])).
% 68.49/10.17 thf(f4410,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_268),
% 68.49/10.17 inference(avatar_component_clause,[],[f4409])).
% 68.49/10.17 thf(f49866,plain,(
% 68.49/10.17 spl93_999 | ~spl93_22 | ~spl93_267),
% 68.49/10.17 inference(avatar_split_clause,[],[f4416,f4405,f1832,f49864])).
% 68.49/10.17 thf(f49864,plain,(
% 68.49/10.17 spl93_999 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X4 : X0,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),X5))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_999])])).
% 68.49/10.17 thf(f4405,plain,(
% 68.49/10.17 spl93_267 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_267])])).
% 68.49/10.17 thf(f4416,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),X5))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_267)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4415])).
% 68.49/10.17 thf(f4415,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),X5))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_267)),
% 68.49/10.17 inference(superposition,[],[f4406,f1833])).
% 68.49/10.17 thf(f4406,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_267),
% 68.49/10.17 inference(avatar_component_clause,[],[f4405])).
% 68.49/10.17 thf(f49461,plain,(
% 68.49/10.17 spl93_998 | ~spl93_22 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4393,f4382,f1832,f49459])).
% 68.49/10.17 thf(f49459,plain,(
% 68.49/10.17 spl93_998 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o,X4,vAPP(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X0,sK62($o,X3,X2,X1,X0),X4)),vAPP(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o)))),product_Pair(X1,product_prod(X2,product_prod(X3,$o))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X1,sK63($o,X3,X2,X1,X0),X4)),vAPP(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o)),vAPP(X2,sTfun(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o))),product_Pair(X2,product_prod(X3,$o)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X2,sK64($o,X3,X2,X1,X0),X4)),vAPP($o,product_prod(X3,$o),vAPP(X3,sTfun($o,product_prod(X3,$o)),product_Pair(X3,$o),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X3,sK65($o,X3,X2,X1,X0),X4)),$true)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),$o,sK66($o,X3,X2,X1,X0),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_998])])).
% 68.49/10.17 thf(f4393,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o,X4,vAPP(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X0,sK62($o,X3,X2,X1,X0),X4)),vAPP(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o)))),product_Pair(X1,product_prod(X2,product_prod(X3,$o))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X1,sK63($o,X3,X2,X1,X0),X4)),vAPP(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o)),vAPP(X2,sTfun(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o))),product_Pair(X2,product_prod(X3,$o)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X2,sK64($o,X3,X2,X1,X0),X4)),vAPP($o,product_prod(X3,$o),vAPP(X3,sTfun($o,product_prod(X3,$o)),product_Pair(X3,$o),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),X3,sK65($o,X3,X2,X1,X0),X4)),$true)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o),$o,sK66($o,X3,X2,X1,X0),X4))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(superposition,[],[f4383,f1833])).
% 68.49/10.17 thf(f49457,plain,(
% 68.49/10.17 spl93_997 | ~spl93_22 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4392,f4382,f1832,f49455])).
% 68.49/10.17 thf(f49455,plain,(
% 68.49/10.17 spl93_997 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o,X4,vAPP(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X0,sK62(X3,$o,X2,X1,X0),X4)),vAPP(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3))),vAPP(X1,sTfun(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3)))),product_Pair(X1,product_prod(X2,product_prod($o,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X1,sK63(X3,$o,X2,X1,X0),X4)),vAPP(product_prod($o,X3),product_prod(X2,product_prod($o,X3)),vAPP(X2,sTfun(product_prod($o,X3),product_prod(X2,product_prod($o,X3))),product_Pair(X2,product_prod($o,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X2,sK64(X3,$o,X2,X1,X0),X4)),vAPP(X3,product_prod($o,X3),vAPP($o,sTfun(X3,product_prod($o,X3)),product_Pair($o,X3),$true),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X3,sK66(X3,$o,X2,X1,X0),X4))))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),$o,sK65(X3,$o,X2,X1,X0),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_997])])).
% 68.49/10.17 thf(f4392,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o,X4,vAPP(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X0,sK62(X3,$o,X2,X1,X0),X4)),vAPP(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3))),vAPP(X1,sTfun(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3)))),product_Pair(X1,product_prod(X2,product_prod($o,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X1,sK63(X3,$o,X2,X1,X0),X4)),vAPP(product_prod($o,X3),product_prod(X2,product_prod($o,X3)),vAPP(X2,sTfun(product_prod($o,X3),product_prod(X2,product_prod($o,X3))),product_Pair(X2,product_prod($o,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X2,sK64(X3,$o,X2,X1,X0),X4)),vAPP(X3,product_prod($o,X3),vAPP($o,sTfun(X3,product_prod($o,X3)),product_Pair($o,X3),$true),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),X3,sK66(X3,$o,X2,X1,X0),X4))))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o),$o,sK65(X3,$o,X2,X1,X0),X4))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(superposition,[],[f4383,f1833])).
% 68.49/10.17 thf(f49453,plain,(
% 68.49/10.17 spl93_996 | ~spl93_22 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4391,f4382,f1832,f49451])).
% 68.49/10.17 thf(f49451,plain,(
% 68.49/10.17 spl93_996 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o,X4,vAPP(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))),product_Pair(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X0,sK62(X3,X2,$o,X1,X0),X4)),vAPP(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3))),vAPP(X1,sTfun(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3)))),product_Pair(X1,product_prod($o,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X1,sK63(X3,X2,$o,X1,X0),X4)),vAPP(product_prod(X2,X3),product_prod($o,product_prod(X2,X3)),vAPP($o,sTfun(product_prod(X2,X3),product_prod($o,product_prod(X2,X3))),product_Pair($o,product_prod(X2,X3)),$true),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,$o,X1,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,$o,X1,X0),X4))))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),$o,sK64(X3,X2,$o,X1,X0),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_996])])).
% 68.49/10.17 thf(f4391,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o,X4,vAPP(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))),product_Pair(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X0,sK62(X3,X2,$o,X1,X0),X4)),vAPP(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3))),vAPP(X1,sTfun(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3)))),product_Pair(X1,product_prod($o,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X1,sK63(X3,X2,$o,X1,X0),X4)),vAPP(product_prod(X2,X3),product_prod($o,product_prod(X2,X3)),vAPP($o,sTfun(product_prod(X2,X3),product_prod($o,product_prod(X2,X3))),product_Pair($o,product_prod(X2,X3)),$true),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,$o,X1,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,$o,X1,X0),X4))))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o),$o,sK64(X3,X2,$o,X1,X0),X4))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(superposition,[],[f4383,f1833])).
% 68.49/10.17 thf(f49449,plain,(
% 68.49/10.17 spl93_995 | ~spl93_22 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4390,f4382,f1832,f49447])).
% 68.49/10.17 thf(f49447,plain,(
% 68.49/10.17 spl93_995 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))) > $o,X5 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))] : (($true != vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o,X4,vAPP(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))),product_Pair(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X0,sK62(X3,X2,X1,$o,X0),X4)),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3))),vAPP($o,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3)))),product_Pair($o,product_prod(X1,product_prod(X2,X3))),$true),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X1,sK64(X3,X2,X1,$o,X0),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,X1,$o,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,X1,$o,X0),X4))))))) | ($true = vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),$o,sK63(X3,X2,X1,$o,X0),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_995])])).
% 68.49/10.17 thf(f4390,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))) > $o,X5 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))] : (($true != vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o,X4,vAPP(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))),product_Pair(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X0,sK62(X3,X2,X1,$o,X0),X4)),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3))),vAPP($o,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3)))),product_Pair($o,product_prod(X1,product_prod(X2,X3))),$true),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X1,sK64(X3,X2,X1,$o,X0),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,X1,$o,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,X1,$o,X0),X4))))))) | ($true = vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o),$o,sK63(X3,X2,X1,$o,X0),X4))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(superposition,[],[f4383,f1833])).
% 68.49/10.17 thf(f49445,plain,(
% 68.49/10.17 spl93_994 | ~spl93_22 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4389,f4382,f1832,f49443])).
% 68.49/10.17 thf(f49443,plain,(
% 68.49/10.17 spl93_994 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))) > $o,X5 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : (($true != vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X4,vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),product_Pair($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$true),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X0,sK63(X3,X2,X1,X0,$o),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X1,sK64(X3,X2,X1,X0,$o),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,X1,X0,$o),X4)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,X1,X0,$o),X4))))))) | ($true = vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),$o,sK62(X3,X2,X1,X0,$o),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_994])])).
% 68.49/10.17 thf(f4389,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))) > $o,X5 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : (($true != vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X4,vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),product_Pair($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$true),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X0,sK63(X3,X2,X1,X0,$o),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X1,sK64(X3,X2,X1,X0,$o),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,X1,X0,$o),X4)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,X1,X0,$o),X4))))))) | ($true = vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X4,X5)) | ($false = vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),$o,sK62(X3,X2,X1,X0,$o),X4))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(superposition,[],[f4383,f1833])).
% 68.49/10.17 thf(f48889,plain,(
% 68.49/10.17 spl93_993 | ~spl93_22 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4401,f4382,f1832,f48887])).
% 68.49/10.17 thf(f48887,plain,(
% 68.49/10.17 spl93_993 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X4 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > $o,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : (($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o,X5,X6)) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o,X5,vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X0,sK62(X4,X3,X2,X1,X0),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X1,sK63(X4,X3,X2,X1,X0),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X2,sK64(X4,X3,X2,X1,X0),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X3,sK65(X4,X3,X2,X1,X0),X5)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X4,sK66(X4,X3,X2,X1,X0),X5))))))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_993])])).
% 68.49/10.17 thf(f4401,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > $o] : (($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o,X5,X6)) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o,X5,vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X0,sK62(X4,X3,X2,X1,X0),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X1,sK63(X4,X3,X2,X1,X0),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X2,sK64(X4,X3,X2,X1,X0),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X3,sK65(X4,X3,X2,X1,X0),X5)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X4,sK66(X4,X3,X2,X1,X0),X5)))))))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4399])).
% 68.49/10.17 thf(f4399,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > $o] : (($true != $true) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o,X5,X6)) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o,X5,vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X0,sK62(X4,X3,X2,X1,X0),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X1,sK63(X4,X3,X2,X1,X0),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X2,sK64(X4,X3,X2,X1,X0),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X3,sK65(X4,X3,X2,X1,X0),X5)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),$o),X4,sK66(X4,X3,X2,X1,X0),X5)))))))) ) | (~spl93_22 | ~spl93_266)),
% 68.49/10.17 inference(superposition,[],[f4383,f1833])).
% 68.49/10.17 thf(f48885,plain,(
% 68.49/10.17 spl93_992 | ~spl93_139 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4396,f4382,f2831,f48883])).
% 68.49/10.17 thf(f48883,plain,(
% 68.49/10.17 spl93_992 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : $tType,X5 : $tType,X7 : product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),X6 : product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))) > $o,X3 : product_prod(X2,product_prod(X0,X1))] : (($true != vAPP(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o,X6,vAPP(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(X4,sTfun(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),product_Pair(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X4,sK62(X1,X0,X2,X5,X4),X6)),vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1))),vAPP(X5,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_Pair(X5,product_prod(X2,product_prod(X0,X1))),vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X5,sK63(X1,X0,X2,X5,X4),X6)),X3)))) | ($true = vAPP(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o,X6,X7)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X1,sK66(X1,X0,X2,X5,X4),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X0,sK65(X1,X0,X2,X5,X4),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X2,sK64(X1,X0,X2,X5,X4),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_992])])).
% 68.49/10.17 thf(f4396,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X6 : product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))) > $o,X7 : product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))] : (($true != vAPP(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o,X6,vAPP(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(X4,sTfun(product_prod(X5,product_prod(X2,product_prod(X0,X1))),product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1))))),product_Pair(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X4,sK62(X1,X0,X2,X5,X4),X6)),vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1))),vAPP(X5,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X5,product_prod(X2,product_prod(X0,X1)))),product_Pair(X5,product_prod(X2,product_prod(X0,X1))),vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X5,sK63(X1,X0,X2,X5,X4),X6)),X3)))) | ($true = vAPP(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o,X6,X7)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X1,sK66(X1,X0,X2,X5,X4),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X0,sK65(X1,X0,X2,X5,X4),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X5,product_prod(X2,product_prod(X0,X1)))),$o),X2,sK64(X1,X0,X2,X5,X4),X6))) ) | (~spl93_139 | ~spl93_266)),
% 68.49/10.17 inference(constrained_superposition,[],[f4383,f2832])).
% 68.49/10.17 thf(f48878,plain,(
% 68.49/10.17 spl93_991 | ~spl93_66 | ~spl93_265),
% 68.49/10.17 inference(avatar_split_clause,[],[f4379,f4330,f2161,f48876])).
% 68.49/10.17 thf(f48876,plain,(
% 68.49/10.17 spl93_991 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_991])])).
% 68.49/10.17 thf(f2161,plain,(
% 68.49/10.17 spl93_66 <=> (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_66])])).
% 68.49/10.17 thf(f4330,plain,(
% 68.49/10.17 spl93_265 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_265])])).
% 68.49/10.17 thf(f4379,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_265)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4374])).
% 68.49/10.17 thf(f4374,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_265)),
% 68.49/10.17 inference(superposition,[],[f4331,f2163])).
% 68.49/10.17 thf(f2163,plain,(
% 68.49/10.17 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true) | ~spl93_66),
% 68.49/10.17 inference(avatar_component_clause,[],[f2161])).
% 68.49/10.17 thf(f4331,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_265),
% 68.49/10.17 inference(avatar_component_clause,[],[f4330])).
% 68.49/10.17 thf(f48871,plain,(
% 68.49/10.17 spl93_990 | ~spl93_66 | ~spl93_264),
% 68.49/10.17 inference(avatar_split_clause,[],[f4371,f4326,f2161,f48869])).
% 68.49/10.17 thf(f48869,plain,(
% 68.49/10.17 spl93_990 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_990])])).
% 68.49/10.17 thf(f4326,plain,(
% 68.49/10.17 spl93_264 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_264])])).
% 68.49/10.17 thf(f4371,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_264)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4366])).
% 68.49/10.17 thf(f4366,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_264)),
% 68.49/10.17 inference(superposition,[],[f4327,f2163])).
% 68.49/10.17 thf(f4327,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_264),
% 68.49/10.17 inference(avatar_component_clause,[],[f4326])).
% 68.49/10.17 thf(f48836,plain,(
% 68.49/10.17 spl93_989 | ~spl93_345 | ~spl93_988),
% 68.49/10.17 inference(avatar_split_clause,[],[f48832,f48827,f6456,f48834])).
% 68.49/10.17 thf(f48834,plain,(
% 68.49/10.17 spl93_989 <=> ! [X2 : a,X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_989])])).
% 68.49/10.17 thf(f48827,plain,(
% 68.49/10.17 spl93_988 <=> ! [X2 : a,X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_988])])).
% 68.49/10.17 thf(f48832,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_345 | ~spl93_988)),
% 68.49/10.17 inference(forward_demodulation,[],[f48831,f6458])).
% 68.49/10.17 thf(f48831,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_345 | ~spl93_988)),
% 68.49/10.17 inference(forward_demodulation,[],[f48830,f6458])).
% 68.49/10.17 thf(f48830,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_345 | ~spl93_988)),
% 68.49/10.17 inference(forward_demodulation,[],[f48828,f6458])).
% 68.49/10.17 thf(f48828,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | ~spl93_988),
% 68.49/10.17 inference(avatar_component_clause,[],[f48827])).
% 68.49/10.17 thf(f48829,plain,(
% 68.49/10.17 spl93_988 | ~spl93_148 | ~spl93_236),
% 68.49/10.17 inference(avatar_split_clause,[],[f4001,f3998,f2904,f48827])).
% 68.49/10.17 thf(f2904,plain,(
% 68.49/10.17 spl93_148 <=> ! [X0 : nat,X1 : a] : (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),X1))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_148])])).
% 68.49/10.17 thf(f3998,plain,(
% 68.49/10.17 spl93_236 <=> ! [X2 : a,X0 : a,X1 : a] : ((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_236])])).
% 68.49/10.17 thf(f4001,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X1 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_148 | ~spl93_236)),
% 68.49/10.17 inference(superposition,[],[f3999,f2905])).
% 68.49/10.17 thf(f2905,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),X1))) ) | ~spl93_148),
% 68.49/10.17 inference(avatar_component_clause,[],[f2904])).
% 68.49/10.17 thf(f3999,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X0 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) ) | ~spl93_236),
% 68.49/10.17 inference(avatar_component_clause,[],[f3998])).
% 68.49/10.17 thf(f48713,plain,(
% 68.49/10.17 spl93_987 | ~spl93_345 | ~spl93_986),
% 68.49/10.17 inference(avatar_split_clause,[],[f48668,f48664,f6456,f48711])).
% 68.49/10.17 thf(f48711,plain,(
% 68.49/10.17 spl93_987 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_987])])).
% 68.49/10.17 thf(f48664,plain,(
% 68.49/10.17 spl93_986 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_986])])).
% 68.49/10.17 thf(f48668,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_986)),
% 68.49/10.17 inference(forward_demodulation,[],[f48667,f6458])).
% 68.49/10.17 thf(f48667,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_986)),
% 68.49/10.17 inference(forward_demodulation,[],[f48665,f6458])).
% 68.49/10.17 thf(f48665,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_986),
% 68.49/10.17 inference(avatar_component_clause,[],[f48664])).
% 68.49/10.17 thf(f48666,plain,(
% 68.49/10.17 spl93_986 | ~spl93_61 | ~spl93_265),
% 68.49/10.17 inference(avatar_split_clause,[],[f4380,f4330,f2136,f48664])).
% 68.49/10.17 thf(f2136,plain,(
% 68.49/10.17 spl93_61 <=> (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_61])])).
% 68.49/10.17 thf(f4380,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_265)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4373])).
% 68.49/10.17 thf(f4373,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_265)),
% 68.49/10.17 inference(superposition,[],[f4331,f2138])).
% 68.49/10.17 thf(f2138,plain,(
% 68.49/10.17 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true) | ~spl93_61),
% 68.49/10.17 inference(avatar_component_clause,[],[f2136])).
% 68.49/10.17 thf(f48554,plain,(
% 68.49/10.17 spl93_985 | ~spl93_345 | ~spl93_984),
% 68.49/10.17 inference(avatar_split_clause,[],[f48550,f48546,f6456,f48552])).
% 68.49/10.17 thf(f48552,plain,(
% 68.49/10.17 spl93_985 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_985])])).
% 68.49/10.17 thf(f48546,plain,(
% 68.49/10.17 spl93_984 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_984])])).
% 68.49/10.17 thf(f48550,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1)))) ) | (~spl93_345 | ~spl93_984)),
% 68.49/10.17 inference(forward_demodulation,[],[f48549,f6458])).
% 68.49/10.17 thf(f48549,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_984)),
% 68.49/10.17 inference(forward_demodulation,[],[f48547,f6458])).
% 68.49/10.17 thf(f48547,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_984),
% 68.49/10.17 inference(avatar_component_clause,[],[f48546])).
% 68.49/10.17 thf(f48548,plain,(
% 68.49/10.17 spl93_984 | ~spl93_61 | ~spl93_264),
% 68.49/10.17 inference(avatar_split_clause,[],[f4372,f4326,f2136,f48546])).
% 68.49/10.17 thf(f4372,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_264)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4365])).
% 68.49/10.17 thf(f4365,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_264)),
% 68.49/10.17 inference(superposition,[],[f4327,f2138])).
% 68.49/10.17 thf(f48474,plain,(
% 68.49/10.17 spl93_983 | ~spl93_206 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4397,f4382,f3634,f48472])).
% 68.49/10.17 thf(f48472,plain,(
% 68.49/10.17 spl93_983 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X2 : $tType,X5 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X7 : product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X6 : product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))) > $o] : (($true != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o,X6,vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),product_Pair(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X5,sK62(X2,X1,X0,X3,X5),X6)),X4))) | ($true = vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o,X6,X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X2,sK66(X2,X1,X0,X3,X5),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X1,sK65(X2,X1,X0,X3,X5),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X0,sK64(X2,X1,X0,X3,X5),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X3,sK63(X2,X1,X0,X3,X5),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_983])])).
% 68.49/10.17 thf(f4397,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))) > $o,X7 : product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2)))] : (($true != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o,X6,vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),product_Pair(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X5,sK62(X2,X1,X0,X3,X5),X6)),X4))) | ($true = vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o,X6,X7)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X2,sK66(X2,X1,X0,X3,X5),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X1,sK65(X2,X1,X0,X3,X5),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X0,sK64(X2,X1,X0,X3,X5),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),$o),X3,sK63(X2,X1,X0,X3,X5),X6))) ) | (~spl93_206 | ~spl93_266)),
% 68.49/10.17 inference(constrained_superposition,[],[f4383,f3635])).
% 68.49/10.17 thf(f48382,plain,(
% 68.49/10.17 spl93_982 | ~spl93_345 | ~spl93_981),
% 68.49/10.17 inference(avatar_split_clause,[],[f48378,f48373,f6456,f48380])).
% 68.49/10.17 thf(f48380,plain,(
% 68.49/10.17 spl93_982 <=> ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_982])])).
% 68.49/10.17 thf(f48373,plain,(
% 68.49/10.17 spl93_981 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_981])])).
% 68.49/10.17 thf(f48378,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)))) ) | (~spl93_345 | ~spl93_981)),
% 68.49/10.17 inference(forward_demodulation,[],[f48377,f6458])).
% 68.49/10.17 thf(f48377,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_981)),
% 68.49/10.17 inference(forward_demodulation,[],[f48376,f6458])).
% 68.49/10.17 thf(f48376,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_981)),
% 68.49/10.17 inference(forward_demodulation,[],[f48374,f6458])).
% 68.49/10.17 thf(f48374,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_981),
% 68.49/10.17 inference(avatar_component_clause,[],[f48373])).
% 68.49/10.17 thf(f48375,plain,(
% 68.49/10.17 spl93_981 | ~spl93_22 | ~spl93_265),
% 68.49/10.17 inference(avatar_split_clause,[],[f4377,f4330,f1832,f48373])).
% 68.49/10.17 thf(f4377,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_265)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4376])).
% 68.49/10.17 thf(f4376,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_265)),
% 68.49/10.17 inference(superposition,[],[f4331,f1833])).
% 68.49/10.17 thf(f48210,plain,(
% 68.49/10.17 spl93_980 | ~spl93_345 | ~spl93_979),
% 68.49/10.17 inference(avatar_split_clause,[],[f48206,f48201,f6456,f48208])).
% 68.49/10.17 thf(f48208,plain,(
% 68.49/10.17 spl93_980 <=> ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_980])])).
% 68.49/10.17 thf(f48201,plain,(
% 68.49/10.17 spl93_979 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_979])])).
% 68.49/10.17 thf(f48206,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)))) ) | (~spl93_345 | ~spl93_979)),
% 68.49/10.17 inference(forward_demodulation,[],[f48205,f6458])).
% 68.49/10.17 thf(f48205,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_979)),
% 68.49/10.17 inference(forward_demodulation,[],[f48204,f6458])).
% 68.49/10.17 thf(f48204,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_979)),
% 68.49/10.17 inference(forward_demodulation,[],[f48202,f6458])).
% 68.49/10.17 thf(f48202,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_979),
% 68.49/10.17 inference(avatar_component_clause,[],[f48201])).
% 68.49/10.17 thf(f48203,plain,(
% 68.49/10.17 spl93_979 | ~spl93_22 | ~spl93_264),
% 68.49/10.17 inference(avatar_split_clause,[],[f4369,f4326,f1832,f48201])).
% 68.49/10.17 thf(f4369,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_264)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4368])).
% 68.49/10.17 thf(f4368,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_264)),
% 68.49/10.17 inference(superposition,[],[f4327,f1833])).
% 68.49/10.17 thf(f48136,plain,(
% 68.49/10.17 spl93_978 | ~spl93_117 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4466,f4448,f2628,f48134])).
% 68.49/10.17 thf(f48134,plain,(
% 68.49/10.17 spl93_978 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_978])])).
% 68.49/10.17 thf(f2628,plain,(
% 68.49/10.17 spl93_117 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r2),s)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_117])])).
% 68.49/10.17 thf(f4466,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_117 | ~spl93_271)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4453])).
% 68.49/10.17 thf(f4453,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_117 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f2630])).
% 68.49/10.17 thf(f2630,plain,(
% 68.49/10.17 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r2),s)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | ~spl93_117),
% 68.49/10.17 inference(avatar_component_clause,[],[f2628])).
% 68.49/10.17 thf(f48132,plain,(
% 68.49/10.17 spl93_977 | ~spl93_118 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4465,f4448,f2633,f48130])).
% 68.49/10.17 thf(f48130,plain,(
% 68.49/10.17 spl93_977 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s2))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_977])])).
% 68.49/10.17 thf(f2633,plain,(
% 68.49/10.17 spl93_118 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r3),s2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_118])])).
% 68.49/10.17 thf(f4465,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s2))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_118 | ~spl93_271)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4454])).
% 68.49/10.17 thf(f4454,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s2))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_118 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f2635])).
% 68.49/10.17 thf(f2635,plain,(
% 68.49/10.17 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r3),s2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | ~spl93_118),
% 68.49/10.17 inference(avatar_component_clause,[],[f2633])).
% 68.49/10.17 thf(f48128,plain,(
% 68.49/10.17 spl93_976 | ~spl93_120 | ~spl93_271),
% 68.49/10.17 inference(avatar_split_clause,[],[f4464,f4448,f2642,f48126])).
% 68.49/10.17 thf(f48126,plain,(
% 68.49/10.17 spl93_976 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_976])])).
% 68.49/10.17 thf(f2642,plain,(
% 68.49/10.17 spl93_120 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r4),s3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_120])])).
% 68.49/10.17 thf(f4464,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_120 | ~spl93_271)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4455])).
% 68.49/10.17 thf(f4455,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) ) | (~spl93_120 | ~spl93_271)),
% 68.49/10.17 inference(superposition,[],[f4449,f2644])).
% 68.49/10.17 thf(f2644,plain,(
% 68.49/10.17 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r4),s3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true) | ~spl93_120),
% 68.49/10.17 inference(avatar_component_clause,[],[f2642])).
% 68.49/10.17 thf(f47800,plain,(
% 68.49/10.17 spl93_975 | ~spl93_75 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4250,f4237,f2256,f47798])).
% 68.49/10.17 thf(f47798,plain,(
% 68.49/10.17 spl93_975 <=> ! [X1 : $tType,X3 : $tType,X4 : $tType,X6 : $tType,X0 : $tType,X2 : $tType,X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X7 : X4 > product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X6] : (vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6,vAPP(X4,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6),X7,vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5)),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5)),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5))))) = vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X6,vAPP(sTfun(X4,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6)),sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X6),product_rec_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6),X7),X5))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_975])])).
% 68.49/10.17 thf(f4250,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X7 : X4 > product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X6,X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6,vAPP(X4,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6),X7,vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5)),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5)),vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5))))) = vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X6,vAPP(sTfun(X4,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6)),sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X6),product_rec_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))),X6),X7),X5))) ) | (~spl93_75 | ~spl93_256)),
% 68.49/10.17 inference(superposition,[],[f2257,f4238])).
% 68.49/10.17 thf(f47679,plain,(
% 68.49/10.17 spl93_974 | ~spl93_22 | ~spl93_260),
% 68.49/10.17 inference(avatar_split_clause,[],[f4302,f4290,f1832,f47677])).
% 68.49/10.17 thf(f47677,plain,(
% 68.49/10.17 spl93_974 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X4 : X0,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_974])])).
% 68.49/10.17 thf(f4290,plain,(
% 68.49/10.17 spl93_260 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_260])])).
% 68.49/10.17 thf(f4302,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_260)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4301])).
% 68.49/10.17 thf(f4301,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_260)),
% 68.49/10.17 inference(superposition,[],[f4291,f1833])).
% 68.49/10.17 thf(f4291,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_260),
% 68.49/10.17 inference(avatar_component_clause,[],[f4290])).
% 68.49/10.17 thf(f46622,plain,(
% 68.49/10.17 spl93_973 | ~spl93_22 | ~spl93_263),
% 68.49/10.17 inference(avatar_split_clause,[],[f4324,f4316,f1832,f46620])).
% 68.49/10.17 thf(f46620,plain,(
% 68.49/10.17 spl93_973 <=> ! [X0 : $tType,X2 : $o,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_973])])).
% 68.49/10.17 thf(f4316,plain,(
% 68.49/10.17 spl93_263 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_263])])).
% 68.49/10.17 thf(f4324,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $o,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_263)),
% 68.49/10.17 inference(inner_rewriting,[],[f4320])).
% 68.49/10.17 thf(f4320,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $o,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_263)),
% 68.49/10.17 inference(superposition,[],[f4317,f1833])).
% 68.49/10.17 thf(f4317,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) ) | ~spl93_263),
% 68.49/10.17 inference(avatar_component_clause,[],[f4316])).
% 68.49/10.17 thf(f46566,plain,(
% 68.49/10.17 spl93_972 | ~spl93_48 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4246,f4237,f2031,f46564])).
% 68.49/10.17 thf(f46564,plain,(
% 68.49/10.17 spl93_972 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : $tType,X6 : product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0))))),product_Pair(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X5,sK57(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X3,sK58(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X4,sK59(X5,X3,X4,X1,X0),X6)),X2))) = X6) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X1,sK60(X5,X3,X4,X1,X0),X6)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X0,sK61(X5,X3,X4,X1,X0),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_972])])).
% 68.49/10.17 thf(f4246,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X6 : product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0))))] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0))))),product_Pair(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X5,sK57(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X3,sK58(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X4,sK59(X5,X3,X4,X1,X0),X6)),X2))) = X6) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X1,sK60(X5,X3,X4,X1,X0),X6)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X0,sK61(X5,X3,X4,X1,X0),X6))) ) | (~spl93_48 | ~spl93_256)),
% 68.49/10.17 inference(constrained_superposition,[],[f4238,f2032])).
% 68.49/10.17 thf(f46562,plain,(
% 68.49/10.17 spl93_971 | ~spl93_47 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4245,f4237,f2027,f46560])).
% 68.49/10.17 thf(f46560,plain,(
% 68.49/10.17 spl93_971 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : $tType,X6 : product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0))))),product_Pair(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X5,sK57(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X3,sK58(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X4,sK59(X5,X3,X4,X1,X0),X6)),X2))) = X6) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X1,sK60(X5,X3,X4,X1,X0),X6)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X0,sK61(X5,X3,X4,X1,X0),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_971])])).
% 68.49/10.17 thf(f4245,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X6 : product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0))))] : ((vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0))))),product_Pair(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X5,sK57(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X3,sK58(X5,X3,X4,X1,X0),X6)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X4,sK59(X5,X3,X4,X1,X0),X6)),X2))) = X6) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X1,sK60(X5,X3,X4,X1,X0),X6)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X5,product_prod(X3,product_prod(X4,product_prod(X1,X0)))),X0,sK61(X5,X3,X4,X1,X0),X6))) ) | (~spl93_47 | ~spl93_256)),
% 68.49/10.17 inference(constrained_superposition,[],[f4238,f2028])).
% 68.49/10.17 thf(f46538,plain,(
% 68.49/10.17 spl93_970 | ~spl93_256 | ~spl93_266),
% 68.49/10.17 inference(avatar_split_clause,[],[f4398,f4382,f4237,f46536])).
% 68.49/10.17 thf(f46536,plain,(
% 68.49/10.17 spl93_970 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X7 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X6 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))) > $o] : (($true != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X6,X5)) | ($true = vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X6,X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X1,sK64(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X0,sK63(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X4,sK62(X3,X2,X1,X0,X4),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_970])])).
% 68.49/10.17 thf(f4398,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))) > $o,X7 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : (($true != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X6,X5)) | ($true = vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,X6,X7)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X3,sK66(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X2,sK65(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X1,sK64(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X0,sK63(X3,X2,X1,X0,X4),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5) != vAPP(sTfun(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o),X4,sK62(X3,X2,X1,X0,X4),X6))) ) | (~spl93_256 | ~spl93_266)),
% 68.49/10.17 inference(constrained_superposition,[],[f4383,f4238])).
% 68.49/10.17 thf(f45980,plain,(
% 68.49/10.17 spl93_969 | ~spl93_22 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4244,f4237,f1832,f45978])).
% 68.49/10.17 thf(f45978,plain,(
% 68.49/10.17 spl93_969 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X0,sK57(X0,X1,X2,X3,$o),X4)),vAPP(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o)))),product_Pair(X1,product_prod(X2,product_prod(X3,$o))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X1,sK58(X0,X1,X2,X3,$o),X4)),vAPP(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o)),vAPP(X2,sTfun(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o))),product_Pair(X2,product_prod(X3,$o)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X2,sK59(X0,X1,X2,X3,$o),X4)),vAPP($o,product_prod(X3,$o),vAPP(X3,sTfun($o,product_prod(X3,$o)),product_Pair(X3,$o),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X3,sK60(X0,X1,X2,X3,$o),X4)),$true)))) = X4) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o,sK61(X0,X1,X2,X3,$o),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_969])])).
% 68.49/10.17 thf(f4244,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,$o))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X0,sK57(X0,X1,X2,X3,$o),X4)),vAPP(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,$o)),product_prod(X1,product_prod(X2,product_prod(X3,$o)))),product_Pair(X1,product_prod(X2,product_prod(X3,$o))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X1,sK58(X0,X1,X2,X3,$o),X4)),vAPP(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o)),vAPP(X2,sTfun(product_prod(X3,$o),product_prod(X2,product_prod(X3,$o))),product_Pair(X2,product_prod(X3,$o)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X2,sK59(X0,X1,X2,X3,$o),X4)),vAPP($o,product_prod(X3,$o),vAPP(X3,sTfun($o,product_prod(X3,$o)),product_Pair(X3,$o),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),X3,sK60(X0,X1,X2,X3,$o),X4)),$true)))) = X4) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,$o)))),$o,sK61(X0,X1,X2,X3,$o),X4))) ) | (~spl93_22 | ~spl93_256)),
% 68.49/10.17 inference(superposition,[],[f4238,f1833])).
% 68.49/10.17 thf(f45976,plain,(
% 68.49/10.17 spl93_968 | ~spl93_22 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4243,f4237,f1832,f45974])).
% 68.49/10.17 thf(f45974,plain,(
% 68.49/10.17 spl93_968 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X0,sK57(X0,X1,X2,$o,X3),X4)),vAPP(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3))),vAPP(X1,sTfun(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3)))),product_Pair(X1,product_prod(X2,product_prod($o,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X1,sK58(X0,X1,X2,$o,X3),X4)),vAPP(product_prod($o,X3),product_prod(X2,product_prod($o,X3)),vAPP(X2,sTfun(product_prod($o,X3),product_prod(X2,product_prod($o,X3))),product_Pair(X2,product_prod($o,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X2,sK59(X0,X1,X2,$o,X3),X4)),vAPP(X3,product_prod($o,X3),vAPP($o,sTfun(X3,product_prod($o,X3)),product_Pair($o,X3),$true),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X3,sK61(X0,X1,X2,$o,X3),X4))))) = X4) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o,sK60(X0,X1,X2,$o,X3),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_968])])).
% 68.49/10.17 thf(f4243,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod($o,X3))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X0,sK57(X0,X1,X2,$o,X3),X4)),vAPP(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3))),vAPP(X1,sTfun(product_prod(X2,product_prod($o,X3)),product_prod(X1,product_prod(X2,product_prod($o,X3)))),product_Pair(X1,product_prod(X2,product_prod($o,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X1,sK58(X0,X1,X2,$o,X3),X4)),vAPP(product_prod($o,X3),product_prod(X2,product_prod($o,X3)),vAPP(X2,sTfun(product_prod($o,X3),product_prod(X2,product_prod($o,X3))),product_Pair(X2,product_prod($o,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X2,sK59(X0,X1,X2,$o,X3),X4)),vAPP(X3,product_prod($o,X3),vAPP($o,sTfun(X3,product_prod($o,X3)),product_Pair($o,X3),$true),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),X3,sK61(X0,X1,X2,$o,X3),X4))))) = X4) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod($o,X3)))),$o,sK60(X0,X1,X2,$o,X3),X4))) ) | (~spl93_22 | ~spl93_256)),
% 68.49/10.17 inference(superposition,[],[f4238,f1833])).
% 68.49/10.17 thf(f45972,plain,(
% 68.49/10.17 spl93_967 | ~spl93_22 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4242,f4237,f1832,f45970])).
% 68.49/10.17 thf(f45970,plain,(
% 68.49/10.17 spl93_967 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))] : ((vAPP(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))),product_Pair(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X0,sK57(X0,X1,$o,X2,X3),X4)),vAPP(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3))),vAPP(X1,sTfun(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3)))),product_Pair(X1,product_prod($o,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X1,sK58(X0,X1,$o,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod($o,product_prod(X2,X3)),vAPP($o,sTfun(product_prod(X2,X3),product_prod($o,product_prod(X2,X3))),product_Pair($o,product_prod(X2,X3)),$true),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X2,sK60(X0,X1,$o,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X3,sK61(X0,X1,$o,X2,X3),X4))))) = X4) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o,sK59(X0,X1,$o,X2,X3),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_967])])).
% 68.49/10.17 thf(f4242,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))] : ((vAPP(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,product_prod(X2,X3))),product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3))))),product_Pair(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X0,sK57(X0,X1,$o,X2,X3),X4)),vAPP(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3))),vAPP(X1,sTfun(product_prod($o,product_prod(X2,X3)),product_prod(X1,product_prod($o,product_prod(X2,X3)))),product_Pair(X1,product_prod($o,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X1,sK58(X0,X1,$o,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod($o,product_prod(X2,X3)),vAPP($o,sTfun(product_prod(X2,X3),product_prod($o,product_prod(X2,X3))),product_Pair($o,product_prod(X2,X3)),$true),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X2,sK60(X0,X1,$o,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),X3,sK61(X0,X1,$o,X2,X3),X4))))) = X4) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod($o,product_prod(X2,X3)))),$o,sK59(X0,X1,$o,X2,X3),X4))) ) | (~spl93_22 | ~spl93_256)),
% 68.49/10.17 inference(superposition,[],[f4238,f1833])).
% 68.49/10.17 thf(f45968,plain,(
% 68.49/10.17 spl93_966 | ~spl93_22 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4241,f4237,f1832,f45966])).
% 68.49/10.17 thf(f45966,plain,(
% 68.49/10.17 spl93_966 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))),product_Pair(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X0,sK57(X0,$o,X1,X2,X3),X4)),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3))),vAPP($o,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3)))),product_Pair($o,product_prod(X1,product_prod(X2,X3))),$true),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X0,$o,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X0,$o,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X0,$o,X1,X2,X3),X4))))) = X4) | ($false = vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o,sK58(X0,$o,X1,X2,X3),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_966])])).
% 68.49/10.17 thf(f4241,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,product_prod(X2,X3))),product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3))))),product_Pair(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X0,sK57(X0,$o,X1,X2,X3),X4)),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3))),vAPP($o,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod($o,product_prod(X1,product_prod(X2,X3)))),product_Pair($o,product_prod(X1,product_prod(X2,X3))),$true),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X0,$o,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X0,$o,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X0,$o,X1,X2,X3),X4))))) = X4) | ($false = vAPP(product_prod(X0,product_prod($o,product_prod(X1,product_prod(X2,X3)))),$o,sK58(X0,$o,X1,X2,X3),X4))) ) | (~spl93_22 | ~spl93_256)),
% 68.49/10.17 inference(superposition,[],[f4238,f1833])).
% 68.49/10.17 thf(f45964,plain,(
% 68.49/10.17 spl93_965 | ~spl93_22 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4240,f4237,f1832,f45962])).
% 68.49/10.17 thf(f45962,plain,(
% 68.49/10.17 spl93_965 <=> ! [X1 : $tType,X2 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),product_Pair($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$true),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58($o,X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59($o,X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60($o,X0,X1,X2,X3),X4)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61($o,X0,X1,X2,X3),X4))))) = X4) | ($false = vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,sK57($o,X0,X1,X2,X3),X4)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_965])])).
% 68.49/10.17 thf(f4240,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3))))),product_Pair($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$true),vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58($o,X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59($o,X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60($o,X0,X1,X2,X3),X4)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61($o,X0,X1,X2,X3),X4))))) = X4) | ($false = vAPP(product_prod($o,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),$o,sK57($o,X0,X1,X2,X3),X4))) ) | (~spl93_22 | ~spl93_256)),
% 68.49/10.17 inference(superposition,[],[f4238,f1833])).
% 68.49/10.17 thf(f45756,plain,(
% 68.49/10.17 spl93_964 | ~spl93_22 | ~spl93_259),
% 68.49/10.17 inference(avatar_split_clause,[],[f4283,f4260,f1832,f45754])).
% 68.49/10.17 thf(f45754,plain,(
% 68.49/10.17 spl93_964 <=> ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X4 : X0,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_964])])).
% 68.49/10.17 thf(f4260,plain,(
% 68.49/10.17 spl93_259 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_259])])).
% 68.49/10.17 thf(f4283,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_259)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4282])).
% 68.49/10.17 thf(f4282,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_259)),
% 68.49/10.17 inference(superposition,[],[f4261,f1833])).
% 68.49/10.17 thf(f4261,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_259),
% 68.49/10.17 inference(avatar_component_clause,[],[f4260])).
% 68.49/10.17 thf(f45752,plain,(
% 68.49/10.17 spl93_963 | ~spl93_22 | ~spl93_258),
% 68.49/10.17 inference(avatar_split_clause,[],[f4275,f4256,f1832,f45750])).
% 68.49/10.17 thf(f45750,plain,(
% 68.49/10.17 spl93_963 <=> ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X4 : X0,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_963])])).
% 68.49/10.17 thf(f4256,plain,(
% 68.49/10.17 spl93_258 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_258])])).
% 68.49/10.17 thf(f4275,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_258)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4274])).
% 68.49/10.17 thf(f4274,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_258)),
% 68.49/10.17 inference(superposition,[],[f4257,f1833])).
% 68.49/10.17 thf(f4257,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_258),
% 68.49/10.17 inference(avatar_component_clause,[],[f4256])).
% 68.49/10.17 thf(f45748,plain,(
% 68.49/10.17 spl93_962 | ~spl93_22 | ~spl93_257),
% 68.49/10.17 inference(avatar_split_clause,[],[f4267,f4252,f1832,f45746])).
% 68.49/10.17 thf(f45746,plain,(
% 68.49/10.17 spl93_962 <=> ! [X2 : $tType,X0 : $tType,X5 : X0,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_962])])).
% 68.49/10.17 thf(f4252,plain,(
% 68.49/10.17 spl93_257 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_257])])).
% 68.49/10.17 thf(f4267,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_257)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4266])).
% 68.49/10.17 thf(f4266,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X5),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_257)),
% 68.49/10.17 inference(superposition,[],[f4253,f1833])).
% 68.49/10.17 thf(f4253,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_257),
% 68.49/10.17 inference(avatar_component_clause,[],[f4252])).
% 68.49/10.17 thf(f45718,plain,(
% 68.49/10.17 spl93_961 | ~spl93_139 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4247,f4237,f2831,f45716])).
% 68.49/10.17 thf(f45716,plain,(
% 68.49/10.17 spl93_961 <=> ! [X1 : $tType,X5 : $tType,X0 : $tType,X4 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X6 : product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1))))] : ((vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),vAPP(X5,sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1))))),product_Pair(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X5,sK57(X5,X4,X2,X0,X1),X6)),vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1))),vAPP(X4,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1)))),product_Pair(X4,product_prod(X2,product_prod(X0,X1))),vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X4,sK58(X5,X4,X2,X0,X1),X6)),X3)) = X6) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X1,sK61(X5,X4,X2,X0,X1),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X0,sK60(X5,X4,X2,X0,X1),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X2,sK59(X5,X4,X2,X0,X1),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_961])])).
% 68.49/10.17 thf(f4247,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X6 : product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1))))] : ((vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),vAPP(X5,sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1))))),product_Pair(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X5,sK57(X5,X4,X2,X0,X1),X6)),vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1))),vAPP(X4,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1)))),product_Pair(X4,product_prod(X2,product_prod(X0,X1))),vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X4,sK58(X5,X4,X2,X0,X1),X6)),X3)) = X6) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X1,sK61(X5,X4,X2,X0,X1),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X0,sK60(X5,X4,X2,X0,X1),X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X5,product_prod(X4,product_prod(X2,product_prod(X0,X1)))),X2,sK59(X5,X4,X2,X0,X1),X6))) ) | (~spl93_139 | ~spl93_256)),
% 68.49/10.17 inference(constrained_superposition,[],[f4238,f2832])).
% 68.49/10.17 thf(f45626,plain,(
% 68.49/10.17 spl93_960 | ~spl93_345 | ~spl93_959),
% 68.49/10.17 inference(avatar_split_clause,[],[f45581,f45576,f6456,f45624])).
% 68.49/10.17 thf(f45624,plain,(
% 68.49/10.17 spl93_960 <=> ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_960])])).
% 68.49/10.17 thf(f45576,plain,(
% 68.49/10.17 spl93_959 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_959])])).
% 68.49/10.17 thf(f45581,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0))) ) | (~spl93_345 | ~spl93_959)),
% 68.49/10.17 inference(forward_demodulation,[],[f45580,f6458])).
% 68.49/10.17 thf(f45580,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_959)),
% 68.49/10.17 inference(forward_demodulation,[],[f45579,f6458])).
% 68.49/10.17 thf(f45579,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_959)),
% 68.49/10.17 inference(forward_demodulation,[],[f45577,f6458])).
% 68.49/10.17 thf(f45577,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_959),
% 68.49/10.17 inference(avatar_component_clause,[],[f45576])).
% 68.49/10.17 thf(f45578,plain,(
% 68.49/10.17 spl93_959 | ~spl93_22 | ~spl93_253),
% 68.49/10.17 inference(avatar_split_clause,[],[f4219,f4200,f1832,f45576])).
% 68.49/10.17 thf(f4200,plain,(
% 68.49/10.17 spl93_253 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_253])])).
% 68.49/10.17 thf(f4219,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_253)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4218])).
% 68.49/10.17 thf(f4218,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_253)),
% 68.49/10.17 inference(superposition,[],[f4201,f1833])).
% 68.49/10.17 thf(f4201,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_253),
% 68.49/10.17 inference(avatar_component_clause,[],[f4200])).
% 68.49/10.17 thf(f45486,plain,(
% 68.49/10.17 spl93_958 | ~spl93_345 | ~spl93_957),
% 68.49/10.17 inference(avatar_split_clause,[],[f45482,f45477,f6456,f45484])).
% 68.49/10.17 thf(f45484,plain,(
% 68.49/10.17 spl93_958 <=> ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_958])])).
% 68.49/10.17 thf(f45477,plain,(
% 68.49/10.17 spl93_957 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_957])])).
% 68.49/10.17 thf(f45482,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)))) ) | (~spl93_345 | ~spl93_957)),
% 68.49/10.17 inference(forward_demodulation,[],[f45481,f6458])).
% 68.49/10.17 thf(f45481,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_957)),
% 68.49/10.17 inference(forward_demodulation,[],[f45480,f6458])).
% 68.49/10.17 thf(f45480,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_957)),
% 68.49/10.17 inference(forward_demodulation,[],[f45478,f6458])).
% 68.49/10.17 thf(f45478,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_957),
% 68.49/10.17 inference(avatar_component_clause,[],[f45477])).
% 68.49/10.17 thf(f45479,plain,(
% 68.49/10.17 spl93_957 | ~spl93_22 | ~spl93_252),
% 68.49/10.17 inference(avatar_split_clause,[],[f4211,f4196,f1832,f45477])).
% 68.49/10.17 thf(f4196,plain,(
% 68.49/10.17 spl93_252 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_252])])).
% 68.49/10.17 thf(f4211,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_252)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4210])).
% 68.49/10.17 thf(f4210,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_252)),
% 68.49/10.17 inference(superposition,[],[f4197,f1833])).
% 68.49/10.17 thf(f4197,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_252),
% 68.49/10.17 inference(avatar_component_clause,[],[f4196])).
% 68.49/10.17 thf(f45449,plain,(
% 68.49/10.17 spl93_956 | ~spl93_206 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4248,f4237,f3634,f45447])).
% 68.49/10.17 thf(f45447,plain,(
% 68.49/10.17 spl93_956 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X5 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X6 : product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))] : ((vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),product_Pair(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X5,sK57(X5,X3,X0,X1,X2),X6)),X4) = X6) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X2,sK61(X5,X3,X0,X1,X2),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X1,sK60(X5,X3,X0,X1,X2),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X0,sK59(X5,X3,X0,X1,X2),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X3,sK58(X5,X3,X0,X1,X2),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_956])])).
% 68.49/10.17 thf(f4248,plain,(
% 68.49/10.17 ( ! [X5 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2)))] : ((vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(X5,sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2))))),product_Pair(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X5,sK57(X5,X3,X0,X1,X2),X6)),X4) = X6) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X2,sK61(X5,X3,X0,X1,X2),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X1,sK60(X5,X3,X0,X1,X2),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X0,sK59(X5,X3,X0,X1,X2),X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(product_prod(X5,product_prod(X3,product_prod(X0,product_prod(X1,X2)))),X3,sK58(X5,X3,X0,X1,X2),X6))) ) | (~spl93_206 | ~spl93_256)),
% 68.49/10.17 inference(constrained_superposition,[],[f4238,f3635])).
% 68.49/10.17 thf(f45442,plain,(
% 68.49/10.17 spl93_955 | ~spl93_66 | ~spl93_253),
% 68.49/10.17 inference(avatar_split_clause,[],[f4221,f4200,f2161,f45440])).
% 68.49/10.17 thf(f45440,plain,(
% 68.49/10.17 spl93_955 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_955])])).
% 68.49/10.17 thf(f4221,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_253)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4216])).
% 68.49/10.17 thf(f4216,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_253)),
% 68.49/10.17 inference(superposition,[],[f4201,f2163])).
% 68.49/10.17 thf(f45435,plain,(
% 68.49/10.17 spl93_954 | ~spl93_66 | ~spl93_252),
% 68.49/10.17 inference(avatar_split_clause,[],[f4213,f4196,f2161,f45433])).
% 68.49/10.17 thf(f45433,plain,(
% 68.49/10.17 spl93_954 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_954])])).
% 68.49/10.17 thf(f4213,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_252)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4208])).
% 68.49/10.17 thf(f4208,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_252)),
% 68.49/10.17 inference(superposition,[],[f4197,f2163])).
% 68.49/10.17 thf(f45406,plain,(
% 68.49/10.17 spl93_953 | ~spl93_345 | ~spl93_952),
% 68.49/10.17 inference(avatar_split_clause,[],[f45361,f45357,f6456,f45404])).
% 68.49/10.17 thf(f45404,plain,(
% 68.49/10.17 spl93_953 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_953])])).
% 68.49/10.17 thf(f45357,plain,(
% 68.49/10.17 spl93_952 <=> ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_952])])).
% 68.49/10.17 thf(f45361,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_345 | ~spl93_952)),
% 68.49/10.17 inference(forward_demodulation,[],[f45360,f6458])).
% 68.49/10.17 thf(f45360,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_345 | ~spl93_952)),
% 68.49/10.17 inference(forward_demodulation,[],[f45358,f6458])).
% 68.49/10.17 thf(f45358,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | ~spl93_952),
% 68.49/10.17 inference(avatar_component_clause,[],[f45357])).
% 68.49/10.17 thf(f45359,plain,(
% 68.49/10.17 spl93_952 | ~spl93_148 | ~spl93_209),
% 68.49/10.17 inference(avatar_split_clause,[],[f3683,f3680,f2904,f45357])).
% 68.49/10.17 thf(f3680,plain,(
% 68.49/10.17 spl93_209 <=> ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_209])])).
% 68.49/10.17 thf(f3683,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))) ) | (~spl93_148 | ~spl93_209)),
% 68.49/10.17 inference(superposition,[],[f3681,f2905])).
% 68.49/10.17 thf(f3681,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) ) | ~spl93_209),
% 68.49/10.17 inference(avatar_component_clause,[],[f3680])).
% 68.49/10.17 thf(f45207,plain,(
% 68.49/10.17 spl93_951 | ~spl93_22 | ~spl93_255),
% 68.49/10.17 inference(avatar_split_clause,[],[f4235,f4227,f1832,f45205])).
% 68.49/10.17 thf(f45205,plain,(
% 68.49/10.17 spl93_951 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),$true)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_951])])).
% 68.49/10.17 thf(f4227,plain,(
% 68.49/10.17 spl93_255 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_255])])).
% 68.49/10.17 thf(f4235,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),$true))) ) | (~spl93_22 | ~spl93_255)),
% 68.49/10.17 inference(inner_rewriting,[],[f4232])).
% 68.49/10.17 thf(f4232,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_255)),
% 68.49/10.17 inference(superposition,[],[f4228,f1833])).
% 68.49/10.17 thf(f4228,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) ) | ~spl93_255),
% 68.49/10.17 inference(avatar_component_clause,[],[f4227])).
% 68.49/10.17 thf(f45203,plain,(
% 68.49/10.17 spl93_950 | ~spl93_22 | ~spl93_255),
% 68.49/10.17 inference(avatar_split_clause,[],[f4231,f4227,f1832,f45201])).
% 68.49/10.17 thf(f45201,plain,(
% 68.49/10.17 spl93_950 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),$true)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_950])])).
% 68.49/10.17 thf(f4231,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),$true)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1))) ) | (~spl93_22 | ~spl93_255)),
% 68.49/10.17 inference(superposition,[],[f4228,f1833])).
% 68.49/10.17 thf(f45111,plain,(
% 68.49/10.17 spl93_949 | ~spl93_345 | ~spl93_948),
% 68.49/10.17 inference(avatar_split_clause,[],[f45107,f45102,f6456,f45109])).
% 68.49/10.17 thf(f45109,plain,(
% 68.49/10.17 spl93_949 <=> ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_949])])).
% 68.49/10.17 thf(f45102,plain,(
% 68.49/10.17 spl93_948 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_948])])).
% 68.49/10.17 thf(f45107,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0))) ) | (~spl93_345 | ~spl93_948)),
% 68.49/10.17 inference(forward_demodulation,[],[f45106,f6458])).
% 68.49/10.17 thf(f45106,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_948)),
% 68.49/10.17 inference(forward_demodulation,[],[f45105,f6458])).
% 68.49/10.17 thf(f45105,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_948)),
% 68.49/10.17 inference(forward_demodulation,[],[f45103,f6458])).
% 68.49/10.17 thf(f45103,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_948),
% 68.49/10.17 inference(avatar_component_clause,[],[f45102])).
% 68.49/10.17 thf(f45104,plain,(
% 68.49/10.17 spl93_948 | ~spl93_22 | ~spl93_250),
% 68.49/10.17 inference(avatar_split_clause,[],[f4169,f4154,f1832,f45102])).
% 68.49/10.17 thf(f4154,plain,(
% 68.49/10.17 spl93_250 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_250])])).
% 68.49/10.17 thf(f4169,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_250)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4168])).
% 68.49/10.17 thf(f4168,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_250)),
% 68.49/10.17 inference(superposition,[],[f4155,f1833])).
% 68.49/10.17 thf(f4155,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_250),
% 68.49/10.17 inference(avatar_component_clause,[],[f4154])).
% 68.49/10.17 thf(f45012,plain,(
% 68.49/10.17 spl93_947 | ~spl93_345 | ~spl93_946),
% 68.49/10.17 inference(avatar_split_clause,[],[f44970,f44965,f6456,f45010])).
% 68.49/10.17 thf(f45010,plain,(
% 68.49/10.17 spl93_947 <=> ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_947])])).
% 68.49/10.17 thf(f44965,plain,(
% 68.49/10.17 spl93_946 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_946])])).
% 68.49/10.17 thf(f44970,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))) ) | (~spl93_345 | ~spl93_946)),
% 68.49/10.17 inference(forward_demodulation,[],[f44969,f6458])).
% 68.49/10.17 thf(f44969,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_946)),
% 68.49/10.17 inference(forward_demodulation,[],[f44968,f6458])).
% 68.49/10.17 thf(f44968,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_946)),
% 68.49/10.17 inference(forward_demodulation,[],[f44966,f6458])).
% 68.49/10.17 thf(f44966,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_946),
% 68.49/10.17 inference(avatar_component_clause,[],[f44965])).
% 68.49/10.17 thf(f44967,plain,(
% 68.49/10.17 spl93_946 | ~spl93_22 | ~spl93_249),
% 68.49/10.17 inference(avatar_split_clause,[],[f4161,f4150,f1832,f44965])).
% 68.49/10.17 thf(f4150,plain,(
% 68.49/10.17 spl93_249 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_249])])).
% 68.49/10.17 thf(f4161,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_249)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4160])).
% 68.49/10.17 thf(f4160,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_249)),
% 68.49/10.17 inference(superposition,[],[f4151,f1833])).
% 68.49/10.17 thf(f4151,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_249),
% 68.49/10.17 inference(avatar_component_clause,[],[f4150])).
% 68.49/10.17 thf(f44855,plain,(
% 68.49/10.17 spl93_945 | ~spl93_345 | ~spl93_944),
% 68.49/10.17 inference(avatar_split_clause,[],[f44851,f44847,f6456,f44853])).
% 68.49/10.17 thf(f44853,plain,(
% 68.49/10.17 spl93_945 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_945])])).
% 68.49/10.17 thf(f44847,plain,(
% 68.49/10.17 spl93_944 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_944])])).
% 68.49/10.17 thf(f44851,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_944)),
% 68.49/10.17 inference(forward_demodulation,[],[f44850,f6458])).
% 68.49/10.17 thf(f44850,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_944)),
% 68.49/10.17 inference(forward_demodulation,[],[f44848,f6458])).
% 68.49/10.17 thf(f44848,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_944),
% 68.49/10.17 inference(avatar_component_clause,[],[f44847])).
% 68.49/10.17 thf(f44849,plain,(
% 68.49/10.17 spl93_944 | ~spl93_61 | ~spl93_253),
% 68.49/10.17 inference(avatar_split_clause,[],[f4222,f4200,f2136,f44847])).
% 68.49/10.17 thf(f4222,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_253)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4215])).
% 68.49/10.17 thf(f4215,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_253)),
% 68.49/10.17 inference(superposition,[],[f4201,f2138])).
% 68.49/10.17 thf(f44737,plain,(
% 68.49/10.17 spl93_943 | ~spl93_345 | ~spl93_942),
% 68.49/10.17 inference(avatar_split_clause,[],[f44733,f44729,f6456,f44735])).
% 68.49/10.17 thf(f44735,plain,(
% 68.49/10.17 spl93_943 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_943])])).
% 68.49/10.17 thf(f44729,plain,(
% 68.49/10.17 spl93_942 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_942])])).
% 68.49/10.17 thf(f44733,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_942)),
% 68.49/10.17 inference(forward_demodulation,[],[f44732,f6458])).
% 68.49/10.17 thf(f44732,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_942)),
% 68.49/10.17 inference(forward_demodulation,[],[f44730,f6458])).
% 68.49/10.17 thf(f44730,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_942),
% 68.49/10.17 inference(avatar_component_clause,[],[f44729])).
% 68.49/10.17 thf(f44731,plain,(
% 68.49/10.17 spl93_942 | ~spl93_61 | ~spl93_252),
% 68.49/10.17 inference(avatar_split_clause,[],[f4214,f4196,f2136,f44729])).
% 68.49/10.17 thf(f4214,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_252)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4207])).
% 68.49/10.17 thf(f4207,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_252)),
% 68.49/10.17 inference(superposition,[],[f4197,f2138])).
% 68.49/10.17 thf(f44612,plain,(
% 68.49/10.17 spl93_941 | ~spl93_345 | ~spl93_940),
% 68.49/10.17 inference(avatar_split_clause,[],[f44608,f44604,f6456,f44610])).
% 68.49/10.17 thf(f44610,plain,(
% 68.49/10.17 spl93_941 <=> ! [X2 : a,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_941])])).
% 68.49/10.17 thf(f44604,plain,(
% 68.49/10.17 spl93_940 <=> ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_940])])).
% 68.49/10.17 thf(f44608,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | (~spl93_345 | ~spl93_940)),
% 68.49/10.17 inference(forward_demodulation,[],[f44607,f6458])).
% 68.49/10.17 thf(f44607,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_940)),
% 68.49/10.17 inference(forward_demodulation,[],[f44605,f6458])).
% 68.49/10.17 thf(f44605,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_940),
% 68.49/10.17 inference(avatar_component_clause,[],[f44604])).
% 68.49/10.17 thf(f44606,plain,(
% 68.49/10.17 spl93_940 | ~spl93_22 | ~spl93_248),
% 68.49/10.17 inference(avatar_split_clause,[],[f4144,f4128,f1832,f44604])).
% 68.49/10.17 thf(f4128,plain,(
% 68.49/10.17 spl93_248 <=> ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_248])])).
% 68.49/10.17 thf(f4144,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_248)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4143])).
% 68.49/10.17 thf(f4143,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_248)),
% 68.49/10.17 inference(superposition,[],[f4129,f1833])).
% 68.49/10.17 thf(f4129,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_248),
% 68.49/10.17 inference(avatar_component_clause,[],[f4128])).
% 68.49/10.17 thf(f44449,plain,(
% 68.49/10.17 spl93_939 | ~spl93_345 | ~spl93_938),
% 68.49/10.17 inference(avatar_split_clause,[],[f44445,f44441,f6456,f44447])).
% 68.49/10.17 thf(f44447,plain,(
% 68.49/10.17 spl93_939 <=> ! [X2 : a,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_939])])).
% 68.49/10.17 thf(f44441,plain,(
% 68.49/10.17 spl93_938 <=> ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_938])])).
% 68.49/10.17 thf(f44445,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)))) ) | (~spl93_345 | ~spl93_938)),
% 68.49/10.17 inference(forward_demodulation,[],[f44444,f6458])).
% 68.49/10.17 thf(f44444,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_938)),
% 68.49/10.17 inference(forward_demodulation,[],[f44442,f6458])).
% 68.49/10.17 thf(f44442,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_938),
% 68.49/10.17 inference(avatar_component_clause,[],[f44441])).
% 68.49/10.17 thf(f44443,plain,(
% 68.49/10.17 spl93_938 | ~spl93_22 | ~spl93_247),
% 68.49/10.17 inference(avatar_split_clause,[],[f4135,f4124,f1832,f44441])).
% 68.49/10.17 thf(f4124,plain,(
% 68.49/10.17 spl93_247 <=> ! [X2 : int,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_247])])).
% 68.49/10.17 thf(f4135,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_247)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4134])).
% 68.49/10.17 thf(f4134,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_247)),
% 68.49/10.17 inference(superposition,[],[f4125,f1833])).
% 68.49/10.17 thf(f4125,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_247),
% 68.49/10.17 inference(avatar_component_clause,[],[f4124])).
% 68.49/10.17 thf(f44209,plain,(
% 68.49/10.17 spl93_937 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_267),
% 68.49/10.17 inference(avatar_split_clause,[],[f6120,f4405,f2247,f2243,f2074,f1868,f44207])).
% 68.49/10.17 thf(f44207,plain,(
% 68.49/10.17 spl93_937 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_937])])).
% 68.49/10.17 thf(f1868,plain,(
% 68.49/10.17 spl93_24 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_24])])).
% 68.49/10.17 thf(f2074,plain,(
% 68.49/10.17 spl93_53 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),units(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_53])])).
% 68.49/10.17 thf(f2243,plain,(
% 68.49/10.17 spl93_73 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_73])])).
% 68.49/10.17 thf(f2247,plain,(
% 68.49/10.17 spl93_74 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true)),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_74])])).
% 68.49/10.17 thf(f6120,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_267)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f6119])).
% 68.49/10.17 thf(f6119,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_267)),
% 68.49/10.17 inference(forward_demodulation,[],[f6118,f1870])).
% 68.49/10.17 thf(f1870,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) = $true) | ~spl93_24),
% 68.49/10.17 inference(avatar_component_clause,[],[f1868])).
% 68.49/10.17 thf(f6118,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_267)),
% 68.49/10.17 inference(forward_demodulation,[],[f6117,f5934])).
% 68.49/10.17 thf(f5934,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) | (~spl93_53 | ~spl93_74)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3121])).
% 68.49/10.17 thf(f3121,plain,(
% 68.49/10.17 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) | (~spl93_53 | ~spl93_74)),
% 68.49/10.17 inference(superposition,[],[f2075,f2249])).
% 68.49/10.17 thf(f2249,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true) | ~spl93_74),
% 68.49/10.17 inference(avatar_component_clause,[],[f2247])).
% 68.49/10.17 thf(f2075,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),units(X1,X0),X2))) ) | ~spl93_53),
% 68.49/10.17 inference(avatar_component_clause,[],[f2074])).
% 68.49/10.17 thf(f6117,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_267)),
% 68.49/10.17 inference(forward_demodulation,[],[f4417,f5934])).
% 68.49/10.17 thf(f4417,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_267)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4414])).
% 68.49/10.17 thf(f4414,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_267)),
% 68.49/10.17 inference(superposition,[],[f4406,f2245])).
% 68.49/10.17 thf(f2245,plain,(
% 68.49/10.17 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_73),
% 68.49/10.17 inference(avatar_component_clause,[],[f2243])).
% 68.49/10.17 thf(f44205,plain,(
% 68.49/10.17 spl93_936 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_268),
% 68.49/10.17 inference(avatar_split_clause,[],[f6114,f4409,f2247,f2243,f2074,f1868,f44203])).
% 68.49/10.17 thf(f44203,plain,(
% 68.49/10.17 spl93_936 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_936])])).
% 68.49/10.17 thf(f6114,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_268)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f6113])).
% 68.49/10.17 thf(f6113,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_268)),
% 68.49/10.17 inference(forward_demodulation,[],[f6112,f1870])).
% 68.49/10.17 thf(f6112,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_268)),
% 68.49/10.17 inference(forward_demodulation,[],[f6111,f5934])).
% 68.49/10.17 thf(f6111,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_268)),
% 68.49/10.17 inference(forward_demodulation,[],[f4425,f5934])).
% 68.49/10.17 thf(f4425,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_268)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4422])).
% 68.49/10.17 thf(f4422,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_268)),
% 68.49/10.17 inference(superposition,[],[f4410,f2245])).
% 68.49/10.17 thf(f44198,plain,(
% 68.49/10.17 spl93_935 | ~spl93_66 | ~spl93_250),
% 68.49/10.17 inference(avatar_split_clause,[],[f4171,f4154,f2161,f44196])).
% 68.49/10.17 thf(f44196,plain,(
% 68.49/10.17 spl93_935 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_935])])).
% 68.49/10.17 thf(f4171,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_250)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4166])).
% 68.49/10.17 thf(f4166,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_250)),
% 68.49/10.17 inference(superposition,[],[f4155,f2163])).
% 68.49/10.17 thf(f44191,plain,(
% 68.49/10.17 spl93_934 | ~spl93_66 | ~spl93_249),
% 68.49/10.17 inference(avatar_split_clause,[],[f4163,f4150,f2161,f44189])).
% 68.49/10.17 thf(f44189,plain,(
% 68.49/10.17 spl93_934 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_934])])).
% 68.49/10.17 thf(f4163,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_249)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4158])).
% 68.49/10.17 thf(f4158,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_249)),
% 68.49/10.17 inference(superposition,[],[f4151,f2163])).
% 68.49/10.17 thf(f44096,plain,(
% 68.49/10.17 spl93_933 | ~spl93_22 | ~spl93_246),
% 68.49/10.17 inference(avatar_split_clause,[],[f4119,f4112,f1832,f44094])).
% 68.49/10.17 thf(f44094,plain,(
% 68.49/10.17 spl93_933 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X4 : X0,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_933])])).
% 68.49/10.17 thf(f4112,plain,(
% 68.49/10.17 spl93_246 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_246])])).
% 68.49/10.17 thf(f4119,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0,X4 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_246)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4118])).
% 68.49/10.17 thf(f4118,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0,X4 : X0,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X5)),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X5),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_246)),
% 68.49/10.17 inference(superposition,[],[f4113,f1833])).
% 68.49/10.17 thf(f4113,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) ) | ~spl93_246),
% 68.49/10.17 inference(avatar_component_clause,[],[f4112])).
% 68.49/10.17 thf(f43552,plain,(
% 68.49/10.17 spl93_932 | ~spl93_22 | ~spl93_244),
% 68.49/10.17 inference(avatar_split_clause,[],[f4088,f4085,f1832,f43550])).
% 68.49/10.17 thf(f43550,plain,(
% 68.49/10.17 spl93_932 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_932])])).
% 68.49/10.17 thf(f4085,plain,(
% 68.49/10.17 spl93_244 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_244])])).
% 68.49/10.17 thf(f4088,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK28(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK29(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,abelian_group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1))) ) | (~spl93_22 | ~spl93_244)),
% 68.49/10.17 inference(superposition,[],[f4086,f1833])).
% 68.49/10.17 thf(f4086,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) ) | ~spl93_244),
% 68.49/10.17 inference(avatar_component_clause,[],[f4085])).
% 68.49/10.17 thf(f43356,plain,(
% 68.49/10.17 spl93_931 | ~spl93_345 | ~spl93_930),
% 68.49/10.17 inference(avatar_split_clause,[],[f43352,f43348,f6456,f43354])).
% 68.49/10.17 thf(f43354,plain,(
% 68.49/10.17 spl93_931 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_931])])).
% 68.49/10.17 thf(f43348,plain,(
% 68.49/10.17 spl93_930 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_930])])).
% 68.49/10.17 thf(f43352,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_930)),
% 68.49/10.17 inference(forward_demodulation,[],[f43351,f6458])).
% 68.49/10.17 thf(f43351,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_930)),
% 68.49/10.17 inference(forward_demodulation,[],[f43349,f6458])).
% 68.49/10.17 thf(f43349,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_930),
% 68.49/10.17 inference(avatar_component_clause,[],[f43348])).
% 68.49/10.17 thf(f43350,plain,(
% 68.49/10.17 spl93_930 | ~spl93_61 | ~spl93_250),
% 68.49/10.17 inference(avatar_split_clause,[],[f4172,f4154,f2136,f43348])).
% 68.49/10.17 thf(f4172,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_250)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4165])).
% 68.49/10.17 thf(f4165,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_250)),
% 68.49/10.17 inference(superposition,[],[f4155,f2138])).
% 68.49/10.17 thf(f43238,plain,(
% 68.49/10.17 spl93_929 | ~spl93_345 | ~spl93_928),
% 68.49/10.17 inference(avatar_split_clause,[],[f43234,f43230,f6456,f43236])).
% 68.49/10.17 thf(f43236,plain,(
% 68.49/10.17 spl93_929 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_929])])).
% 68.49/10.17 thf(f43230,plain,(
% 68.49/10.17 spl93_928 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_928])])).
% 68.49/10.17 thf(f43234,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_928)),
% 68.49/10.17 inference(forward_demodulation,[],[f43233,f6458])).
% 68.49/10.17 thf(f43233,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_928)),
% 68.49/10.17 inference(forward_demodulation,[],[f43231,f6458])).
% 68.49/10.17 thf(f43231,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_928),
% 68.49/10.17 inference(avatar_component_clause,[],[f43230])).
% 68.49/10.17 thf(f43232,plain,(
% 68.49/10.17 spl93_928 | ~spl93_61 | ~spl93_249),
% 68.49/10.17 inference(avatar_split_clause,[],[f4164,f4150,f2136,f43230])).
% 68.49/10.17 thf(f4164,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_249)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4157])).
% 68.49/10.17 thf(f4157,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_249)),
% 68.49/10.17 inference(superposition,[],[f4151,f2138])).
% 68.49/10.17 thf(f43139,plain,(
% 68.49/10.17 spl93_927 | ~spl93_66 | ~spl93_248),
% 68.49/10.17 inference(avatar_split_clause,[],[f4146,f4128,f2161,f43137])).
% 68.49/10.17 thf(f43137,plain,(
% 68.49/10.17 spl93_927 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_927])])).
% 68.49/10.17 thf(f4146,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_248)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4141])).
% 68.49/10.17 thf(f4141,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_248)),
% 68.49/10.17 inference(superposition,[],[f4129,f2163])).
% 68.49/10.17 thf(f43132,plain,(
% 68.49/10.17 spl93_926 | ~spl93_66 | ~spl93_247),
% 68.49/10.17 inference(avatar_split_clause,[],[f4137,f4124,f2161,f43130])).
% 68.49/10.17 thf(f43130,plain,(
% 68.49/10.17 spl93_926 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_926])])).
% 68.49/10.17 thf(f4137,plain,(
% 68.49/10.17 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_247)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4132])).
% 68.49/10.17 thf(f4132,plain,(
% 68.49/10.17 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_247)),
% 68.49/10.17 inference(superposition,[],[f4125,f2163])).
% 68.49/10.17 thf(f43128,plain,(
% 68.49/10.17 spl93_925 | ~spl93_22 | ~spl93_241),
% 68.49/10.17 inference(avatar_split_clause,[],[f4058,f4043,f1832,f43126])).
% 68.49/10.17 thf(f43126,plain,(
% 68.49/10.17 spl93_925 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK25(X0,$o),X1)),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK26(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK27(X0,$o),X1)))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK25(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK26(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK27(X0,$o),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_925])])).
% 68.49/10.17 thf(f4043,plain,(
% 68.49/10.17 spl93_241 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_241])])).
% 68.49/10.17 thf(f4058,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK25(X0,$o),X1)),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK26(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK27(X0,$o),X1)))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP2(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK25(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK26(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK27(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_241)),
% 68.49/10.17 inference(superposition,[],[f4044,f1833])).
% 68.49/10.17 thf(f4044,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0))) ) | ~spl93_241),
% 68.49/10.17 inference(avatar_component_clause,[],[f4043])).
% 68.49/10.17 thf(f43097,plain,(
% 68.49/10.17 spl93_924 | ~spl93_256),
% 68.49/10.17 inference(avatar_split_clause,[],[f4249,f4237,f43095])).
% 68.49/10.17 thf(f43095,plain,(
% 68.49/10.17 spl93_924 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X6 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((X5 = X6) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X6)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_924])])).
% 68.49/10.17 thf(f4249,plain,(
% 68.49/10.17 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X5 : product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3))))] : ((X5 = X6) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X3,sK61(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X2,sK60(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X1,sK59(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X0,sK58(X4,X0,X1,X2,X3),X6)) | (vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X5) != vAPP(product_prod(X4,product_prod(X0,product_prod(X1,product_prod(X2,X3)))),X4,sK57(X4,X0,X1,X2,X3),X6))) ) | ~spl93_256),
% 68.49/10.17 inference(constrained_superposition,[],[f4238,f4238])).
% 68.49/10.17 thf(f43023,plain,(
% 68.49/10.17 spl93_923 | ~spl93_345 | ~spl93_922),
% 68.49/10.17 inference(avatar_split_clause,[],[f43019,f43016,f6456,f43021])).
% 68.49/10.17 thf(f43021,plain,(
% 68.49/10.17 spl93_923 <=> ! [X2 : nat,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_923])])).
% 68.49/10.17 thf(f43016,plain,(
% 68.49/10.17 spl93_922 <=> ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_922])])).
% 68.49/10.17 thf(f43019,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | (~spl93_345 | ~spl93_922)),
% 68.49/10.17 inference(forward_demodulation,[],[f43017,f6458])).
% 68.49/10.17 thf(f43017,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_922),
% 68.49/10.17 inference(avatar_component_clause,[],[f43016])).
% 68.49/10.17 thf(f43018,plain,(
% 68.49/10.17 spl93_922 | ~spl93_22 | ~spl93_245),
% 68.49/10.17 inference(avatar_split_clause,[],[f4101,f4094,f1832,f43016])).
% 68.49/10.17 thf(f4094,plain,(
% 68.49/10.17 spl93_245 <=> ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_245])])).
% 68.49/10.17 thf(f4101,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_245)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4100])).
% 68.49/10.17 thf(f4100,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_245)),
% 68.49/10.17 inference(superposition,[],[f4095,f1833])).
% 68.49/10.17 thf(f4095,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | ~spl93_245),
% 68.49/10.17 inference(avatar_component_clause,[],[f4094])).
% 68.49/10.17 thf(f42802,plain,(
% 68.49/10.17 spl93_921 | ~spl93_22 | ~spl93_244),
% 68.49/10.17 inference(avatar_split_clause,[],[f4091,f4085,f1832,f42800])).
% 68.49/10.17 thf(f42800,plain,(
% 68.49/10.17 spl93_921 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK28(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK29(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,abelian_group(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_921])])).
% 68.49/10.17 thf(f4091,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK28(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK29(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,abelian_group(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2)))) ) | (~spl93_22 | ~spl93_244)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4090])).
% 68.49/10.17 thf(f4090,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK28(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK29(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,abelian_group(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2)))) ) | (~spl93_22 | ~spl93_244)),
% 68.49/10.17 inference(superposition,[],[f4086,f1833])).
% 68.49/10.17 thf(f42619,plain,(
% 68.49/10.17 spl93_920 | ~spl93_22 | ~spl93_243),
% 68.49/10.17 inference(avatar_split_clause,[],[f4080,f4051,f1832,f42617])).
% 68.49/10.17 thf(f42617,plain,(
% 68.49/10.17 spl93_920 <=> ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X4 : nat,X5 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_920])])).
% 68.49/10.17 thf(f4051,plain,(
% 68.49/10.17 spl93_243 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : nat,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_243])])).
% 68.49/10.17 thf(f4080,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : nat,X5 : X0] : ((vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_243)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4079])).
% 68.49/10.17 thf(f4079,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : nat,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),X5)),X1)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_243)),
% 68.49/10.17 inference(superposition,[],[f4052,f1833])).
% 68.49/10.17 thf(f4052,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_243),
% 68.49/10.17 inference(avatar_component_clause,[],[f4051])).
% 68.49/10.17 thf(f42615,plain,(
% 68.49/10.17 spl93_919 | ~spl93_22 | ~spl93_242),
% 68.49/10.17 inference(avatar_split_clause,[],[f4071,f4047,f1832,f42613])).
% 68.49/10.17 thf(f42613,plain,(
% 68.49/10.17 spl93_919 <=> ! [X2 : $tType,X0 : $tType,X5 : X0,X4 : nat,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_919])])).
% 68.49/10.17 thf(f4047,plain,(
% 68.49/10.17 spl93_242 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : nat,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_242])])).
% 68.49/10.17 thf(f4071,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : nat,X5 : X0] : ((vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_242)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4070])).
% 68.49/10.17 thf(f4070,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : nat,X5 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X5),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X3),X4),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_242)),
% 68.49/10.17 inference(superposition,[],[f4048,f1833])).
% 68.49/10.17 thf(f4048,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_242),
% 68.49/10.17 inference(avatar_component_clause,[],[f4047])).
% 68.49/10.17 thf(f42559,plain,(
% 68.49/10.17 spl93_918 | ~spl93_22 | ~spl93_237),
% 68.49/10.17 inference(avatar_split_clause,[],[f4010,f4003,f1832,f42557])).
% 68.49/10.17 thf(f42557,plain,(
% 68.49/10.17 spl93_918 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_918])])).
% 68.49/10.17 thf(f4003,plain,(
% 68.49/10.17 spl93_237 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_237])])).
% 68.49/10.17 thf(f4010,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_237)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4009])).
% 68.49/10.17 thf(f4009,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_237)),
% 68.49/10.17 inference(superposition,[],[f4004,f1833])).
% 68.49/10.17 thf(f4004,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_237),
% 68.49/10.17 inference(avatar_component_clause,[],[f4003])).
% 68.49/10.17 thf(f42534,plain,(
% 68.49/10.17 spl93_917 | ~spl93_46 | ~spl93_72 | ~spl93_208),
% 68.49/10.17 inference(avatar_split_clause,[],[f3676,f3667,f2239,f2023,f42532])).
% 68.49/10.17 thf(f42532,plain,(
% 68.49/10.17 spl93_917 <=> ! [X1 : $tType,X0 : $tType,X4 : X0,X3 : X0,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X4),X3)) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_917])])).
% 68.49/10.17 thf(f3667,plain,(
% 68.49/10.17 spl93_208 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_208])])).
% 68.49/10.17 thf(f3676,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X3 : X0,X4 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X4),X3)) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_72 | ~spl93_208)),
% 68.49/10.17 inference(forward_demodulation,[],[f3675,f2024])).
% 68.49/10.17 thf(f3675,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X3 : X0,X4 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X4),X3)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_46 | ~spl93_72 | ~spl93_208)),
% 68.49/10.17 inference(forward_demodulation,[],[f3670,f2024])).
% 68.49/10.17 thf(f3670,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X3 : X0,X4 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X3),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),X4),X3)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,group(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_72 | ~spl93_208)),
% 68.49/10.17 inference(superposition,[],[f3668,f2240])).
% 68.49/10.17 thf(f3668,plain,(
% 68.49/10.17 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) ) | ~spl93_208),
% 68.49/10.17 inference(avatar_component_clause,[],[f3667])).
% 68.49/10.17 thf(f42504,plain,(
% 68.49/10.17 spl93_916 | ~spl93_345 | ~spl93_915),
% 68.49/10.17 inference(avatar_split_clause,[],[f42459,f42455,f6456,f42502])).
% 68.49/10.17 thf(f42502,plain,(
% 68.49/10.17 spl93_916 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_916])])).
% 68.49/10.17 thf(f42455,plain,(
% 68.49/10.17 spl93_915 <=> ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_915])])).
% 68.49/10.17 thf(f42459,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))) ) | (~spl93_345 | ~spl93_915)),
% 68.49/10.17 inference(forward_demodulation,[],[f42458,f6458])).
% 68.49/10.17 thf(f42458,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))) ) | (~spl93_345 | ~spl93_915)),
% 68.49/10.17 inference(forward_demodulation,[],[f42456,f6458])).
% 68.49/10.17 thf(f42456,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))) ) | ~spl93_915),
% 68.49/10.17 inference(avatar_component_clause,[],[f42455])).
% 68.49/10.17 thf(f42457,plain,(
% 68.49/10.17 spl93_915 | ~spl93_148 | ~spl93_195),
% 68.49/10.17 inference(avatar_split_clause,[],[f3531,f3528,f2904,f42455])).
% 68.49/10.17 thf(f3528,plain,(
% 68.49/10.17 spl93_195 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_195])])).
% 68.49/10.17 thf(f3531,plain,(
% 68.49/10.17 ( ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1))) ) | (~spl93_148 | ~spl93_195)),
% 68.49/10.17 inference(superposition,[],[f3529,f2905])).
% 68.49/10.17 thf(f3529,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0)) ) | ~spl93_195),
% 68.49/10.17 inference(avatar_component_clause,[],[f3528])).
% 68.49/10.17 thf(f41912,plain,(
% 68.49/10.17 spl93_914 | ~spl93_22 | ~spl93_240),
% 68.49/10.17 inference(avatar_split_clause,[],[f4041,f4031,f1832,f41910])).
% 68.49/10.17 thf(f41910,plain,(
% 68.49/10.17 spl93_914 <=> ! [X0 : $tType,X2 : $o,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_914])])).
% 68.49/10.17 thf(f4041,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $o,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_240)),
% 68.49/10.17 inference(inner_rewriting,[],[f4036])).
% 68.49/10.17 thf(f4036,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X2 : $o,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),X2),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_240)),
% 68.49/10.17 inference(superposition,[],[f4032,f1833])).
% 68.49/10.17 thf(f41793,plain,(
% 68.49/10.17 spl93_913 | ~spl93_345 | ~spl93_912),
% 68.49/10.17 inference(avatar_split_clause,[],[f41789,f41785,f6456,f41791])).
% 68.49/10.17 thf(f41791,plain,(
% 68.49/10.17 spl93_913 <=> ! [X2 : a,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_913])])).
% 68.49/10.17 thf(f41785,plain,(
% 68.49/10.17 spl93_912 <=> ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_912])])).
% 68.49/10.17 thf(f41789,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0))) ) | (~spl93_345 | ~spl93_912)),
% 68.49/10.17 inference(forward_demodulation,[],[f41788,f6458])).
% 68.49/10.17 thf(f41788,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_912)),
% 68.49/10.17 inference(forward_demodulation,[],[f41786,f6458])).
% 68.49/10.17 thf(f41786,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_912),
% 68.49/10.17 inference(avatar_component_clause,[],[f41785])).
% 68.49/10.17 thf(f41787,plain,(
% 68.49/10.17 spl93_912 | ~spl93_22 | ~spl93_234),
% 68.49/10.17 inference(avatar_split_clause,[],[f3993,f3956,f1832,f41785])).
% 68.49/10.17 thf(f3956,plain,(
% 68.49/10.17 spl93_234 <=> ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_234])])).
% 68.49/10.17 thf(f3993,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_234)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3992])).
% 68.49/10.17 thf(f3992,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_234)),
% 68.49/10.17 inference(superposition,[],[f3957,f1833])).
% 68.49/10.17 thf(f3957,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_234),
% 68.49/10.17 inference(avatar_component_clause,[],[f3956])).
% 68.49/10.17 thf(f41695,plain,(
% 68.49/10.17 spl93_911 | ~spl93_345 | ~spl93_910),
% 68.49/10.17 inference(avatar_split_clause,[],[f41691,f41687,f6456,f41693])).
% 68.49/10.17 thf(f41693,plain,(
% 68.49/10.17 spl93_911 <=> ! [X2 : a,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_911])])).
% 68.49/10.17 thf(f41687,plain,(
% 68.49/10.17 spl93_910 <=> ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_910])])).
% 68.49/10.17 thf(f41691,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)))) ) | (~spl93_345 | ~spl93_910)),
% 68.49/10.17 inference(forward_demodulation,[],[f41690,f6458])).
% 68.49/10.17 thf(f41690,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_910)),
% 68.49/10.17 inference(forward_demodulation,[],[f41688,f6458])).
% 68.49/10.17 thf(f41688,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_910),
% 68.49/10.17 inference(avatar_component_clause,[],[f41687])).
% 68.49/10.17 thf(f41689,plain,(
% 68.49/10.17 spl93_910 | ~spl93_22 | ~spl93_233),
% 68.49/10.17 inference(avatar_split_clause,[],[f3984,f3952,f1832,f41687])).
% 68.49/10.17 thf(f3952,plain,(
% 68.49/10.17 spl93_233 <=> ! [X2 : int,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_233])])).
% 68.49/10.17 thf(f3984,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_233)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3983])).
% 68.49/10.17 thf(f3983,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_233)),
% 68.49/10.17 inference(superposition,[],[f3953,f1833])).
% 68.49/10.17 thf(f3953,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_233),
% 68.49/10.17 inference(avatar_component_clause,[],[f3952])).
% 68.49/10.17 thf(f41556,plain,(
% 68.49/10.17 spl93_909 | ~spl93_345 | ~spl93_908),
% 68.49/10.17 inference(avatar_split_clause,[],[f41552,f41548,f6456,f41554])).
% 68.49/10.17 thf(f41554,plain,(
% 68.49/10.17 spl93_909 <=> ! [X2 : a,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_909])])).
% 68.49/10.17 thf(f41548,plain,(
% 68.49/10.17 spl93_908 <=> ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_908])])).
% 68.49/10.17 thf(f41552,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | (~spl93_345 | ~spl93_908)),
% 68.49/10.17 inference(forward_demodulation,[],[f41551,f6458])).
% 68.49/10.17 thf(f41551,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_908)),
% 68.49/10.17 inference(forward_demodulation,[],[f41549,f6458])).
% 68.49/10.17 thf(f41549,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_908),
% 68.49/10.17 inference(avatar_component_clause,[],[f41548])).
% 68.49/10.17 thf(f41550,plain,(
% 68.49/10.17 spl93_908 | ~spl93_22 | ~spl93_232),
% 68.49/10.17 inference(avatar_split_clause,[],[f3975,f3948,f1832,f41548])).
% 68.49/10.17 thf(f3948,plain,(
% 68.49/10.17 spl93_232 <=> ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_232])])).
% 68.49/10.17 thf(f3975,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_232)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3974])).
% 68.49/10.17 thf(f3974,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_232)),
% 68.49/10.17 inference(superposition,[],[f3949,f1833])).
% 68.49/10.17 thf(f3949,plain,(
% 68.49/10.17 ( ! [X2 : nat,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_232),
% 68.49/10.17 inference(avatar_component_clause,[],[f3948])).
% 68.49/10.17 thf(f41431,plain,(
% 68.49/10.17 spl93_907 | ~spl93_345 | ~spl93_906),
% 68.49/10.17 inference(avatar_split_clause,[],[f41427,f41423,f6456,f41429])).
% 68.49/10.17 thf(f41429,plain,(
% 68.49/10.17 spl93_907 <=> ! [X2 : a,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_907])])).
% 68.49/10.17 thf(f41423,plain,(
% 68.49/10.17 spl93_906 <=> ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_906])])).
% 68.49/10.17 thf(f41427,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0))) ) | (~spl93_345 | ~spl93_906)),
% 68.49/10.17 inference(forward_demodulation,[],[f41426,f6458])).
% 68.49/10.17 thf(f41426,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_906)),
% 68.49/10.17 inference(forward_demodulation,[],[f41424,f6458])).
% 68.49/10.17 thf(f41424,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_906),
% 68.49/10.17 inference(avatar_component_clause,[],[f41423])).
% 68.49/10.17 thf(f41425,plain,(
% 68.49/10.17 spl93_906 | ~spl93_22 | ~spl93_231),
% 68.49/10.17 inference(avatar_split_clause,[],[f3967,f3944,f1832,f41423])).
% 68.49/10.17 thf(f3944,plain,(
% 68.49/10.17 spl93_231 <=> ! [X2 : int,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_231])])).
% 68.49/10.17 thf(f3967,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_231)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3966])).
% 68.49/10.17 thf(f3966,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_231)),
% 68.49/10.17 inference(superposition,[],[f3945,f1833])).
% 68.49/10.17 thf(f3945,plain,(
% 68.49/10.17 ( ! [X2 : int,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_231),
% 68.49/10.17 inference(avatar_component_clause,[],[f3944])).
% 68.49/10.17 thf(f41193,plain,(
% 68.49/10.17 spl93_905 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_252),
% 68.49/10.17 inference(avatar_split_clause,[],[f6158,f4196,f2247,f2243,f2074,f41191])).
% 68.49/10.17 thf(f41191,plain,(
% 68.49/10.17 spl93_905 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_905])])).
% 68.49/10.17 thf(f6158,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_252)),
% 68.49/10.17 inference(forward_demodulation,[],[f6157,f5934])).
% 68.49/10.17 thf(f6157,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_252)),
% 68.49/10.17 inference(forward_demodulation,[],[f4212,f5934])).
% 68.49/10.17 thf(f4212,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_252)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4209])).
% 68.49/10.17 thf(f4209,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_252)),
% 68.49/10.17 inference(superposition,[],[f4197,f2245])).
% 68.49/10.17 thf(f41189,plain,(
% 68.49/10.17 spl93_904 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_260),
% 68.49/10.17 inference(avatar_split_clause,[],[f6134,f4290,f2247,f2243,f2074,f1868,f41187])).
% 68.49/10.17 thf(f41187,plain,(
% 68.49/10.17 spl93_904 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_904])])).
% 68.49/10.17 thf(f6134,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_260)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f6133])).
% 68.49/10.17 thf(f6133,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_260)),
% 68.49/10.17 inference(forward_demodulation,[],[f6132,f1870])).
% 68.49/10.17 thf(f6132,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_260)),
% 68.49/10.17 inference(forward_demodulation,[],[f6131,f5934])).
% 68.49/10.17 thf(f6131,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_260)),
% 68.49/10.17 inference(forward_demodulation,[],[f4303,f5934])).
% 68.49/10.17 thf(f4303,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_260)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4300])).
% 68.49/10.17 thf(f4300,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_260)),
% 68.49/10.17 inference(superposition,[],[f4291,f2245])).
% 68.49/10.17 thf(f41185,plain,(
% 68.49/10.17 ~spl93_61 | spl93_903 | ~spl93_566 | ~spl93_61 | ~spl93_125 | ~spl93_238),
% 68.49/10.17 inference(avatar_split_clause,[],[f4025,f4016,f2688,f2136,f25119,f41183,f2136])).
% 68.49/10.17 thf(f41183,plain,(
% 68.49/10.17 spl93_903 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_903])])).
% 68.49/10.17 thf(f25119,plain,(
% 68.49/10.17 spl93_566 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_566])])).
% 68.49/10.17 thf(f2688,plain,(
% 68.49/10.17 spl93_125 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_125])])).
% 68.49/10.17 thf(f4016,plain,(
% 68.49/10.17 spl93_238 <=> ! [X2 : a,X0 : a,X1 : a] : ((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_238])])).
% 68.49/10.17 thf(f4025,plain,(
% 68.49/10.17 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_61 | ~spl93_125 | ~spl93_238)),
% 68.49/10.17 inference(inner_rewriting,[],[f4024])).
% 68.49/10.17 thf(f4024,plain,(
% 68.49/10.17 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_61 | ~spl93_125 | ~spl93_238)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f4023])).
% 68.49/10.17 thf(f4023,plain,(
% 68.49/10.17 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_61 | ~spl93_125 | ~spl93_238)),
% 68.49/10.17 inference(forward_demodulation,[],[f4019,f2138])).
% 68.49/10.17 thf(f4019,plain,(
% 68.49/10.17 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_125 | ~spl93_238)),
% 68.49/10.17 inference(superposition,[],[f4017,f2690])).
% 68.49/10.17 thf(f2690,plain,(
% 68.49/10.17 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ~spl93_125),
% 68.49/10.17 inference(avatar_component_clause,[],[f2688])).
% 68.49/10.17 thf(f4017,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (X0 = X2) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1))) ) | ~spl93_238),
% 68.49/10.17 inference(avatar_component_clause,[],[f4016])).
% 68.49/10.17 thf(f40980,plain,(
% 68.49/10.17 spl93_902 | ~spl93_345 | ~spl93_901),
% 68.49/10.17 inference(avatar_split_clause,[],[f40976,f40972,f6456,f40978])).
% 68.49/10.17 thf(f40978,plain,(
% 68.49/10.17 spl93_902 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_902])])).
% 68.49/10.17 thf(f40972,plain,(
% 68.49/10.17 spl93_901 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_901])])).
% 68.49/10.17 thf(f40976,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))) ) | (~spl93_345 | ~spl93_901)),
% 68.49/10.17 inference(forward_demodulation,[],[f40975,f6458])).
% 68.49/10.17 thf(f40975,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_901)),
% 68.49/10.17 inference(forward_demodulation,[],[f40973,f6458])).
% 68.49/10.17 thf(f40973,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_901),
% 68.49/10.17 inference(avatar_component_clause,[],[f40972])).
% 68.49/10.17 thf(f40974,plain,(
% 68.49/10.17 spl93_901 | ~spl93_22 | ~spl93_230),
% 68.49/10.17 inference(avatar_split_clause,[],[f3938,f3922,f1832,f40972])).
% 68.49/10.17 thf(f3922,plain,(
% 68.49/10.17 spl93_230 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_230])])).
% 68.49/10.17 thf(f3938,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_230)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3937])).
% 68.49/10.17 thf(f3937,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_230)),
% 68.49/10.17 inference(superposition,[],[f3923,f1833])).
% 68.49/10.17 thf(f3923,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_230),
% 68.49/10.17 inference(avatar_component_clause,[],[f3922])).
% 68.49/10.17 thf(f40857,plain,(
% 68.49/10.17 spl93_900 | ~spl93_345 | ~spl93_899),
% 68.49/10.17 inference(avatar_split_clause,[],[f40853,f40849,f6456,f40855])).
% 68.49/10.17 thf(f40855,plain,(
% 68.49/10.17 spl93_900 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_900])])).
% 68.49/10.17 thf(f40849,plain,(
% 68.49/10.17 spl93_899 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_899])])).
% 68.49/10.17 thf(f40853,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))) ) | (~spl93_345 | ~spl93_899)),
% 68.49/10.17 inference(forward_demodulation,[],[f40852,f6458])).
% 68.49/10.17 thf(f40852,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_899)),
% 68.49/10.17 inference(forward_demodulation,[],[f40850,f6458])).
% 68.49/10.17 thf(f40850,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_899),
% 68.49/10.17 inference(avatar_component_clause,[],[f40849])).
% 68.49/10.17 thf(f40851,plain,(
% 68.49/10.17 spl93_899 | ~spl93_22 | ~spl93_229),
% 68.49/10.17 inference(avatar_split_clause,[],[f3929,f3918,f1832,f40849])).
% 68.49/10.17 thf(f3918,plain,(
% 68.49/10.17 spl93_229 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_229])])).
% 68.49/10.17 thf(f3929,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_229)),
% 68.49/10.17 inference(trivial_inequality_removal,[],[f3928])).
% 68.49/10.17 thf(f3928,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_229)),
% 68.49/10.17 inference(superposition,[],[f3919,f1833])).
% 68.49/10.17 thf(f3919,plain,(
% 68.49/10.17 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_229),
% 68.49/10.17 inference(avatar_component_clause,[],[f3918])).
% 68.49/10.17 thf(f40847,plain,(
% 68.49/10.17 spl93_898 | ~spl93_22 | ~spl93_225),
% 68.49/10.17 inference(avatar_split_clause,[],[f3875,f3863,f1832,f40845])).
% 68.49/10.17 thf(f40845,plain,(
% 68.49/10.17 spl93_898 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK16(X0,$o),X1)),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK17(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK18(X0,$o),X1)))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK16(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK17(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK18(X0,$o),X1))))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_898])])).
% 68.49/10.17 thf(f3875,plain,(
% 68.49/10.17 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK16(X0,$o),X1)),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK17(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK18(X0,$o),X1)))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK16(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK17(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK18(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_225)),
% 68.49/10.17 inference(superposition,[],[f3864,f1833])).
% 68.49/10.17 thf(f40716,plain,(
% 68.49/10.17 spl93_897 | ~spl93_345 | ~spl93_896),
% 68.49/10.17 inference(avatar_split_clause,[],[f40672,f40667,f6456,f40714])).
% 68.49/10.17 thf(f40714,plain,(
% 68.49/10.17 spl93_897 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_897])])).
% 68.49/10.17 thf(f40667,plain,(
% 68.49/10.17 spl93_896 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1))),
% 68.49/10.17 introduced(avatar_definition,[new_symbols(naming,[spl93_896])])).
% 68.49/10.17 thf(f40672,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1)) ) | (~spl93_345 | ~spl93_896)),
% 68.49/10.17 inference(forward_demodulation,[],[f40671,f6458])).
% 68.49/10.17 thf(f40671,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1)) ) | (~spl93_345 | ~spl93_896)),
% 68.49/10.17 inference(forward_demodulation,[],[f40670,f6458])).
% 68.49/10.17 thf(f40670,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1)) ) | (~spl93_345 | ~spl93_896)),
% 68.49/10.17 inference(forward_demodulation,[],[f40668,f6458])).
% 68.49/10.17 thf(f40668,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1)) ) | ~spl93_896),
% 68.49/10.17 inference(avatar_component_clause,[],[f40667])).
% 68.49/10.17 thf(f40669,plain,(
% 68.49/10.17 spl93_896),
% 68.49/10.17 inference(avatar_split_clause,[],[f1601,f40667])).
% 68.49/10.17 thf(f1601,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) != X1)) )),
% 68.49/10.17 inference(equality_proxy_clausification,[],[f1600])).
% 68.49/10.17 thf(f1600,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1))) )),
% 68.49/10.17 inference(equality_proxy_clausification,[],[f1596])).
% 68.49/10.17 thf(f1596,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1))) )),
% 68.49/10.17 inference(binary_proxy_clausification,[],[f1379])).
% 68.49/10.17 thf(f1379,plain,(
% 68.49/10.17 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.17 inference(cnf_transformation,[],[f957])).
% 68.49/10.17 thf(f957,plain,(
% 68.49/10.17 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.17 inference(flattening,[],[f956])).
% 68.49/10.17 thf(f956,plain,(
% 68.49/10.17 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 inference(ennf_transformation,[],[f545])).
% 68.49/10.18 thf(f545,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1)))))),
% 68.49/10.18 inference(fool_elimination,[],[f544])).
% 68.49/10.18 thf(f544,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) = X0) = (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1)))))),
% 68.49/10.18 inference(rectify,[],[f201])).
% 68.49/10.18 thf(f201,axiom,(
% 68.49/10.18 ! [X6 : a,X7 : a,X8 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X8),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X7),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X8)) = X6) = (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X6),X8) = X7)))))),
% 68.49/10.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_200_add_Oinv__solve__right)).
% 68.49/10.18 thf(f40631,plain,(
% 68.49/10.18 spl93_895 | ~spl93_345 | ~spl93_894),
% 68.49/10.18 inference(avatar_split_clause,[],[f40627,f40622,f6456,f40629])).
% 68.49/10.18 thf(f40629,plain,(
% 68.49/10.18 spl93_895 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_895])])).
% 68.49/10.18 thf(f40622,plain,(
% 68.49/10.18 spl93_894 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_894])])).
% 68.49/10.18 thf(f40627,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1)) ) | (~spl93_345 | ~spl93_894)),
% 68.49/10.18 inference(forward_demodulation,[],[f40626,f6458])).
% 68.49/10.18 thf(f40626,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1)) ) | (~spl93_345 | ~spl93_894)),
% 68.49/10.18 inference(forward_demodulation,[],[f40625,f6458])).
% 68.49/10.18 thf(f40625,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1)) ) | (~spl93_345 | ~spl93_894)),
% 68.49/10.18 inference(forward_demodulation,[],[f40623,f6458])).
% 68.49/10.18 thf(f40623,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1)) ) | ~spl93_894),
% 68.49/10.18 inference(avatar_component_clause,[],[f40622])).
% 68.49/10.18 thf(f40624,plain,(
% 68.49/10.18 spl93_894),
% 68.49/10.18 inference(avatar_split_clause,[],[f1599,f40622])).
% 68.49/10.18 thf(f1599,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2) = X1)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1598])).
% 68.49/10.18 thf(f1598,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2)) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1597])).
% 68.49/10.18 thf(f1597,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2)),X1))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1379])).
% 68.49/10.18 thf(f40516,plain,(
% 68.49/10.18 spl93_893 | ~spl93_345 | ~spl93_892),
% 68.49/10.18 inference(avatar_split_clause,[],[f40512,f40507,f6456,f40514])).
% 68.49/10.18 thf(f40514,plain,(
% 68.49/10.18 spl93_893 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_893])])).
% 68.49/10.18 thf(f40507,plain,(
% 68.49/10.18 spl93_892 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_892])])).
% 68.49/10.18 thf(f40512,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2)) ) | (~spl93_345 | ~spl93_892)),
% 68.49/10.18 inference(forward_demodulation,[],[f40511,f6458])).
% 68.49/10.18 thf(f40511,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2)) ) | (~spl93_345 | ~spl93_892)),
% 68.49/10.18 inference(forward_demodulation,[],[f40510,f6458])).
% 68.49/10.18 thf(f40510,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2)) ) | (~spl93_345 | ~spl93_892)),
% 68.49/10.18 inference(forward_demodulation,[],[f40508,f6458])).
% 68.49/10.18 thf(f40508,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2)) ) | ~spl93_892),
% 68.49/10.18 inference(avatar_component_clause,[],[f40507])).
% 68.49/10.18 thf(f40509,plain,(
% 68.49/10.18 spl93_892),
% 68.49/10.18 inference(avatar_split_clause,[],[f1589,f40507])).
% 68.49/10.18 thf(f1589,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X2)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1588])).
% 68.49/10.18 thf(f1588,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1584])).
% 68.49/10.18 thf(f1584,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1381])).
% 68.49/10.18 thf(f1381,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.18 inference(cnf_transformation,[],[f961])).
% 68.49/10.18 thf(f961,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 inference(flattening,[],[f960])).
% 68.49/10.18 thf(f960,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 inference(ennf_transformation,[],[f549])).
% 68.49/10.18 thf(f549,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2)))))),
% 68.49/10.18 inference(fool_elimination,[],[f548])).
% 68.49/10.18 thf(f548,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) = X0) = (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2)))))),
% 68.49/10.18 inference(rectify,[],[f202])).
% 68.49/10.18 thf(f202,axiom,(
% 68.49/10.18 ! [X6 : a,X7 : a,X8 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X8),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X7)),X8) = X6) = (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X7),X6) = X8)))))),
% 68.49/10.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_201_add_Oinv__solve__left_H)).
% 68.49/10.18 thf(f40472,plain,(
% 68.49/10.18 spl93_891 | ~spl93_345 | ~spl93_890),
% 68.49/10.18 inference(avatar_split_clause,[],[f40468,f40463,f6456,f40470])).
% 68.49/10.18 thf(f40470,plain,(
% 68.49/10.18 spl93_891 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_891])])).
% 68.49/10.18 thf(f40463,plain,(
% 68.49/10.18 spl93_890 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_890])])).
% 68.49/10.18 thf(f40468,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2)) ) | (~spl93_345 | ~spl93_890)),
% 68.49/10.18 inference(forward_demodulation,[],[f40467,f6458])).
% 68.49/10.18 thf(f40467,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2)) ) | (~spl93_345 | ~spl93_890)),
% 68.49/10.18 inference(forward_demodulation,[],[f40466,f6458])).
% 68.49/10.18 thf(f40466,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2)) ) | (~spl93_345 | ~spl93_890)),
% 68.49/10.18 inference(forward_demodulation,[],[f40464,f6458])).
% 68.49/10.18 thf(f40464,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2)) ) | ~spl93_890),
% 68.49/10.18 inference(avatar_component_clause,[],[f40463])).
% 68.49/10.18 thf(f40465,plain,(
% 68.49/10.18 spl93_890),
% 68.49/10.18 inference(avatar_split_clause,[],[f1587,f40463])).
% 68.49/10.18 thf(f1587,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X2)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1586])).
% 68.49/10.18 thf(f1586,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1585])).
% 68.49/10.18 thf(f1585,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X2))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1381])).
% 68.49/10.18 thf(f40304,plain,(
% 68.49/10.18 spl93_889 | ~spl93_66 | ~spl93_234),
% 68.49/10.18 inference(avatar_split_clause,[],[f3995,f3956,f2161,f40302])).
% 68.49/10.18 thf(f40302,plain,(
% 68.49/10.18 spl93_889 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_889])])).
% 68.49/10.18 thf(f3995,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_234)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3990])).
% 68.49/10.18 thf(f3990,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_234)),
% 68.49/10.18 inference(superposition,[],[f3957,f2163])).
% 68.49/10.18 thf(f40297,plain,(
% 68.49/10.18 spl93_888 | ~spl93_66 | ~spl93_233),
% 68.49/10.18 inference(avatar_split_clause,[],[f3986,f3952,f2161,f40295])).
% 68.49/10.18 thf(f40295,plain,(
% 68.49/10.18 spl93_888 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_888])])).
% 68.49/10.18 thf(f3986,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_233)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3981])).
% 68.49/10.18 thf(f3981,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_233)),
% 68.49/10.18 inference(superposition,[],[f3953,f2163])).
% 68.49/10.18 thf(f40290,plain,(
% 68.49/10.18 spl93_887 | ~spl93_66 | ~spl93_232),
% 68.49/10.18 inference(avatar_split_clause,[],[f3977,f3948,f2161,f40288])).
% 68.49/10.18 thf(f40288,plain,(
% 68.49/10.18 spl93_887 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_887])])).
% 68.49/10.18 thf(f3977,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_232)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3972])).
% 68.49/10.18 thf(f3972,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_232)),
% 68.49/10.18 inference(superposition,[],[f3949,f2163])).
% 68.49/10.18 thf(f40284,plain,(
% 68.49/10.18 spl93_886 | ~spl93_66 | ~spl93_231),
% 68.49/10.18 inference(avatar_split_clause,[],[f3969,f3944,f2161,f40282])).
% 68.49/10.18 thf(f40282,plain,(
% 68.49/10.18 spl93_886 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_886])])).
% 68.49/10.18 thf(f3969,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_231)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3964])).
% 68.49/10.18 thf(f3964,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_231)),
% 68.49/10.18 inference(superposition,[],[f3945,f2163])).
% 68.49/10.18 thf(f40280,plain,(
% 68.49/10.18 spl93_885 | ~spl93_48 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3817,f3805,f2031,f40278])).
% 68.49/10.18 thf(f40278,plain,(
% 68.49/10.18 spl93_885 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X6 : product_prod(X3,product_prod(X4,product_prod(X1,X0))),X5 : product_prod(X3,product_prod(X4,product_prod(X1,X0))) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X4,X3),X5)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X4,sK54(X0,X1,X4,X3),X5)),X2)))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,X6)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X4,X3),X5)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X4,X3),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_885])])).
% 68.49/10.18 thf(f3817,plain,(
% 68.49/10.18 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X6 : product_prod(X3,product_prod(X4,product_prod(X1,X0))),X5 : product_prod(X3,product_prod(X4,product_prod(X1,X0))) > $o] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X4,X3),X5)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X4,sK54(X0,X1,X4,X3),X5)),X2)))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,X6)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X4,X3),X5)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X4,X3),X5))) ) | (~spl93_48 | ~spl93_220)),
% 68.49/10.18 inference(constrained_superposition,[],[f3806,f2032])).
% 68.49/10.18 thf(f40276,plain,(
% 68.49/10.18 spl93_884 | ~spl93_47 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3816,f3805,f2027,f40274])).
% 68.49/10.18 thf(f40274,plain,(
% 68.49/10.18 spl93_884 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X6 : product_prod(X3,product_prod(X4,product_prod(X1,X0))),X5 : product_prod(X3,product_prod(X4,product_prod(X1,X0))) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X4,X3),X5)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X4,sK54(X0,X1,X4,X3),X5)),X2)))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,X6)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X4,X3),X5)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X4,X3),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_884])])).
% 68.49/10.18 thf(f3816,plain,(
% 68.49/10.18 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X6 : product_prod(X3,product_prod(X4,product_prod(X1,X0))),X5 : product_prod(X3,product_prod(X4,product_prod(X1,X0))) > $o] : (($true != vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,vAPP(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X4,product_prod(X1,X0)),product_prod(X3,product_prod(X4,product_prod(X1,X0)))),product_Pair(X3,product_prod(X4,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X4,X3),X5)),vAPP(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0)),vAPP(X4,sTfun(product_prod(X1,X0),product_prod(X4,product_prod(X1,X0))),product_Pair(X4,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X4,sK54(X0,X1,X4,X3),X5)),X2)))) | ($true = vAPP(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o,X5,X6)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X4,X3),X5)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X4,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X4,X3),X5))) ) | (~spl93_47 | ~spl93_220)),
% 68.49/10.18 inference(constrained_superposition,[],[f3806,f2028])).
% 68.49/10.18 thf(f40218,plain,(
% 68.49/10.18 spl93_883 | ~spl93_345 | ~spl93_882),
% 68.49/10.18 inference(avatar_split_clause,[],[f40139,f40136,f6456,f40216])).
% 68.49/10.18 thf(f40216,plain,(
% 68.49/10.18 spl93_883 <=> ! [X2 : int,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_883])])).
% 68.49/10.18 thf(f40136,plain,(
% 68.49/10.18 spl93_882 <=> ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_882])])).
% 68.49/10.18 thf(f40139,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))))) ) | (~spl93_345 | ~spl93_882)),
% 68.49/10.18 inference(forward_demodulation,[],[f40137,f6458])).
% 68.49/10.18 thf(f40137,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_882),
% 68.49/10.18 inference(avatar_component_clause,[],[f40136])).
% 68.49/10.18 thf(f40138,plain,(
% 68.49/10.18 spl93_882 | ~spl93_22 | ~spl93_226),
% 68.49/10.18 inference(avatar_split_clause,[],[f3888,f3867,f1832,f40136])).
% 68.49/10.18 thf(f3867,plain,(
% 68.49/10.18 spl93_226 <=> ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_226])])).
% 68.49/10.18 thf(f3888,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_226)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3887])).
% 68.49/10.18 thf(f3887,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_226)),
% 68.49/10.18 inference(superposition,[],[f3868,f1833])).
% 68.49/10.18 thf(f3868,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))))) ) | ~spl93_226),
% 68.49/10.18 inference(avatar_component_clause,[],[f3867])).
% 68.49/10.18 thf(f39870,plain,(
% 68.49/10.18 spl93_881 | ~spl93_22 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3815,f3805,f1832,f39868])).
% 68.49/10.18 thf(f39868,plain,(
% 68.49/10.18 spl93_881 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,$o))),X3 : product_prod(X0,product_prod(X1,product_prod(X2,$o))) > $o] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o,X3,vAPP(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o)))),product_Pair(X0,product_prod(X1,product_prod(X2,$o))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),X0,sK53($o,X2,X1,X0),X3)),vAPP(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o)),vAPP(X1,sTfun(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o))),product_Pair(X1,product_prod(X2,$o)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),X1,sK54($o,X2,X1,X0),X3)),vAPP($o,product_prod(X2,$o),vAPP(X2,sTfun($o,product_prod(X2,$o)),product_Pair(X2,$o),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),X2,sK55($o,X2,X1,X0),X3)),$true))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),$o,sK56($o,X2,X1,X0),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_881])])).
% 68.49/10.18 thf(f3815,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,product_prod(X2,$o))) > $o,X4 : product_prod(X0,product_prod(X1,product_prod(X2,$o)))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o,X3,vAPP(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o)))),product_Pair(X0,product_prod(X1,product_prod(X2,$o))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),X0,sK53($o,X2,X1,X0),X3)),vAPP(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o)),vAPP(X1,sTfun(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o))),product_Pair(X1,product_prod(X2,$o)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),X1,sK54($o,X2,X1,X0),X3)),vAPP($o,product_prod(X2,$o),vAPP(X2,sTfun($o,product_prod(X2,$o)),product_Pair(X2,$o),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),X2,sK55($o,X2,X1,X0),X3)),$true))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o),$o,sK56($o,X2,X1,X0),X3))) ) | (~spl93_22 | ~spl93_220)),
% 68.49/10.18 inference(superposition,[],[f3806,f1833])).
% 68.49/10.18 thf(f39866,plain,(
% 68.49/10.18 spl93_880 | ~spl93_22 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3814,f3805,f1832,f39864])).
% 68.49/10.18 thf(f39864,plain,(
% 68.49/10.18 spl93_880 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod($o,X2))),X3 : product_prod(X0,product_prod(X1,product_prod($o,X2))) > $o] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o,X3,vAPP(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2)))),product_Pair(X0,product_prod(X1,product_prod($o,X2))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),X0,sK53(X2,$o,X1,X0),X3)),vAPP(product_prod($o,X2),product_prod(X1,product_prod($o,X2)),vAPP(X1,sTfun(product_prod($o,X2),product_prod(X1,product_prod($o,X2))),product_Pair(X1,product_prod($o,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),X1,sK54(X2,$o,X1,X0),X3)),vAPP(X2,product_prod($o,X2),vAPP($o,sTfun(X2,product_prod($o,X2)),product_Pair($o,X2),$true),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),X2,sK56(X2,$o,X1,X0),X3)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),$o,sK55(X2,$o,X1,X0),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_880])])).
% 68.49/10.18 thf(f3814,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,product_prod($o,X2))) > $o,X4 : product_prod(X0,product_prod(X1,product_prod($o,X2)))] : (($true != vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o,X3,vAPP(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2)))),product_Pair(X0,product_prod(X1,product_prod($o,X2))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),X0,sK53(X2,$o,X1,X0),X3)),vAPP(product_prod($o,X2),product_prod(X1,product_prod($o,X2)),vAPP(X1,sTfun(product_prod($o,X2),product_prod(X1,product_prod($o,X2))),product_Pair(X1,product_prod($o,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),X1,sK54(X2,$o,X1,X0),X3)),vAPP(X2,product_prod($o,X2),vAPP($o,sTfun(X2,product_prod($o,X2)),product_Pair($o,X2),$true),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),X2,sK56(X2,$o,X1,X0),X3)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o),$o,sK55(X2,$o,X1,X0),X3))) ) | (~spl93_22 | ~spl93_220)),
% 68.49/10.18 inference(superposition,[],[f3806,f1833])).
% 68.49/10.18 thf(f39862,plain,(
% 68.49/10.18 spl93_879 | ~spl93_22 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3813,f3805,f1832,f39860])).
% 68.49/10.18 thf(f39860,plain,(
% 68.49/10.18 spl93_879 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod($o,product_prod(X1,X2))),X3 : product_prod(X0,product_prod($o,product_prod(X1,X2))) > $o] : (($true != vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o,X3,vAPP(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2)))),product_Pair(X0,product_prod($o,product_prod(X1,X2))),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),X0,sK53(X2,X1,$o,X0),X3)),vAPP(product_prod(X1,X2),product_prod($o,product_prod(X1,X2)),vAPP($o,sTfun(product_prod(X1,X2),product_prod($o,product_prod(X1,X2))),product_Pair($o,product_prod(X1,X2)),$true),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),X1,sK55(X2,X1,$o,X0),X3)),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),X2,sK56(X2,X1,$o,X0),X3)))))) | ($true = vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),$o,sK54(X2,X1,$o,X0),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_879])])).
% 68.49/10.18 thf(f3813,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod($o,product_prod(X1,X2))) > $o,X4 : product_prod(X0,product_prod($o,product_prod(X1,X2)))] : (($true != vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o,X3,vAPP(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2)))),product_Pair(X0,product_prod($o,product_prod(X1,X2))),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),X0,sK53(X2,X1,$o,X0),X3)),vAPP(product_prod(X1,X2),product_prod($o,product_prod(X1,X2)),vAPP($o,sTfun(product_prod(X1,X2),product_prod($o,product_prod(X1,X2))),product_Pair($o,product_prod(X1,X2)),$true),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),X1,sK55(X2,X1,$o,X0),X3)),vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),X2,sK56(X2,X1,$o,X0),X3)))))) | ($true = vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o),$o,sK54(X2,X1,$o,X0),X3))) ) | (~spl93_22 | ~spl93_220)),
% 68.49/10.18 inference(superposition,[],[f3806,f1833])).
% 68.49/10.18 thf(f39858,plain,(
% 68.49/10.18 spl93_878 | ~spl93_22 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3812,f3805,f1832,f39856])).
% 68.49/10.18 thf(f39856,plain,(
% 68.49/10.18 spl93_878 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod($o,product_prod(X0,product_prod(X1,X2))),X3 : product_prod($o,product_prod(X0,product_prod(X1,X2))) > $o] : (($true != vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o,X3,vAPP(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2)))),product_Pair($o,product_prod(X0,product_prod(X1,X2))),$true),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),X0,sK54(X2,X1,X0,$o),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),X1,sK55(X2,X1,X0,$o),X3)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),X2,sK56(X2,X1,X0,$o),X3)))))) | ($true = vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),$o,sK53(X2,X1,X0,$o),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_878])])).
% 68.49/10.18 thf(f3812,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod($o,product_prod(X0,product_prod(X1,X2))) > $o,X4 : product_prod($o,product_prod(X0,product_prod(X1,X2)))] : (($true != vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o,X3,vAPP(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2)))),product_Pair($o,product_prod(X0,product_prod(X1,X2))),$true),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),X0,sK54(X2,X1,X0,$o),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),X1,sK55(X2,X1,X0,$o),X3)),vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),X2,sK56(X2,X1,X0,$o),X3)))))) | ($true = vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o,X3,X4)) | ($false = vAPP(sTfun(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o),$o,sK53(X2,X1,X0,$o),X3))) ) | (~spl93_22 | ~spl93_220)),
% 68.49/10.18 inference(superposition,[],[f3806,f1833])).
% 68.49/10.18 thf(f39666,plain,(
% 68.49/10.18 spl93_877 | ~spl93_345 | ~spl93_876),
% 68.49/10.18 inference(avatar_split_clause,[],[f39662,f39659,f6456,f39664])).
% 68.49/10.18 thf(f39664,plain,(
% 68.49/10.18 spl93_877 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_877])])).
% 68.49/10.18 thf(f39659,plain,(
% 68.49/10.18 spl93_876 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_876])])).
% 68.49/10.18 thf(f39662,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_876)),
% 68.49/10.18 inference(forward_demodulation,[],[f39660,f6458])).
% 68.49/10.18 thf(f39660,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_876),
% 68.49/10.18 inference(avatar_component_clause,[],[f39659])).
% 68.49/10.18 thf(f39661,plain,(
% 68.49/10.18 spl93_876 | ~spl93_61 | ~spl93_234),
% 68.49/10.18 inference(avatar_split_clause,[],[f3996,f3956,f2136,f39659])).
% 68.49/10.18 thf(f3996,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_234)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3989])).
% 68.49/10.18 thf(f3989,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_234)),
% 68.49/10.18 inference(superposition,[],[f3957,f2138])).
% 68.49/10.18 thf(f39510,plain,(
% 68.49/10.18 spl93_875 | ~spl93_345 | ~spl93_874),
% 68.49/10.18 inference(avatar_split_clause,[],[f39506,f39503,f6456,f39508])).
% 68.49/10.18 thf(f39508,plain,(
% 68.49/10.18 spl93_875 <=> ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_875])])).
% 68.49/10.18 thf(f39503,plain,(
% 68.49/10.18 spl93_874 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_874])])).
% 68.49/10.18 thf(f39506,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_874)),
% 68.49/10.18 inference(forward_demodulation,[],[f39504,f6458])).
% 68.49/10.18 thf(f39504,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_874),
% 68.49/10.18 inference(avatar_component_clause,[],[f39503])).
% 68.49/10.18 thf(f39505,plain,(
% 68.49/10.18 spl93_874 | ~spl93_61 | ~spl93_231),
% 68.49/10.18 inference(avatar_split_clause,[],[f3970,f3944,f2136,f39503])).
% 68.49/10.18 thf(f3970,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_231)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3963])).
% 68.49/10.18 thf(f3963,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_231)),
% 68.49/10.18 inference(superposition,[],[f3945,f2138])).
% 68.49/10.18 thf(f39498,plain,(
% 68.49/10.18 spl93_873 | ~spl93_66 | ~spl93_230),
% 68.49/10.18 inference(avatar_split_clause,[],[f3940,f3922,f2161,f39496])).
% 68.49/10.18 thf(f39496,plain,(
% 68.49/10.18 spl93_873 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_873])])).
% 68.49/10.18 thf(f3940,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_230)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3935])).
% 68.49/10.18 thf(f3935,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_230)),
% 68.49/10.18 inference(superposition,[],[f3923,f2163])).
% 68.49/10.18 thf(f39491,plain,(
% 68.49/10.18 spl93_872 | ~spl93_66 | ~spl93_229),
% 68.49/10.18 inference(avatar_split_clause,[],[f3931,f3918,f2161,f39489])).
% 68.49/10.18 thf(f39489,plain,(
% 68.49/10.18 spl93_872 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_872])])).
% 68.49/10.18 thf(f3931,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_229)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3926])).
% 68.49/10.18 thf(f3926,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_229)),
% 68.49/10.18 inference(superposition,[],[f3919,f2163])).
% 68.49/10.18 thf(f39261,plain,(
% 68.49/10.18 spl93_871 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_257),
% 68.49/10.18 inference(avatar_split_clause,[],[f6150,f4252,f2247,f2243,f2074,f1868,f39259])).
% 68.49/10.18 thf(f39259,plain,(
% 68.49/10.18 spl93_871 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_871])])).
% 68.49/10.18 thf(f6150,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_257)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f6149])).
% 68.49/10.18 thf(f6149,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_257)),
% 68.49/10.18 inference(forward_demodulation,[],[f6148,f1870])).
% 68.49/10.18 thf(f6148,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_257)),
% 68.49/10.18 inference(forward_demodulation,[],[f6147,f5934])).
% 68.49/10.18 thf(f6147,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_257)),
% 68.49/10.18 inference(forward_demodulation,[],[f4268,f5934])).
% 68.49/10.18 thf(f4268,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_257)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4265])).
% 68.49/10.18 thf(f4265,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_257)),
% 68.49/10.18 inference(superposition,[],[f4253,f2245])).
% 68.49/10.18 thf(f39257,plain,(
% 68.49/10.18 spl93_870 | ~spl93_276 | ~spl93_617),
% 68.49/10.18 inference(avatar_split_clause,[],[f30441,f26464,f4534,f39255])).
% 68.49/10.18 thf(f39255,plain,(
% 68.49/10.18 spl93_870 <=> ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = X1))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_870])])).
% 68.49/10.18 thf(f26464,plain,(
% 68.49/10.18 spl93_617 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),X1) != X0) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_617])])).
% 68.49/10.18 thf(f30441,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = X1)) ) | (~spl93_276 | ~spl93_617)),
% 68.49/10.18 inference(superposition,[],[f26465,f4535])).
% 68.49/10.18 thf(f26465,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),X1) != X0) | (X1 = X2)) ) | ~spl93_617),
% 68.49/10.18 inference(avatar_component_clause,[],[f26464])).
% 68.49/10.18 thf(f39253,plain,(
% 68.49/10.18 spl93_869 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_259),
% 68.49/10.18 inference(avatar_split_clause,[],[f6140,f4260,f2247,f2243,f2074,f1873,f39251])).
% 68.49/10.18 thf(f39251,plain,(
% 68.49/10.18 spl93_869 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_869])])).
% 68.49/10.18 thf(f1873,plain,(
% 68.49/10.18 spl93_25 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) = $true)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_25])])).
% 68.49/10.18 thf(f6140,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_259)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f6139])).
% 68.49/10.18 thf(f6139,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_259)),
% 68.49/10.18 inference(forward_demodulation,[],[f6138,f1875])).
% 68.49/10.18 thf(f1875,plain,(
% 68.49/10.18 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) = $true) | ~spl93_25),
% 68.49/10.18 inference(avatar_component_clause,[],[f1873])).
% 68.49/10.18 thf(f6138,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_259)),
% 68.49/10.18 inference(forward_demodulation,[],[f6137,f5934])).
% 68.49/10.18 thf(f6137,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_259)),
% 68.49/10.18 inference(forward_demodulation,[],[f4284,f5934])).
% 68.49/10.18 thf(f4284,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_259)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4281])).
% 68.49/10.18 thf(f4281,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_259)),
% 68.49/10.18 inference(superposition,[],[f4261,f2245])).
% 68.49/10.18 thf(f38892,plain,(
% 68.49/10.18 spl93_868 | ~spl93_66 | ~spl93_177 | ~spl93_226),
% 68.49/10.18 inference(avatar_split_clause,[],[f3896,f3867,f3305,f2161,f38890])).
% 68.49/10.18 thf(f38890,plain,(
% 68.49/10.18 spl93_868 <=> ! [X0 : int,X1 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_868])])).
% 68.49/10.18 thf(f3305,plain,(
% 68.49/10.18 spl93_177 <=> ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_177])])).
% 68.49/10.18 thf(f3896,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_177 | ~spl93_226)),
% 68.49/10.18 inference(forward_demodulation,[],[f3890,f3338])).
% 68.49/10.18 thf(f3338,plain,(
% 68.49/10.18 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_66 | ~spl93_177)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3333])).
% 68.49/10.18 thf(f3333,plain,(
% 68.49/10.18 ( ! [X0 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_66 | ~spl93_177)),
% 68.49/10.18 inference(superposition,[],[f3306,f2163])).
% 68.49/10.18 thf(f3306,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0))) ) | ~spl93_177),
% 68.49/10.18 inference(avatar_component_clause,[],[f3305])).
% 68.49/10.18 thf(f3890,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))))) ) | (~spl93_66 | ~spl93_226)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3885])).
% 68.49/10.18 thf(f3885,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))))) ) | (~spl93_66 | ~spl93_226)),
% 68.49/10.18 inference(superposition,[],[f3868,f2163])).
% 68.49/10.18 thf(f38888,plain,(
% 68.49/10.18 spl93_867 | ~spl93_22 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3822,f3805,f1832,f38886])).
% 68.49/10.18 thf(f38886,plain,(
% 68.49/10.18 spl93_867 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,X4,X5)) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,X4,vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),X4)))))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_867])])).
% 68.49/10.18 thf(f3822,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,X4,X5)) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,X4,vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),X4))))))) ) | (~spl93_22 | ~spl93_220)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3820])).
% 68.49/10.18 thf(f3820,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3))) > $o,X5 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (($true != $true) | ($true = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,X4,X5)) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o,X4,vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X0,sK53(X3,X2,X1,X0),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X1,sK54(X3,X2,X1,X0),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X2,sK55(X3,X2,X1,X0),X4)),vAPP(sTfun(product_prod(X0,product_prod(X1,product_prod(X2,X3))),$o),X3,sK56(X3,X2,X1,X0),X4))))))) ) | (~spl93_22 | ~spl93_220)),
% 68.49/10.18 inference(superposition,[],[f3806,f1833])).
% 68.49/10.18 thf(f38884,plain,(
% 68.49/10.18 spl93_866 | ~spl93_139 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3818,f3805,f2831,f38882])).
% 68.49/10.18 thf(f38882,plain,(
% 68.49/10.18 spl93_866 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X6 : product_prod(X4,product_prod(X2,product_prod(X0,X1))),X5 : product_prod(X4,product_prod(X2,product_prod(X0,X1))) > $o] : (($true != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o,X5,vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1))),vAPP(X4,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1)))),product_Pair(X4,product_prod(X2,product_prod(X0,X1))),vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X4,sK53(X1,X0,X2,X4),X5)),X3))) | ($true = vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o,X5,X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X1,sK56(X1,X0,X2,X4),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X0,sK55(X1,X0,X2,X4),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X2,sK54(X1,X0,X2,X4),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_866])])).
% 68.49/10.18 thf(f3818,plain,(
% 68.49/10.18 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X6 : product_prod(X4,product_prod(X2,product_prod(X0,X1))),X5 : product_prod(X4,product_prod(X2,product_prod(X0,X1))) > $o] : (($true != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o,X5,vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1))),vAPP(X4,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1)))),product_Pair(X4,product_prod(X2,product_prod(X0,X1))),vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X4,sK53(X1,X0,X2,X4),X5)),X3))) | ($true = vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o,X5,X6)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X1,sK56(X1,X0,X2,X4),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X0,sK55(X1,X0,X2,X4),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X4,product_prod(X2,product_prod(X0,X1))),$o),X2,sK54(X1,X0,X2,X4),X5))) ) | (~spl93_139 | ~spl93_220)),
% 68.49/10.18 inference(constrained_superposition,[],[f3806,f2832])).
% 68.49/10.18 thf(f38518,plain,(
% 68.49/10.18 spl93_865 | ~spl93_270 | ~spl93_617),
% 68.49/10.18 inference(avatar_split_clause,[],[f30416,f26464,f4444,f38516])).
% 68.49/10.18 thf(f38516,plain,(
% 68.49/10.18 spl93_865 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0)),X2) != X0) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_865])])).
% 68.49/10.18 thf(f4444,plain,(
% 68.49/10.18 spl93_270 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_270])])).
% 68.49/10.18 thf(f30416,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0)),X2) != X0) | (X1 = X2)) ) | (~spl93_270 | ~spl93_617)),
% 68.49/10.18 inference(superposition,[],[f26465,f4445])).
% 68.49/10.18 thf(f4445,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0))) ) | ~spl93_270),
% 68.49/10.18 inference(avatar_component_clause,[],[f4444])).
% 68.49/10.18 thf(f38514,plain,(
% 68.49/10.18 spl93_864 | ~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_795 | ~spl93_863),
% 68.49/10.18 inference(avatar_split_clause,[],[f38510,f38507,f34330,f27603,f23000,f13821,f7374,f3689,f38512])).
% 68.49/10.18 thf(f38512,plain,(
% 68.49/10.18 spl93_864 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_864])])).
% 68.49/10.18 thf(f7374,plain,(
% 68.49/10.18 spl93_369 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_369])])).
% 68.49/10.18 thf(f23000,plain,(
% 68.49/10.18 spl93_520 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_520])])).
% 68.49/10.18 thf(f27603,plain,(
% 68.49/10.18 spl93_646 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_646])])).
% 68.49/10.18 thf(f34330,plain,(
% 68.49/10.18 spl93_795 <=> ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_795])])).
% 68.49/10.18 thf(f38507,plain,(
% 68.49/10.18 spl93_863 <=> ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_863])])).
% 68.49/10.18 thf(f38510,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_795 | ~spl93_863)),
% 68.49/10.18 inference(forward_demodulation,[],[f38508,f34413])).
% 68.49/10.18 thf(f34413,plain,(
% 68.49/10.18 ( ! [X0 : int] : ((sK6 = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))) ) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_795)),
% 68.49/10.18 inference(forward_demodulation,[],[f34398,f27626])).
% 68.49/10.18 thf(f27626,plain,(
% 68.49/10.18 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646)),
% 68.49/10.18 inference(forward_demodulation,[],[f27625,f13823])).
% 68.49/10.18 thf(f27625,plain,(
% 68.49/10.18 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f27624])).
% 68.49/10.18 thf(f27624,plain,(
% 68.49/10.18 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646)),
% 68.49/10.18 inference(forward_demodulation,[],[f27623,f7376])).
% 68.49/10.18 thf(f7376,plain,(
% 68.49/10.18 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ~spl93_369),
% 68.49/10.18 inference(avatar_component_clause,[],[f7374])).
% 68.49/10.18 thf(f27623,plain,(
% 68.49/10.18 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_440 | ~spl93_520 | ~spl93_646)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f27622])).
% 68.49/10.18 thf(f27622,plain,(
% 68.49/10.18 ($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_440 | ~spl93_520 | ~spl93_646)),
% 68.49/10.18 inference(forward_demodulation,[],[f27621,f23002])).
% 68.49/10.18 thf(f23002,plain,(
% 68.49/10.18 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ~spl93_520),
% 68.49/10.18 inference(avatar_component_clause,[],[f23000])).
% 68.49/10.18 thf(f27621,plain,(
% 68.49/10.18 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_440 | ~spl93_646)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f27620])).
% 68.49/10.18 thf(f27620,plain,(
% 68.49/10.18 (sK6 != sK6) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_440 | ~spl93_646)),
% 68.49/10.18 inference(forward_demodulation,[],[f27610,f13823])).
% 68.49/10.18 thf(f27610,plain,(
% 68.49/10.18 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != sK6) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_210 | ~spl93_646)),
% 68.49/10.18 inference(superposition,[],[f3690,f27605])).
% 68.49/10.18 thf(f27605,plain,(
% 68.49/10.18 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | ~spl93_646),
% 68.49/10.18 inference(avatar_component_clause,[],[f27603])).
% 68.49/10.18 thf(f34398,plain,(
% 68.49/10.18 ( ! [X0 : int] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_520 | ~spl93_795)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f34339])).
% 68.49/10.18 thf(f34339,plain,(
% 68.49/10.18 ( ! [X0 : int] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_520 | ~spl93_795)),
% 68.49/10.18 inference(superposition,[],[f34331,f23002])).
% 68.49/10.18 thf(f34331,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | ~spl93_795),
% 68.49/10.18 inference(avatar_component_clause,[],[f34330])).
% 68.49/10.18 thf(f38508,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)))) ) | ~spl93_863),
% 68.49/10.18 inference(avatar_component_clause,[],[f38507])).
% 68.49/10.18 thf(f38509,plain,(
% 68.49/10.18 spl93_863 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_247),
% 68.49/10.18 inference(avatar_split_clause,[],[f6171,f4124,f2247,f2243,f2074,f38507])).
% 68.49/10.18 thf(f6171,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_247)),
% 68.49/10.18 inference(forward_demodulation,[],[f4136,f5934])).
% 68.49/10.18 thf(f4136,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_247)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4133])).
% 68.49/10.18 thf(f4133,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_247)),
% 68.49/10.18 inference(superposition,[],[f4125,f2245])).
% 68.49/10.18 thf(f38351,plain,(
% 68.49/10.18 spl93_862 | ~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_793 | ~spl93_861),
% 68.49/10.18 inference(avatar_split_clause,[],[f38347,f38344,f34214,f27603,f23000,f13821,f7374,f3689,f38349])).
% 68.49/10.18 thf(f38349,plain,(
% 68.49/10.18 spl93_862 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_862])])).
% 68.49/10.18 thf(f34214,plain,(
% 68.49/10.18 spl93_793 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_793])])).
% 68.49/10.18 thf(f38344,plain,(
% 68.49/10.18 spl93_861 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_861])])).
% 68.49/10.18 thf(f38347,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_793 | ~spl93_861)),
% 68.49/10.18 inference(forward_demodulation,[],[f38345,f34297])).
% 68.49/10.18 thf(f34297,plain,(
% 68.49/10.18 ( ! [X0 : nat] : ((sK6 = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))) ) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_793)),
% 68.49/10.18 inference(forward_demodulation,[],[f34282,f27626])).
% 68.49/10.18 thf(f34282,plain,(
% 68.49/10.18 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_520 | ~spl93_793)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f34223])).
% 68.49/10.18 thf(f34223,plain,(
% 68.49/10.18 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_520 | ~spl93_793)),
% 68.49/10.18 inference(superposition,[],[f34215,f23002])).
% 68.49/10.18 thf(f34215,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | ~spl93_793),
% 68.49/10.18 inference(avatar_component_clause,[],[f34214])).
% 68.49/10.18 thf(f38345,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | ~spl93_861),
% 68.49/10.18 inference(avatar_component_clause,[],[f38344])).
% 68.49/10.18 thf(f38346,plain,(
% 68.49/10.18 spl93_861 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_248),
% 68.49/10.18 inference(avatar_split_clause,[],[f6169,f4128,f2247,f2243,f2074,f38344])).
% 68.49/10.18 thf(f6169,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_248)),
% 68.49/10.18 inference(forward_demodulation,[],[f4145,f5934])).
% 68.49/10.18 thf(f4145,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_248)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4142])).
% 68.49/10.18 thf(f4142,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_248)),
% 68.49/10.18 inference(superposition,[],[f4129,f2245])).
% 68.49/10.18 thf(f38342,plain,(
% 68.49/10.18 spl93_860 | ~spl93_22 | ~spl93_228),
% 68.49/10.18 inference(avatar_split_clause,[],[f3916,f3903,f1832,f38340])).
% 68.49/10.18 thf(f38340,plain,(
% 68.49/10.18 spl93_860 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),$true)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_860])])).
% 68.49/10.18 thf(f3916,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),$true))) ) | (~spl93_22 | ~spl93_228)),
% 68.49/10.18 inference(inner_rewriting,[],[f3910])).
% 68.49/10.18 thf(f3910,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_228)),
% 68.49/10.18 inference(superposition,[],[f3904,f1833])).
% 68.49/10.18 thf(f38338,plain,(
% 68.49/10.18 spl93_859 | ~spl93_22 | ~spl93_228),
% 68.49/10.18 inference(avatar_split_clause,[],[f3909,f3903,f1832,f38336])).
% 68.49/10.18 thf(f38336,plain,(
% 68.49/10.18 spl93_859 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),$true)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_859])])).
% 68.49/10.18 thf(f3909,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),$true)) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1))) ) | (~spl93_22 | ~spl93_228)),
% 68.49/10.18 inference(superposition,[],[f3904,f1833])).
% 68.49/10.18 thf(f38334,plain,(
% 68.49/10.18 spl93_858 | ~spl93_75 | ~spl93_170),
% 68.49/10.18 inference(avatar_split_clause,[],[f3231,f3201,f2256,f38332])).
% 68.49/10.18 thf(f38332,plain,(
% 68.49/10.18 spl93_858 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,X2)),X3 : X0 > product_prod(X1,X2) > $o] : (($true != vAPP(product_prod(X1,X2),$o,vAPP(X0,sTfun(product_prod(X1,X2),$o),X3,vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3))),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3))))) | ($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3),X4)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_858])])).
% 68.49/10.18 thf(f3231,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > product_prod(X1,X2) > $o,X4 : product_prod(X0,product_prod(X1,X2))] : (($true != vAPP(product_prod(X1,X2),$o,vAPP(X0,sTfun(product_prod(X1,X2),$o),X3,vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3))),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3))))) | ($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,vAPP(sTfun(X0,sTfun(product_prod(X1,X2),$o)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),product_rec_prod(X0,product_prod(X1,X2),$o),X3),X4))) ) | (~spl93_75 | ~spl93_170)),
% 68.49/10.18 inference(superposition,[],[f3202,f2257])).
% 68.49/10.18 thf(f38189,plain,(
% 68.49/10.18 spl93_857 | ~spl93_345 | ~spl93_855),
% 68.49/10.18 inference(avatar_split_clause,[],[f38181,f38178,f6456,f38187])).
% 68.49/10.18 thf(f38187,plain,(
% 68.49/10.18 spl93_857 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_857])])).
% 68.49/10.18 thf(f38178,plain,(
% 68.49/10.18 spl93_855 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_855])])).
% 68.49/10.18 thf(f38181,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_855)),
% 68.49/10.18 inference(forward_demodulation,[],[f38179,f6458])).
% 68.49/10.18 thf(f38179,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_855),
% 68.49/10.18 inference(avatar_component_clause,[],[f38178])).
% 68.49/10.18 thf(f38185,plain,(
% 68.49/10.18 spl93_856 | ~spl93_235 | ~spl93_617),
% 68.49/10.18 inference(avatar_split_clause,[],[f30411,f26464,f3960,f38183])).
% 68.49/10.18 thf(f38183,plain,(
% 68.49/10.18 spl93_856 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_856])])).
% 68.49/10.18 thf(f3960,plain,(
% 68.49/10.18 spl93_235 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X1)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_235])])).
% 68.49/10.18 thf(f30411,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2)) ) | (~spl93_235 | ~spl93_617)),
% 68.49/10.18 inference(superposition,[],[f26465,f3961])).
% 68.49/10.18 thf(f3961,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X1)) ) | ~spl93_235),
% 68.49/10.18 inference(avatar_component_clause,[],[f3960])).
% 68.49/10.18 thf(f38180,plain,(
% 68.49/10.18 spl93_855 | ~spl93_61 | ~spl93_100 | ~spl93_248),
% 68.49/10.18 inference(avatar_split_clause,[],[f4148,f4128,f2484,f2136,f38178])).
% 68.49/10.18 thf(f2484,plain,(
% 68.49/10.18 spl93_100 <=> ! [X0 : nat] : (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_100])])).
% 68.49/10.18 thf(f4148,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_100 | ~spl93_248)),
% 68.49/10.18 inference(forward_demodulation,[],[f4147,f2485])).
% 68.49/10.18 thf(f2485,plain,(
% 68.49/10.18 ( ! [X0 : nat] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | ~spl93_100),
% 68.49/10.18 inference(avatar_component_clause,[],[f2484])).
% 68.49/10.18 thf(f4147,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_248)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4140])).
% 68.49/10.18 thf(f4140,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_248)),
% 68.49/10.18 inference(superposition,[],[f4129,f2138])).
% 68.49/10.18 thf(f38037,plain,(
% 68.49/10.18 spl93_854 | ~spl93_345 | ~spl93_853),
% 68.49/10.18 inference(avatar_split_clause,[],[f38033,f38030,f6456,f38035])).
% 68.49/10.18 thf(f38035,plain,(
% 68.49/10.18 spl93_854 <=> ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_854])])).
% 68.49/10.18 thf(f38030,plain,(
% 68.49/10.18 spl93_853 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_853])])).
% 68.49/10.18 thf(f38033,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_853)),
% 68.49/10.18 inference(forward_demodulation,[],[f38031,f6458])).
% 68.49/10.18 thf(f38031,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_853),
% 68.49/10.18 inference(avatar_component_clause,[],[f38030])).
% 68.49/10.18 thf(f38032,plain,(
% 68.49/10.18 spl93_853 | ~spl93_61 | ~spl93_99 | ~spl93_247),
% 68.49/10.18 inference(avatar_split_clause,[],[f4139,f4124,f2480,f2136,f38030])).
% 68.49/10.18 thf(f2480,plain,(
% 68.49/10.18 spl93_99 <=> ! [X0 : int] : (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_99])])).
% 68.49/10.18 thf(f4139,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_99 | ~spl93_247)),
% 68.49/10.18 inference(forward_demodulation,[],[f4138,f2481])).
% 68.49/10.18 thf(f2481,plain,(
% 68.49/10.18 ( ! [X0 : int] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | ~spl93_99),
% 68.49/10.18 inference(avatar_component_clause,[],[f2480])).
% 68.49/10.18 thf(f4138,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_247)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4131])).
% 68.49/10.18 thf(f4131,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_247)),
% 68.49/10.18 inference(superposition,[],[f4125,f2138])).
% 68.49/10.18 thf(f38027,plain,(
% 68.49/10.18 spl93_852 | ~spl93_66 | ~spl93_212 | ~spl93_245),
% 68.49/10.18 inference(avatar_split_clause,[],[f4109,f4094,f3701,f2161,f38025])).
% 68.49/10.18 thf(f38025,plain,(
% 68.49/10.18 spl93_852 <=> ! [X0 : nat,X1 : nat] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_852])])).
% 68.49/10.18 thf(f3701,plain,(
% 68.49/10.18 spl93_212 <=> ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_212])])).
% 68.49/10.18 thf(f4109,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_66 | ~spl93_212 | ~spl93_245)),
% 68.49/10.18 inference(forward_demodulation,[],[f4103,f3733])).
% 68.49/10.18 thf(f3733,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_66 | ~spl93_212)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3728])).
% 68.49/10.18 thf(f3728,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_66 | ~spl93_212)),
% 68.49/10.18 inference(superposition,[],[f3702,f2163])).
% 68.49/10.18 thf(f3702,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0))) ) | ~spl93_212),
% 68.49/10.18 inference(avatar_component_clause,[],[f3701])).
% 68.49/10.18 thf(f4103,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_245)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4098])).
% 68.49/10.18 thf(f4098,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_245)),
% 68.49/10.18 inference(superposition,[],[f4095,f2163])).
% 68.49/10.18 thf(f38022,plain,(
% 68.49/10.18 spl93_851 | ~spl93_66 | ~spl93_212),
% 68.49/10.18 inference(avatar_split_clause,[],[f3733,f3701,f2161,f38020])).
% 68.49/10.18 thf(f38020,plain,(
% 68.49/10.18 spl93_851 <=> ! [X0 : nat,X1 : nat] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_851])])).
% 68.49/10.18 thf(f38017,plain,(
% 68.49/10.18 spl93_850 | ~spl93_66 | ~spl93_211),
% 68.49/10.18 inference(avatar_split_clause,[],[f3722,f3697,f2161,f38015])).
% 68.49/10.18 thf(f38015,plain,(
% 68.49/10.18 spl93_850 <=> ! [X0 : int,X1 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_850])])).
% 68.49/10.18 thf(f3697,plain,(
% 68.49/10.18 spl93_211 <=> ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_211])])).
% 68.49/10.18 thf(f3722,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_211)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3717])).
% 68.49/10.18 thf(f3717,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_211)),
% 68.49/10.18 inference(superposition,[],[f3698,f2163])).
% 68.49/10.18 thf(f3698,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) ) | ~spl93_211),
% 68.49/10.18 inference(avatar_component_clause,[],[f3697])).
% 68.49/10.18 thf(f37925,plain,(
% 68.49/10.18 spl93_849 | ~spl93_345 | ~spl93_848),
% 68.49/10.18 inference(avatar_split_clause,[],[f37921,f37917,f6456,f37923])).
% 68.49/10.18 thf(f37923,plain,(
% 68.49/10.18 spl93_849 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_849])])).
% 68.49/10.18 thf(f37917,plain,(
% 68.49/10.18 spl93_848 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_848])])).
% 68.49/10.18 thf(f37921,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | (~spl93_345 | ~spl93_848)),
% 68.49/10.18 inference(forward_demodulation,[],[f37920,f6458])).
% 68.49/10.18 thf(f37920,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_848)),
% 68.49/10.18 inference(forward_demodulation,[],[f37918,f6458])).
% 68.49/10.18 thf(f37918,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_848),
% 68.49/10.18 inference(avatar_component_clause,[],[f37917])).
% 68.49/10.18 thf(f37919,plain,(
% 68.49/10.18 spl93_848 | ~spl93_22 | ~spl93_219),
% 68.49/10.18 inference(avatar_split_clause,[],[f3799,f3784,f1832,f37917])).
% 68.49/10.18 thf(f3784,plain,(
% 68.49/10.18 spl93_219 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_219])])).
% 68.49/10.18 thf(f3799,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_219)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3798])).
% 68.49/10.18 thf(f3798,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_219)),
% 68.49/10.18 inference(superposition,[],[f3785,f1833])).
% 68.49/10.18 thf(f3785,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_219),
% 68.49/10.18 inference(avatar_component_clause,[],[f3784])).
% 68.49/10.18 thf(f37915,plain,(
% 68.49/10.18 spl93_847 | ~spl93_227 | ~spl93_617),
% 68.49/10.18 inference(avatar_split_clause,[],[f30401,f26464,f3899,f37913])).
% 68.49/10.18 thf(f37913,plain,(
% 68.49/10.18 spl93_847 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_847])])).
% 68.49/10.18 thf(f3899,plain,(
% 68.49/10.18 spl93_227 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X1) = X0)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_227])])).
% 68.49/10.18 thf(f30401,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)) | (X1 = X2)) ) | (~spl93_227 | ~spl93_617)),
% 68.49/10.18 inference(superposition,[],[f26465,f3900])).
% 68.49/10.18 thf(f3900,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X1) = X0)) ) | ~spl93_227),
% 68.49/10.18 inference(avatar_component_clause,[],[f3899])).
% 68.49/10.18 thf(f37796,plain,(
% 68.49/10.18 spl93_846 | ~spl93_345 | ~spl93_845),
% 68.49/10.18 inference(avatar_split_clause,[],[f37792,f37788,f6456,f37794])).
% 68.49/10.18 thf(f37794,plain,(
% 68.49/10.18 spl93_846 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_846])])).
% 68.49/10.18 thf(f37788,plain,(
% 68.49/10.18 spl93_845 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_845])])).
% 68.49/10.18 thf(f37792,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0))) ) | (~spl93_345 | ~spl93_845)),
% 68.49/10.18 inference(forward_demodulation,[],[f37791,f6458])).
% 68.49/10.18 thf(f37791,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_845)),
% 68.49/10.18 inference(forward_demodulation,[],[f37789,f6458])).
% 68.49/10.18 thf(f37789,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_845),
% 68.49/10.18 inference(avatar_component_clause,[],[f37788])).
% 68.49/10.18 thf(f37790,plain,(
% 68.49/10.18 spl93_845 | ~spl93_22 | ~spl93_218),
% 68.49/10.18 inference(avatar_split_clause,[],[f3791,f3780,f1832,f37788])).
% 68.49/10.18 thf(f3780,plain,(
% 68.49/10.18 spl93_218 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_218])])).
% 68.49/10.18 thf(f3791,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_218)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3790])).
% 68.49/10.18 thf(f3790,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_218)),
% 68.49/10.18 inference(superposition,[],[f3781,f1833])).
% 68.49/10.18 thf(f3781,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_218),
% 68.49/10.18 inference(avatar_component_clause,[],[f3780])).
% 68.49/10.18 thf(f37502,plain,(
% 68.49/10.18 spl93_844 | ~spl93_22 | ~spl93_217),
% 68.49/10.18 inference(avatar_split_clause,[],[f3772,f3768,f1832,f37500])).
% 68.49/10.18 thf(f37500,plain,(
% 68.49/10.18 spl93_844 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_844])])).
% 68.49/10.18 thf(f3772,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK19(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK20(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP0(X0,$o),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,group($o,X0),X1)) | ($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1))) ) | (~spl93_22 | ~spl93_217)),
% 68.49/10.18 inference(superposition,[],[f3769,f1833])).
% 68.49/10.18 thf(f37396,plain,(
% 68.49/10.18 spl93_843 | ~spl93_345 | ~spl93_842),
% 68.49/10.18 inference(avatar_split_clause,[],[f37392,f37388,f6456,f37394])).
% 68.49/10.18 thf(f37394,plain,(
% 68.49/10.18 spl93_843 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_843])])).
% 68.49/10.18 thf(f37388,plain,(
% 68.49/10.18 spl93_842 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_842])])).
% 68.49/10.18 thf(f37392,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2)) ) | (~spl93_345 | ~spl93_842)),
% 68.49/10.18 inference(forward_demodulation,[],[f37391,f6458])).
% 68.49/10.18 thf(f37391,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2)) ) | (~spl93_345 | ~spl93_842)),
% 68.49/10.18 inference(forward_demodulation,[],[f37389,f6458])).
% 68.49/10.18 thf(f37389,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2)) ) | ~spl93_842),
% 68.49/10.18 inference(avatar_component_clause,[],[f37388])).
% 68.49/10.18 thf(f37390,plain,(
% 68.49/10.18 spl93_842),
% 68.49/10.18 inference(avatar_split_clause,[],[f1607,f37388])).
% 68.49/10.18 thf(f1607,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1606])).
% 68.49/10.18 thf(f1606,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1602])).
% 68.49/10.18 thf(f1602,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1360])).
% 68.49/10.18 thf(f1360,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.18 inference(cnf_transformation,[],[f923])).
% 68.49/10.18 thf(f923,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 inference(flattening,[],[f922])).
% 68.49/10.18 thf(f922,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 inference(ennf_transformation,[],[f507])).
% 68.49/10.18 thf(f507,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2)))))),
% 68.49/10.18 inference(fool_elimination,[],[f506])).
% 68.49/10.18 thf(f506,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) = (X1 = X2)))))),
% 68.49/10.18 inference(rectify,[],[f184])).
% 68.49/10.18 thf(f184,axiom,(
% 68.49/10.18 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14)) = (X14 = X15)))))),
% 68.49/10.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_Units__l__cancel)).
% 68.49/10.18 thf(f37286,plain,(
% 68.49/10.18 spl93_841 | ~spl93_345 | ~spl93_839),
% 68.49/10.18 inference(avatar_split_clause,[],[f37278,f37274,f6456,f37284])).
% 68.49/10.18 thf(f37284,plain,(
% 68.49/10.18 spl93_841 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_841])])).
% 68.49/10.18 thf(f37274,plain,(
% 68.49/10.18 spl93_839 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_839])])).
% 68.49/10.18 thf(f37278,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2)) ) | (~spl93_345 | ~spl93_839)),
% 68.49/10.18 inference(forward_demodulation,[],[f37277,f6458])).
% 68.49/10.18 thf(f37277,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2)) ) | (~spl93_345 | ~spl93_839)),
% 68.49/10.18 inference(forward_demodulation,[],[f37275,f6458])).
% 68.49/10.18 thf(f37275,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2)) ) | ~spl93_839),
% 68.49/10.18 inference(avatar_component_clause,[],[f37274])).
% 68.49/10.18 thf(f37282,plain,(
% 68.49/10.18 spl93_840 | ~spl93_216 | ~spl93_610),
% 68.49/10.18 inference(avatar_split_clause,[],[f30075,f26363,f3748,f37280])).
% 68.49/10.18 thf(f37280,plain,(
% 68.49/10.18 spl93_840 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) != X0) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_840])])).
% 68.49/10.18 thf(f26363,plain,(
% 68.49/10.18 spl93_610 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) != X0) | (X1 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_610])])).
% 68.49/10.18 thf(f30075,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) != X0) | (X1 = X2)) ) | (~spl93_216 | ~spl93_610)),
% 68.49/10.18 inference(superposition,[],[f26364,f3749])).
% 68.49/10.18 thf(f26364,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) != X0) | (X1 = X2)) ) | ~spl93_610),
% 68.49/10.18 inference(avatar_component_clause,[],[f26363])).
% 68.49/10.18 thf(f37276,plain,(
% 68.49/10.18 spl93_839),
% 68.49/10.18 inference(avatar_split_clause,[],[f1605,f37274])).
% 68.49/10.18 thf(f1605,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1604])).
% 68.49/10.18 thf(f1604,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1603])).
% 68.49/10.18 thf(f1603,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1360])).
% 68.49/10.18 thf(f37254,plain,(
% 68.49/10.18 spl93_838 | ~spl93_206 | ~spl93_220),
% 68.49/10.18 inference(avatar_split_clause,[],[f3819,f3805,f3634,f37252])).
% 68.49/10.18 thf(f37252,plain,(
% 68.49/10.18 spl93_838 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X6 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5 : product_prod(X3,product_prod(X0,product_prod(X1,X2))) > $o] : (($true != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o,X5,X4)) | ($true = vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o,X5,X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X2,sK56(X2,X1,X0,X3),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X1,sK55(X2,X1,X0,X3),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X0,sK54(X2,X1,X0,X3),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X3,sK53(X2,X1,X0,X3),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_838])])).
% 68.49/10.18 thf(f3819,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5 : product_prod(X3,product_prod(X0,product_prod(X1,X2))) > $o] : (($true != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o,X5,X4)) | ($true = vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o,X5,X6)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X2,sK56(X2,X1,X0,X3),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X1,sK55(X2,X1,X0,X3),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X0,sK54(X2,X1,X0,X3),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),$o),X3,sK53(X2,X1,X0,X3),X5))) ) | (~spl93_206 | ~spl93_220)),
% 68.49/10.18 inference(constrained_superposition,[],[f3806,f3635])).
% 68.49/10.18 thf(f37135,plain,(
% 68.49/10.18 spl93_837 | ~spl93_345 | ~spl93_836),
% 68.49/10.18 inference(avatar_split_clause,[],[f37131,f37126,f6456,f37133])).
% 68.49/10.18 thf(f37133,plain,(
% 68.49/10.18 spl93_837 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_837])])).
% 68.49/10.18 thf(f37126,plain,(
% 68.49/10.18 spl93_836 <=> ! [X2 : a,X0 : a,X1 : a] : ((X1 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_836])])).
% 68.49/10.18 thf(f37131,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | (~spl93_345 | ~spl93_836)),
% 68.49/10.18 inference(forward_demodulation,[],[f37130,f6458])).
% 68.49/10.18 thf(f37130,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | (~spl93_345 | ~spl93_836)),
% 68.49/10.18 inference(forward_demodulation,[],[f37129,f6458])).
% 68.49/10.18 thf(f37129,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | (~spl93_345 | ~spl93_836)),
% 68.49/10.18 inference(forward_demodulation,[],[f37127,f6458])).
% 68.49/10.18 thf(f37127,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((X1 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | ~spl93_836),
% 68.49/10.18 inference(avatar_component_clause,[],[f37126])).
% 68.49/10.18 thf(f37128,plain,(
% 68.49/10.18 spl93_836),
% 68.49/10.18 inference(avatar_split_clause,[],[f1577,f37126])).
% 68.49/10.18 thf(f1577,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((X1 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1576])).
% 68.49/10.18 thf(f1576,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((X1 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1572])).
% 68.49/10.18 thf(f1572,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1383])).
% 68.49/10.18 thf(f1383,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.18 inference(cnf_transformation,[],[f965])).
% 68.49/10.18 thf(f965,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 inference(flattening,[],[f964])).
% 68.49/10.18 thf(f964,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 inference(ennf_transformation,[],[f553])).
% 68.49/10.18 thf(f553,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))))))),
% 68.49/10.18 inference(fool_elimination,[],[f552])).
% 68.49/10.18 thf(f552,plain,(
% 68.49/10.18 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)) = (X1 = X2)))))),
% 68.49/10.18 inference(rectify,[],[f38])).
% 68.49/10.18 thf(f38,axiom,(
% 68.49/10.18 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X13) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X15),X13)) = (X14 = X15)))))),
% 68.49/10.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_local_Oadd_Oright__cancel)).
% 68.49/10.18 thf(f37020,plain,(
% 68.49/10.18 spl93_835 | ~spl93_345 | ~spl93_834),
% 68.49/10.18 inference(avatar_split_clause,[],[f37016,f37011,f6456,f37018])).
% 68.49/10.18 thf(f37018,plain,(
% 68.49/10.18 spl93_835 <=> ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_835])])).
% 68.49/10.18 thf(f37011,plain,(
% 68.49/10.18 spl93_834 <=> ! [X2 : a,X0 : a,X1 : a] : ((X1 != X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_834])])).
% 68.49/10.18 thf(f37016,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | (~spl93_345 | ~spl93_834)),
% 68.49/10.18 inference(forward_demodulation,[],[f37015,f6458])).
% 68.49/10.18 thf(f37015,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | (~spl93_345 | ~spl93_834)),
% 68.49/10.18 inference(forward_demodulation,[],[f37014,f6458])).
% 68.49/10.18 thf(f37014,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (X1 != X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | (~spl93_345 | ~spl93_834)),
% 68.49/10.18 inference(forward_demodulation,[],[f37012,f6458])).
% 68.49/10.18 thf(f37012,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((X1 != X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) ) | ~spl93_834),
% 68.49/10.18 inference(avatar_component_clause,[],[f37011])).
% 68.49/10.18 thf(f37013,plain,(
% 68.49/10.18 spl93_834),
% 68.49/10.18 inference(avatar_split_clause,[],[f1575,f37011])).
% 68.49/10.18 thf(f1575,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((X1 != X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1574])).
% 68.49/10.18 thf(f1574,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : ((X1 != X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1573])).
% 68.49/10.18 thf(f1573,plain,(
% 68.49/10.18 ( ! [X2 : a,X0 : a,X1 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),X1),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),X0)))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1383])).
% 68.49/10.18 thf(f36803,plain,(
% 68.49/10.18 spl93_833 | ~spl93_221 | ~spl93_610),
% 68.49/10.18 inference(avatar_split_clause,[],[f30074,f26363,f3826,f36801])).
% 68.49/10.18 thf(f36801,plain,(
% 68.49/10.18 spl93_833 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X2) | (X0 = X1))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_833])])).
% 68.49/10.18 thf(f30074,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X2) | (X0 = X1)) ) | (~spl93_221 | ~spl93_610)),
% 68.49/10.18 inference(superposition,[],[f26364,f3827])).
% 68.49/10.18 thf(f36420,plain,(
% 68.49/10.18 spl93_832 | ~spl93_345 | ~spl93_440 | ~spl93_771 | ~spl93_831),
% 68.49/10.18 inference(avatar_split_clause,[],[f36416,f36411,f33243,f13821,f6456,f36418])).
% 68.49/10.18 thf(f36418,plain,(
% 68.49/10.18 spl93_832 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_832])])).
% 68.49/10.18 thf(f33243,plain,(
% 68.49/10.18 spl93_771 <=> (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_771])])).
% 68.49/10.18 thf(f36411,plain,(
% 68.49/10.18 spl93_831 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_831])])).
% 68.49/10.18 thf(f36416,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)))) ) | (~spl93_345 | ~spl93_440 | ~spl93_771 | ~spl93_831)),
% 68.49/10.18 inference(forward_demodulation,[],[f36415,f6458])).
% 68.49/10.18 thf(f36415,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_440 | ~spl93_771 | ~spl93_831)),
% 68.49/10.18 inference(forward_demodulation,[],[f36414,f33245])).
% 68.49/10.18 thf(f33245,plain,(
% 68.49/10.18 (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)) | ~spl93_771),
% 68.49/10.18 inference(avatar_component_clause,[],[f33243])).
% 68.49/10.18 thf(f36414,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_440 | ~spl93_831)),
% 68.49/10.18 inference(forward_demodulation,[],[f36412,f13823])).
% 68.49/10.18 thf(f36412,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_831),
% 68.49/10.18 inference(avatar_component_clause,[],[f36411])).
% 68.49/10.18 thf(f36413,plain,(
% 68.49/10.18 spl93_831 | ~spl93_66 | ~spl93_219),
% 68.49/10.18 inference(avatar_split_clause,[],[f3801,f3784,f2161,f36411])).
% 68.49/10.18 thf(f3801,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_219)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3796])).
% 68.49/10.18 thf(f3796,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_219)),
% 68.49/10.18 inference(superposition,[],[f3785,f2163])).
% 68.49/10.18 thf(f36407,plain,(
% 68.49/10.18 spl93_830 | ~spl93_66 | ~spl93_218),
% 68.49/10.18 inference(avatar_split_clause,[],[f3793,f3780,f2161,f36405])).
% 68.49/10.18 thf(f36405,plain,(
% 68.49/10.18 spl93_830 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_830])])).
% 68.49/10.18 thf(f3793,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_218)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3788])).
% 68.49/10.18 thf(f3788,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_218)),
% 68.49/10.18 inference(superposition,[],[f3781,f2163])).
% 68.49/10.18 thf(f36403,plain,(
% 68.49/10.18 spl93_829 | ~spl93_22 | ~spl93_217),
% 68.49/10.18 inference(avatar_split_clause,[],[f3775,f3768,f1832,f36401])).
% 68.49/10.18 thf(f36401,plain,(
% 68.49/10.18 spl93_829 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK19(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK20(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,group(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_829])])).
% 68.49/10.18 thf(f3775,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK19(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK20(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,group(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2)))) ) | (~spl93_22 | ~spl93_217)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3774])).
% 68.49/10.18 thf(f3774,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK19(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK20(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,group(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2)))) ) | (~spl93_22 | ~spl93_217)),
% 68.49/10.18 inference(superposition,[],[f3769,f1833])).
% 68.49/10.18 thf(f36399,plain,(
% 68.49/10.18 spl93_828 | ~spl93_75 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3656,f3634,f2256,f36397])).
% 68.49/10.18 thf(f36397,plain,(
% 68.49/10.18 spl93_828 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X5 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X6 : X3 > product_prod(X0,product_prod(X1,X2)) > X5] : (vAPP(product_prod(X0,product_prod(X1,X2)),X5,vAPP(X3,sTfun(product_prod(X0,product_prod(X1,X2)),X5),X6,vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4)),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4)),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4)))) = vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5,vAPP(sTfun(X3,sTfun(product_prod(X0,product_prod(X1,X2)),X5)),sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5),product_rec_prod(X3,product_prod(X0,product_prod(X1,X2)),X5),X6),X4))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_828])])).
% 68.49/10.18 thf(f3656,plain,(
% 68.49/10.18 ( ! [X5 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : X3 > product_prod(X0,product_prod(X1,X2)) > X5,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2)))] : ((vAPP(product_prod(X0,product_prod(X1,X2)),X5,vAPP(X3,sTfun(product_prod(X0,product_prod(X1,X2)),X5),X6,vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4)),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4)),vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4)))) = vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5,vAPP(sTfun(X3,sTfun(product_prod(X0,product_prod(X1,X2)),X5)),sTfun(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5),product_rec_prod(X3,product_prod(X0,product_prod(X1,X2)),X5),X6),X4))) ) | (~spl93_75 | ~spl93_206)),
% 68.49/10.18 inference(superposition,[],[f2257,f3635])).
% 68.49/10.18 thf(f36240,plain,(
% 68.49/10.18 spl93_827 | ~spl93_276 | ~spl93_610),
% 68.49/10.18 inference(avatar_split_clause,[],[f30050,f26363,f4534,f36238])).
% 68.49/10.18 thf(f36238,plain,(
% 68.49/10.18 spl93_827 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_827])])).
% 68.49/10.18 thf(f30050,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X0)) ) | (~spl93_276 | ~spl93_610)),
% 68.49/10.18 inference(superposition,[],[f26364,f4535])).
% 68.49/10.18 thf(f35922,plain,(
% 68.49/10.18 spl93_826 | ~spl93_22 | ~spl93_215),
% 68.49/10.18 inference(avatar_split_clause,[],[f3763,f3713,f1832,f35920])).
% 68.49/10.18 thf(f35920,plain,(
% 68.49/10.18 spl93_826 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_826])])).
% 68.49/10.18 thf(f3713,plain,(
% 68.49/10.18 spl93_215 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_215])])).
% 68.49/10.18 thf(f3763,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_215)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3762])).
% 68.49/10.18 thf(f3762,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_215)),
% 68.49/10.18 inference(superposition,[],[f3714,f1833])).
% 68.49/10.18 thf(f3714,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_215),
% 68.49/10.18 inference(avatar_component_clause,[],[f3713])).
% 68.49/10.18 thf(f35918,plain,(
% 68.49/10.18 spl93_825 | ~spl93_22 | ~spl93_214),
% 68.49/10.18 inference(avatar_split_clause,[],[f3755,f3709,f1832,f35916])).
% 68.49/10.18 thf(f35916,plain,(
% 68.49/10.18 spl93_825 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),X1)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_825])])).
% 68.49/10.18 thf(f3709,plain,(
% 68.49/10.18 spl93_214 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_214])])).
% 68.49/10.18 thf(f3755,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),X1)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_214)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3754])).
% 68.49/10.18 thf(f3754,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X4)),X1)) = X1) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_214)),
% 68.49/10.18 inference(superposition,[],[f3710,f1833])).
% 68.49/10.18 thf(f3710,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_214),
% 68.49/10.18 inference(avatar_component_clause,[],[f3709])).
% 68.49/10.18 thf(f35868,plain,(
% 68.49/10.18 spl93_824 | ~spl93_345 | ~spl93_823),
% 68.49/10.18 inference(avatar_split_clause,[],[f35864,f35861,f6456,f35866])).
% 68.49/10.18 thf(f35866,plain,(
% 68.49/10.18 spl93_824 <=> ! [X2 : nat,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_824])])).
% 68.49/10.18 thf(f35861,plain,(
% 68.49/10.18 spl93_823 <=> ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_823])])).
% 68.49/10.18 thf(f35864,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0))) ) | (~spl93_345 | ~spl93_823)),
% 68.49/10.18 inference(forward_demodulation,[],[f35862,f6458])).
% 68.49/10.18 thf(f35862,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_823),
% 68.49/10.18 inference(avatar_component_clause,[],[f35861])).
% 68.49/10.18 thf(f35863,plain,(
% 68.49/10.18 spl93_823 | ~spl93_22 | ~spl93_212),
% 68.49/10.18 inference(avatar_split_clause,[],[f3731,f3701,f1832,f35861])).
% 68.49/10.18 thf(f3731,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_212)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3730])).
% 68.49/10.18 thf(f3730,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_212)),
% 68.49/10.18 inference(superposition,[],[f3702,f1833])).
% 68.49/10.18 thf(f35811,plain,(
% 68.49/10.18 spl93_822 | ~spl93_345 | ~spl93_821),
% 68.49/10.18 inference(avatar_split_clause,[],[f35807,f35804,f6456,f35809])).
% 68.49/10.18 thf(f35809,plain,(
% 68.49/10.18 spl93_822 <=> ! [X2 : int,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_822])])).
% 68.49/10.18 thf(f35804,plain,(
% 68.49/10.18 spl93_821 <=> ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_821])])).
% 68.49/10.18 thf(f35807,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) ) | (~spl93_345 | ~spl93_821)),
% 68.49/10.18 inference(forward_demodulation,[],[f35805,f6458])).
% 68.49/10.18 thf(f35805,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_821),
% 68.49/10.18 inference(avatar_component_clause,[],[f35804])).
% 68.49/10.18 thf(f35806,plain,(
% 68.49/10.18 spl93_821 | ~spl93_22 | ~spl93_211),
% 68.49/10.18 inference(avatar_split_clause,[],[f3720,f3697,f1832,f35804])).
% 68.49/10.18 thf(f3720,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_211)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3719])).
% 68.49/10.18 thf(f3719,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_211)),
% 68.49/10.18 inference(superposition,[],[f3698,f1833])).
% 68.49/10.18 thf(f35802,plain,(
% 68.49/10.18 spl93_820),
% 68.49/10.18 inference(avatar_split_clause,[],[f1524,f35800])).
% 68.49/10.18 thf(f35800,plain,(
% 68.49/10.18 spl93_820 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (X4 != X5))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_820])])).
% 68.49/10.18 thf(f1524,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (X4 != X5)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1523])).
% 68.49/10.18 thf(f1523,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1519])).
% 68.49/10.18 thf(f1519,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1439])).
% 68.49/10.18 thf(f1439,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.18 inference(cnf_transformation,[],[f1051])).
% 68.49/10.18 thf(f1051,plain,(
% 68.49/10.18 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.18 inference(flattening,[],[f1050])).
% 68.49/10.18 thf(f1050,plain,(
% 68.49/10.18 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.18 inference(ennf_transformation,[],[f641])).
% 68.49/10.18 thf(f641,plain,(
% 68.49/10.18 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5))))))),
% 68.49/10.18 inference(fool_elimination,[],[f640])).
% 68.49/10.18 thf(f640,plain,(
% 68.49/10.18 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) = (X4 = X5))))))),
% 68.49/10.18 inference(rectify,[],[f188])).
% 68.49/10.18 thf(f188,axiom,(
% 68.49/10.18 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X14),X13) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X15),X13)) = (X14 = X15))))))),
% 68.49/10.18 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_187_Group_Ogroup_Oright__cancel)).
% 68.49/10.18 thf(f35798,plain,(
% 68.49/10.18 spl93_819 | ~spl93_216 | ~spl93_610),
% 68.49/10.18 inference(avatar_split_clause,[],[f30043,f26363,f3748,f35796])).
% 68.49/10.18 thf(f30043,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X1)) ) | (~spl93_216 | ~spl93_610)),
% 68.49/10.18 inference(superposition,[],[f26364,f3749])).
% 68.49/10.18 thf(f35794,plain,(
% 68.49/10.18 spl93_818),
% 68.49/10.18 inference(avatar_split_clause,[],[f1522,f35792])).
% 68.49/10.18 thf(f35792,plain,(
% 68.49/10.18 spl93_818 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X4 : X1,X5 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (X4 = X5))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_818])])).
% 68.49/10.18 thf(f1522,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (X4 = X5)) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1521])).
% 68.49/10.18 thf(f1521,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5))) )),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f1520])).
% 68.49/10.18 thf(f1520,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X3))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X4),X5))) )),
% 68.49/10.18 inference(binary_proxy_clausification,[],[f1439])).
% 68.49/10.18 thf(f35611,plain,(
% 68.49/10.18 spl93_817 | ~spl93_345 | ~spl93_816),
% 68.49/10.18 inference(avatar_split_clause,[],[f35607,f35604,f6456,f35609])).
% 68.49/10.18 thf(f35609,plain,(
% 68.49/10.18 spl93_817 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_817])])).
% 68.49/10.18 thf(f35604,plain,(
% 68.49/10.18 spl93_816 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_816])])).
% 68.49/10.18 thf(f35607,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_816)),
% 68.49/10.18 inference(forward_demodulation,[],[f35605,f6458])).
% 68.49/10.18 thf(f35605,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_816),
% 68.49/10.18 inference(avatar_component_clause,[],[f35604])).
% 68.49/10.18 thf(f35606,plain,(
% 68.49/10.18 spl93_816 | ~spl93_61 | ~spl93_218),
% 68.49/10.18 inference(avatar_split_clause,[],[f3794,f3780,f2136,f35604])).
% 68.49/10.18 thf(f3794,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_218)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3787])).
% 68.49/10.18 thf(f3787,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_218)),
% 68.49/10.18 inference(superposition,[],[f3781,f2138])).
% 68.49/10.18 thf(f35602,plain,(
% 68.49/10.18 spl93_815 | ~spl93_170),
% 68.49/10.18 inference(avatar_split_clause,[],[f3234,f3201,f35600])).
% 68.49/10.18 thf(f35600,plain,(
% 68.49/10.18 spl93_815 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,X2)),X3 : product_prod(X0,product_prod(X1,X2))] : ((vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3)))) != X3) | (X3 = X4))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_815])])).
% 68.49/10.18 thf(f3234,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2)),X4 : product_prod(X0,product_prod(X1,X2))] : ((vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3)))) != X3) | (X3 = X4)) ) | ~spl93_170),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f3233])).
% 68.49/10.18 thf(f3233,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2)),X4 : product_prod(X0,product_prod(X1,X2))] : ((vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3)))) != X3) | ($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3),X4))) ) | ~spl93_170),
% 68.49/10.18 inference(equality_proxy_clausification,[],[f3223])).
% 68.49/10.18 thf(f3223,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2)),X4 : product_prod(X0,product_prod(X1,X2))] : (($true != vAPP(product_prod(X0,product_prod(X1,X2)),$o,vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3))),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3)))))) | ($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,vAPP(product_prod(X0,product_prod(X1,X2)),sTfun(product_prod(X0,product_prod(X1,X2)),$o),vEQ(product_prod(X0,product_prod(X1,X2))),X3),X4))) ) | ~spl93_170),
% 68.49/10.18 inference(primitive_instantiation,[],[f3202])).
% 68.49/10.18 thf(f35554,plain,(
% 68.49/10.18 spl93_814 | ~spl93_48 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3653,f3634,f2031,f35552])).
% 68.49/10.18 thf(f35552,plain,(
% 68.49/10.18 spl93_814 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X1,X0))),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0)))),product_Pair(X4,product_prod(X3,product_prod(X1,X0))),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X4,sK49(X4,X3,X1,X0),X5)),vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X3,sK50(X4,X3,X1,X0),X5)),X2)) = X5) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X1,sK51(X4,X3,X1,X0),X5)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X0,sK52(X4,X3,X1,X0),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_814])])).
% 68.49/10.18 thf(f3653,plain,(
% 68.49/10.18 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X5 : product_prod(X4,product_prod(X3,product_prod(X1,X0)))] : ((vAPP(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0)))),product_Pair(X4,product_prod(X3,product_prod(X1,X0))),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X4,sK49(X4,X3,X1,X0),X5)),vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X3,sK50(X4,X3,X1,X0),X5)),X2)) = X5) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X1,sK51(X4,X3,X1,X0),X5)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X0,sK52(X4,X3,X1,X0),X5))) ) | (~spl93_48 | ~spl93_206)),
% 68.49/10.18 inference(constrained_superposition,[],[f3635,f2032])).
% 68.49/10.18 thf(f35550,plain,(
% 68.49/10.18 spl93_813 | ~spl93_47 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3652,f3634,f2027,f35548])).
% 68.49/10.18 thf(f35548,plain,(
% 68.49/10.18 spl93_813 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X3 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X1,X0))),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0)))),product_Pair(X4,product_prod(X3,product_prod(X1,X0))),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X4,sK49(X4,X3,X1,X0),X5)),vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X3,sK50(X4,X3,X1,X0),X5)),X2)) = X5) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X1,sK51(X4,X3,X1,X0),X5)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X0,sK52(X4,X3,X1,X0),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_813])])).
% 68.49/10.18 thf(f3652,plain,(
% 68.49/10.18 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X5 : product_prod(X4,product_prod(X3,product_prod(X1,X0)))] : ((vAPP(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0))),vAPP(X4,sTfun(product_prod(X3,product_prod(X1,X0)),product_prod(X4,product_prod(X3,product_prod(X1,X0)))),product_Pair(X4,product_prod(X3,product_prod(X1,X0))),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X4,sK49(X4,X3,X1,X0),X5)),vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X3,sK50(X4,X3,X1,X0),X5)),X2)) = X5) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X1,sK51(X4,X3,X1,X0),X5)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X4,product_prod(X3,product_prod(X1,X0))),X0,sK52(X4,X3,X1,X0),X5))) ) | (~spl93_47 | ~spl93_206)),
% 68.49/10.18 inference(constrained_superposition,[],[f3635,f2028])).
% 68.49/10.18 thf(f35546,plain,(
% 68.49/10.18 spl93_812 | ~spl93_221 | ~spl93_610),
% 68.49/10.18 inference(avatar_split_clause,[],[f30042,f26363,f3826,f35544])).
% 68.49/10.18 thf(f30042,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X0)) ) | (~spl93_221 | ~spl93_610)),
% 68.49/10.18 inference(superposition,[],[f26364,f3827])).
% 68.49/10.18 thf(f35409,plain,(
% 68.49/10.18 spl93_811 | ~spl93_345 | ~spl93_810),
% 68.49/10.18 inference(avatar_split_clause,[],[f35405,f35402,f6456,f35407])).
% 68.49/10.18 thf(f35407,plain,(
% 68.49/10.18 spl93_811 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_811])])).
% 68.49/10.18 thf(f35402,plain,(
% 68.49/10.18 spl93_810 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_810])])).
% 68.49/10.18 thf(f35405,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_810)),
% 68.49/10.18 inference(forward_demodulation,[],[f35403,f6458])).
% 68.49/10.18 thf(f35403,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_810),
% 68.49/10.18 inference(avatar_component_clause,[],[f35402])).
% 68.49/10.18 thf(f35404,plain,(
% 68.49/10.18 spl93_810 | ~spl93_60 | ~spl93_61 | ~spl93_230),
% 68.49/10.18 inference(avatar_split_clause,[],[f3942,f3922,f2136,f2131,f35402])).
% 68.49/10.18 thf(f2131,plain,(
% 68.49/10.18 spl93_60 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_60])])).
% 68.49/10.18 thf(f3942,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_60 | ~spl93_61 | ~spl93_230)),
% 68.49/10.18 inference(forward_demodulation,[],[f3941,f2133])).
% 68.49/10.18 thf(f2133,plain,(
% 68.49/10.18 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ~spl93_60),
% 68.49/10.18 inference(avatar_component_clause,[],[f2131])).
% 68.49/10.18 thf(f3941,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_230)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3934])).
% 68.49/10.18 thf(f3934,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_230)),
% 68.49/10.18 inference(superposition,[],[f3923,f2138])).
% 68.49/10.18 thf(f35268,plain,(
% 68.49/10.18 spl93_809 | ~spl93_345 | ~spl93_808),
% 68.49/10.18 inference(avatar_split_clause,[],[f35264,f35261,f6456,f35266])).
% 68.49/10.18 thf(f35266,plain,(
% 68.49/10.18 spl93_809 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_809])])).
% 68.49/10.18 thf(f35261,plain,(
% 68.49/10.18 spl93_808 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_808])])).
% 68.49/10.18 thf(f35264,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | (~spl93_345 | ~spl93_808)),
% 68.49/10.18 inference(forward_demodulation,[],[f35262,f6458])).
% 68.49/10.18 thf(f35262,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_808),
% 68.49/10.18 inference(avatar_component_clause,[],[f35261])).
% 68.49/10.18 thf(f35263,plain,(
% 68.49/10.18 spl93_808 | ~spl93_60 | ~spl93_61 | ~spl93_229),
% 68.49/10.18 inference(avatar_split_clause,[],[f3933,f3918,f2136,f2131,f35261])).
% 68.49/10.18 thf(f3933,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_60 | ~spl93_61 | ~spl93_229)),
% 68.49/10.18 inference(forward_demodulation,[],[f3932,f2133])).
% 68.49/10.18 thf(f3932,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_229)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3925])).
% 68.49/10.18 thf(f3925,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_229)),
% 68.49/10.18 inference(superposition,[],[f3919,f2138])).
% 68.49/10.18 thf(f34991,plain,(
% 68.49/10.18 spl93_807 | ~spl93_221 | ~spl93_536),
% 68.49/10.18 inference(avatar_split_clause,[],[f28265,f24478,f3826,f34989])).
% 68.49/10.18 thf(f34989,plain,(
% 68.49/10.18 spl93_807 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_807])])).
% 68.49/10.18 thf(f24478,plain,(
% 68.49/10.18 spl93_536 <=> ! [X2 : int,X1 : int,X3 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X3)) | (X2 = X3))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_536])])).
% 68.49/10.18 thf(f28265,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X0)) ) | (~spl93_221 | ~spl93_536)),
% 68.49/10.18 inference(superposition,[],[f24479,f3827])).
% 68.49/10.18 thf(f24479,plain,(
% 68.49/10.18 ( ! [X2 : int,X3 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X3)) | (X2 = X3)) ) | ~spl93_536),
% 68.49/10.18 inference(avatar_component_clause,[],[f24478])).
% 68.49/10.18 thf(f34987,plain,(
% 68.49/10.18 spl93_806 | ~spl93_22 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3651,f3634,f1832,f34985])).
% 68.49/10.18 thf(f34985,plain,(
% 68.49/10.18 spl93_806 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,product_prod(X2,$o)))] : ((vAPP(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o)))),product_Pair(X0,product_prod(X1,product_prod(X2,$o))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),X0,sK49(X0,X1,X2,$o),X3)),vAPP(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o)),vAPP(X1,sTfun(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o))),product_Pair(X1,product_prod(X2,$o)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),X1,sK50(X0,X1,X2,$o),X3)),vAPP($o,product_prod(X2,$o),vAPP(X2,sTfun($o,product_prod(X2,$o)),product_Pair(X2,$o),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),X2,sK51(X0,X1,X2,$o),X3)),$true))) = X3) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o,sK52(X0,X1,X2,$o),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_806])])).
% 68.49/10.18 thf(f3651,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,product_prod(X2,$o)))] : ((vAPP(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,$o)),product_prod(X0,product_prod(X1,product_prod(X2,$o)))),product_Pair(X0,product_prod(X1,product_prod(X2,$o))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),X0,sK49(X0,X1,X2,$o),X3)),vAPP(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o)),vAPP(X1,sTfun(product_prod(X2,$o),product_prod(X1,product_prod(X2,$o))),product_Pair(X1,product_prod(X2,$o)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),X1,sK50(X0,X1,X2,$o),X3)),vAPP($o,product_prod(X2,$o),vAPP(X2,sTfun($o,product_prod(X2,$o)),product_Pair(X2,$o),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),X2,sK51(X0,X1,X2,$o),X3)),$true))) = X3) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod(X2,$o))),$o,sK52(X0,X1,X2,$o),X3))) ) | (~spl93_22 | ~spl93_206)),
% 68.49/10.18 inference(superposition,[],[f3635,f1833])).
% 68.49/10.18 thf(f34983,plain,(
% 68.49/10.18 spl93_805 | ~spl93_22 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3650,f3634,f1832,f34981])).
% 68.49/10.18 thf(f34981,plain,(
% 68.49/10.18 spl93_805 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,product_prod($o,X2)))] : ((vAPP(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2)))),product_Pair(X0,product_prod(X1,product_prod($o,X2))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),X0,sK49(X0,X1,$o,X2),X3)),vAPP(product_prod($o,X2),product_prod(X1,product_prod($o,X2)),vAPP(X1,sTfun(product_prod($o,X2),product_prod(X1,product_prod($o,X2))),product_Pair(X1,product_prod($o,X2)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),X1,sK50(X0,X1,$o,X2),X3)),vAPP(X2,product_prod($o,X2),vAPP($o,sTfun(X2,product_prod($o,X2)),product_Pair($o,X2),$true),vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),X2,sK52(X0,X1,$o,X2),X3)))) = X3) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o,sK51(X0,X1,$o,X2),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_805])])).
% 68.49/10.18 thf(f3650,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,product_prod($o,X2)))] : ((vAPP(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2))),vAPP(X0,sTfun(product_prod(X1,product_prod($o,X2)),product_prod(X0,product_prod(X1,product_prod($o,X2)))),product_Pair(X0,product_prod(X1,product_prod($o,X2))),vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),X0,sK49(X0,X1,$o,X2),X3)),vAPP(product_prod($o,X2),product_prod(X1,product_prod($o,X2)),vAPP(X1,sTfun(product_prod($o,X2),product_prod(X1,product_prod($o,X2))),product_Pair(X1,product_prod($o,X2)),vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),X1,sK50(X0,X1,$o,X2),X3)),vAPP(X2,product_prod($o,X2),vAPP($o,sTfun(X2,product_prod($o,X2)),product_Pair($o,X2),$true),vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),X2,sK52(X0,X1,$o,X2),X3)))) = X3) | ($false = vAPP(product_prod(X0,product_prod(X1,product_prod($o,X2))),$o,sK51(X0,X1,$o,X2),X3))) ) | (~spl93_22 | ~spl93_206)),
% 68.49/10.18 inference(superposition,[],[f3635,f1833])).
% 68.49/10.18 thf(f34979,plain,(
% 68.49/10.18 spl93_804 | ~spl93_22 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3649,f3634,f1832,f34977])).
% 68.49/10.18 thf(f34977,plain,(
% 68.49/10.18 spl93_804 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod($o,product_prod(X1,X2)))] : ((vAPP(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2)))),product_Pair(X0,product_prod($o,product_prod(X1,X2))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),X0,sK49(X0,$o,X1,X2),X3)),vAPP(product_prod(X1,X2),product_prod($o,product_prod(X1,X2)),vAPP($o,sTfun(product_prod(X1,X2),product_prod($o,product_prod(X1,X2))),product_Pair($o,product_prod(X1,X2)),$true),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),X1,sK51(X0,$o,X1,X2),X3)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),X2,sK52(X0,$o,X1,X2),X3)))) = X3) | ($false = vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o,sK50(X0,$o,X1,X2),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_804])])).
% 68.49/10.18 thf(f3649,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod($o,product_prod(X1,X2)))] : ((vAPP(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2))),vAPP(X0,sTfun(product_prod($o,product_prod(X1,X2)),product_prod(X0,product_prod($o,product_prod(X1,X2)))),product_Pair(X0,product_prod($o,product_prod(X1,X2))),vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),X0,sK49(X0,$o,X1,X2),X3)),vAPP(product_prod(X1,X2),product_prod($o,product_prod(X1,X2)),vAPP($o,sTfun(product_prod(X1,X2),product_prod($o,product_prod(X1,X2))),product_Pair($o,product_prod(X1,X2)),$true),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),X1,sK51(X0,$o,X1,X2),X3)),vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),X2,sK52(X0,$o,X1,X2),X3)))) = X3) | ($false = vAPP(product_prod(X0,product_prod($o,product_prod(X1,X2))),$o,sK50(X0,$o,X1,X2),X3))) ) | (~spl93_22 | ~spl93_206)),
% 68.49/10.18 inference(superposition,[],[f3635,f1833])).
% 68.49/10.18 thf(f34975,plain,(
% 68.49/10.18 spl93_803 | ~spl93_22 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3648,f3634,f1832,f34973])).
% 68.49/10.18 thf(f34973,plain,(
% 68.49/10.18 spl93_803 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : product_prod($o,product_prod(X0,product_prod(X1,X2)))] : ((vAPP(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2)))),product_Pair($o,product_prod(X0,product_prod(X1,X2))),$true),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),X0,sK50($o,X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),X1,sK51($o,X0,X1,X2),X3)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),X2,sK52($o,X0,X1,X2),X3)))) = X3) | ($false = vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o,sK49($o,X0,X1,X2),X3)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_803])])).
% 68.49/10.18 thf(f3648,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod($o,product_prod(X0,product_prod(X1,X2)))] : ((vAPP(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2))),vAPP($o,sTfun(product_prod(X0,product_prod(X1,X2)),product_prod($o,product_prod(X0,product_prod(X1,X2)))),product_Pair($o,product_prod(X0,product_prod(X1,X2))),$true),vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),X0,sK50($o,X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),X1,sK51($o,X0,X1,X2),X3)),vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),X2,sK52($o,X0,X1,X2),X3)))) = X3) | ($false = vAPP(product_prod($o,product_prod(X0,product_prod(X1,X2))),$o,sK49($o,X0,X1,X2),X3))) ) | (~spl93_22 | ~spl93_206)),
% 68.49/10.18 inference(superposition,[],[f3635,f1833])).
% 68.49/10.18 thf(f34715,plain,(
% 68.49/10.18 spl93_802 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_231),
% 68.49/10.18 inference(avatar_split_clause,[],[f6197,f3944,f2247,f2243,f2074,f34713])).
% 68.49/10.18 thf(f34713,plain,(
% 68.49/10.18 spl93_802 <=> ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),sK6)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_802])])).
% 68.49/10.18 thf(f6197,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),sK6))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_231)),
% 68.49/10.18 inference(forward_demodulation,[],[f3968,f5934])).
% 68.49/10.18 thf(f3968,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_231)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3965])).
% 68.49/10.18 thf(f3965,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_231)),
% 68.49/10.18 inference(superposition,[],[f3945,f2245])).
% 68.49/10.18 thf(f34600,plain,(
% 68.49/10.18 spl93_801 | ~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_795 | ~spl93_800),
% 68.49/10.18 inference(avatar_split_clause,[],[f34596,f34593,f34330,f27603,f23000,f13821,f7374,f3689,f34598])).
% 68.49/10.18 thf(f34598,plain,(
% 68.49/10.18 spl93_801 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_801])])).
% 68.49/10.18 thf(f34593,plain,(
% 68.49/10.18 spl93_800 <=> ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_800])])).
% 68.49/10.18 thf(f34596,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_795 | ~spl93_800)),
% 68.49/10.18 inference(forward_demodulation,[],[f34594,f34413])).
% 68.49/10.18 thf(f34594,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)))) ) | ~spl93_800),
% 68.49/10.18 inference(avatar_component_clause,[],[f34593])).
% 68.49/10.18 thf(f34595,plain,(
% 68.49/10.18 spl93_800 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_233),
% 68.49/10.18 inference(avatar_split_clause,[],[f6193,f3952,f2247,f2243,f2074,f34593])).
% 68.49/10.18 thf(f6193,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_233)),
% 68.49/10.18 inference(forward_demodulation,[],[f3985,f5934])).
% 68.49/10.18 thf(f3985,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_233)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3982])).
% 68.49/10.18 thf(f3982,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_233)),
% 68.49/10.18 inference(superposition,[],[f3953,f2245])).
% 68.49/10.18 thf(f34591,plain,(
% 68.49/10.18 spl93_799 | ~spl93_427 | ~spl93_528),
% 68.49/10.18 inference(avatar_split_clause,[],[f28052,f24381,f10110,f34589])).
% 68.49/10.18 thf(f34589,plain,(
% 68.49/10.18 spl93_799 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_799])])).
% 68.49/10.18 thf(f10110,plain,(
% 68.49/10.18 spl93_427 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)),X0) = X0)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_427])])).
% 68.49/10.18 thf(f24381,plain,(
% 68.49/10.18 spl93_528 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) != X0) | (X0 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_528])])).
% 68.49/10.18 thf(f28052,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0) = X2)) ) | (~spl93_427 | ~spl93_528)),
% 68.49/10.18 inference(superposition,[],[f24382,f10111])).
% 68.49/10.18 thf(f10111,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)),X0) = X0)) ) | ~spl93_427),
% 68.49/10.18 inference(avatar_component_clause,[],[f10110])).
% 68.49/10.18 thf(f24382,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) != X0) | (X0 = X2)) ) | ~spl93_528),
% 68.49/10.18 inference(avatar_component_clause,[],[f24381])).
% 68.49/10.18 thf(f34476,plain,(
% 68.49/10.18 spl93_798 | ~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_793 | ~spl93_797),
% 68.49/10.18 inference(avatar_split_clause,[],[f34472,f34469,f34214,f27603,f23000,f13821,f7374,f3689,f34474])).
% 68.49/10.18 thf(f34474,plain,(
% 68.49/10.18 spl93_798 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_798])])).
% 68.49/10.18 thf(f34469,plain,(
% 68.49/10.18 spl93_797 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_797])])).
% 68.49/10.18 thf(f34472,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_793 | ~spl93_797)),
% 68.49/10.18 inference(forward_demodulation,[],[f34470,f34297])).
% 68.49/10.18 thf(f34470,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | ~spl93_797),
% 68.49/10.18 inference(avatar_component_clause,[],[f34469])).
% 68.49/10.18 thf(f34471,plain,(
% 68.49/10.18 spl93_797 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_242),
% 68.49/10.18 inference(avatar_split_clause,[],[f6185,f4047,f2247,f2243,f2074,f1868,f34469])).
% 68.49/10.18 thf(f6185,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_242)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f6184])).
% 68.49/10.18 thf(f6184,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_242)),
% 68.49/10.18 inference(forward_demodulation,[],[f6183,f1870])).
% 68.49/10.18 thf(f6183,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_242)),
% 68.49/10.18 inference(forward_demodulation,[],[f4072,f5934])).
% 68.49/10.18 thf(f4072,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_242)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4069])).
% 68.49/10.18 thf(f4069,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_242)),
% 68.49/10.18 inference(superposition,[],[f4048,f2245])).
% 68.49/10.18 thf(f34467,plain,(
% 68.49/10.18 spl93_796 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_243),
% 68.49/10.18 inference(avatar_split_clause,[],[f6181,f4051,f2247,f2243,f2074,f1868,f34465])).
% 68.49/10.18 thf(f34465,plain,(
% 68.49/10.18 spl93_796 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_796])])).
% 68.49/10.18 thf(f6181,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_243)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f6180])).
% 68.49/10.18 thf(f6180,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_243)),
% 68.49/10.18 inference(forward_demodulation,[],[f6179,f1870])).
% 68.49/10.18 thf(f6179,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_243)),
% 68.49/10.18 inference(forward_demodulation,[],[f4081,f5934])).
% 68.49/10.18 thf(f4081,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_243)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4078])).
% 68.49/10.18 thf(f4078,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_243)),
% 68.49/10.18 inference(superposition,[],[f4052,f2245])).
% 68.49/10.18 thf(f34332,plain,(
% 68.49/10.18 spl93_795 | ~spl93_345 | ~spl93_794),
% 68.49/10.18 inference(avatar_split_clause,[],[f34328,f34325,f6456,f34330])).
% 68.49/10.18 thf(f34325,plain,(
% 68.49/10.18 spl93_794 <=> ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_794])])).
% 68.49/10.18 thf(f34328,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_794)),
% 68.49/10.18 inference(forward_demodulation,[],[f34326,f6458])).
% 68.49/10.18 thf(f34326,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_794),
% 68.49/10.18 inference(avatar_component_clause,[],[f34325])).
% 68.49/10.18 thf(f34327,plain,(
% 68.49/10.18 spl93_794 | ~spl93_61 | ~spl93_99 | ~spl93_233),
% 68.49/10.18 inference(avatar_split_clause,[],[f3988,f3952,f2480,f2136,f34325])).
% 68.49/10.18 thf(f3988,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_99 | ~spl93_233)),
% 68.49/10.18 inference(forward_demodulation,[],[f3987,f2481])).
% 68.49/10.18 thf(f3987,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_233)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3980])).
% 68.49/10.18 thf(f3980,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_233)),
% 68.49/10.18 inference(superposition,[],[f3953,f2138])).
% 68.49/10.18 thf(f34216,plain,(
% 68.49/10.18 spl93_793 | ~spl93_345 | ~spl93_791),
% 68.49/10.18 inference(avatar_split_clause,[],[f34208,f34205,f6456,f34214])).
% 68.49/10.18 thf(f34205,plain,(
% 68.49/10.18 spl93_791 <=> ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_791])])).
% 68.49/10.18 thf(f34208,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_791)),
% 68.49/10.18 inference(forward_demodulation,[],[f34206,f6458])).
% 68.49/10.18 thf(f34206,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_791),
% 68.49/10.18 inference(avatar_component_clause,[],[f34205])).
% 68.49/10.18 thf(f34212,plain,(
% 68.49/10.18 spl93_792 | ~spl93_396 | ~spl93_524),
% 68.49/10.18 inference(avatar_split_clause,[],[f27907,f23758,f9070,f34210])).
% 68.49/10.18 thf(f34210,plain,(
% 68.49/10.18 spl93_792 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_792])])).
% 68.49/10.18 thf(f9070,plain,(
% 68.49/10.18 spl93_396 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_396])])).
% 68.49/10.18 thf(f23758,plain,(
% 68.49/10.18 spl93_524 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) != X1) | (X0 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_524])])).
% 68.49/10.18 thf(f27907,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X0)) ) | (~spl93_396 | ~spl93_524)),
% 68.49/10.18 inference(superposition,[],[f23759,f9071])).
% 68.49/10.18 thf(f9071,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))) ) | ~spl93_396),
% 68.49/10.18 inference(avatar_component_clause,[],[f9070])).
% 68.49/10.18 thf(f23759,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) != X1) | (X0 = X2)) ) | ~spl93_524),
% 68.49/10.18 inference(avatar_component_clause,[],[f23758])).
% 68.49/10.18 thf(f34207,plain,(
% 68.49/10.18 spl93_791 | ~spl93_61 | ~spl93_100 | ~spl93_232),
% 68.49/10.18 inference(avatar_split_clause,[],[f3979,f3948,f2484,f2136,f34205])).
% 68.49/10.18 thf(f3979,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_100 | ~spl93_232)),
% 68.49/10.18 inference(forward_demodulation,[],[f3978,f2485])).
% 68.49/10.18 thf(f3978,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_232)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3971])).
% 68.49/10.18 thf(f3971,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_232)),
% 68.49/10.18 inference(superposition,[],[f3949,f2138])).
% 68.49/10.18 thf(f34117,plain,(
% 68.49/10.18 spl93_790 | ~spl93_345 | ~spl93_789),
% 68.49/10.18 inference(avatar_split_clause,[],[f34113,f34108,f6456,f34115])).
% 68.49/10.18 thf(f34115,plain,(
% 68.49/10.18 spl93_790 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_790])])).
% 68.49/10.18 thf(f34108,plain,(
% 68.49/10.18 spl93_789 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_789])])).
% 68.49/10.18 thf(f34113,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_789)),
% 68.49/10.18 inference(forward_demodulation,[],[f34112,f6458])).
% 68.49/10.18 thf(f34112,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_789)),
% 68.49/10.18 inference(forward_demodulation,[],[f34111,f6458])).
% 68.49/10.18 thf(f34111,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_789)),
% 68.49/10.18 inference(forward_demodulation,[],[f34109,f6458])).
% 68.49/10.18 thf(f34109,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_789),
% 68.49/10.18 inference(avatar_component_clause,[],[f34108])).
% 68.49/10.18 thf(f34110,plain,(
% 68.49/10.18 spl93_789 | ~spl93_22 | ~spl93_207),
% 68.49/10.18 inference(avatar_split_clause,[],[f3661,f3638,f1832,f34108])).
% 68.49/10.18 thf(f3638,plain,(
% 68.49/10.18 spl93_207 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_207])])).
% 68.49/10.18 thf(f3661,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_207)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3660])).
% 68.49/10.18 thf(f3660,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_207)),
% 68.49/10.18 inference(superposition,[],[f3639,f1833])).
% 68.49/10.18 thf(f3639,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_207),
% 68.49/10.18 inference(avatar_component_clause,[],[f3638])).
% 68.49/10.18 thf(f34106,plain,(
% 68.49/10.18 spl93_788 | ~spl93_139 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3654,f3634,f2831,f34104])).
% 68.49/10.18 thf(f34104,plain,(
% 68.49/10.18 spl93_788 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X5 : product_prod(X4,product_prod(X2,product_prod(X0,X1)))] : ((vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1))),vAPP(X4,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1)))),product_Pair(X4,product_prod(X2,product_prod(X0,X1))),vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X4,sK49(X4,X2,X0,X1),X5)),X3) = X5) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X1,sK52(X4,X2,X0,X1),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X0,sK51(X4,X2,X0,X1),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X2,sK50(X4,X2,X0,X1),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_788])])).
% 68.49/10.18 thf(f3654,plain,(
% 68.49/10.18 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X5 : product_prod(X4,product_prod(X2,product_prod(X0,X1)))] : ((vAPP(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1))),vAPP(X4,sTfun(product_prod(X2,product_prod(X0,X1)),product_prod(X4,product_prod(X2,product_prod(X0,X1)))),product_Pair(X4,product_prod(X2,product_prod(X0,X1))),vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X4,sK49(X4,X2,X0,X1),X5)),X3) = X5) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X1,sK52(X4,X2,X0,X1),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X0,sK51(X4,X2,X0,X1),X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X4,product_prod(X2,product_prod(X0,X1))),X2,sK50(X4,X2,X0,X1),X5))) ) | (~spl93_139 | ~spl93_206)),
% 68.49/10.18 inference(constrained_superposition,[],[f3635,f2832])).
% 68.49/10.18 thf(f34008,plain,(
% 68.49/10.18 spl93_787 | ~spl93_22 | ~spl93_203),
% 68.49/10.18 inference(avatar_split_clause,[],[f3617,f3610,f1832,f34006])).
% 68.49/10.18 thf(f34006,plain,(
% 68.49/10.18 spl93_787 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_787])])).
% 68.49/10.18 thf(f3610,plain,(
% 68.49/10.18 spl93_203 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_203])])).
% 68.49/10.18 thf(f3617,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_203)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3616])).
% 68.49/10.18 thf(f3616,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_203)),
% 68.49/10.18 inference(superposition,[],[f3611,f1833])).
% 68.49/10.18 thf(f3611,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_203),
% 68.49/10.18 inference(avatar_component_clause,[],[f3610])).
% 68.49/10.18 thf(f34004,plain,(
% 68.49/10.18 spl93_786 | ~spl93_72 | ~spl93_145),
% 68.49/10.18 inference(avatar_split_clause,[],[f2888,f2885,f2239,f34002])).
% 68.49/10.18 thf(f34002,plain,(
% 68.49/10.18 spl93_786 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK14(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK15(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_786])])).
% 68.49/10.18 thf(f2885,plain,(
% 68.49/10.18 spl93_145 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_145])])).
% 68.49/10.18 thf(f2888,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK14(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,sK15(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),set(X0),partial_carrier(X0,monoid_ext(X0,product_unit)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),$o,sP1(product_unit,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X1),X2)))) ) | (~spl93_72 | ~spl93_145)),
% 68.49/10.18 inference(superposition,[],[f2886,f2240])).
% 68.49/10.18 thf(f2886,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0))) ) | ~spl93_145),
% 68.49/10.18 inference(avatar_component_clause,[],[f2885])).
% 68.49/10.18 thf(f33949,plain,(
% 68.49/10.18 spl93_785 | ~spl93_396 | ~spl93_524),
% 68.49/10.18 inference(avatar_split_clause,[],[f27878,f23758,f9070,f33947])).
% 68.49/10.18 thf(f33947,plain,(
% 68.49/10.18 spl93_785 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) != X0) | (X0 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_785])])).
% 68.49/10.18 thf(f27878,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) != X0) | (X0 = X2)) ) | (~spl93_396 | ~spl93_524)),
% 68.49/10.18 inference(superposition,[],[f23759,f9071])).
% 68.49/10.18 thf(f33758,plain,(
% 68.49/10.18 spl93_784 | ~spl93_771 | ~spl93_783),
% 68.49/10.18 inference(avatar_split_clause,[],[f33754,f33751,f33243,f33756])).
% 68.49/10.18 thf(f33756,plain,(
% 68.49/10.18 spl93_784 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_784])])).
% 68.49/10.18 thf(f33751,plain,(
% 68.49/10.18 spl93_783 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_783])])).
% 68.49/10.18 thf(f33754,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_771 | ~spl93_783)),
% 68.49/10.18 inference(forward_demodulation,[],[f33752,f33245])).
% 68.49/10.18 thf(f33752,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | ~spl93_783),
% 68.49/10.18 inference(avatar_component_clause,[],[f33751])).
% 68.49/10.18 thf(f33753,plain,(
% 68.49/10.18 spl93_783 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_229),
% 68.49/10.18 inference(avatar_split_clause,[],[f6201,f3918,f2247,f2243,f2074,f33751])).
% 68.49/10.18 thf(f6201,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_229)),
% 68.49/10.18 inference(forward_demodulation,[],[f3930,f5934])).
% 68.49/10.18 thf(f3930,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_229)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3927])).
% 68.49/10.18 thf(f3927,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_229)),
% 68.49/10.18 inference(superposition,[],[f3919,f2245])).
% 68.49/10.18 thf(f33614,plain,(
% 68.49/10.18 spl93_782 | ~spl93_771 | ~spl93_781),
% 68.49/10.18 inference(avatar_split_clause,[],[f33610,f33607,f33243,f33612])).
% 68.49/10.18 thf(f33612,plain,(
% 68.49/10.18 spl93_782 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_782])])).
% 68.49/10.18 thf(f33607,plain,(
% 68.49/10.18 spl93_781 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_781])])).
% 68.49/10.18 thf(f33610,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_771 | ~spl93_781)),
% 68.49/10.18 inference(forward_demodulation,[],[f33608,f33245])).
% 68.49/10.18 thf(f33608,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | ~spl93_781),
% 68.49/10.18 inference(avatar_component_clause,[],[f33607])).
% 68.49/10.18 thf(f33609,plain,(
% 68.49/10.18 spl93_781 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_237),
% 68.49/10.18 inference(avatar_split_clause,[],[f6189,f4003,f2247,f2243,f2074,f1873,f33607])).
% 68.49/10.18 thf(f6189,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_237)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f6188])).
% 68.49/10.18 thf(f6188,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_237)),
% 68.49/10.18 inference(forward_demodulation,[],[f6187,f1875])).
% 68.49/10.18 thf(f6187,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_237)),
% 68.49/10.18 inference(forward_demodulation,[],[f4011,f5934])).
% 68.49/10.18 thf(f4011,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_237)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4008])).
% 68.49/10.18 thf(f4008,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_237)),
% 68.49/10.18 inference(superposition,[],[f4004,f2245])).
% 68.49/10.18 thf(f33605,plain,(
% 68.49/10.18 spl93_780 | ~spl93_22 | ~spl93_202),
% 68.49/10.18 inference(avatar_split_clause,[],[f3605,f3590,f1832,f33603])).
% 68.49/10.18 thf(f33603,plain,(
% 68.49/10.18 spl93_780 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_780])])).
% 68.49/10.18 thf(f3590,plain,(
% 68.49/10.18 spl93_202 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_202])])).
% 68.49/10.18 thf(f3605,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_202)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3604])).
% 68.49/10.18 thf(f3604,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_202)),
% 68.49/10.18 inference(superposition,[],[f3591,f1833])).
% 68.49/10.18 thf(f3591,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_202),
% 68.49/10.18 inference(avatar_component_clause,[],[f3590])).
% 68.49/10.18 thf(f33601,plain,(
% 68.49/10.18 spl93_779 | ~spl93_22 | ~spl93_201),
% 68.49/10.18 inference(avatar_split_clause,[],[f3597,f3586,f1832,f33599])).
% 68.49/10.18 thf(f33599,plain,(
% 68.49/10.18 spl93_779 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_779])])).
% 68.49/10.18 thf(f3586,plain,(
% 68.49/10.18 spl93_201 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_201])])).
% 68.49/10.18 thf(f3597,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_201)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3596])).
% 68.49/10.18 thf(f3596,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_201)),
% 68.49/10.18 inference(superposition,[],[f3587,f1833])).
% 68.49/10.18 thf(f3587,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_201),
% 68.49/10.18 inference(avatar_component_clause,[],[f3586])).
% 68.49/10.18 thf(f33596,plain,(
% 68.49/10.18 spl93_778 | ~spl93_73 | ~spl93_226),
% 68.49/10.18 inference(avatar_split_clause,[],[f3889,f3867,f2243,f33594])).
% 68.49/10.18 thf(f33594,plain,(
% 68.49/10.18 spl93_778 <=> ! [X0 : int,X1 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_778])])).
% 68.49/10.18 thf(f3889,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),sK6))))) ) | (~spl93_73 | ~spl93_226)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3886])).
% 68.49/10.18 thf(f3886,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),sK6))))) ) | (~spl93_73 | ~spl93_226)),
% 68.49/10.18 inference(superposition,[],[f3868,f2245])).
% 68.49/10.18 thf(f33473,plain,(
% 68.49/10.18 spl93_777 | ~spl93_345 | ~spl93_776),
% 68.49/10.18 inference(avatar_split_clause,[],[f33469,f33465,f6456,f33471])).
% 68.49/10.18 thf(f33471,plain,(
% 68.49/10.18 spl93_777 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_777])])).
% 68.49/10.18 thf(f33465,plain,(
% 68.49/10.18 spl93_776 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_776])])).
% 68.49/10.18 thf(f33469,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0)) ) | (~spl93_345 | ~spl93_776)),
% 68.49/10.18 inference(forward_demodulation,[],[f33468,f6458])).
% 68.49/10.18 thf(f33468,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_776)),
% 68.49/10.18 inference(forward_demodulation,[],[f33466,f6458])).
% 68.49/10.18 thf(f33466,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_776),
% 68.49/10.18 inference(avatar_component_clause,[],[f33465])).
% 68.49/10.18 thf(f33467,plain,(
% 68.49/10.18 spl93_776 | ~spl93_22 | ~spl93_199),
% 68.49/10.18 inference(avatar_split_clause,[],[f3581,f3561,f1832,f33465])).
% 68.49/10.18 thf(f3561,plain,(
% 68.49/10.18 spl93_199 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_199])])).
% 68.49/10.18 thf(f3581,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_199)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3580])).
% 68.49/10.18 thf(f3580,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_199)),
% 68.49/10.18 inference(superposition,[],[f3562,f1833])).
% 68.49/10.18 thf(f3562,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_199),
% 68.49/10.18 inference(avatar_component_clause,[],[f3561])).
% 68.49/10.18 thf(f33364,plain,(
% 68.49/10.18 spl93_775 | ~spl93_345 | ~spl93_774),
% 68.49/10.18 inference(avatar_split_clause,[],[f33360,f33356,f6456,f33362])).
% 68.49/10.18 thf(f33362,plain,(
% 68.49/10.18 spl93_775 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_775])])).
% 68.49/10.18 thf(f33356,plain,(
% 68.49/10.18 spl93_774 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_774])])).
% 68.49/10.18 thf(f33360,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0)) ) | (~spl93_345 | ~spl93_774)),
% 68.49/10.18 inference(forward_demodulation,[],[f33359,f6458])).
% 68.49/10.18 thf(f33359,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_774)),
% 68.49/10.18 inference(forward_demodulation,[],[f33357,f6458])).
% 68.49/10.18 thf(f33357,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_774),
% 68.49/10.18 inference(avatar_component_clause,[],[f33356])).
% 68.49/10.18 thf(f33358,plain,(
% 68.49/10.18 spl93_774 | ~spl93_22 | ~spl93_198),
% 68.49/10.18 inference(avatar_split_clause,[],[f3573,f3557,f1832,f33356])).
% 68.49/10.18 thf(f3557,plain,(
% 68.49/10.18 spl93_198 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_198])])).
% 68.49/10.18 thf(f3573,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_198)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3572])).
% 68.49/10.18 thf(f3572,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_198)),
% 68.49/10.18 inference(superposition,[],[f3558,f1833])).
% 68.49/10.18 thf(f3558,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_198),
% 68.49/10.18 inference(avatar_component_clause,[],[f3557])).
% 68.49/10.18 thf(f33254,plain,(
% 68.49/10.18 spl93_773 | ~spl93_22 | ~spl93_197),
% 68.49/10.18 inference(avatar_split_clause,[],[f3552,f3537,f1832,f33252])).
% 68.49/10.18 thf(f33252,plain,(
% 68.49/10.18 spl93_773 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_773])])).
% 68.49/10.18 thf(f3537,plain,(
% 68.49/10.18 spl93_197 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_197])])).
% 68.49/10.18 thf(f3552,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_197)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3551])).
% 68.49/10.18 thf(f3551,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_197)),
% 68.49/10.18 inference(superposition,[],[f3538,f1833])).
% 68.49/10.18 thf(f3538,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_197),
% 68.49/10.18 inference(avatar_component_clause,[],[f3537])).
% 68.49/10.18 thf(f33250,plain,(
% 68.49/10.18 spl93_772 | ~spl93_22 | ~spl93_196),
% 68.49/10.18 inference(avatar_split_clause,[],[f3544,f3533,f1832,f33248])).
% 68.49/10.18 thf(f33248,plain,(
% 68.49/10.18 spl93_772 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_772])])).
% 68.49/10.18 thf(f3533,plain,(
% 68.49/10.18 spl93_196 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_196])])).
% 68.49/10.18 thf(f3544,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_196)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3543])).
% 68.49/10.18 thf(f3543,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0,X4 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_196)),
% 68.49/10.18 inference(superposition,[],[f3534,f1833])).
% 68.49/10.18 thf(f3534,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_196),
% 68.49/10.18 inference(avatar_component_clause,[],[f3533])).
% 68.49/10.18 thf(f33246,plain,(
% 68.49/10.18 spl93_771 | ~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_770),
% 68.49/10.18 inference(avatar_split_clause,[],[f33217,f33134,f27603,f23000,f13821,f7374,f3689,f33243])).
% 68.49/10.18 thf(f33134,plain,(
% 68.49/10.18 spl93_770 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_770])])).
% 68.49/10.18 thf(f33217,plain,(
% 68.49/10.18 (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)) | (~spl93_210 | ~spl93_369 | ~spl93_440 | ~spl93_520 | ~spl93_646 | ~spl93_770)),
% 68.49/10.18 inference(forward_demodulation,[],[f33202,f27626])).
% 68.49/10.18 thf(f33202,plain,(
% 68.49/10.18 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | (~spl93_520 | ~spl93_770)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f33143])).
% 68.49/10.18 thf(f33143,plain,(
% 68.49/10.18 ($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | (~spl93_520 | ~spl93_770)),
% 68.49/10.18 inference(superposition,[],[f33135,f23002])).
% 68.49/10.18 thf(f33135,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | ~spl93_770),
% 68.49/10.18 inference(avatar_component_clause,[],[f33134])).
% 68.49/10.18 thf(f33136,plain,(
% 68.49/10.18 spl93_770 | ~spl93_345 | ~spl93_769),
% 68.49/10.18 inference(avatar_split_clause,[],[f33132,f33129,f6456,f33134])).
% 68.49/10.18 thf(f33129,plain,(
% 68.49/10.18 spl93_769 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_769])])).
% 68.49/10.18 thf(f33132,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_769)),
% 68.49/10.18 inference(forward_demodulation,[],[f33130,f6458])).
% 68.49/10.18 thf(f33130,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_769),
% 68.49/10.18 inference(avatar_component_clause,[],[f33129])).
% 68.49/10.18 thf(f33131,plain,(
% 68.49/10.18 spl93_769 | ~spl93_60 | ~spl93_61 | ~spl93_219),
% 68.49/10.18 inference(avatar_split_clause,[],[f3803,f3784,f2136,f2131,f33129])).
% 68.49/10.18 thf(f3803,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_60 | ~spl93_61 | ~spl93_219)),
% 68.49/10.18 inference(forward_demodulation,[],[f3802,f2133])).
% 68.49/10.18 thf(f3802,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_219)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3795])).
% 68.49/10.18 thf(f3795,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_219)),
% 68.49/10.18 inference(superposition,[],[f3785,f2138])).
% 68.49/10.18 thf(f33125,plain,(
% 68.49/10.18 spl93_768 | ~spl93_66 | ~spl93_199),
% 68.49/10.18 inference(avatar_split_clause,[],[f3583,f3561,f2161,f33123])).
% 68.49/10.18 thf(f33123,plain,(
% 68.49/10.18 spl93_768 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_768])])).
% 68.49/10.18 thf(f3583,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_199)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3578])).
% 68.49/10.18 thf(f3578,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_199)),
% 68.49/10.18 inference(superposition,[],[f3562,f2163])).
% 68.49/10.18 thf(f33119,plain,(
% 68.49/10.18 spl93_767 | ~spl93_66 | ~spl93_198),
% 68.49/10.18 inference(avatar_split_clause,[],[f3575,f3557,f2161,f33117])).
% 68.49/10.18 thf(f33117,plain,(
% 68.49/10.18 spl93_767 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_767])])).
% 68.49/10.18 thf(f3575,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_198)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3570])).
% 68.49/10.18 thf(f3570,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_198)),
% 68.49/10.18 inference(superposition,[],[f3558,f2163])).
% 68.49/10.18 thf(f32954,plain,(
% 68.49/10.18 spl93_766 | ~spl93_206),
% 68.49/10.18 inference(avatar_split_clause,[],[f3655,f3634,f32952])).
% 68.49/10.18 thf(f32952,plain,(
% 68.49/10.18 spl93_766 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X3 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5 : product_prod(X3,product_prod(X0,product_prod(X1,X2)))] : ((X4 = X5) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X5)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_766])])).
% 68.49/10.18 thf(f3655,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X3,product_prod(X0,product_prod(X1,X2))),X5 : product_prod(X3,product_prod(X0,product_prod(X1,X2)))] : ((X4 = X5) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X2,sK52(X3,X0,X1,X2),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X1,sK51(X3,X0,X1,X2),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X0,sK50(X3,X0,X1,X2),X5)) | (vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X4) != vAPP(product_prod(X3,product_prod(X0,product_prod(X1,X2))),X3,sK49(X3,X0,X1,X2),X5))) ) | ~spl93_206),
% 68.49/10.18 inference(constrained_superposition,[],[f3635,f3635])).
% 68.49/10.18 thf(f32950,plain,(
% 68.49/10.18 spl93_765 | ~spl93_102),
% 68.49/10.18 inference(avatar_split_clause,[],[f2512,f2492,f32948])).
% 68.49/10.18 thf(f32948,plain,(
% 68.49/10.18 spl93_765 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : (vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))) = X2)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_765])])).
% 68.49/10.18 thf(f2492,plain,(
% 68.49/10.18 spl93_102 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0) > $o] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X2)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_102])])).
% 68.49/10.18 thf(f2512,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))) = X2)) ) | ~spl93_102),
% 68.49/10.18 inference(leibniz_equality_elimination,[],[f2493])).
% 68.49/10.18 thf(f2493,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X2)))) | ($true = vAPP(product_prod(X1,X0),$o,X2,X3))) ) | ~spl93_102),
% 68.49/10.18 inference(avatar_component_clause,[],[f2492])).
% 68.49/10.18 thf(f32946,plain,(
% 68.49/10.18 spl93_764 | ~spl93_276 | ~spl93_524),
% 68.49/10.18 inference(avatar_split_clause,[],[f27875,f23758,f4534,f32944])).
% 68.49/10.18 thf(f32944,plain,(
% 68.49/10.18 spl93_764 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) | (X0 = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_764])])).
% 68.49/10.18 thf(f27875,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) | (X0 = X2)) ) | (~spl93_276 | ~spl93_524)),
% 68.49/10.18 inference(superposition,[],[f23759,f4535])).
% 68.49/10.18 thf(f32942,plain,(
% 68.49/10.18 spl93_763 | ~spl93_101),
% 68.49/10.18 inference(avatar_split_clause,[],[f2499,f2488,f32940])).
% 68.49/10.18 thf(f32940,plain,(
% 68.49/10.18 spl93_763 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : (vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))) = X2)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_763])])).
% 68.49/10.18 thf(f2488,plain,(
% 68.49/10.18 spl93_101 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0) > $o] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X2)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_101])])).
% 68.49/10.18 thf(f2499,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),vAPP(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o),vAPP(sTfun($o,$o),sTfun(sTfun(product_prod(X1,X0),$o),sTfun(product_prod(X1,X0),$o)),bCOMB,vNOT),vAPP(product_prod(X1,X0),sTfun(product_prod(X1,X0),$o),vEQ(product_prod(X1,X0)),X2)))) = X2)) ) | ~spl93_101),
% 68.49/10.18 inference(leibniz_equality_elimination,[],[f2489])).
% 68.49/10.18 thf(f2489,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X2)))) | ($true = vAPP(product_prod(X1,X0),$o,X2,X3))) ) | ~spl93_101),
% 68.49/10.18 inference(avatar_component_clause,[],[f2488])).
% 68.49/10.18 thf(f32829,plain,(
% 68.49/10.18 spl93_762 | ~spl93_345 | ~spl93_761),
% 68.49/10.18 inference(avatar_split_clause,[],[f32825,f32822,f6456,f32827])).
% 68.49/10.18 thf(f32827,plain,(
% 68.49/10.18 spl93_762 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_762])])).
% 68.49/10.18 thf(f32822,plain,(
% 68.49/10.18 spl93_761 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_761])])).
% 68.49/10.18 thf(f32825,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_761)),
% 68.49/10.18 inference(forward_demodulation,[],[f32823,f6458])).
% 68.49/10.18 thf(f32823,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_761),
% 68.49/10.18 inference(avatar_component_clause,[],[f32822])).
% 68.49/10.18 thf(f32824,plain,(
% 68.49/10.18 spl93_761 | ~spl93_61 | ~spl93_199),
% 68.49/10.18 inference(avatar_split_clause,[],[f3584,f3561,f2136,f32822])).
% 68.49/10.18 thf(f3584,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_199)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3577])).
% 68.49/10.18 thf(f3577,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_199)),
% 68.49/10.18 inference(superposition,[],[f3562,f2138])).
% 68.49/10.18 thf(f32713,plain,(
% 68.49/10.18 spl93_760 | ~spl93_345 | ~spl93_759),
% 68.49/10.18 inference(avatar_split_clause,[],[f32709,f32706,f6456,f32711])).
% 68.49/10.18 thf(f32711,plain,(
% 68.49/10.18 spl93_760 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_760])])).
% 68.49/10.18 thf(f32706,plain,(
% 68.49/10.18 spl93_759 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_759])])).
% 68.49/10.18 thf(f32709,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))) ) | (~spl93_345 | ~spl93_759)),
% 68.49/10.18 inference(forward_demodulation,[],[f32707,f6458])).
% 68.49/10.18 thf(f32707,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_759),
% 68.49/10.18 inference(avatar_component_clause,[],[f32706])).
% 68.49/10.18 thf(f32708,plain,(
% 68.49/10.18 spl93_759 | ~spl93_61 | ~spl93_198),
% 68.49/10.18 inference(avatar_split_clause,[],[f3576,f3557,f2136,f32706])).
% 68.49/10.18 thf(f3576,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_198)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3569])).
% 68.49/10.18 thf(f3569,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_198)),
% 68.49/10.18 inference(superposition,[],[f3558,f2138])).
% 68.49/10.18 thf(f32703,plain,(
% 68.49/10.18 spl93_758 | ~spl93_66 | ~spl93_184),
% 68.49/10.18 inference(avatar_split_clause,[],[f3401,f3392,f2161,f32701])).
% 68.49/10.18 thf(f32701,plain,(
% 68.49/10.18 spl93_758 <=> ! [X0 : nat] : (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_758])])).
% 68.49/10.18 thf(f3392,plain,(
% 68.49/10.18 spl93_184 <=> ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_184])])).
% 68.49/10.18 thf(f3401,plain,(
% 68.49/10.18 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_184)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3396])).
% 68.49/10.18 thf(f3396,plain,(
% 68.49/10.18 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_184)),
% 68.49/10.18 inference(superposition,[],[f3393,f2163])).
% 68.49/10.18 thf(f3393,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | ~spl93_184),
% 68.49/10.18 inference(avatar_component_clause,[],[f3392])).
% 68.49/10.18 thf(f32680,plain,(
% 68.49/10.18 spl93_757 | ~spl93_345 | ~spl93_755),
% 68.49/10.18 inference(avatar_split_clause,[],[f32672,f32668,f6456,f32678])).
% 68.49/10.18 thf(f32678,plain,(
% 68.49/10.18 spl93_757 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_757])])).
% 68.49/10.18 thf(f32668,plain,(
% 68.49/10.18 spl93_755 <=> ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_755])])).
% 68.49/10.18 thf(f32672,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1)) ) | (~spl93_345 | ~spl93_755)),
% 68.49/10.18 inference(forward_demodulation,[],[f32671,f6458])).
% 68.49/10.18 thf(f32671,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_755)),
% 68.49/10.18 inference(forward_demodulation,[],[f32669,f6458])).
% 68.49/10.18 thf(f32669,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_755),
% 68.49/10.18 inference(avatar_component_clause,[],[f32668])).
% 68.49/10.18 thf(f32676,plain,(
% 68.49/10.18 spl93_756 | ~spl93_216 | ~spl93_524),
% 68.49/10.18 inference(avatar_split_clause,[],[f27868,f23758,f3748,f32674])).
% 68.49/10.18 thf(f32674,plain,(
% 68.49/10.18 spl93_756 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_756])])).
% 68.49/10.18 thf(f27868,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X2)) ) | (~spl93_216 | ~spl93_524)),
% 68.49/10.18 inference(superposition,[],[f23759,f3749])).
% 68.49/10.18 thf(f32670,plain,(
% 68.49/10.18 spl93_755 | ~spl93_25 | ~spl93_278 | ~spl93_282),
% 68.49/10.18 inference(avatar_split_clause,[],[f4627,f4618,f4557,f1873,f32668])).
% 68.49/10.18 thf(f4557,plain,(
% 68.49/10.18 spl93_278 <=> ! [X0 : a,X1 : a] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X1))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_278])])).
% 68.49/10.18 thf(f4618,plain,(
% 68.49/10.18 spl93_282 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((X3 = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_282])])).
% 68.49/10.18 thf(f4627,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_25 | ~spl93_278 | ~spl93_282)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4626])).
% 68.49/10.18 thf(f4626,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_25 | ~spl93_278 | ~spl93_282)),
% 68.49/10.18 inference(forward_demodulation,[],[f4623,f1875])).
% 68.49/10.18 thf(f4623,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_278 | ~spl93_282)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4622])).
% 68.49/10.18 thf(f4622,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | (X0 = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (a_inv(a,b) != a_inv(a,b)) | (vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b))) != vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b))))) ) | (~spl93_278 | ~spl93_282)),
% 68.49/10.18 inference(constrained_superposition,[],[f4619,f4558])).
% 68.49/10.18 thf(f4558,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X1))) ) | ~spl93_278),
% 68.49/10.18 inference(avatar_component_clause,[],[f4557])).
% 68.49/10.18 thf(f4619,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)) | (X3 = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_282),
% 68.49/10.18 inference(avatar_component_clause,[],[f4618])).
% 68.49/10.18 thf(f32663,plain,(
% 68.49/10.18 spl93_754 | ~spl93_22 | ~spl93_194),
% 68.49/10.18 inference(avatar_split_clause,[],[f3523,f3516,f1832,f32661])).
% 68.49/10.18 thf(f32661,plain,(
% 68.49/10.18 spl93_754 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_754])])).
% 68.49/10.18 thf(f3516,plain,(
% 68.49/10.18 spl93_194 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_194])])).
% 68.49/10.18 thf(f3523,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_194)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3522])).
% 68.49/10.18 thf(f3522,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_194)),
% 68.49/10.18 inference(superposition,[],[f3517,f1833])).
% 68.49/10.18 thf(f3517,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_194),
% 68.49/10.18 inference(avatar_component_clause,[],[f3516])).
% 68.49/10.18 thf(f32380,plain,(
% 68.49/10.18 spl93_753 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_218),
% 68.49/10.18 inference(avatar_split_clause,[],[f6205,f3780,f2247,f2243,f2074,f32378])).
% 68.49/10.18 thf(f32378,plain,(
% 68.49/10.18 spl93_753 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_753])])).
% 68.49/10.18 thf(f6205,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_218)),
% 68.49/10.18 inference(forward_demodulation,[],[f3792,f5934])).
% 68.49/10.18 thf(f3792,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_218)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3789])).
% 68.49/10.18 thf(f3789,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_218)),
% 68.49/10.18 inference(superposition,[],[f3781,f2245])).
% 68.49/10.18 thf(f32376,plain,(
% 68.49/10.18 spl93_752 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_219),
% 68.49/10.18 inference(avatar_split_clause,[],[f6203,f3784,f2247,f2243,f2074,f32374])).
% 68.49/10.18 thf(f32374,plain,(
% 68.49/10.18 spl93_752 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_752])])).
% 68.49/10.18 thf(f6203,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_219)),
% 68.49/10.18 inference(forward_demodulation,[],[f3800,f5934])).
% 68.49/10.18 thf(f3800,plain,(
% 68.49/10.18 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_219)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3797])).
% 68.49/10.18 thf(f3797,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_219)),
% 68.49/10.18 inference(superposition,[],[f3785,f2245])).
% 68.49/10.18 thf(f32372,plain,(
% 68.49/10.18 spl93_751 | ~spl93_73 | ~spl93_177 | ~spl93_226),
% 68.49/10.18 inference(avatar_split_clause,[],[f3897,f3867,f3305,f2243,f32370])).
% 68.49/10.18 thf(f32370,plain,(
% 68.49/10.18 spl93_751 <=> ! [X0 : int,X1 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),sK6)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_751])])).
% 68.49/10.18 thf(f3897,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),sK6)))) ) | (~spl93_73 | ~spl93_177 | ~spl93_226)),
% 68.49/10.18 inference(forward_demodulation,[],[f3889,f3337])).
% 68.49/10.18 thf(f3337,plain,(
% 68.49/10.18 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),sK6))) ) | (~spl93_73 | ~spl93_177)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3334])).
% 68.49/10.18 thf(f3334,plain,(
% 68.49/10.18 ( ! [X0 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),sK6))) ) | (~spl93_73 | ~spl93_177)),
% 68.49/10.18 inference(superposition,[],[f3306,f2245])).
% 68.49/10.18 thf(f32343,plain,(
% 68.49/10.18 spl93_750 | ~spl93_345 | ~spl93_748),
% 68.49/10.18 inference(avatar_split_clause,[],[f32335,f32332,f6456,f32341])).
% 68.49/10.18 thf(f32341,plain,(
% 68.49/10.18 spl93_750 <=> ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_750])])).
% 68.49/10.18 thf(f32332,plain,(
% 68.49/10.18 spl93_748 <=> ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_748])])).
% 68.49/10.18 thf(f32335,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | (~spl93_345 | ~spl93_748)),
% 68.49/10.18 inference(forward_demodulation,[],[f32333,f6458])).
% 68.49/10.18 thf(f32333,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_748),
% 68.49/10.18 inference(avatar_component_clause,[],[f32332])).
% 68.49/10.18 thf(f32339,plain,(
% 68.49/10.18 spl93_749 | ~spl93_221 | ~spl93_524),
% 68.49/10.18 inference(avatar_split_clause,[],[f27867,f23758,f3826,f32337])).
% 68.49/10.18 thf(f32337,plain,(
% 68.49/10.18 spl93_749 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_749])])).
% 68.49/10.18 thf(f27867,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = X2)) ) | (~spl93_221 | ~spl93_524)),
% 68.49/10.18 inference(superposition,[],[f23759,f3827])).
% 68.49/10.18 thf(f32334,plain,(
% 68.49/10.18 spl93_748 | ~spl93_22 | ~spl93_192),
% 68.49/10.18 inference(avatar_split_clause,[],[f3502,f3483,f1832,f32332])).
% 68.49/10.18 thf(f3483,plain,(
% 68.49/10.18 spl93_192 <=> ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_192])])).
% 68.49/10.18 thf(f3502,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_192)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3501])).
% 68.49/10.18 thf(f3501,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_192)),
% 68.49/10.18 inference(superposition,[],[f3484,f1833])).
% 68.49/10.18 thf(f3484,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | ~spl93_192),
% 68.49/10.18 inference(avatar_component_clause,[],[f3483])).
% 68.49/10.18 thf(f32312,plain,(
% 68.49/10.18 spl93_747 | ~spl93_345 | ~spl93_746),
% 68.49/10.18 inference(avatar_split_clause,[],[f32308,f32305,f6456,f32310])).
% 68.49/10.18 thf(f32310,plain,(
% 68.49/10.18 spl93_747 <=> ! [X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_747])])).
% 68.49/10.18 thf(f32305,plain,(
% 68.49/10.18 spl93_746 <=> ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_746])])).
% 68.49/10.18 thf(f32308,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | (~spl93_345 | ~spl93_746)),
% 68.49/10.18 inference(forward_demodulation,[],[f32306,f6458])).
% 68.49/10.18 thf(f32306,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_746),
% 68.49/10.18 inference(avatar_component_clause,[],[f32305])).
% 68.49/10.18 thf(f32307,plain,(
% 68.49/10.18 spl93_746 | ~spl93_22 | ~spl93_191),
% 68.49/10.18 inference(avatar_split_clause,[],[f3490,f3479,f1832,f32305])).
% 68.49/10.18 thf(f3479,plain,(
% 68.49/10.18 spl93_191 <=> ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_191])])).
% 68.49/10.18 thf(f3490,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_191)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3489])).
% 68.49/10.18 thf(f3489,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_191)),
% 68.49/10.18 inference(superposition,[],[f3480,f1833])).
% 68.49/10.18 thf(f3480,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | ~spl93_191),
% 68.49/10.18 inference(avatar_component_clause,[],[f3479])).
% 68.49/10.18 thf(f32219,plain,(
% 68.49/10.18 spl93_745 | ~spl93_345 | ~spl93_744),
% 68.49/10.18 inference(avatar_split_clause,[],[f32215,f32210,f6456,f32217])).
% 68.49/10.18 thf(f32217,plain,(
% 68.49/10.18 spl93_745 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_745])])).
% 68.49/10.18 thf(f32210,plain,(
% 68.49/10.18 spl93_744 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_744])])).
% 68.49/10.18 thf(f32215,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_744)),
% 68.49/10.18 inference(forward_demodulation,[],[f32214,f6458])).
% 68.49/10.18 thf(f32214,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_744)),
% 68.49/10.18 inference(forward_demodulation,[],[f32213,f6458])).
% 68.49/10.18 thf(f32213,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_744)),
% 68.49/10.18 inference(forward_demodulation,[],[f32211,f6458])).
% 68.49/10.18 thf(f32211,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_744),
% 68.49/10.18 inference(avatar_component_clause,[],[f32210])).
% 68.49/10.18 thf(f32212,plain,(
% 68.49/10.18 spl93_744 | ~spl93_22 | ~spl93_190),
% 68.49/10.18 inference(avatar_split_clause,[],[f3474,f3459,f1832,f32210])).
% 68.49/10.18 thf(f3459,plain,(
% 68.49/10.18 spl93_190 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_190])])).
% 68.49/10.18 thf(f3474,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_190)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3473])).
% 68.49/10.18 thf(f3473,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_190)),
% 68.49/10.18 inference(superposition,[],[f3460,f1833])).
% 68.49/10.18 thf(f3460,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_190),
% 68.49/10.18 inference(avatar_component_clause,[],[f3459])).
% 68.49/10.18 thf(f32124,plain,(
% 68.49/10.18 spl93_743 | ~spl93_345 | ~spl93_742),
% 68.49/10.18 inference(avatar_split_clause,[],[f32120,f32116,f6456,f32122])).
% 68.49/10.18 thf(f32122,plain,(
% 68.49/10.18 spl93_743 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_743])])).
% 68.49/10.18 thf(f32116,plain,(
% 68.49/10.18 spl93_742 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_742])])).
% 68.49/10.18 thf(f32120,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))) ) | (~spl93_345 | ~spl93_742)),
% 68.49/10.18 inference(forward_demodulation,[],[f32119,f6458])).
% 68.49/10.18 thf(f32119,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_742)),
% 68.49/10.18 inference(forward_demodulation,[],[f32117,f6458])).
% 68.49/10.18 thf(f32117,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_742),
% 68.49/10.18 inference(avatar_component_clause,[],[f32116])).
% 68.49/10.18 thf(f32118,plain,(
% 68.49/10.18 spl93_742 | ~spl93_22 | ~spl93_189),
% 68.49/10.18 inference(avatar_split_clause,[],[f3466,f3455,f1832,f32116])).
% 68.49/10.18 thf(f3455,plain,(
% 68.49/10.18 spl93_189 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_189])])).
% 68.49/10.18 thf(f3466,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_189)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3465])).
% 68.49/10.18 thf(f3465,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_189)),
% 68.49/10.18 inference(superposition,[],[f3456,f1833])).
% 68.49/10.18 thf(f3456,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_189),
% 68.49/10.18 inference(avatar_component_clause,[],[f3455])).
% 68.49/10.18 thf(f32114,plain,(
% 68.49/10.18 spl93_741 | ~spl93_21 | ~spl93_312 | ~spl93_432),
% 68.49/10.18 inference(avatar_split_clause,[],[f15979,f11066,f5040,f1827,f32112])).
% 68.49/10.18 thf(f32112,plain,(
% 68.49/10.18 spl93_741 <=> ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_741])])).
% 68.49/10.18 thf(f5040,plain,(
% 68.49/10.18 spl93_312 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = X1) | (group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_312])])).
% 68.49/10.18 thf(f11066,plain,(
% 68.49/10.18 spl93_432 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_432])])).
% 68.49/10.18 thf(f15979,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_21 | ~spl93_312 | ~spl93_432)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f15978])).
% 68.49/10.18 thf(f15978,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_21 | ~spl93_312 | ~spl93_432)),
% 68.49/10.18 inference(forward_demodulation,[],[f15913,f1829])).
% 68.49/10.18 thf(f15913,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_312 | ~spl93_432)),
% 68.49/10.18 inference(superposition,[],[f5041,f11067])).
% 68.49/10.18 thf(f11067,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | ~spl93_432),
% 68.49/10.18 inference(avatar_component_clause,[],[f11066])).
% 68.49/10.18 thf(f5041,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2) | (group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = X1)) ) | ~spl93_312),
% 68.49/10.18 inference(avatar_component_clause,[],[f5040])).
% 68.49/10.18 thf(f31430,plain,(
% 68.49/10.18 spl93_740 | ~spl93_66 | ~spl93_207),
% 68.49/10.18 inference(avatar_split_clause,[],[f3663,f3638,f2161,f31428])).
% 68.49/10.18 thf(f31428,plain,(
% 68.49/10.18 spl93_740 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_740])])).
% 68.49/10.18 thf(f3663,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_207)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3658])).
% 68.49/10.18 thf(f3658,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_207)),
% 68.49/10.18 inference(superposition,[],[f3639,f2163])).
% 68.49/10.18 thf(f31426,plain,(
% 68.49/10.18 spl93_739 | ~spl93_22 | ~spl93_188),
% 68.49/10.18 inference(avatar_split_clause,[],[f3450,f3443,f1832,f31424])).
% 68.49/10.18 thf(f31424,plain,(
% 68.49/10.18 spl93_739 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_739])])).
% 68.49/10.18 thf(f3443,plain,(
% 68.49/10.18 spl93_188 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_188])])).
% 68.49/10.18 thf(f3450,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0,X4 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_188)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3449])).
% 68.49/10.18 thf(f3449,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_188)),
% 68.49/10.18 inference(superposition,[],[f3444,f1833])).
% 68.49/10.18 thf(f3444,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) ) | ~spl93_188),
% 68.49/10.18 inference(avatar_component_clause,[],[f3443])).
% 68.49/10.18 thf(f31422,plain,(
% 68.49/10.18 spl93_738 | ~spl93_65 | ~spl93_97),
% 68.49/10.18 inference(avatar_split_clause,[],[f2470,f2436,f2157,f31420])).
% 68.49/10.18 thf(f31420,plain,(
% 68.49/10.18 spl93_738 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2)))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_738])])).
% 68.49/10.18 thf(f2157,plain,(
% 68.49/10.18 spl93_65 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_65])])).
% 68.49/10.18 thf(f2436,plain,(
% 68.49/10.18 spl93_97 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_97])])).
% 68.49/10.18 thf(f2470,plain,(
% 68.49/10.18 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2)) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2)))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2)) ) | (~spl93_65 | ~spl93_97)),
% 68.49/10.18 inference(superposition,[],[f2437,f2158])).
% 68.49/10.18 thf(f2158,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | ~spl93_65),
% 68.49/10.18 inference(avatar_component_clause,[],[f2157])).
% 68.49/10.18 thf(f2437,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2))) | (X2 = X3)) ) | ~spl93_97),
% 68.49/10.18 inference(avatar_component_clause,[],[f2436])).
% 68.49/10.18 thf(f31418,plain,(
% 68.49/10.18 spl93_737 | ~spl93_70 | ~spl93_97),
% 68.49/10.18 inference(avatar_split_clause,[],[f2469,f2436,f2181,f31416])).
% 68.49/10.18 thf(f31416,plain,(
% 68.49/10.18 spl93_737 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2)),X1)) != vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_737])])).
% 68.49/10.18 thf(f2181,plain,(
% 68.49/10.18 spl93_70 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_70])])).
% 68.49/10.18 thf(f2469,plain,(
% 68.49/10.18 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2)),X1)) != vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X2))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2)) ) | (~spl93_70 | ~spl93_97)),
% 68.49/10.18 inference(superposition,[],[f2437,f2182])).
% 68.49/10.18 thf(f2182,plain,(
% 68.49/10.18 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) ) | ~spl93_70),
% 68.49/10.18 inference(avatar_component_clause,[],[f2181])).
% 68.49/10.18 thf(f31414,plain,(
% 68.49/10.18 spl93_736 | ~spl93_65 | ~spl93_97),
% 68.49/10.18 inference(avatar_split_clause,[],[f2462,f2436,f2157,f31412])).
% 68.49/10.18 thf(f31412,plain,(
% 68.49/10.18 spl93_736 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_736])])).
% 68.49/10.18 thf(f2462,plain,(
% 68.49/10.18 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2)) ) | (~spl93_65 | ~spl93_97)),
% 68.49/10.18 inference(superposition,[],[f2437,f2158])).
% 68.49/10.18 thf(f31410,plain,(
% 68.49/10.18 spl93_735 | ~spl93_21 | ~spl93_309 | ~spl93_432),
% 68.49/10.18 inference(avatar_split_clause,[],[f15977,f11066,f5028,f1827,f31408])).
% 68.49/10.18 thf(f31408,plain,(
% 68.49/10.18 spl93_735 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_735])])).
% 68.49/10.18 thf(f5028,plain,(
% 68.49/10.18 spl93_309 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | (X2 = X3))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_309])])).
% 68.49/10.18 thf(f15977,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = X2)) ) | (~spl93_21 | ~spl93_309 | ~spl93_432)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f15976])).
% 68.49/10.18 thf(f15976,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = X2)) ) | (~spl93_21 | ~spl93_309 | ~spl93_432)),
% 68.49/10.18 inference(forward_demodulation,[],[f15911,f1829])).
% 68.49/10.18 thf(f15911,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X0) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = X2)) ) | (~spl93_309 | ~spl93_432)),
% 68.49/10.18 inference(superposition,[],[f5029,f11067])).
% 68.49/10.18 thf(f5029,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | (X2 = X3)) ) | ~spl93_309),
% 68.49/10.18 inference(avatar_component_clause,[],[f5028])).
% 68.49/10.18 thf(f31406,plain,(
% 68.49/10.18 spl93_734 | ~spl93_70 | ~spl93_97),
% 68.49/10.18 inference(avatar_split_clause,[],[f2461,f2436,f2181,f31404])).
% 68.49/10.18 thf(f31404,plain,(
% 68.49/10.18 spl93_734 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),X1)) != vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_734])])).
% 68.49/10.18 thf(f2461,plain,(
% 68.49/10.18 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))),X1)) != vAPP(nat,nat,X2,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X2),vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))))) | (vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)) = X2)) ) | (~spl93_70 | ~spl93_97)),
% 68.49/10.18 inference(superposition,[],[f2437,f2182])).
% 68.49/10.18 thf(f31353,plain,(
% 68.49/10.18 spl93_733 | ~spl93_22 | ~spl93_187),
% 68.49/10.18 inference(avatar_split_clause,[],[f3435,f3428,f1832,f31351])).
% 68.49/10.18 thf(f31351,plain,(
% 68.49/10.18 spl93_733 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_733])])).
% 68.49/10.18 thf(f3428,plain,(
% 68.49/10.18 spl93_187 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_187])])).
% 68.49/10.18 thf(f3435,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_187)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3434])).
% 68.49/10.18 thf(f3434,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0,X4 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X1),X4)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X4),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_187)),
% 68.49/10.18 inference(superposition,[],[f3429,f1833])).
% 68.49/10.18 thf(f3429,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) ) | ~spl93_187),
% 68.49/10.18 inference(avatar_component_clause,[],[f3428])).
% 68.49/10.18 thf(f31348,plain,(
% 68.49/10.18 spl93_732 | ~spl93_116 | ~spl93_185),
% 68.49/10.18 inference(avatar_split_clause,[],[f3417,f3406,f2623,f31346])).
% 68.49/10.18 thf(f31346,plain,(
% 68.49/10.18 spl93_732 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_732])])).
% 68.49/10.18 thf(f2623,plain,(
% 68.49/10.18 spl93_116 <=> (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_116])])).
% 68.49/10.18 thf(f3406,plain,(
% 68.49/10.18 spl93_185 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_185])])).
% 68.49/10.18 thf(f3417,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_116 | ~spl93_185)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3414])).
% 68.49/10.18 thf(f3414,plain,(
% 68.49/10.18 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_116 | ~spl93_185)),
% 68.49/10.18 inference(superposition,[],[f3407,f2625])).
% 68.49/10.18 thf(f2625,plain,(
% 68.49/10.18 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true) | ~spl93_116),
% 68.49/10.18 inference(avatar_component_clause,[],[f2623])).
% 68.49/10.18 thf(f3407,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | ~spl93_185),
% 68.49/10.18 inference(avatar_component_clause,[],[f3406])).
% 68.49/10.18 thf(f31125,plain,(
% 68.49/10.18 spl93_731 | ~spl93_21 | ~spl93_312 | ~spl93_427),
% 68.49/10.18 inference(avatar_split_clause,[],[f13779,f10110,f5040,f1827,f31123])).
% 68.49/10.18 thf(f31123,plain,(
% 68.49/10.18 spl93_731 <=> ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_731])])).
% 68.49/10.18 thf(f13779,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))) ) | (~spl93_21 | ~spl93_312 | ~spl93_427)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f13778])).
% 68.49/10.18 thf(f13778,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))) ) | (~spl93_21 | ~spl93_312 | ~spl93_427)),
% 68.49/10.18 inference(forward_demodulation,[],[f13713,f1829])).
% 68.49/10.18 thf(f13713,plain,(
% 68.49/10.18 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))) ) | (~spl93_312 | ~spl93_427)),
% 68.49/10.18 inference(superposition,[],[f5041,f10111])).
% 68.49/10.18 thf(f31121,plain,(
% 68.49/10.18 spl93_730 | ~spl93_73 | ~spl93_212 | ~spl93_245),
% 68.49/10.18 inference(avatar_split_clause,[],[f6177,f4094,f3701,f2243,f31119])).
% 68.49/10.18 thf(f31119,plain,(
% 68.49/10.18 spl93_730 <=> ! [X0 : nat,X1 : nat] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),sK6))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_730])])).
% 68.49/10.18 thf(f6177,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),sK6))) ) | (~spl93_73 | ~spl93_212 | ~spl93_245)),
% 68.49/10.18 inference(forward_demodulation,[],[f4102,f4110])).
% 68.49/10.18 thf(f4110,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),sK6))) ) | (~spl93_73 | ~spl93_212 | ~spl93_245)),
% 68.49/10.18 inference(forward_demodulation,[],[f4102,f3732])).
% 68.49/10.18 thf(f3732,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),sK6))) ) | (~spl93_73 | ~spl93_212)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3729])).
% 68.49/10.18 thf(f3729,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),sK6))) ) | (~spl93_73 | ~spl93_212)),
% 68.49/10.18 inference(superposition,[],[f3702,f2245])).
% 68.49/10.18 thf(f4102,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_245)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f4099])).
% 68.49/10.18 thf(f4099,plain,(
% 68.49/10.18 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_245)),
% 68.49/10.18 inference(superposition,[],[f4095,f2245])).
% 68.49/10.18 thf(f31117,plain,(
% 68.49/10.18 spl93_729 | ~spl93_73 | ~spl93_212 | ~spl93_245),
% 68.49/10.18 inference(avatar_split_clause,[],[f4110,f4094,f3701,f2243,f31115])).
% 68.49/10.18 thf(f31115,plain,(
% 68.49/10.18 spl93_729 <=> ! [X0 : nat,X1 : nat] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),sK6))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_729])])).
% 68.49/10.18 thf(f31113,plain,(
% 68.49/10.18 spl93_728 | ~spl93_73 | ~spl93_211),
% 68.49/10.18 inference(avatar_split_clause,[],[f3721,f3697,f2243,f31111])).
% 68.49/10.18 thf(f31111,plain,(
% 68.49/10.18 spl93_728 <=> ! [X0 : int,X1 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),sK6)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_728])])).
% 68.49/10.18 thf(f3721,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),sK6)))) ) | (~spl93_73 | ~spl93_211)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3718])).
% 68.49/10.18 thf(f3718,plain,(
% 68.49/10.18 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),sK6)))) ) | (~spl93_73 | ~spl93_211)),
% 68.49/10.18 inference(superposition,[],[f3698,f2245])).
% 68.49/10.18 thf(f31025,plain,(
% 68.49/10.18 spl93_727 | ~spl93_345 | ~spl93_726),
% 68.49/10.18 inference(avatar_split_clause,[],[f31021,f31017,f6456,f31023])).
% 68.49/10.18 thf(f31023,plain,(
% 68.49/10.18 spl93_727 <=> ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_727])])).
% 68.49/10.18 thf(f31017,plain,(
% 68.49/10.18 spl93_726 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_726])])).
% 68.49/10.18 thf(f31021,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) ) | (~spl93_345 | ~spl93_726)),
% 68.49/10.18 inference(forward_demodulation,[],[f31020,f6458])).
% 68.49/10.18 thf(f31020,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_726)),
% 68.49/10.18 inference(forward_demodulation,[],[f31018,f6458])).
% 68.49/10.18 thf(f31018,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_726),
% 68.49/10.18 inference(avatar_component_clause,[],[f31017])).
% 68.49/10.18 thf(f31019,plain,(
% 68.49/10.18 spl93_726 | ~spl93_22 | ~spl93_186),
% 68.49/10.18 inference(avatar_split_clause,[],[f3423,f3410,f1832,f31017])).
% 68.49/10.18 thf(f3410,plain,(
% 68.49/10.18 spl93_186 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_186])])).
% 68.49/10.18 thf(f3423,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_186)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3422])).
% 68.49/10.18 thf(f3422,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_186)),
% 68.49/10.18 inference(superposition,[],[f3411,f1833])).
% 68.49/10.18 thf(f3411,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_186),
% 68.49/10.18 inference(avatar_component_clause,[],[f3410])).
% 68.49/10.18 thf(f31015,plain,(
% 68.49/10.18 spl93_725 | ~spl93_22 | ~spl93_185),
% 68.49/10.18 inference(avatar_split_clause,[],[f3416,f3406,f1832,f31013])).
% 68.49/10.18 thf(f31013,plain,(
% 68.49/10.18 spl93_725 <=> ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_725])])).
% 68.49/10.18 thf(f3416,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_185)),
% 68.49/10.18 inference(trivial_inequality_removal,[],[f3415])).
% 68.49/10.18 thf(f3415,plain,(
% 68.49/10.18 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_185)),
% 68.49/10.18 inference(superposition,[],[f3407,f1833])).
% 68.49/10.18 thf(f31011,plain,(
% 68.49/10.18 spl93_724 | ~spl93_22 | ~spl93_181),
% 68.49/10.18 inference(avatar_split_clause,[],[f3376,f3361,f1832,f31009])).
% 68.49/10.18 thf(f31009,plain,(
% 68.49/10.18 spl93_724 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK21(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK22(X0,$o),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK22(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK21(X0,$o),X1))))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_724])])).
% 68.49/10.18 thf(f3361,plain,(
% 68.49/10.18 spl93_181 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)))),
% 68.49/10.18 introduced(avatar_definition,[new_symbols(naming,[spl93_181])])).
% 68.49/10.18 thf(f3376,plain,(
% 68.49/10.18 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK21(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK22(X0,$o),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP4(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK22(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK21(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_181)),
% 68.49/10.18 inference(superposition,[],[f3362,f1833])).
% 68.49/10.18 thf(f3362,plain,(
% 68.49/10.18 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0))) ) | ~spl93_181),
% 68.49/10.18 inference(avatar_component_clause,[],[f3361])).
% 68.49/10.18 thf(f31007,plain,(
% 68.49/10.18 spl93_723 | ~spl93_49 | ~spl93_97),
% 68.49/10.18 inference(avatar_split_clause,[],[f2468,f2436,f2044,f31005])).
% 68.49/10.18 thf(f31005,plain,(
% 68.49/10.18 spl93_723 <=> ! [X0 : $tType,X2 : (X0 > $o) > set(X0),X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),X2,vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),collect(X0)),X2)) != X1) | (collect(X0) = X2) | (vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1) != vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),collect(X0)),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_723])])).
% 68.49/10.19 thf(f2044,plain,(
% 68.49/10.19 spl93_49 <=> ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_49])])).
% 68.49/10.19 thf(f2468,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : (X0 > $o) > set(X0),X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),X2,vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),collect(X0)),X2)) != X1) | (collect(X0) = X2) | (vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1) != vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),collect(X0)),X2))) ) | (~spl93_49 | ~spl93_97)),
% 68.49/10.19 inference(constrained_superposition,[],[f2437,f2045])).
% 68.49/10.19 thf(f2045,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)) ) | ~spl93_49),
% 68.49/10.19 inference(avatar_component_clause,[],[f2044])).
% 68.49/10.19 thf(f31003,plain,(
% 68.49/10.19 spl93_722 | ~spl93_21 | ~spl93_309 | ~spl93_427),
% 68.49/10.19 inference(avatar_split_clause,[],[f13777,f10110,f5028,f1827,f31001])).
% 68.49/10.19 thf(f13777,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X2) != X1) | (X1 = X2)) ) | (~spl93_21 | ~spl93_309 | ~spl93_427)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f13776])).
% 68.49/10.19 thf(f13776,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X2) != X1) | (X1 = X2)) ) | (~spl93_21 | ~spl93_309 | ~spl93_427)),
% 68.49/10.19 inference(forward_demodulation,[],[f13711,f1829])).
% 68.49/10.19 thf(f13711,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0)),X2) != X1) | (group_add(int) != $true) | (X1 = X2)) ) | (~spl93_309 | ~spl93_427)),
% 68.49/10.19 inference(superposition,[],[f5029,f10111])).
% 68.49/10.19 thf(f30999,plain,(
% 68.49/10.19 spl93_721 | ~spl93_49 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2460,f2436,f2044,f30997])).
% 68.49/10.19 thf(f30997,plain,(
% 68.49/10.19 spl93_721 <=> ! [X0 : $tType,X2 : (X0 > $o) > set(X0),X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),X2,vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),X2),collect(X0))) != X1) | (collect(X0) = X2) | (vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1) != vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),X2),collect(X0))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_721])])).
% 68.49/10.19 thf(f2460,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : (X0 > $o) > set(X0),X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),X2,vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),X2),collect(X0))) != X1) | (collect(X0) = X2) | (vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1) != vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o),vAPP(sTfun(sTfun(X0,$o),set(X0)),sTfun(sTfun(sTfun(X0,$o),set(X0)),sTfun(X0,$o)),sK35(set(X0),sTfun(X0,$o)),X2),collect(X0)))) ) | (~spl93_49 | ~spl93_97)),
% 68.49/10.19 inference(constrained_superposition,[],[f2437,f2045])).
% 68.49/10.19 thf(f30993,plain,(
% 68.49/10.19 spl93_720 | ~spl93_66 | ~spl93_189),
% 68.49/10.19 inference(avatar_split_clause,[],[f3468,f3455,f2161,f30991])).
% 68.49/10.19 thf(f30991,plain,(
% 68.49/10.19 spl93_720 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_720])])).
% 68.49/10.19 thf(f3468,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_189)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3463])).
% 68.49/10.19 thf(f3463,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_189)),
% 68.49/10.19 inference(superposition,[],[f3456,f2163])).
% 68.49/10.19 thf(f30958,plain,(
% 68.49/10.19 spl93_719 | ~spl93_345 | ~spl93_718),
% 68.49/10.19 inference(avatar_split_clause,[],[f30954,f30951,f6456,f30956])).
% 68.49/10.19 thf(f30956,plain,(
% 68.49/10.19 spl93_719 <=> ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_719])])).
% 68.49/10.19 thf(f30951,plain,(
% 68.49/10.19 spl93_718 <=> ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_718])])).
% 68.49/10.19 thf(f30954,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | (~spl93_345 | ~spl93_718)),
% 68.49/10.19 inference(forward_demodulation,[],[f30952,f6458])).
% 68.49/10.19 thf(f30952,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_718),
% 68.49/10.19 inference(avatar_component_clause,[],[f30951])).
% 68.49/10.19 thf(f30953,plain,(
% 68.49/10.19 spl93_718 | ~spl93_22 | ~spl93_184),
% 68.49/10.19 inference(avatar_split_clause,[],[f3399,f3392,f1832,f30951])).
% 68.49/10.19 thf(f3399,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_184)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3398])).
% 68.49/10.19 thf(f3398,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_184)),
% 68.49/10.19 inference(superposition,[],[f3393,f1833])).
% 68.49/10.19 thf(f30938,plain,(
% 68.49/10.19 spl93_717 | ~spl93_345 | ~spl93_716),
% 68.49/10.19 inference(avatar_split_clause,[],[f30934,f30931,f6456,f30936])).
% 68.49/10.19 thf(f30936,plain,(
% 68.49/10.19 spl93_717 <=> ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_717])])).
% 68.49/10.19 thf(f30931,plain,(
% 68.49/10.19 spl93_716 <=> ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_716])])).
% 68.49/10.19 thf(f30934,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | (~spl93_345 | ~spl93_716)),
% 68.49/10.19 inference(forward_demodulation,[],[f30932,f6458])).
% 68.49/10.19 thf(f30932,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_716),
% 68.49/10.19 inference(avatar_component_clause,[],[f30931])).
% 68.49/10.19 thf(f30933,plain,(
% 68.49/10.19 spl93_716 | ~spl93_22 | ~spl93_180),
% 68.49/10.19 inference(avatar_split_clause,[],[f3368,f3357,f1832,f30931])).
% 68.49/10.19 thf(f3357,plain,(
% 68.49/10.19 spl93_180 <=> ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_180])])).
% 68.49/10.19 thf(f3368,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_180)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3367])).
% 68.49/10.19 thf(f3367,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_180)),
% 68.49/10.19 inference(superposition,[],[f3358,f1833])).
% 68.49/10.19 thf(f3358,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)))) ) | ~spl93_180),
% 68.49/10.19 inference(avatar_component_clause,[],[f3357])).
% 68.49/10.19 thf(f30836,plain,(
% 68.49/10.19 spl93_715 | ~spl93_345 | ~spl93_713),
% 68.49/10.19 inference(avatar_split_clause,[],[f30828,f30825,f6456,f30834])).
% 68.49/10.19 thf(f30834,plain,(
% 68.49/10.19 spl93_715 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_715])])).
% 68.49/10.19 thf(f30825,plain,(
% 68.49/10.19 spl93_713 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_713])])).
% 68.49/10.19 thf(f30828,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) ) | (~spl93_345 | ~spl93_713)),
% 68.49/10.19 inference(forward_demodulation,[],[f30826,f6458])).
% 68.49/10.19 thf(f30826,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_713),
% 68.49/10.19 inference(avatar_component_clause,[],[f30825])).
% 68.49/10.19 thf(f30832,plain,(
% 68.49/10.19 spl93_714 | ~spl93_317 | ~spl93_427),
% 68.49/10.19 inference(avatar_split_clause,[],[f13702,f10110,f5217,f30830])).
% 68.49/10.19 thf(f30830,plain,(
% 68.49/10.19 spl93_714 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0) = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_714])])).
% 68.49/10.19 thf(f5217,plain,(
% 68.49/10.19 spl93_317 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) != X1) | (X0 = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_317])])).
% 68.49/10.19 thf(f13702,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0) = X2)) ) | (~spl93_317 | ~spl93_427)),
% 68.49/10.19 inference(superposition,[],[f5218,f10111])).
% 68.49/10.19 thf(f5218,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) != X1) | (X0 = X2)) ) | ~spl93_317),
% 68.49/10.19 inference(avatar_component_clause,[],[f5217])).
% 68.49/10.19 thf(f30827,plain,(
% 68.49/10.19 spl93_713 | ~spl93_61 | ~spl93_189),
% 68.49/10.19 inference(avatar_split_clause,[],[f3469,f3455,f2136,f30825])).
% 68.49/10.19 thf(f3469,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_189)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3462])).
% 68.49/10.19 thf(f3462,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_189)),
% 68.49/10.19 inference(superposition,[],[f3456,f2138])).
% 68.49/10.19 thf(f30821,plain,(
% 68.49/10.19 spl93_712 | ~spl93_66 | ~spl93_186),
% 68.49/10.19 inference(avatar_split_clause,[],[f3425,f3410,f2161,f30819])).
% 68.49/10.19 thf(f30819,plain,(
% 68.49/10.19 spl93_712 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_712])])).
% 68.49/10.19 thf(f3425,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_186)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3420])).
% 68.49/10.19 thf(f3420,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_186)),
% 68.49/10.19 inference(superposition,[],[f3411,f2163])).
% 68.49/10.19 thf(f30805,plain,(
% 68.49/10.19 spl93_711 | ~spl93_66 | ~spl93_180 | ~spl93_192),
% 68.49/10.19 inference(avatar_split_clause,[],[f3508,f3483,f3357,f2161,f30803])).
% 68.49/10.19 thf(f30803,plain,(
% 68.49/10.19 spl93_711 <=> ! [X0 : nat] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_711])])).
% 68.49/10.19 thf(f3508,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_180 | ~spl93_192)),
% 68.49/10.19 inference(forward_demodulation,[],[f3504,f3370])).
% 68.49/10.19 thf(f3370,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_180)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3365])).
% 68.49/10.19 thf(f3365,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_180)),
% 68.49/10.19 inference(superposition,[],[f3358,f2163])).
% 68.49/10.19 thf(f3504,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_192)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3499])).
% 68.49/10.19 thf(f3499,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_192)),
% 68.49/10.19 inference(superposition,[],[f3484,f2163])).
% 68.49/10.19 thf(f30800,plain,(
% 68.49/10.19 spl93_710 | ~spl93_66 | ~spl93_180),
% 68.49/10.19 inference(avatar_split_clause,[],[f3370,f3357,f2161,f30798])).
% 68.49/10.19 thf(f30798,plain,(
% 68.49/10.19 spl93_710 <=> ! [X0 : nat] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_710])])).
% 68.49/10.19 thf(f30796,plain,(
% 68.49/10.19 spl93_709 | ~spl93_22 | ~spl93_179),
% 68.49/10.19 inference(avatar_split_clause,[],[f3346,f3329,f1832,f30794])).
% 68.49/10.19 thf(f30794,plain,(
% 68.49/10.19 spl93_709 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0),sK42(X2,X0),X1),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_709])])).
% 68.49/10.19 thf(f3329,plain,(
% 68.49/10.19 spl93_179 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_179])])).
% 68.49/10.19 thf(f3346,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0),sK42(X2,X0),X1),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_179)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3345])).
% 68.49/10.19 thf(f3345,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0),sK42(X2,X0),X1),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_179)),
% 68.49/10.19 inference(superposition,[],[f3330,f1833])).
% 68.49/10.19 thf(f3330,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),X3)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_179),
% 68.49/10.19 inference(avatar_component_clause,[],[f3329])).
% 68.49/10.19 thf(f30791,plain,(
% 68.49/10.19 spl93_708 | ~spl93_22 | ~spl93_177),
% 68.49/10.19 inference(avatar_split_clause,[],[f3336,f3305,f1832,f30789])).
% 68.49/10.19 thf(f30789,plain,(
% 68.49/10.19 spl93_708 <=> ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_708])])).
% 68.49/10.19 thf(f3336,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_177)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3335])).
% 68.49/10.19 thf(f3335,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_177)),
% 68.49/10.19 inference(superposition,[],[f3306,f1833])).
% 68.49/10.19 thf(f30759,plain,(
% 68.49/10.19 spl93_707 | ~spl93_440 | ~spl93_706),
% 68.49/10.19 inference(avatar_split_clause,[],[f30754,f30750,f13821,f30756])).
% 68.49/10.19 thf(f30756,plain,(
% 68.49/10.19 spl93_707 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_707])])).
% 68.49/10.19 thf(f30750,plain,(
% 68.49/10.19 spl93_706 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_706])])).
% 68.49/10.19 thf(f30754,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) | (~spl93_440 | ~spl93_706)),
% 68.49/10.19 inference(forward_demodulation,[],[f30752,f13823])).
% 68.49/10.19 thf(f30752,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) | ~spl93_706),
% 68.49/10.19 inference(avatar_component_clause,[],[f30750])).
% 68.49/10.19 thf(f30753,plain,(
% 68.49/10.19 spl93_706 | ~spl93_116 | ~spl93_138),
% 68.49/10.19 inference(avatar_split_clause,[],[f2828,f2815,f2623,f30750])).
% 68.49/10.19 thf(f2815,plain,(
% 68.49/10.19 spl93_138 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_138])])).
% 68.49/10.19 thf(f2828,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) | (~spl93_116 | ~spl93_138)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2825])).
% 68.49/10.19 thf(f2825,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) | (~spl93_116 | ~spl93_138)),
% 68.49/10.19 inference(superposition,[],[f2816,f2625])).
% 68.49/10.19 thf(f2816,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0)))) ) | ~spl93_138),
% 68.49/10.19 inference(avatar_component_clause,[],[f2815])).
% 68.49/10.19 thf(f30719,plain,(
% 68.49/10.19 spl93_705 | ~spl93_440 | ~spl93_704),
% 68.49/10.19 inference(avatar_split_clause,[],[f30714,f30710,f13821,f30716])).
% 68.49/10.19 thf(f30716,plain,(
% 68.49/10.19 spl93_705 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_705])])).
% 68.49/10.19 thf(f30710,plain,(
% 68.49/10.19 spl93_704 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_704])])).
% 68.49/10.19 thf(f30714,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (~spl93_440 | ~spl93_704)),
% 68.49/10.19 inference(forward_demodulation,[],[f30712,f13823])).
% 68.49/10.19 thf(f30712,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ~spl93_704),
% 68.49/10.19 inference(avatar_component_clause,[],[f30710])).
% 68.49/10.19 thf(f30713,plain,(
% 68.49/10.19 spl93_704 | ~spl93_116 | ~spl93_137),
% 68.49/10.19 inference(avatar_split_clause,[],[f2822,f2811,f2623,f30710])).
% 68.49/10.19 thf(f2811,plain,(
% 68.49/10.19 spl93_137 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_137])])).
% 68.49/10.19 thf(f2822,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_116 | ~spl93_137)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2819])).
% 68.49/10.19 thf(f2819,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_116 | ~spl93_137)),
% 68.49/10.19 inference(superposition,[],[f2812,f2625])).
% 68.49/10.19 thf(f2812,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0))) ) | ~spl93_137),
% 68.49/10.19 inference(avatar_component_clause,[],[f2811])).
% 68.49/10.19 thf(f30614,plain,(
% 68.49/10.19 spl93_703 | ~spl93_345 | ~spl93_702),
% 68.49/10.19 inference(avatar_split_clause,[],[f30610,f30607,f6456,f30612])).
% 68.49/10.19 thf(f30612,plain,(
% 68.49/10.19 spl93_703 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_703])])).
% 68.49/10.19 thf(f30607,plain,(
% 68.49/10.19 spl93_702 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_702])])).
% 68.49/10.19 thf(f30610,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) ) | (~spl93_345 | ~spl93_702)),
% 68.49/10.19 inference(forward_demodulation,[],[f30608,f6458])).
% 68.49/10.19 thf(f30608,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_702),
% 68.49/10.19 inference(avatar_component_clause,[],[f30607])).
% 68.49/10.19 thf(f30609,plain,(
% 68.49/10.19 spl93_702 | ~spl93_61 | ~spl93_186),
% 68.49/10.19 inference(avatar_split_clause,[],[f3426,f3410,f2136,f30607])).
% 68.49/10.19 thf(f3426,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_186)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3419])).
% 68.49/10.19 thf(f3419,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_186)),
% 68.49/10.19 inference(superposition,[],[f3411,f2138])).
% 68.49/10.19 thf(f30356,plain,(
% 68.49/10.19 spl93_701 | ~spl93_22 | ~spl93_178),
% 68.49/10.19 inference(avatar_split_clause,[],[f5955,f3310,f1832,f30354])).
% 68.49/10.19 thf(f30354,plain,(
% 68.49/10.19 spl93_701 <=> ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_701])])).
% 68.49/10.19 thf(f3310,plain,(
% 68.49/10.19 spl93_178 <=> ! [X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_178])])).
% 68.49/10.19 thf(f5955,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_178)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f5954])).
% 68.49/10.19 thf(f5954,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_178)),
% 68.49/10.19 inference(superposition,[],[f3311,f1833])).
% 68.49/10.19 thf(f3311,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0))) ) | ~spl93_178),
% 68.49/10.19 inference(avatar_component_clause,[],[f3310])).
% 68.49/10.19 thf(f30352,plain,(
% 68.49/10.19 spl93_700),
% 68.49/10.19 inference(avatar_split_clause,[],[f1571,f30350])).
% 68.49/10.19 thf(f30350,plain,(
% 68.49/10.19 spl93_700 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != X4))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_700])])).
% 68.49/10.19 thf(f1571,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != X4)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1570])).
% 68.49/10.19 thf(f1570,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1566])).
% 68.49/10.19 thf(f1566,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1413])).
% 68.49/10.19 thf(f1413,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X3) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.19 inference(cnf_transformation,[],[f1011])).
% 68.49/10.19 thf(f1011,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X3) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 inference(flattening,[],[f1010])).
% 68.49/10.19 thf(f1010,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X3) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 inference(ennf_transformation,[],[f597])).
% 68.49/10.19 thf(f597,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X3) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4)))))),
% 68.49/10.19 inference(fool_elimination,[],[f596])).
% 68.49/10.19 thf(f596,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = X3) = (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4)))))),
% 68.49/10.19 inference(rectify,[],[f193])).
% 68.49/10.19 thf(f193,axiom,(
% 68.49/10.19 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X6 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),X6) = X13) = (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = X6)))))),
% 68.49/10.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_group_Ol__cancel__one)).
% 68.49/10.19 thf(f30348,plain,(
% 68.49/10.19 spl93_699),
% 68.49/10.19 inference(avatar_split_clause,[],[f1569,f30346])).
% 68.49/10.19 thf(f30346,plain,(
% 68.49/10.19 spl93_699 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_699])])).
% 68.49/10.19 thf(f1569,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1568])).
% 68.49/10.19 thf(f1568,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1567])).
% 68.49/10.19 thf(f1567,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1413])).
% 68.49/10.19 thf(f30344,plain,(
% 68.49/10.19 spl93_698),
% 68.49/10.19 inference(avatar_split_clause,[],[f1565,f30342])).
% 68.49/10.19 thf(f30342,plain,(
% 68.49/10.19 spl93_698 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) != X3))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_698])])).
% 68.49/10.19 thf(f1565,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) != X3)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1564])).
% 68.49/10.19 thf(f1564,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1560])).
% 68.49/10.19 thf(f1560,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1414])).
% 68.49/10.19 thf(f1414,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.19 inference(cnf_transformation,[],[f1013])).
% 68.49/10.19 thf(f1013,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 inference(flattening,[],[f1012])).
% 68.49/10.19 thf(f1012,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((((vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 inference(ennf_transformation,[],[f599])).
% 68.49/10.19 thf(f599,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4) = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3)))))),
% 68.49/10.19 inference(fool_elimination,[],[f598])).
% 68.49/10.19 thf(f598,plain,(
% 68.49/10.19 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = X3) = (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = X4)))))),
% 68.49/10.19 inference(rectify,[],[f192])).
% 68.49/10.19 thf(f192,axiom,(
% 68.49/10.19 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X6 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X6),X13) = X13) = (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = X6)))))),
% 68.49/10.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_group_Or__cancel__one)).
% 68.49/10.19 thf(f30340,plain,(
% 68.49/10.19 spl93_697),
% 68.49/10.19 inference(avatar_split_clause,[],[f1563,f30338])).
% 68.49/10.19 thf(f30338,plain,(
% 68.49/10.19 spl93_697 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = X3))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_697])])).
% 68.49/10.19 thf(f1563,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3) = X3)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1562])).
% 68.49/10.19 thf(f1562,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1561])).
% 68.49/10.19 thf(f1561,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)),X3))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1414])).
% 68.49/10.19 thf(f30226,plain,(
% 68.49/10.19 spl93_696 | ~spl93_345 | ~spl93_695),
% 68.49/10.19 inference(avatar_split_clause,[],[f30222,f30218,f6456,f30224])).
% 68.49/10.19 thf(f30224,plain,(
% 68.49/10.19 spl93_696 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_696])])).
% 68.49/10.19 thf(f30218,plain,(
% 68.49/10.19 spl93_695 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_695])])).
% 68.49/10.19 thf(f30222,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1)) ) | (~spl93_345 | ~spl93_695)),
% 68.49/10.19 inference(forward_demodulation,[],[f30221,f6458])).
% 68.49/10.19 thf(f30221,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1)) ) | (~spl93_345 | ~spl93_695)),
% 68.49/10.19 inference(forward_demodulation,[],[f30219,f6458])).
% 68.49/10.19 thf(f30219,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1)) ) | ~spl93_695),
% 68.49/10.19 inference(avatar_component_clause,[],[f30218])).
% 68.49/10.19 thf(f30220,plain,(
% 68.49/10.19 spl93_695),
% 68.49/10.19 inference(avatar_split_clause,[],[f1635,f30218])).
% 68.49/10.19 thf(f1635,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1634])).
% 68.49/10.19 thf(f1634,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1630])).
% 68.49/10.19 thf(f1630,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1299])).
% 68.49/10.19 thf(f1299,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.19 inference(cnf_transformation,[],[f877])).
% 68.49/10.19 thf(f877,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 inference(flattening,[],[f876])).
% 68.49/10.19 thf(f876,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : (((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 inference(ennf_transformation,[],[f457])).
% 68.49/10.19 thf(f457,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X0) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))))),
% 68.49/10.19 inference(fool_elimination,[],[f456])).
% 68.49/10.19 thf(f456,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X0) = (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1))))),
% 68.49/10.19 inference(rectify,[],[f52])).
% 68.49/10.19 thf(f52,axiom,(
% 68.49/10.19 ! [X13 : a,X6 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X6) = X13) = (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X6))))),
% 68.49/10.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_add_Ol__cancel__one)).
% 68.49/10.19 thf(f30041,plain,(
% 68.49/10.19 spl93_694 | ~spl93_345 | ~spl93_693),
% 68.49/10.19 inference(avatar_split_clause,[],[f30037,f30033,f6456,f30039])).
% 68.49/10.19 thf(f30039,plain,(
% 68.49/10.19 spl93_694 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_694])])).
% 68.49/10.19 thf(f30033,plain,(
% 68.49/10.19 spl93_693 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_693])])).
% 68.49/10.19 thf(f30037,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1)) ) | (~spl93_345 | ~spl93_693)),
% 68.49/10.19 inference(forward_demodulation,[],[f30036,f6458])).
% 68.49/10.19 thf(f30036,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1)) ) | (~spl93_345 | ~spl93_693)),
% 68.49/10.19 inference(forward_demodulation,[],[f30034,f6458])).
% 68.49/10.19 thf(f30034,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1)) ) | ~spl93_693),
% 68.49/10.19 inference(avatar_component_clause,[],[f30033])).
% 68.49/10.19 thf(f30035,plain,(
% 68.49/10.19 spl93_693),
% 68.49/10.19 inference(avatar_split_clause,[],[f1633,f30033])).
% 68.49/10.19 thf(f1633,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1632])).
% 68.49/10.19 thf(f1632,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1631])).
% 68.49/10.19 thf(f1631,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1299])).
% 68.49/10.19 thf(f29936,plain,(
% 68.49/10.19 spl93_692 | ~spl93_345 | ~spl93_691),
% 68.49/10.19 inference(avatar_split_clause,[],[f29932,f29928,f6456,f29934])).
% 68.49/10.19 thf(f29934,plain,(
% 68.49/10.19 spl93_692 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_692])])).
% 68.49/10.19 thf(f29928,plain,(
% 68.49/10.19 spl93_691 <=> ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_691])])).
% 68.49/10.19 thf(f29932,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X0)) ) | (~spl93_345 | ~spl93_691)),
% 68.49/10.19 inference(forward_demodulation,[],[f29931,f6458])).
% 68.49/10.19 thf(f29931,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X0)) ) | (~spl93_345 | ~spl93_691)),
% 68.49/10.19 inference(forward_demodulation,[],[f29929,f6458])).
% 68.49/10.19 thf(f29929,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X0)) ) | ~spl93_691),
% 68.49/10.19 inference(avatar_component_clause,[],[f29928])).
% 68.49/10.19 thf(f29930,plain,(
% 68.49/10.19 spl93_691),
% 68.49/10.19 inference(avatar_split_clause,[],[f1623,f29928])).
% 68.49/10.19 thf(f1623,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) != X0)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1622])).
% 68.49/10.19 thf(f1622,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1618])).
% 68.49/10.19 thf(f1618,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1301])).
% 68.49/10.19 thf(f1301,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.19 inference(cnf_transformation,[],[f881])).
% 68.49/10.19 thf(f881,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 inference(flattening,[],[f880])).
% 68.49/10.19 thf(f880,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : (((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 inference(ennf_transformation,[],[f461])).
% 68.49/10.19 thf(f461,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0))))),
% 68.49/10.19 inference(fool_elimination,[],[f460])).
% 68.49/10.19 thf(f460,plain,(
% 68.49/10.19 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0) = (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X1))))),
% 68.49/10.19 inference(rectify,[],[f50])).
% 68.49/10.19 thf(f50,axiom,(
% 68.49/10.19 ! [X13 : a,X6 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X6),X13) = X13) = (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X6))))),
% 68.49/10.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_add_Or__cancel__one)).
% 68.49/10.19 thf(f29825,plain,(
% 68.49/10.19 spl93_690 | ~spl93_345 | ~spl93_689),
% 68.49/10.19 inference(avatar_split_clause,[],[f29821,f29817,f6456,f29823])).
% 68.49/10.19 thf(f29823,plain,(
% 68.49/10.19 spl93_690 <=> ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_690])])).
% 68.49/10.19 thf(f29817,plain,(
% 68.49/10.19 spl93_689 <=> ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_689])])).
% 68.49/10.19 thf(f29821,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0)) ) | (~spl93_345 | ~spl93_689)),
% 68.49/10.19 inference(forward_demodulation,[],[f29820,f6458])).
% 68.49/10.19 thf(f29820,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0)) ) | (~spl93_345 | ~spl93_689)),
% 68.49/10.19 inference(forward_demodulation,[],[f29818,f6458])).
% 68.49/10.19 thf(f29818,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0)) ) | ~spl93_689),
% 68.49/10.19 inference(avatar_component_clause,[],[f29817])).
% 68.49/10.19 thf(f29819,plain,(
% 68.49/10.19 spl93_689),
% 68.49/10.19 inference(avatar_split_clause,[],[f1621,f29817])).
% 68.49/10.19 thf(f1621,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0) = X0)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1620])).
% 68.49/10.19 thf(f1620,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1619])).
% 68.49/10.19 thf(f1619,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)),X0))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1301])).
% 68.49/10.19 thf(f29564,plain,(
% 68.49/10.19 spl93_688 | ~spl93_22 | ~spl93_176),
% 68.49/10.19 inference(avatar_split_clause,[],[f3302,f3293,f1832,f29562])).
% 68.49/10.19 thf(f29562,plain,(
% 68.49/10.19 spl93_688 <=> ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (group_add(X0) = $false))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_688])])).
% 68.49/10.19 thf(f3293,plain,(
% 68.49/10.19 spl93_176 <=> ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (group_add(X0) != $true))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_176])])).
% 68.49/10.19 thf(f3302,plain,(
% 68.49/10.19 ( ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_176)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3301])).
% 68.49/10.19 thf(f3301,plain,(
% 68.49/10.19 ( ! [X0 : $tType] : (($true != $true) | (minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_176)),
% 68.49/10.19 inference(superposition,[],[f3294,f1833])).
% 68.49/10.19 thf(f3294,plain,(
% 68.49/10.19 ( ! [X0 : $tType] : ((group_add(X0) != $true) | (minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0)))) ) | ~spl93_176),
% 68.49/10.19 inference(avatar_component_clause,[],[f3293])).
% 68.49/10.19 thf(f29560,plain,(
% 68.49/10.19 spl93_687 | ~spl93_22 | ~spl93_175),
% 68.49/10.19 inference(avatar_split_clause,[],[f3298,f3289,f1832,f29558])).
% 68.49/10.19 thf(f29558,plain,(
% 68.49/10.19 spl93_687 <=> ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (ab_group_add(X0) = $false))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_687])])).
% 68.49/10.19 thf(f3289,plain,(
% 68.49/10.19 spl93_175 <=> ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (ab_group_add(X0) != $true))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_175])])).
% 68.49/10.19 thf(f3298,plain,(
% 68.49/10.19 ( ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_175)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3297])).
% 68.49/10.19 thf(f3297,plain,(
% 68.49/10.19 ( ! [X0 : $tType] : (($true != $true) | (minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_175)),
% 68.49/10.19 inference(superposition,[],[f3290,f1833])).
% 68.49/10.19 thf(f3290,plain,(
% 68.49/10.19 ( ! [X0 : $tType] : ((ab_group_add(X0) != $true) | (minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0)))) ) | ~spl93_175),
% 68.49/10.19 inference(avatar_component_clause,[],[f3289])).
% 68.49/10.19 thf(f29556,plain,(
% 68.49/10.19 spl93_686 | ~spl93_48 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3228,f3201,f2031,f29554])).
% 68.49/10.19 thf(f29554,plain,(
% 68.49/10.19 spl93_686 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X5 : product_prod(X3,product_prod(X1,X0)),X4 : product_prod(X3,product_prod(X1,X0)) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X3,sK46(X0,X1,X3),X4)),X2))) | ($true = vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,X5)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X3),X4)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X3),X4)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_686])])).
% 68.49/10.19 thf(f3228,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X4 : product_prod(X3,product_prod(X1,X0)) > $o,X5 : product_prod(X3,product_prod(X1,X0))] : (($true != vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X3,sK46(X0,X1,X3),X4)),X2))) | ($true = vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,X5)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X3),X4)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X3),X4))) ) | (~spl93_48 | ~spl93_170)),
% 68.49/10.19 inference(constrained_superposition,[],[f3202,f2032])).
% 68.49/10.19 thf(f29552,plain,(
% 68.49/10.19 spl93_685 | ~spl93_47 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3227,f3201,f2027,f29550])).
% 68.49/10.19 thf(f29550,plain,(
% 68.49/10.19 spl93_685 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X5 : product_prod(X3,product_prod(X1,X0)),X4 : product_prod(X3,product_prod(X1,X0)) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X3,sK46(X0,X1,X3),X4)),X2))) | ($true = vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,X5)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X3),X4)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X3),X4)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_685])])).
% 68.49/10.19 thf(f3227,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X4 : product_prod(X3,product_prod(X1,X0)) > $o,X5 : product_prod(X3,product_prod(X1,X0))] : (($true != vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X3,sK46(X0,X1,X3),X4)),X2))) | ($true = vAPP(product_prod(X3,product_prod(X1,X0)),$o,X4,X5)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X3),X4)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X3,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X3),X4))) ) | (~spl93_47 | ~spl93_170)),
% 68.49/10.19 inference(constrained_superposition,[],[f3202,f2028])).
% 68.49/10.19 thf(f29548,plain,(
% 68.49/10.19 spl93_684 | ~spl93_50),
% 68.49/10.19 inference(avatar_split_clause,[],[f2052,f2048,f29546])).
% 68.49/10.19 thf(f29546,plain,(
% 68.49/10.19 spl93_684 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = vAPP(sTfun(nat,$o),nat,sK30,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_684])])).
% 68.49/10.19 thf(f2048,plain,(
% 68.49/10.19 spl93_50 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0))) | ($true != vAPP(nat,$o,X0,X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_50])])).
% 68.49/10.19 thf(f2052,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))),X0)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = vAPP(sTfun(nat,$o),nat,sK30,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)))))) ) | ~spl93_50),
% 68.49/10.19 inference(leibniz_equality_elimination,[],[f2049])).
% 68.49/10.19 thf(f2049,plain,(
% 68.49/10.19 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,X0,X1))) ) | ~spl93_50),
% 68.49/10.19 inference(avatar_component_clause,[],[f2048])).
% 68.49/10.19 thf(f29543,plain,(
% 68.49/10.19 spl93_683 | ~spl93_21 | ~spl93_66 | ~spl93_85 | ~spl93_86 | ~spl93_116 | ~spl93_177 | ~spl93_178 | ~spl93_191 | ~spl93_216 | ~spl93_276 | ~spl93_300 | ~spl93_301 | ~spl93_333),
% 68.49/10.19 inference(avatar_split_clause,[],[f5960,f5865,f4916,f4912,f4534,f3748,f3479,f3310,f3305,f2623,f2306,f2302,f2161,f1827,f29541])).
% 68.49/10.19 thf(f29541,plain,(
% 68.49/10.19 spl93_683 <=> ! [X0 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_683])])).
% 68.49/10.19 thf(f2302,plain,(
% 68.49/10.19 spl93_85 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | (group_add(X0) != $true))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_85])])).
% 68.49/10.19 thf(f2306,plain,(
% 68.49/10.19 spl93_86 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) != $true))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_86])])).
% 68.49/10.19 thf(f4912,plain,(
% 68.49/10.19 spl93_300 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,uminus_uminus(int),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_300])])).
% 68.49/10.19 thf(f5865,plain,(
% 68.49/10.19 spl93_333 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_333])])).
% 68.49/10.19 thf(f5960,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_21 | ~spl93_66 | ~spl93_85 | ~spl93_86 | ~spl93_116 | ~spl93_177 | ~spl93_178 | ~spl93_191 | ~spl93_216 | ~spl93_276 | ~spl93_300 | ~spl93_301 | ~spl93_333)),
% 68.49/10.19 inference(forward_demodulation,[],[f5959,f3496])).
% 68.49/10.19 thf(f3496,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_177 | ~spl93_191)),
% 68.49/10.19 inference(forward_demodulation,[],[f3492,f3338])).
% 68.49/10.19 thf(f3492,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_191)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3487])).
% 68.49/10.19 thf(f3487,plain,(
% 68.49/10.19 ( ! [X0 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_66 | ~spl93_191)),
% 68.49/10.19 inference(superposition,[],[f3480,f2163])).
% 68.49/10.19 thf(f5959,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))))) ) | (~spl93_21 | ~spl93_66 | ~spl93_85 | ~spl93_86 | ~spl93_116 | ~spl93_177 | ~spl93_178 | ~spl93_191 | ~spl93_216 | ~spl93_276 | ~spl93_300 | ~spl93_301 | ~spl93_333)),
% 68.49/10.19 inference(forward_demodulation,[],[f5958,f5895])).
% 68.49/10.19 thf(f5895,plain,(
% 68.49/10.19 ( ! [X1 : int] : ((vAPP(int,int,uminus_uminus(int),vAPP(int,int,uminus_uminus(int),X1)) = X1)) ) | (~spl93_21 | ~spl93_85 | ~spl93_86 | ~spl93_216 | ~spl93_276 | ~spl93_300 | ~spl93_301 | ~spl93_333)),
% 68.49/10.19 inference(forward_demodulation,[],[f5894,f4967])).
% 68.49/10.19 thf(f4967,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,uminus_uminus(int),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)))) ) | (~spl93_216 | ~spl93_301)),
% 68.49/10.19 inference(superposition,[],[f4917,f3749])).
% 68.49/10.19 thf(f5894,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0))) = X1)) ) | (~spl93_21 | ~spl93_85 | ~spl93_86 | ~spl93_276 | ~spl93_300 | ~spl93_333)),
% 68.49/10.19 inference(forward_demodulation,[],[f5893,f4913])).
% 68.49/10.19 thf(f4913,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,uminus_uminus(int),X1)))) ) | ~spl93_300),
% 68.49/10.19 inference(avatar_component_clause,[],[f4912])).
% 68.49/10.19 thf(f5893,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),vAPP(int,int,uminus_uminus(int),X0)))) = X1)) ) | (~spl93_21 | ~spl93_85 | ~spl93_86 | ~spl93_276 | ~spl93_333)),
% 68.49/10.19 inference(forward_demodulation,[],[f5874,f2383])).
% 68.49/10.19 thf(f2383,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)))) ) | (~spl93_21 | ~spl93_85 | ~spl93_86)),
% 68.49/10.19 inference(forward_demodulation,[],[f2382,f2378])).
% 68.49/10.19 thf(f2378,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))) ) | (~spl93_21 | ~spl93_85)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2375])).
% 68.49/10.19 thf(f2375,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))) ) | (~spl93_21 | ~spl93_85)),
% 68.49/10.19 inference(superposition,[],[f2303,f1829])).
% 68.49/10.19 thf(f2303,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)))) ) | ~spl93_85),
% 68.49/10.19 inference(avatar_component_clause,[],[f2302])).
% 68.49/10.19 thf(f2382,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)))) ) | (~spl93_21 | ~spl93_86)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2379])).
% 68.49/10.19 thf(f2379,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)))) ) | (~spl93_21 | ~spl93_86)),
% 68.49/10.19 inference(superposition,[],[f2307,f1829])).
% 68.49/10.19 thf(f2307,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3))) ) | ~spl93_86),
% 68.49/10.19 inference(avatar_component_clause,[],[f2306])).
% 68.49/10.19 thf(f5874,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1))) = X1)) ) | (~spl93_276 | ~spl93_333)),
% 68.49/10.19 inference(superposition,[],[f5866,f4535])).
% 68.49/10.19 thf(f5866,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)))) ) | ~spl93_333),
% 68.49/10.19 inference(avatar_component_clause,[],[f5865])).
% 68.49/10.19 thf(f5958,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(int,int,uminus_uminus(int),X0))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) ) | (~spl93_66 | ~spl93_116 | ~spl93_177 | ~spl93_178 | ~spl93_191)),
% 68.49/10.19 inference(forward_demodulation,[],[f5956,f3496])).
% 68.49/10.19 thf(f5956,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_116 | ~spl93_178)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f5953])).
% 68.49/10.19 thf(f5953,plain,(
% 68.49/10.19 ( ! [X0 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))) ) | (~spl93_116 | ~spl93_178)),
% 68.49/10.19 inference(superposition,[],[f3311,f2625])).
% 68.49/10.19 thf(f29536,plain,(
% 68.49/10.19 spl93_682 | ~spl93_66 | ~spl93_194),
% 68.49/10.19 inference(avatar_split_clause,[],[f3525,f3516,f2161,f29534])).
% 68.49/10.19 thf(f29534,plain,(
% 68.49/10.19 spl93_682 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_682])])).
% 68.49/10.19 thf(f3525,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_194)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3520])).
% 68.49/10.19 thf(f3520,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_194)),
% 68.49/10.19 inference(superposition,[],[f3517,f2163])).
% 68.49/10.19 thf(f29530,plain,(
% 68.49/10.19 spl93_681 | ~spl93_66 | ~spl93_177 | ~spl93_191),
% 68.49/10.19 inference(avatar_split_clause,[],[f3496,f3479,f3305,f2161,f29528])).
% 68.49/10.19 thf(f29528,plain,(
% 68.49/10.19 spl93_681 <=> ! [X0 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_681])])).
% 68.49/10.19 thf(f29525,plain,(
% 68.49/10.19 spl93_680 | ~spl93_66 | ~spl93_177),
% 68.49/10.19 inference(avatar_split_clause,[],[f3338,f3305,f2161,f29523])).
% 68.49/10.19 thf(f29523,plain,(
% 68.49/10.19 spl93_680 <=> ! [X0 : int] : (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_680])])).
% 68.49/10.19 thf(f29499,plain,(
% 68.49/10.19 spl93_679 | ~spl93_22 | ~spl93_174),
% 68.49/10.19 inference(avatar_split_clause,[],[f3283,f3267,f1832,f29497])).
% 68.49/10.19 thf(f29497,plain,(
% 68.49/10.19 spl93_679 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_679])])).
% 68.49/10.19 thf(f3267,plain,(
% 68.49/10.19 spl93_174 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_174])])).
% 68.49/10.19 thf(f3283,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_174)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3282])).
% 68.49/10.19 thf(f3282,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_174)),
% 68.49/10.19 inference(superposition,[],[f3268,f1833])).
% 68.49/10.19 thf(f3268,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_174),
% 68.49/10.19 inference(avatar_component_clause,[],[f3267])).
% 68.49/10.19 thf(f29495,plain,(
% 68.49/10.19 spl93_678 | ~spl93_22 | ~spl93_173),
% 68.49/10.19 inference(avatar_split_clause,[],[f3274,f3263,f1832,f29493])).
% 68.49/10.19 thf(f29493,plain,(
% 68.49/10.19 spl93_678 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_678])])).
% 68.49/10.19 thf(f3263,plain,(
% 68.49/10.19 spl93_173 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_173])])).
% 68.49/10.19 thf(f3274,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_173)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3273])).
% 68.49/10.19 thf(f3273,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_173)),
% 68.49/10.19 inference(superposition,[],[f3264,f1833])).
% 68.49/10.19 thf(f3264,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_173),
% 68.49/10.19 inference(avatar_component_clause,[],[f3263])).
% 68.49/10.19 thf(f29244,plain,(
% 68.49/10.19 spl93_677 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_278 | ~spl93_283),
% 68.49/10.19 inference(avatar_split_clause,[],[f6104,f4629,f4557,f2247,f2243,f2074,f1873,f29242])).
% 68.49/10.19 thf(f29242,plain,(
% 68.49/10.19 spl93_677 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_677])])).
% 68.49/10.19 thf(f4629,plain,(
% 68.49/10.19 spl93_283 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_283])])).
% 68.49/10.19 thf(f6104,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_278 | ~spl93_283)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f6103])).
% 68.49/10.19 thf(f6103,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_278 | ~spl93_283)),
% 68.49/10.19 inference(forward_demodulation,[],[f6102,f1875])).
% 68.49/10.19 thf(f6102,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_278 | ~spl93_283)),
% 68.49/10.19 inference(forward_demodulation,[],[f6101,f5934])).
% 68.49/10.19 thf(f6101,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_278 | ~spl93_283)),
% 68.49/10.19 inference(forward_demodulation,[],[f4643,f5934])).
% 68.49/10.19 thf(f4643,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_278 | ~spl93_283)),
% 68.49/10.19 inference(forward_demodulation,[],[f4637,f4558])).
% 68.49/10.19 thf(f4637,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_283)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f4634])).
% 68.49/10.19 thf(f4634,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_283)),
% 68.49/10.19 inference(superposition,[],[f4630,f2245])).
% 68.49/10.19 thf(f4630,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_283),
% 68.49/10.19 inference(avatar_component_clause,[],[f4629])).
% 68.49/10.19 thf(f29238,plain,(
% 68.49/10.19 spl93_676 | ~spl93_61 | ~spl93_194),
% 68.49/10.19 inference(avatar_split_clause,[],[f3526,f3516,f2136,f29236])).
% 68.49/10.19 thf(f29236,plain,(
% 68.49/10.19 spl93_676 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_676])])).
% 68.49/10.19 thf(f3526,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_194)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3519])).
% 68.49/10.19 thf(f3519,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_194)),
% 68.49/10.19 inference(superposition,[],[f3517,f2138])).
% 68.49/10.19 thf(f29231,plain,(
% 68.49/10.19 spl93_675 | ~spl93_66 | ~spl93_190),
% 68.49/10.19 inference(avatar_split_clause,[],[f3476,f3459,f2161,f29229])).
% 68.49/10.19 thf(f29229,plain,(
% 68.49/10.19 spl93_675 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_675])])).
% 68.49/10.19 thf(f3476,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_190)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3471])).
% 68.49/10.19 thf(f3471,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_190)),
% 68.49/10.19 inference(superposition,[],[f3460,f2163])).
% 68.49/10.19 thf(f29227,plain,(
% 68.49/10.19 spl93_674 | ~spl93_22 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3226,f3201,f1832,f29225])).
% 68.49/10.19 thf(f29225,plain,(
% 68.49/10.19 spl93_674 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,$o)),X2 : product_prod(X0,product_prod(X1,$o)) > $o] : (($true != vAPP(product_prod(X0,product_prod(X1,$o)),$o,X2,vAPP(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o)),vAPP(X0,sTfun(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o))),product_Pair(X0,product_prod(X1,$o)),vAPP(sTfun(product_prod(X0,product_prod(X1,$o)),$o),X0,sK46($o,X1,X0),X2)),vAPP($o,product_prod(X1,$o),vAPP(X1,sTfun($o,product_prod(X1,$o)),product_Pair(X1,$o),vAPP(sTfun(product_prod(X0,product_prod(X1,$o)),$o),X1,sK47($o,X1,X0),X2)),$true)))) | ($true = vAPP(product_prod(X0,product_prod(X1,$o)),$o,X2,X3)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,$o)),$o),$o,sK48($o,X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_674])])).
% 68.49/10.19 thf(f3226,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,product_prod(X1,$o)) > $o,X3 : product_prod(X0,product_prod(X1,$o))] : (($true != vAPP(product_prod(X0,product_prod(X1,$o)),$o,X2,vAPP(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o)),vAPP(X0,sTfun(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o))),product_Pair(X0,product_prod(X1,$o)),vAPP(sTfun(product_prod(X0,product_prod(X1,$o)),$o),X0,sK46($o,X1,X0),X2)),vAPP($o,product_prod(X1,$o),vAPP(X1,sTfun($o,product_prod(X1,$o)),product_Pair(X1,$o),vAPP(sTfun(product_prod(X0,product_prod(X1,$o)),$o),X1,sK47($o,X1,X0),X2)),$true)))) | ($true = vAPP(product_prod(X0,product_prod(X1,$o)),$o,X2,X3)) | ($false = vAPP(sTfun(product_prod(X0,product_prod(X1,$o)),$o),$o,sK48($o,X1,X0),X2))) ) | (~spl93_22 | ~spl93_170)),
% 68.49/10.19 inference(superposition,[],[f3202,f1833])).
% 68.49/10.19 thf(f29223,plain,(
% 68.49/10.19 spl93_673 | ~spl93_22 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3225,f3201,f1832,f29221])).
% 68.49/10.19 thf(f29221,plain,(
% 68.49/10.19 spl93_673 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod($o,X1)),X2 : product_prod(X0,product_prod($o,X1)) > $o] : (($true != vAPP(product_prod(X0,product_prod($o,X1)),$o,X2,vAPP(product_prod($o,X1),product_prod(X0,product_prod($o,X1)),vAPP(X0,sTfun(product_prod($o,X1),product_prod(X0,product_prod($o,X1))),product_Pair(X0,product_prod($o,X1)),vAPP(sTfun(product_prod(X0,product_prod($o,X1)),$o),X0,sK46(X1,$o,X0),X2)),vAPP(X1,product_prod($o,X1),vAPP($o,sTfun(X1,product_prod($o,X1)),product_Pair($o,X1),$true),vAPP(sTfun(product_prod(X0,product_prod($o,X1)),$o),X1,sK48(X1,$o,X0),X2))))) | ($true = vAPP(product_prod(X0,product_prod($o,X1)),$o,X2,X3)) | ($false = vAPP(sTfun(product_prod(X0,product_prod($o,X1)),$o),$o,sK47(X1,$o,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_673])])).
% 68.49/10.19 thf(f3225,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,product_prod($o,X1)) > $o,X3 : product_prod(X0,product_prod($o,X1))] : (($true != vAPP(product_prod(X0,product_prod($o,X1)),$o,X2,vAPP(product_prod($o,X1),product_prod(X0,product_prod($o,X1)),vAPP(X0,sTfun(product_prod($o,X1),product_prod(X0,product_prod($o,X1))),product_Pair(X0,product_prod($o,X1)),vAPP(sTfun(product_prod(X0,product_prod($o,X1)),$o),X0,sK46(X1,$o,X0),X2)),vAPP(X1,product_prod($o,X1),vAPP($o,sTfun(X1,product_prod($o,X1)),product_Pair($o,X1),$true),vAPP(sTfun(product_prod(X0,product_prod($o,X1)),$o),X1,sK48(X1,$o,X0),X2))))) | ($true = vAPP(product_prod(X0,product_prod($o,X1)),$o,X2,X3)) | ($false = vAPP(sTfun(product_prod(X0,product_prod($o,X1)),$o),$o,sK47(X1,$o,X0),X2))) ) | (~spl93_22 | ~spl93_170)),
% 68.49/10.19 inference(superposition,[],[f3202,f1833])).
% 68.49/10.19 thf(f29219,plain,(
% 68.49/10.19 spl93_672 | ~spl93_22 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3224,f3201,f1832,f29217])).
% 68.49/10.19 thf(f29217,plain,(
% 68.49/10.19 spl93_672 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod($o,product_prod(X0,X1)),X2 : product_prod($o,product_prod(X0,X1)) > $o] : (($true != vAPP(product_prod($o,product_prod(X0,X1)),$o,X2,vAPP(product_prod(X0,X1),product_prod($o,product_prod(X0,X1)),vAPP($o,sTfun(product_prod(X0,X1),product_prod($o,product_prod(X0,X1))),product_Pair($o,product_prod(X0,X1)),$true),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod($o,product_prod(X0,X1)),$o),X0,sK47(X1,X0,$o),X2)),vAPP(sTfun(product_prod($o,product_prod(X0,X1)),$o),X1,sK48(X1,X0,$o),X2))))) | ($true = vAPP(product_prod($o,product_prod(X0,X1)),$o,X2,X3)) | ($false = vAPP(sTfun(product_prod($o,product_prod(X0,X1)),$o),$o,sK46(X1,X0,$o),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_672])])).
% 68.49/10.19 thf(f3224,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod($o,product_prod(X0,X1)) > $o,X3 : product_prod($o,product_prod(X0,X1))] : (($true != vAPP(product_prod($o,product_prod(X0,X1)),$o,X2,vAPP(product_prod(X0,X1),product_prod($o,product_prod(X0,X1)),vAPP($o,sTfun(product_prod(X0,X1),product_prod($o,product_prod(X0,X1))),product_Pair($o,product_prod(X0,X1)),$true),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod($o,product_prod(X0,X1)),$o),X0,sK47(X1,X0,$o),X2)),vAPP(sTfun(product_prod($o,product_prod(X0,X1)),$o),X1,sK48(X1,X0,$o),X2))))) | ($true = vAPP(product_prod($o,product_prod(X0,X1)),$o,X2,X3)) | ($false = vAPP(sTfun(product_prod($o,product_prod(X0,X1)),$o),$o,sK46(X1,X0,$o),X2))) ) | (~spl93_22 | ~spl93_170)),
% 68.49/10.19 inference(superposition,[],[f3202,f1833])).
% 68.49/10.19 thf(f29193,plain,(
% 68.49/10.19 spl93_671 | ~spl93_20 | ~spl93_175),
% 68.49/10.19 inference(avatar_split_clause,[],[f3299,f3289,f1822,f29190])).
% 68.49/10.19 thf(f29190,plain,(
% 68.49/10.19 spl93_671 <=> (minus_minus(int) = vAPP(sTfun(int,int),sTfun(int,sTfun(int,int)),vAPP(sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,int),sTfun(int,sTfun(int,int))),cCOMB,vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),vAPP(sTfun(sTfun(int,int),sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int)))),bCOMB,bCOMB),plus_plus(int))),uminus_uminus(int)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_671])])).
% 68.49/10.19 thf(f3299,plain,(
% 68.49/10.19 (minus_minus(int) = vAPP(sTfun(int,int),sTfun(int,sTfun(int,int)),vAPP(sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,int),sTfun(int,sTfun(int,int))),cCOMB,vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),vAPP(sTfun(sTfun(int,int),sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int)))),bCOMB,bCOMB),plus_plus(int))),uminus_uminus(int))) | (~spl93_20 | ~spl93_175)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3296])).
% 68.49/10.19 thf(f3296,plain,(
% 68.49/10.19 ($true != $true) | (minus_minus(int) = vAPP(sTfun(int,int),sTfun(int,sTfun(int,int)),vAPP(sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,int),sTfun(int,sTfun(int,int))),cCOMB,vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int))),vAPP(sTfun(sTfun(int,int),sTfun(sTfun(int,int),sTfun(int,int))),sTfun(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(sTfun(int,int),sTfun(int,int)))),bCOMB,bCOMB),plus_plus(int))),uminus_uminus(int))) | (~spl93_20 | ~spl93_175)),
% 68.49/10.19 inference(superposition,[],[f3290,f1824])).
% 68.49/10.19 thf(f29188,plain,(
% 68.49/10.19 spl93_670 | ~spl93_22 | ~spl93_171),
% 68.49/10.19 inference(avatar_split_clause,[],[f3243,f3236,f1832,f29186])).
% 68.49/10.19 thf(f29186,plain,(
% 68.49/10.19 spl93_670 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0),sK42(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_670])])).
% 68.49/10.19 thf(f3236,plain,(
% 68.49/10.19 spl93_171 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_171])])).
% 68.49/10.19 thf(f3243,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0),sK42(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_171)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3242])).
% 68.49/10.19 thf(f3242,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0),sK42(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_171)),
% 68.49/10.19 inference(superposition,[],[f3237,f1833])).
% 68.49/10.19 thf(f3237,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_171),
% 68.49/10.19 inference(avatar_component_clause,[],[f3236])).
% 68.49/10.19 thf(f28938,plain,(
% 68.49/10.19 spl93_669 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_214),
% 68.49/10.19 inference(avatar_split_clause,[],[f6213,f3709,f2247,f2243,f2074,f1873,f28936])).
% 68.49/10.19 thf(f28936,plain,(
% 68.49/10.19 spl93_669 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_669])])).
% 68.49/10.19 thf(f6213,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_214)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f6212])).
% 68.49/10.19 thf(f6212,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_214)),
% 68.49/10.19 inference(forward_demodulation,[],[f6211,f1875])).
% 68.49/10.19 thf(f6211,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_214)),
% 68.49/10.19 inference(forward_demodulation,[],[f3756,f5934])).
% 68.49/10.19 thf(f3756,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_214)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3753])).
% 68.49/10.19 thf(f3753,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_214)),
% 68.49/10.19 inference(superposition,[],[f3710,f2245])).
% 68.49/10.19 thf(f28934,plain,(
% 68.49/10.19 spl93_668 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_215),
% 68.49/10.19 inference(avatar_split_clause,[],[f6209,f3713,f2247,f2243,f2074,f1873,f28932])).
% 68.49/10.19 thf(f28932,plain,(
% 68.49/10.19 spl93_668 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_668])])).
% 68.49/10.19 thf(f6209,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_215)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f6208])).
% 68.49/10.19 thf(f6208,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_215)),
% 68.49/10.19 inference(forward_demodulation,[],[f6207,f1875])).
% 68.49/10.19 thf(f6207,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_215)),
% 68.49/10.19 inference(forward_demodulation,[],[f3764,f5934])).
% 68.49/10.19 thf(f3764,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_215)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3761])).
% 68.49/10.19 thf(f3761,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_215)),
% 68.49/10.19 inference(superposition,[],[f3714,f2245])).
% 68.49/10.19 thf(f28928,plain,(
% 68.49/10.19 spl93_667 | ~spl93_61 | ~spl93_190),
% 68.49/10.19 inference(avatar_split_clause,[],[f3477,f3459,f2136,f28926])).
% 68.49/10.19 thf(f28926,plain,(
% 68.49/10.19 spl93_667 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_667])])).
% 68.49/10.19 thf(f3477,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_190)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3470])).
% 68.49/10.19 thf(f3470,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_61 | ~spl93_190)),
% 68.49/10.19 inference(superposition,[],[f3460,f2138])).
% 68.49/10.19 thf(f28923,plain,(
% 68.49/10.19 spl93_666 | ~spl93_62 | ~spl93_185),
% 68.49/10.19 inference(avatar_split_clause,[],[f3418,f3406,f2141,f28921])).
% 68.49/10.19 thf(f28921,plain,(
% 68.49/10.19 spl93_666 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_666])])).
% 68.49/10.19 thf(f2141,plain,(
% 68.49/10.19 spl93_62 <=> (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_62])])).
% 68.49/10.19 thf(f3418,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_62 | ~spl93_185)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3413])).
% 68.49/10.19 thf(f3413,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_62 | ~spl93_185)),
% 68.49/10.19 inference(superposition,[],[f3407,f2143])).
% 68.49/10.19 thf(f2143,plain,(
% 68.49/10.19 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true) | ~spl93_62),
% 68.49/10.19 inference(avatar_component_clause,[],[f2141])).
% 68.49/10.19 thf(f28616,plain,(
% 68.49/10.19 spl93_665 | ~spl93_22 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3232,f3201,f1832,f28614])).
% 68.49/10.19 thf(f28614,plain,(
% 68.49/10.19 spl93_665 <=> ! [X1 : $tType,X2 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,X2)),X3 : product_prod(X0,product_prod(X1,X2)) > $o] : (($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,X3,X4)) | ($false = vAPP(product_prod(X0,product_prod(X1,X2)),$o,X3,vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),X3))))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_665])])).
% 68.49/10.19 thf(f3232,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2)) > $o,X4 : product_prod(X0,product_prod(X1,X2))] : (($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,X3,X4)) | ($false = vAPP(product_prod(X0,product_prod(X1,X2)),$o,X3,vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),X3)))))) ) | (~spl93_22 | ~spl93_170)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3230])).
% 68.49/10.19 thf(f3230,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2)) > $o,X4 : product_prod(X0,product_prod(X1,X2))] : (($true != $true) | ($true = vAPP(product_prod(X0,product_prod(X1,X2)),$o,X3,X4)) | ($false = vAPP(product_prod(X0,product_prod(X1,X2)),$o,X3,vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X0,sK46(X2,X1,X0),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X1,sK47(X2,X1,X0),X3)),vAPP(sTfun(product_prod(X0,product_prod(X1,X2)),$o),X2,sK48(X2,X1,X0),X3)))))) ) | (~spl93_22 | ~spl93_170)),
% 68.49/10.19 inference(superposition,[],[f3202,f1833])).
% 68.49/10.19 thf(f28612,plain,(
% 68.49/10.19 spl93_664 | ~spl93_139 | ~spl93_170),
% 68.49/10.19 inference(avatar_split_clause,[],[f3229,f3201,f2831,f28610])).
% 68.49/10.19 thf(f28610,plain,(
% 68.49/10.19 spl93_664 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X2,product_prod(X0,X1)) > $o,X3 : product_prod(X2,product_prod(X0,X1)),X5 : product_prod(X2,product_prod(X0,X1))] : (($true != vAPP(product_prod(X2,product_prod(X0,X1)),$o,X4,X3)) | ($true = vAPP(product_prod(X2,product_prod(X0,X1)),$o,X4,X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X1,sK48(X1,X0,X2),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X0,sK47(X1,X0,X2),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X2,sK46(X1,X0,X2),X4)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_664])])).
% 68.49/10.19 thf(f3229,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X4 : product_prod(X2,product_prod(X0,X1)) > $o,X5 : product_prod(X2,product_prod(X0,X1))] : (($true != vAPP(product_prod(X2,product_prod(X0,X1)),$o,X4,X3)) | ($true = vAPP(product_prod(X2,product_prod(X0,X1)),$o,X4,X5)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X1,sK48(X1,X0,X2),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X0,sK47(X1,X0,X2),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(sTfun(product_prod(X2,product_prod(X0,X1)),$o),X2,sK46(X1,X0,X2),X4))) ) | (~spl93_139 | ~spl93_170)),
% 68.49/10.19 inference(constrained_superposition,[],[f3202,f2832])).
% 68.49/10.19 thf(f28608,plain,(
% 68.49/10.19 spl93_663 | ~spl93_22 | ~spl93_169),
% 68.49/10.19 inference(avatar_split_clause,[],[f3216,f3197,f1832,f28606])).
% 68.49/10.19 thf(f28606,plain,(
% 68.49/10.19 spl93_663 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_663])])).
% 68.49/10.19 thf(f3197,plain,(
% 68.49/10.19 spl93_169 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_169])])).
% 68.49/10.19 thf(f3216,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_169)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3215])).
% 68.49/10.19 thf(f3215,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_169)),
% 68.49/10.19 inference(superposition,[],[f3198,f1833])).
% 68.49/10.19 thf(f3198,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_169),
% 68.49/10.19 inference(avatar_component_clause,[],[f3197])).
% 68.49/10.19 thf(f28604,plain,(
% 68.49/10.19 spl93_662 | ~spl93_22 | ~spl93_168),
% 68.49/10.19 inference(avatar_split_clause,[],[f3208,f3193,f1832,f28602])).
% 68.49/10.19 thf(f28602,plain,(
% 68.49/10.19 spl93_662 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_662])])).
% 68.49/10.19 thf(f3193,plain,(
% 68.49/10.19 spl93_168 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_168])])).
% 68.49/10.19 thf(f3208,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_168)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3207])).
% 68.49/10.19 thf(f3207,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_168)),
% 68.49/10.19 inference(superposition,[],[f3194,f1833])).
% 68.49/10.19 thf(f3194,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_168),
% 68.49/10.19 inference(avatar_component_clause,[],[f3193])).
% 68.49/10.19 thf(f28330,plain,(
% 68.49/10.19 spl93_661 | ~spl93_22 | ~spl93_164),
% 68.49/10.19 inference(avatar_split_clause,[],[f3135,f3130,f1832,f28328])).
% 68.49/10.19 thf(f28328,plain,(
% 68.49/10.19 spl93_661 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK23(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK24(X0,$o),X1))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_661])])).
% 68.49/10.19 thf(f3130,plain,(
% 68.49/10.19 spl93_164 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_164])])).
% 68.49/10.19 thf(f3135,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK23(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK24(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_164)),
% 68.49/10.19 inference(superposition,[],[f3131,f1833])).
% 68.49/10.19 thf(f3131,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0))) ) | ~spl93_164),
% 68.49/10.19 inference(avatar_component_clause,[],[f3130])).
% 68.49/10.19 thf(f28326,plain,(
% 68.49/10.19 spl93_660 | ~spl93_22 | ~spl93_164),
% 68.49/10.19 inference(avatar_split_clause,[],[f3134,f3130,f1832,f28324])).
% 68.49/10.19 thf(f28324,plain,(
% 68.49/10.19 spl93_660 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK23(X0,$o),X1)),$true)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK24(X0,$o),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_660])])).
% 68.49/10.19 thf(f3134,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK23(X0,$o),X1)),$true)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK24(X0,$o),X1))) ) | (~spl93_22 | ~spl93_164)),
% 68.49/10.19 inference(superposition,[],[f3131,f1833])).
% 68.49/10.19 thf(f28322,plain,(
% 68.49/10.19 spl93_659 | ~spl93_22 | ~spl93_164),
% 68.49/10.19 inference(avatar_split_clause,[],[f3133,f3130,f1832,f28320])).
% 68.49/10.19 thf(f28320,plain,(
% 68.49/10.19 spl93_659 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK24(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK23(X0,$o),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_659])])).
% 68.49/10.19 thf(f3133,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),sTfun($o,sTfun($o,$o)),add($o,X0),X1),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK24(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),set($o),partial_carrier($o,monoid_ext($o,ring_ext($o,X0))),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sP3(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,sK23(X0,$o),X1))) ) | (~spl93_22 | ~spl93_164)),
% 68.49/10.19 inference(superposition,[],[f3131,f1833])).
% 68.49/10.19 thf(f28112,plain,(
% 68.49/10.19 spl93_658 | ~spl93_22 | ~spl93_167),
% 68.49/10.19 inference(avatar_split_clause,[],[f3184,f3147,f1832,f28110])).
% 68.49/10.19 thf(f28110,plain,(
% 68.49/10.19 spl93_658 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_658])])).
% 68.49/10.19 thf(f3147,plain,(
% 68.49/10.19 spl93_167 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_167])])).
% 68.49/10.19 thf(f3184,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_167)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3183])).
% 68.49/10.19 thf(f3183,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_167)),
% 68.49/10.19 inference(superposition,[],[f3148,f1833])).
% 68.49/10.19 thf(f3148,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_167),
% 68.49/10.19 inference(avatar_component_clause,[],[f3147])).
% 68.49/10.19 thf(f28107,plain,(
% 68.49/10.19 spl93_657 | ~spl93_66 | ~spl93_74 | ~spl93_166),
% 68.49/10.19 inference(avatar_split_clause,[],[f3177,f3143,f2247,f2161,f28104])).
% 68.49/10.19 thf(f28104,plain,(
% 68.49/10.19 spl93_657 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_657])])).
% 68.49/10.19 thf(f3143,plain,(
% 68.49/10.19 spl93_166 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_166])])).
% 68.49/10.19 thf(f3177,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r))) | (~spl93_66 | ~spl93_74 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3176])).
% 68.49/10.19 thf(f3176,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r))) | (~spl93_66 | ~spl93_74 | ~spl93_166)),
% 68.49/10.19 inference(forward_demodulation,[],[f3172,f2249])).
% 68.49/10.19 thf(f3172,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3167])).
% 68.49/10.19 thf(f3167,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_166)),
% 68.49/10.19 inference(superposition,[],[f3144,f2163])).
% 68.49/10.19 thf(f3144,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) ) | ~spl93_166),
% 68.49/10.19 inference(avatar_component_clause,[],[f3143])).
% 68.49/10.19 thf(f28102,plain,(
% 68.49/10.19 spl93_656 | ~spl93_22 | ~spl93_166),
% 68.49/10.19 inference(avatar_split_clause,[],[f3170,f3143,f1832,f28100])).
% 68.49/10.19 thf(f28100,plain,(
% 68.49/10.19 spl93_656 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK41(X2,X0),X1),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_656])])).
% 68.49/10.19 thf(f3170,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK41(X2,X0),X1),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3169])).
% 68.49/10.19 thf(f3169,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK41(X2,X0),X1),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_166)),
% 68.49/10.19 inference(superposition,[],[f3144,f1833])).
% 68.49/10.19 thf(f28027,plain,(
% 68.49/10.19 spl93_655 | ~spl93_66 | ~spl93_74 | ~spl93_165),
% 68.49/10.19 inference(avatar_split_clause,[],[f3161,f3139,f2247,f2161,f28024])).
% 68.49/10.19 thf(f28024,plain,(
% 68.49/10.19 spl93_655 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_655])])).
% 68.49/10.19 thf(f3139,plain,(
% 68.49/10.19 spl93_165 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_165])])).
% 68.49/10.19 thf(f3161,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_74 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3160])).
% 68.49/10.19 thf(f3160,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_74 | ~spl93_165)),
% 68.49/10.19 inference(forward_demodulation,[],[f3156,f2249])).
% 68.49/10.19 thf(f3156,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3151])).
% 68.49/10.19 thf(f3151,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_165)),
% 68.49/10.19 inference(superposition,[],[f3140,f2163])).
% 68.49/10.19 thf(f3140,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),X3)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) ) | ~spl93_165),
% 68.49/10.19 inference(avatar_component_clause,[],[f3139])).
% 68.49/10.19 thf(f28022,plain,(
% 68.49/10.19 spl93_654 | ~spl93_22 | ~spl93_165),
% 68.49/10.19 inference(avatar_split_clause,[],[f3154,f3139,f1832,f28020])).
% 68.49/10.19 thf(f28020,plain,(
% 68.49/10.19 spl93_654 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK40(X2,X0),X1),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_654])])).
% 68.49/10.19 thf(f3154,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK40(X2,X0),X1),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3153])).
% 68.49/10.19 thf(f3153,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK40(X2,X0),X1),X3)),X1)) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_165)),
% 68.49/10.19 inference(superposition,[],[f3140,f1833])).
% 68.49/10.19 thf(f28018,plain,(
% 68.49/10.19 spl93_653 | ~spl93_48 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2478,f2436,f2031,f28016])).
% 68.49/10.19 thf(f28016,plain,(
% 68.49/10.19 spl93_653 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2))),X3)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_653])])).
% 68.49/10.19 thf(f2478,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2))),X3))) ) | (~spl93_48 | ~spl93_97)),
% 68.49/10.19 inference(inner_rewriting,[],[f2473])).
% 68.49/10.19 thf(f2473,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2))),X3)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2))),X3))) ) | (~spl93_48 | ~spl93_97)),
% 68.49/10.19 inference(constrained_superposition,[],[f2437,f2032])).
% 68.49/10.19 thf(f28014,plain,(
% 68.49/10.19 spl93_652 | ~spl93_47 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2477,f2436,f2027,f28012])).
% 68.49/10.19 thf(f28012,plain,(
% 68.49/10.19 spl93_652 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2))),X3)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_652])])).
% 68.49/10.19 thf(f2477,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2))),X3))) ) | (~spl93_47 | ~spl93_97)),
% 68.49/10.19 inference(inner_rewriting,[],[f2472])).
% 68.49/10.19 thf(f2472,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2))),X3)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2))),X3))) ) | (~spl93_47 | ~spl93_97)),
% 68.49/10.19 inference(constrained_superposition,[],[f2437,f2028])).
% 68.49/10.19 thf(f28010,plain,(
% 68.49/10.19 spl93_651 | ~spl93_48 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2476,f2436,f2031,f28008])).
% 68.49/10.19 thf(f28008,plain,(
% 68.49/10.19 spl93_651 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_651])])).
% 68.49/10.19 thf(f2476,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2))))) ) | (~spl93_48 | ~spl93_97)),
% 68.49/10.19 inference(inner_rewriting,[],[f2465])).
% 68.49/10.19 thf(f2465,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)))) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2))))) ) | (~spl93_48 | ~spl93_97)),
% 68.49/10.19 inference(constrained_superposition,[],[f2437,f2032])).
% 68.49/10.19 thf(f28006,plain,(
% 68.49/10.19 spl93_650 | ~spl93_47 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2475,f2436,f2027,f28004])).
% 68.49/10.19 thf(f28004,plain,(
% 68.49/10.19 spl93_650 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_650])])).
% 68.49/10.19 thf(f2475,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2)) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2))))) ) | (~spl93_47 | ~spl93_97)),
% 68.49/10.19 inference(inner_rewriting,[],[f2464])).
% 68.49/10.19 thf(f2464,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : X0 > product_prod(X1,X0)] : ((vAPP(X0,product_prod(X1,X0),X3,vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)))) != X2) | (vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)) = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(X0,product_prod(X1,X0)),X0,vAPP(sTfun(X0,product_prod(X1,X0)),sTfun(sTfun(X0,product_prod(X1,X0)),X0),sK35(product_prod(X1,X0),X0),X3),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2))))) ) | (~spl93_47 | ~spl93_97)),
% 68.49/10.19 inference(constrained_superposition,[],[f2437,f2028])).
% 68.49/10.19 thf(f27994,plain,(
% 68.49/10.19 spl93_649 | ~spl93_22 | ~spl93_164),
% 68.49/10.19 inference(avatar_split_clause,[],[f3137,f3130,f1832,f27992])).
% 68.49/10.19 thf(f27992,plain,(
% 68.49/10.19 spl93_649 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),add(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK23(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK24(X1,X0),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_649])])).
% 68.49/10.19 thf(f3137,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),add(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK23(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK24(X1,X0),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2)))) ) | (~spl93_22 | ~spl93_164)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3136])).
% 68.49/10.19 thf(f3136,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),add(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK23(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK24(X1,X0),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2)))) ) | (~spl93_22 | ~spl93_164)),
% 68.49/10.19 inference(superposition,[],[f3131,f1833])).
% 68.49/10.19 thf(f27866,plain,(
% 68.49/10.19 spl93_648 | ~spl93_39 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2471,f2436,f1964,f27864])).
% 68.49/10.19 thf(f27864,plain,(
% 68.49/10.19 spl93_648 <=> ! [X0 : nat,X1 : nat > nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))),X1))) != vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))),X1))) | (vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)) = X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_648])])).
% 68.49/10.19 thf(f1964,plain,(
% 68.49/10.19 spl93_39 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_39])])).
% 68.49/10.19 thf(f2471,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : nat > nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))),X1))) != vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))),X1))) | (vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl93_39 | ~spl93_97)),
% 68.49/10.19 inference(superposition,[],[f2437,f1965])).
% 68.49/10.19 thf(f1965,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1))) ) | ~spl93_39),
% 68.49/10.19 inference(avatar_component_clause,[],[f1964])).
% 68.49/10.19 thf(f27862,plain,(
% 68.49/10.19 spl93_647 | ~spl93_39 | ~spl93_97),
% 68.49/10.19 inference(avatar_split_clause,[],[f2463,f2436,f1964,f27860])).
% 68.49/10.19 thf(f27860,plain,(
% 68.49/10.19 spl93_647 <=> ! [X0 : nat,X1 : nat > nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X1),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))))) != vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X1),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))))) | (vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)) = X1))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_647])])).
% 68.49/10.19 thf(f2463,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : nat > nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X1),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))))) != vAPP(nat,nat,X1,vAPP(sTfun(nat,nat),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,nat),nat),sK35(nat,nat),X1),vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0))))) | (vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl93_39 | ~spl93_97)),
% 68.49/10.19 inference(superposition,[],[f2437,f1965])).
% 68.49/10.19 thf(f27606,plain,(
% 68.49/10.19 spl93_646 | ~spl93_440 | ~spl93_645),
% 68.49/10.19 inference(avatar_split_clause,[],[f27601,f27597,f13821,f27603])).
% 68.49/10.19 thf(f27597,plain,(
% 68.49/10.19 spl93_645 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_645])])).
% 68.49/10.19 thf(f27601,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | (~spl93_440 | ~spl93_645)),
% 68.49/10.19 inference(forward_demodulation,[],[f27599,f13823])).
% 68.49/10.19 thf(f27599,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | ~spl93_645),
% 68.49/10.19 inference(avatar_component_clause,[],[f27597])).
% 68.49/10.19 thf(f27600,plain,(
% 68.49/10.19 spl93_645 | ~spl93_61 | ~spl93_74 | ~spl93_166),
% 68.49/10.19 inference(avatar_split_clause,[],[f3175,f3143,f2247,f2136,f27597])).
% 68.49/10.19 thf(f3175,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | (~spl93_61 | ~spl93_74 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3174])).
% 68.49/10.19 thf(f3174,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | (~spl93_61 | ~spl93_74 | ~spl93_166)),
% 68.49/10.19 inference(forward_demodulation,[],[f3173,f2249])).
% 68.49/10.19 thf(f3173,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3166])).
% 68.49/10.19 thf(f3166,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_166)),
% 68.49/10.19 inference(superposition,[],[f3144,f2138])).
% 68.49/10.19 thf(f27567,plain,(
% 68.49/10.19 spl93_644 | ~spl93_440 | ~spl93_643),
% 68.49/10.19 inference(avatar_split_clause,[],[f27562,f27558,f13821,f27564])).
% 68.49/10.19 thf(f27564,plain,(
% 68.49/10.19 spl93_644 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_644])])).
% 68.49/10.19 thf(f27558,plain,(
% 68.49/10.19 spl93_643 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_643])])).
% 68.49/10.19 thf(f27562,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_440 | ~spl93_643)),
% 68.49/10.19 inference(forward_demodulation,[],[f27560,f13823])).
% 68.49/10.19 thf(f27560,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ~spl93_643),
% 68.49/10.19 inference(avatar_component_clause,[],[f27558])).
% 68.49/10.19 thf(f27561,plain,(
% 68.49/10.19 spl93_643 | ~spl93_61 | ~spl93_74 | ~spl93_165),
% 68.49/10.19 inference(avatar_split_clause,[],[f3159,f3139,f2247,f2136,f27558])).
% 68.49/10.19 thf(f3159,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_74 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3158])).
% 68.49/10.19 thf(f3158,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_74 | ~spl93_165)),
% 68.49/10.19 inference(forward_demodulation,[],[f3157,f2249])).
% 68.49/10.19 thf(f3157,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3150])).
% 68.49/10.19 thf(f3150,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_165)),
% 68.49/10.19 inference(superposition,[],[f3140,f2138])).
% 68.49/10.19 thf(f27556,plain,(
% 68.49/10.19 spl93_642 | ~spl93_75 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2840,f2831,f2256,f27554])).
% 68.49/10.19 thf(f27554,plain,(
% 68.49/10.19 spl93_642 <=> ! [X1 : $tType,X0 : $tType,X4 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X5 : X2 > product_prod(X0,X1) > X4] : (vAPP(product_prod(X0,X1),X4,vAPP(X2,sTfun(product_prod(X0,X1),X4),X5,vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3)),vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3))) = vAPP(product_prod(X2,product_prod(X0,X1)),X4,vAPP(sTfun(X2,sTfun(product_prod(X0,X1),X4)),sTfun(product_prod(X2,product_prod(X0,X1)),X4),product_rec_prod(X2,product_prod(X0,X1),X4),X5),X3))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_642])])).
% 68.49/10.19 thf(f2840,plain,(
% 68.49/10.19 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X5 : X2 > product_prod(X0,X1) > X4] : ((vAPP(product_prod(X0,X1),X4,vAPP(X2,sTfun(product_prod(X0,X1),X4),X5,vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3)),vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3))) = vAPP(product_prod(X2,product_prod(X0,X1)),X4,vAPP(sTfun(X2,sTfun(product_prod(X0,X1),X4)),sTfun(product_prod(X2,product_prod(X0,X1)),X4),product_rec_prod(X2,product_prod(X0,X1),X4),X5),X3))) ) | (~spl93_75 | ~spl93_139)),
% 68.49/10.19 inference(superposition,[],[f2257,f2832])).
% 68.49/10.19 thf(f27464,plain,(
% 68.49/10.19 spl93_641 | ~spl93_25 | ~spl93_66 | ~spl93_179),
% 68.49/10.19 inference(avatar_split_clause,[],[f3353,f3329,f2161,f1873,f27461])).
% 68.49/10.19 thf(f27461,plain,(
% 68.49/10.19 spl93_641 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_641])])).
% 68.49/10.19 thf(f3353,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_66 | ~spl93_179)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3352])).
% 68.49/10.19 thf(f3352,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_66 | ~spl93_179)),
% 68.49/10.19 inference(forward_demodulation,[],[f3348,f1875])).
% 68.49/10.19 thf(f3348,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_66 | ~spl93_179)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3343])).
% 68.49/10.19 thf(f3343,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_66 | ~spl93_179)),
% 68.49/10.19 inference(superposition,[],[f3330,f2163])).
% 68.49/10.19 thf(f27459,plain,(
% 68.49/10.19 spl93_640 | ~spl93_22 | ~spl93_162),
% 68.49/10.19 inference(avatar_split_clause,[],[f3091,f3064,f1832,f27457])).
% 68.49/10.19 thf(f27457,plain,(
% 68.49/10.19 spl93_640 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,one(X0,ring_ext(X0,X2)),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_640])])).
% 68.49/10.19 thf(f3064,plain,(
% 68.49/10.19 spl93_162 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_162])])).
% 68.49/10.19 thf(f3091,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,one(X0,ring_ext(X0,X2)),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_162)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3090])).
% 68.49/10.19 thf(f3090,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,one(X0,ring_ext(X0,X2)),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_162)),
% 68.49/10.19 inference(superposition,[],[f3065,f1833])).
% 68.49/10.19 thf(f3065,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_162),
% 68.49/10.19 inference(avatar_component_clause,[],[f3064])).
% 68.49/10.19 thf(f27409,plain,(
% 68.49/10.19 spl93_639 | ~spl93_345 | ~spl93_638),
% 68.49/10.19 inference(avatar_split_clause,[],[f27405,f27401,f6456,f27407])).
% 68.49/10.19 thf(f27407,plain,(
% 68.49/10.19 spl93_639 <=> ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_639])])).
% 68.49/10.19 thf(f27401,plain,(
% 68.49/10.19 spl93_638 <=> ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_638])])).
% 68.49/10.19 thf(f27405,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_638)),
% 68.49/10.19 inference(forward_demodulation,[],[f27404,f6458])).
% 68.49/10.19 thf(f27404,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_638)),
% 68.49/10.19 inference(forward_demodulation,[],[f27402,f6458])).
% 68.49/10.19 thf(f27402,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_638),
% 68.49/10.19 inference(avatar_component_clause,[],[f27401])).
% 68.49/10.19 thf(f27403,plain,(
% 68.49/10.19 spl93_638 | ~spl93_22 | ~spl93_161),
% 68.49/10.19 inference(avatar_split_clause,[],[f3080,f3060,f1832,f27401])).
% 68.49/10.19 thf(f3060,plain,(
% 68.49/10.19 spl93_161 <=> ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_161])])).
% 68.49/10.19 thf(f3080,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_161)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3079])).
% 68.49/10.19 thf(f3079,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_161)),
% 68.49/10.19 inference(superposition,[],[f3061,f1833])).
% 68.49/10.19 thf(f3061,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : nat] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_161),
% 68.49/10.19 inference(avatar_component_clause,[],[f3060])).
% 68.49/10.19 thf(f27353,plain,(
% 68.49/10.19 spl93_637 | ~spl93_345 | ~spl93_636),
% 68.49/10.19 inference(avatar_split_clause,[],[f27349,f27345,f6456,f27351])).
% 68.49/10.19 thf(f27351,plain,(
% 68.49/10.19 spl93_637 <=> ! [X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_637])])).
% 68.49/10.19 thf(f27345,plain,(
% 68.49/10.19 spl93_636 <=> ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_636])])).
% 68.49/10.19 thf(f27349,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_636)),
% 68.49/10.19 inference(forward_demodulation,[],[f27348,f6458])).
% 68.49/10.19 thf(f27348,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_636)),
% 68.49/10.19 inference(forward_demodulation,[],[f27346,f6458])).
% 68.49/10.19 thf(f27346,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_636),
% 68.49/10.19 inference(avatar_component_clause,[],[f27345])).
% 68.49/10.19 thf(f27347,plain,(
% 68.49/10.19 spl93_636 | ~spl93_22 | ~spl93_160),
% 68.49/10.19 inference(avatar_split_clause,[],[f3071,f3056,f1832,f27345])).
% 68.49/10.19 thf(f3056,plain,(
% 68.49/10.19 spl93_160 <=> ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_160])])).
% 68.49/10.19 thf(f3071,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_160)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3070])).
% 68.49/10.19 thf(f3070,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_160)),
% 68.49/10.19 inference(superposition,[],[f3057,f1833])).
% 68.49/10.19 thf(f3057,plain,(
% 68.49/10.19 ( ! [X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_160),
% 68.49/10.19 inference(avatar_component_clause,[],[f3056])).
% 68.49/10.19 thf(f27313,plain,(
% 68.49/10.19 spl93_635 | ~spl93_345 | ~spl93_634),
% 68.49/10.19 inference(avatar_split_clause,[],[f27309,f27306,f6456,f27311])).
% 68.49/10.19 thf(f27311,plain,(
% 68.49/10.19 spl93_635 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_635])])).
% 68.49/10.19 thf(f27306,plain,(
% 68.49/10.19 spl93_634 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_634])])).
% 68.49/10.19 thf(f27309,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0))) ) | (~spl93_345 | ~spl93_634)),
% 68.49/10.19 inference(forward_demodulation,[],[f27307,f6458])).
% 68.49/10.19 thf(f27307,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_634),
% 68.49/10.19 inference(avatar_component_clause,[],[f27306])).
% 68.49/10.19 thf(f27308,plain,(
% 68.49/10.19 spl93_634 | ~spl93_22 | ~spl93_159),
% 68.49/10.19 inference(avatar_split_clause,[],[f3050,f3034,f1832,f27306])).
% 68.49/10.19 thf(f3034,plain,(
% 68.49/10.19 spl93_159 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_159])])).
% 68.49/10.19 thf(f3050,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_159)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3049])).
% 68.49/10.19 thf(f3049,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_159)),
% 68.49/10.19 inference(superposition,[],[f3035,f1833])).
% 68.49/10.19 thf(f3035,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0))) ) | ~spl93_159),
% 68.49/10.19 inference(avatar_component_clause,[],[f3034])).
% 68.49/10.19 thf(f27285,plain,(
% 68.49/10.19 spl93_633 | ~spl93_345 | ~spl93_632),
% 68.49/10.19 inference(avatar_split_clause,[],[f27281,f27278,f6456,f27283])).
% 68.49/10.19 thf(f27283,plain,(
% 68.49/10.19 spl93_633 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_633])])).
% 68.49/10.19 thf(f27278,plain,(
% 68.49/10.19 spl93_632 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_632])])).
% 68.49/10.19 thf(f27281,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | (~spl93_345 | ~spl93_632)),
% 68.49/10.19 inference(forward_demodulation,[],[f27279,f6458])).
% 68.49/10.19 thf(f27279,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_632),
% 68.49/10.19 inference(avatar_component_clause,[],[f27278])).
% 68.49/10.19 thf(f27280,plain,(
% 68.49/10.19 spl93_632 | ~spl93_22 | ~spl93_158),
% 68.49/10.19 inference(avatar_split_clause,[],[f3041,f3030,f1832,f27278])).
% 68.49/10.19 thf(f3030,plain,(
% 68.49/10.19 spl93_158 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_158])])).
% 68.49/10.19 thf(f3041,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_158)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3040])).
% 68.49/10.19 thf(f3040,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_158)),
% 68.49/10.19 inference(superposition,[],[f3031,f1833])).
% 68.49/10.19 thf(f3031,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))) ) | ~spl93_158),
% 68.49/10.19 inference(avatar_component_clause,[],[f3030])).
% 68.49/10.19 thf(f27244,plain,(
% 68.49/10.19 spl93_631 | ~spl93_22 | ~spl93_157),
% 68.49/10.19 inference(avatar_split_clause,[],[f3022,f3002,f1832,f27242])).
% 68.49/10.19 thf(f27242,plain,(
% 68.49/10.19 spl93_631 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK41(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_631])])).
% 68.49/10.19 thf(f3002,plain,(
% 68.49/10.19 spl93_157 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_157])])).
% 68.49/10.19 thf(f3022,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK41(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_157)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3021])).
% 68.49/10.19 thf(f3021,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK41(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_157)),
% 68.49/10.19 inference(superposition,[],[f3003,f1833])).
% 68.49/10.19 thf(f3003,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) ) | ~spl93_157),
% 68.49/10.19 inference(avatar_component_clause,[],[f3002])).
% 68.49/10.19 thf(f27240,plain,(
% 68.49/10.19 spl93_630 | ~spl93_22 | ~spl93_156),
% 68.49/10.19 inference(avatar_split_clause,[],[f3009,f2998,f1832,f27238])).
% 68.49/10.19 thf(f27238,plain,(
% 68.49/10.19 spl93_630 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK40(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_630])])).
% 68.49/10.19 thf(f2998,plain,(
% 68.49/10.19 spl93_156 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_156])])).
% 68.49/10.19 thf(f3009,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK40(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_156)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3008])).
% 68.49/10.19 thf(f3008,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X1 : X0] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,vAPP(X0,sTfun(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0),sK40(X2,X0),X1),X3)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3))) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X3)))) ) | (~spl93_22 | ~spl93_156)),
% 68.49/10.19 inference(superposition,[],[f2999,f1833])).
% 68.49/10.19 thf(f2999,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) ) | ~spl93_156),
% 68.49/10.19 inference(avatar_component_clause,[],[f2998])).
% 68.49/10.19 thf(f26964,plain,(
% 68.49/10.19 spl93_629 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_189),
% 68.49/10.19 inference(avatar_split_clause,[],[f6257,f3455,f2247,f2243,f2074,f26962])).
% 68.49/10.19 thf(f26962,plain,(
% 68.49/10.19 spl93_629 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_629])])).
% 68.49/10.19 thf(f6257,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_189)),
% 68.49/10.19 inference(forward_demodulation,[],[f3467,f5934])).
% 68.49/10.19 thf(f3467,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_189)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3464])).
% 68.49/10.19 thf(f3464,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_189)),
% 68.49/10.19 inference(superposition,[],[f3456,f2245])).
% 68.49/10.19 thf(f26960,plain,(
% 68.49/10.19 spl93_628 | ~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_203),
% 68.49/10.19 inference(avatar_split_clause,[],[f6222,f3610,f2247,f2243,f2074,f1868,f26958])).
% 68.49/10.19 thf(f26958,plain,(
% 68.49/10.19 spl93_628 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_628])])).
% 68.49/10.19 thf(f6222,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_203)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f6221])).
% 68.49/10.19 thf(f6221,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_24 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_203)),
% 68.49/10.19 inference(forward_demodulation,[],[f6220,f1870])).
% 68.49/10.19 thf(f6220,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_203)),
% 68.49/10.19 inference(forward_demodulation,[],[f6219,f5934])).
% 68.49/10.19 thf(f6219,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_203)),
% 68.49/10.19 inference(forward_demodulation,[],[f3618,f5934])).
% 68.49/10.19 thf(f3618,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_203)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3615])).
% 68.49/10.19 thf(f3615,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_203)),
% 68.49/10.19 inference(superposition,[],[f3611,f2245])).
% 68.49/10.19 thf(f26954,plain,(
% 68.49/10.19 ~spl93_74 | spl93_627 | ~spl93_66 | ~spl93_157),
% 68.49/10.19 inference(avatar_split_clause,[],[f3024,f3002,f2161,f26951,f2247])).
% 68.49/10.19 thf(f26951,plain,(
% 68.49/10.19 spl93_627 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_627])])).
% 68.49/10.19 thf(f3024,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_157)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3019])).
% 68.49/10.19 thf(f3019,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_157)),
% 68.49/10.19 inference(superposition,[],[f3003,f2163])).
% 68.49/10.19 thf(f26947,plain,(
% 68.49/10.19 ~spl93_74 | spl93_626 | ~spl93_66 | ~spl93_156),
% 68.49/10.19 inference(avatar_split_clause,[],[f3011,f2998,f2161,f26944,f2247])).
% 68.49/10.19 thf(f26944,plain,(
% 68.49/10.19 spl93_626 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_626])])).
% 68.49/10.19 thf(f3011,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_156)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3006])).
% 68.49/10.19 thf(f3006,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_66 | ~spl93_156)),
% 68.49/10.19 inference(superposition,[],[f2999,f2163])).
% 68.49/10.19 thf(f26816,plain,(
% 68.49/10.19 spl93_625 | ~spl93_21 | ~spl93_301 | ~spl93_327 | ~spl93_368),
% 68.49/10.19 inference(avatar_split_clause,[],[f17659,f7370,f5387,f4916,f1827,f26814])).
% 68.49/10.19 thf(f26814,plain,(
% 68.49/10.19 spl93_625 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)),X2) = X1) | (X0 != X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_625])])).
% 68.49/10.19 thf(f7370,plain,(
% 68.49/10.19 spl93_368 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X0) | (X1 = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_368])])).
% 68.49/10.19 thf(f17659,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)),X2) = X1) | (X0 != X2)) ) | (~spl93_21 | ~spl93_301 | ~spl93_327 | ~spl93_368)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f17658])).
% 68.49/10.19 thf(f17658,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true = $false) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)),X2) = X1) | (X0 != X2)) ) | (~spl93_21 | ~spl93_301 | ~spl93_327 | ~spl93_368)),
% 68.49/10.19 inference(forward_demodulation,[],[f17657,f1829])).
% 68.49/10.19 thf(f17657,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)),X2) = X1) | (X0 != X2) | (group_add(int) = $false)) ) | (~spl93_301 | ~spl93_327 | ~spl93_368)),
% 68.49/10.19 inference(forward_demodulation,[],[f17641,f4917])).
% 68.49/10.19 thf(f17641,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1))),X2) = X1) | (group_add(int) = $false)) ) | (~spl93_327 | ~spl93_368)),
% 68.49/10.19 inference(superposition,[],[f7371,f5388])).
% 68.49/10.19 thf(f7371,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X0) | (X1 = X2)) ) | ~spl93_368),
% 68.49/10.19 inference(avatar_component_clause,[],[f7370])).
% 68.49/10.19 thf(f26592,plain,(
% 68.49/10.19 spl93_624 | ~spl93_25 | ~spl93_61 | ~spl93_179),
% 68.49/10.19 inference(avatar_split_clause,[],[f3351,f3329,f2136,f1873,f26589])).
% 68.49/10.19 thf(f26589,plain,(
% 68.49/10.19 spl93_624 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_624])])).
% 68.49/10.19 thf(f3351,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_25 | ~spl93_61 | ~spl93_179)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3350])).
% 68.49/10.19 thf(f3350,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_25 | ~spl93_61 | ~spl93_179)),
% 68.49/10.19 inference(forward_demodulation,[],[f3349,f1875])).
% 68.49/10.19 thf(f3349,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_61 | ~spl93_179)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3342])).
% 68.49/10.19 thf(f3342,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_61 | ~spl93_179)),
% 68.49/10.19 inference(superposition,[],[f3330,f2138])).
% 68.49/10.19 thf(f26587,plain,(
% 68.49/10.19 spl93_623 | ~spl93_22 | ~spl93_155),
% 68.49/10.19 inference(avatar_split_clause,[],[f2993,f2970,f1832,f26585])).
% 68.49/10.19 thf(f26585,plain,(
% 68.49/10.19 spl93_623 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_623])])).
% 68.49/10.19 thf(f2970,plain,(
% 68.49/10.19 spl93_155 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_155])])).
% 68.49/10.19 thf(f2993,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_155)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2992])).
% 68.49/10.19 thf(f2992,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_155)),
% 68.49/10.19 inference(superposition,[],[f2971,f1833])).
% 68.49/10.19 thf(f2971,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_155),
% 68.49/10.19 inference(avatar_component_clause,[],[f2970])).
% 68.49/10.19 thf(f26583,plain,(
% 68.49/10.19 spl93_622 | ~spl93_22 | ~spl93_154),
% 68.49/10.19 inference(avatar_split_clause,[],[f2985,f2966,f1832,f26581])).
% 68.49/10.19 thf(f26581,plain,(
% 68.49/10.19 spl93_622 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_622])])).
% 68.49/10.19 thf(f2966,plain,(
% 68.49/10.19 spl93_154 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_154])])).
% 68.49/10.19 thf(f2985,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_154)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2984])).
% 68.49/10.19 thf(f2984,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)),X1) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_154)),
% 68.49/10.19 inference(superposition,[],[f2967,f1833])).
% 68.49/10.19 thf(f2967,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_154),
% 68.49/10.19 inference(avatar_component_clause,[],[f2966])).
% 68.49/10.19 thf(f26579,plain,(
% 68.49/10.19 spl93_621 | ~spl93_22 | ~spl93_153),
% 68.49/10.19 inference(avatar_split_clause,[],[f2977,f2962,f1832,f26577])).
% 68.49/10.19 thf(f26577,plain,(
% 68.49/10.19 spl93_621 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_621])])).
% 68.49/10.19 thf(f2962,plain,(
% 68.49/10.19 spl93_153 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_153])])).
% 68.49/10.19 thf(f2977,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_153)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2976])).
% 68.49/10.19 thf(f2976,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X3),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X3)) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_153)),
% 68.49/10.19 inference(superposition,[],[f2963,f1833])).
% 68.49/10.19 thf(f2963,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) ) | ~spl93_153),
% 68.49/10.19 inference(avatar_component_clause,[],[f2962])).
% 68.49/10.19 thf(f26575,plain,(
% 68.49/10.19 spl93_620 | ~spl93_22 | ~spl93_145),
% 68.49/10.19 inference(avatar_split_clause,[],[f2891,f2885,f1832,f26573])).
% 68.49/10.19 thf(f26573,plain,(
% 68.49/10.19 spl93_620 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK14(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK15(X0,$o),X1))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_620])])).
% 68.49/10.19 thf(f2891,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK14(X0,$o),X1)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK15(X0,$o),X1)))) ) | (~spl93_22 | ~spl93_145)),
% 68.49/10.19 inference(superposition,[],[f2886,f1833])).
% 68.49/10.19 thf(f26571,plain,(
% 68.49/10.19 spl93_619 | ~spl93_22 | ~spl93_145),
% 68.49/10.19 inference(avatar_split_clause,[],[f2890,f2885,f1832,f26569])).
% 68.49/10.19 thf(f26569,plain,(
% 68.49/10.19 spl93_619 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK14(X0,$o),X1)),$true)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK15(X0,$o),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_619])])).
% 68.49/10.19 thf(f2890,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK14(X0,$o),X1)),$true)),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK15(X0,$o),X1))) ) | (~spl93_22 | ~spl93_145)),
% 68.49/10.19 inference(superposition,[],[f2886,f1833])).
% 68.49/10.19 thf(f26567,plain,(
% 68.49/10.19 spl93_618 | ~spl93_22 | ~spl93_145),
% 68.49/10.19 inference(avatar_split_clause,[],[f2889,f2885,f1832,f26565])).
% 68.49/10.19 thf(f26565,plain,(
% 68.49/10.19 spl93_618 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK15(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK14(X0,$o),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_618])])).
% 68.49/10.19 thf(f2889,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true != vAPP(set($o),$o,vAPP($o,sTfun(set($o),$o),member($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),sTfun($o,sTfun($o,$o)),mult($o,X0),X1),$true),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK15(X0,$o),X1))),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),set($o),partial_carrier($o,monoid_ext($o,X0)),X1))) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sP1(X0,$o),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,sK14(X0,$o),X1))) ) | (~spl93_22 | ~spl93_145)),
% 68.49/10.19 inference(superposition,[],[f2886,f1833])).
% 68.49/10.19 thf(f26466,plain,(
% 68.49/10.19 spl93_617 | ~spl93_20 | ~spl93_368 | ~spl93_417),
% 68.49/10.19 inference(avatar_split_clause,[],[f17656,f9957,f7370,f1822,f26464])).
% 68.49/10.19 thf(f17656,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),X1) != X0) | (X1 = X2)) ) | (~spl93_20 | ~spl93_368 | ~spl93_417)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f17655])).
% 68.49/10.19 thf(f17655,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true = $false) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),X1) != X0) | (X1 = X2)) ) | (~spl93_20 | ~spl93_368 | ~spl93_417)),
% 68.49/10.19 inference(forward_demodulation,[],[f17640,f1824])).
% 68.49/10.19 thf(f17640,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),X1) != X0) | (X1 = X2) | (ab_group_add(int) = $false)) ) | (~spl93_368 | ~spl93_417)),
% 68.49/10.19 inference(superposition,[],[f7371,f9958])).
% 68.49/10.19 thf(f26426,plain,(
% 68.49/10.19 spl93_616 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_202),
% 68.49/10.19 inference(avatar_split_clause,[],[f6228,f3590,f2247,f2243,f2074,f1873,f26424])).
% 68.49/10.19 thf(f26424,plain,(
% 68.49/10.19 spl93_616 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_616])])).
% 68.49/10.19 thf(f6228,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_202)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f6227])).
% 68.49/10.19 thf(f6227,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_202)),
% 68.49/10.19 inference(forward_demodulation,[],[f6226,f1875])).
% 68.49/10.19 thf(f6226,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_202)),
% 68.49/10.19 inference(forward_demodulation,[],[f6225,f5934])).
% 68.49/10.19 thf(f6225,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_202)),
% 68.49/10.19 inference(forward_demodulation,[],[f3606,f5934])).
% 68.49/10.19 thf(f3606,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_202)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3603])).
% 68.49/10.19 thf(f3603,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_202)),
% 68.49/10.19 inference(superposition,[],[f3591,f2245])).
% 68.49/10.19 thf(f26421,plain,(
% 68.49/10.19 ~spl93_74 | spl93_615 | ~spl93_61 | ~spl93_157),
% 68.49/10.19 inference(avatar_split_clause,[],[f3025,f3002,f2136,f26418,f2247])).
% 68.49/10.19 thf(f26418,plain,(
% 68.49/10.19 spl93_615 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_615])])).
% 68.49/10.19 thf(f3025,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_157)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3018])).
% 68.49/10.19 thf(f3018,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_157)),
% 68.49/10.19 inference(superposition,[],[f3003,f2138])).
% 68.49/10.19 thf(f26415,plain,(
% 68.49/10.19 ~spl93_74 | spl93_614 | ~spl93_61 | ~spl93_156),
% 68.49/10.19 inference(avatar_split_clause,[],[f3012,f2998,f2136,f26412,f2247])).
% 68.49/10.19 thf(f26412,plain,(
% 68.49/10.19 spl93_614 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_614])])).
% 68.49/10.19 thf(f3012,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_156)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3005])).
% 68.49/10.19 thf(f3005,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_61 | ~spl93_156)),
% 68.49/10.19 inference(superposition,[],[f2999,f2138])).
% 68.49/10.19 thf(f26389,plain,(
% 68.49/10.19 spl93_613 | ~spl93_345 | ~spl93_612),
% 68.49/10.19 inference(avatar_split_clause,[],[f26385,f26382,f6456,f26387])).
% 68.49/10.19 thf(f26387,plain,(
% 68.49/10.19 spl93_613 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_613])])).
% 68.49/10.19 thf(f26382,plain,(
% 68.49/10.19 spl93_612 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_612])])).
% 68.49/10.19 thf(f26385,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) ) | (~spl93_345 | ~spl93_612)),
% 68.49/10.19 inference(forward_demodulation,[],[f26383,f6458])).
% 68.49/10.19 thf(f26383,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_612),
% 68.49/10.19 inference(avatar_component_clause,[],[f26382])).
% 68.49/10.19 thf(f26384,plain,(
% 68.49/10.19 spl93_612 | ~spl93_22 | ~spl93_151),
% 68.49/10.19 inference(avatar_split_clause,[],[f2949,f2934,f1832,f26382])).
% 68.49/10.19 thf(f2934,plain,(
% 68.49/10.19 spl93_151 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_151])])).
% 68.49/10.19 thf(f2949,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_151)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2948])).
% 68.49/10.19 thf(f2948,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_151)),
% 68.49/10.19 inference(superposition,[],[f2935,f1833])).
% 68.49/10.19 thf(f2935,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) ) | ~spl93_151),
% 68.49/10.19 inference(avatar_component_clause,[],[f2934])).
% 68.49/10.19 thf(f26369,plain,(
% 68.49/10.19 spl93_611 | ~spl93_345 | ~spl93_609),
% 68.49/10.19 inference(avatar_split_clause,[],[f26361,f26358,f6456,f26367])).
% 68.49/10.19 thf(f26367,plain,(
% 68.49/10.19 spl93_611 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_611])])).
% 68.49/10.19 thf(f26358,plain,(
% 68.49/10.19 spl93_609 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_609])])).
% 68.49/10.19 thf(f26361,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | (~spl93_345 | ~spl93_609)),
% 68.49/10.19 inference(forward_demodulation,[],[f26359,f6458])).
% 68.49/10.19 thf(f26359,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_609),
% 68.49/10.19 inference(avatar_component_clause,[],[f26358])).
% 68.49/10.19 thf(f26365,plain,(
% 68.49/10.19 spl93_610 | ~spl93_368 | ~spl93_395),
% 68.49/10.19 inference(avatar_split_clause,[],[f17630,f8867,f7370,f26363])).
% 68.49/10.19 thf(f17630,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) != X0) | (X1 = X2)) ) | (~spl93_368 | ~spl93_395)),
% 68.49/10.19 inference(superposition,[],[f7371,f8868])).
% 68.49/10.19 thf(f26360,plain,(
% 68.49/10.19 spl93_609 | ~spl93_22 | ~spl93_150),
% 68.49/10.19 inference(avatar_split_clause,[],[f2941,f2930,f1832,f26358])).
% 68.49/10.19 thf(f2930,plain,(
% 68.49/10.19 spl93_150 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_150])])).
% 68.49/10.19 thf(f2941,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_150)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2940])).
% 68.49/10.19 thf(f2940,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_150)),
% 68.49/10.19 inference(superposition,[],[f2931,f1833])).
% 68.49/10.19 thf(f2931,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) ) | ~spl93_150),
% 68.49/10.19 inference(avatar_component_clause,[],[f2930])).
% 68.49/10.19 thf(f26356,plain,(
% 68.49/10.19 spl93_608 | ~spl93_48 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2838,f2831,f2031,f26354])).
% 68.49/10.19 thf(f26354,plain,(
% 68.49/10.19 spl93_608 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X3,product_prod(X1,X0)),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X3,product_prod(X1,X0)),X3,sK43(X3,X1,X0),X4)),X2) = X4) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X1,sK44(X3,X1,X0),X4)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X0,sK45(X3,X1,X0),X4)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_608])])).
% 68.49/10.19 thf(f2838,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X4 : product_prod(X3,product_prod(X1,X0))] : ((vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X3,product_prod(X1,X0)),X3,sK43(X3,X1,X0),X4)),X2) = X4) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X1,sK44(X3,X1,X0),X4)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X0,sK45(X3,X1,X0),X4))) ) | (~spl93_48 | ~spl93_139)),
% 68.49/10.19 inference(constrained_superposition,[],[f2832,f2032])).
% 68.49/10.19 thf(f26352,plain,(
% 68.49/10.19 spl93_607 | ~spl93_47 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2837,f2831,f2027,f26350])).
% 68.49/10.19 thf(f26350,plain,(
% 68.49/10.19 spl93_607 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X4 : product_prod(X3,product_prod(X1,X0)),X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X3,product_prod(X1,X0)),X3,sK43(X3,X1,X0),X4)),X2) = X4) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X1,sK44(X3,X1,X0),X4)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X0,sK45(X3,X1,X0),X4)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_607])])).
% 68.49/10.19 thf(f2837,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X4 : product_prod(X3,product_prod(X1,X0))] : ((vAPP(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0)),vAPP(X3,sTfun(product_prod(X1,X0),product_prod(X3,product_prod(X1,X0))),product_Pair(X3,product_prod(X1,X0)),vAPP(product_prod(X3,product_prod(X1,X0)),X3,sK43(X3,X1,X0),X4)),X2) = X4) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X1,sK44(X3,X1,X0),X4)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X3,product_prod(X1,X0)),X0,sK45(X3,X1,X0),X4))) ) | (~spl93_47 | ~spl93_139)),
% 68.49/10.19 inference(constrained_superposition,[],[f2832,f2028])).
% 68.49/10.19 thf(f25941,plain,(
% 68.49/10.19 spl93_606 | ~spl93_73 | ~spl93_184),
% 68.49/10.19 inference(avatar_split_clause,[],[f3400,f3392,f2243,f25939])).
% 68.49/10.19 thf(f25939,plain,(
% 68.49/10.19 spl93_606 <=> ! [X0 : nat] : (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_606])])).
% 68.49/10.19 thf(f3400,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_184)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3397])).
% 68.49/10.19 thf(f3397,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_184)),
% 68.49/10.19 inference(superposition,[],[f3393,f2245])).
% 68.49/10.19 thf(f25936,plain,(
% 68.49/10.19 spl93_605 | ~spl93_66 | ~spl93_159),
% 68.49/10.19 inference(avatar_split_clause,[],[f3052,f3034,f2161,f25933])).
% 68.49/10.19 thf(f25933,plain,(
% 68.49/10.19 spl93_605 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_605])])).
% 68.49/10.19 thf(f3052,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_159)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3047])).
% 68.49/10.19 thf(f3047,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_159)),
% 68.49/10.19 inference(superposition,[],[f3035,f2163])).
% 68.49/10.19 thf(f25930,plain,(
% 68.49/10.19 spl93_604 | ~spl93_66 | ~spl93_158),
% 68.49/10.19 inference(avatar_split_clause,[],[f3043,f3030,f2161,f25927])).
% 68.49/10.19 thf(f25927,plain,(
% 68.49/10.19 spl93_604 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_604])])).
% 68.49/10.19 thf(f3043,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_66 | ~spl93_158)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3038])).
% 68.49/10.19 thf(f3038,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_66 | ~spl93_158)),
% 68.49/10.19 inference(superposition,[],[f3031,f2163])).
% 68.49/10.19 thf(f25925,plain,(
% 68.49/10.19 spl93_603 | ~spl93_216 | ~spl93_368),
% 68.49/10.19 inference(avatar_split_clause,[],[f17598,f7370,f3748,f25923])).
% 68.49/10.19 thf(f25923,plain,(
% 68.49/10.19 spl93_603 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)) | (X1 = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_603])])).
% 68.49/10.19 thf(f17598,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)) | (X1 = X2)) ) | (~spl93_216 | ~spl93_368)),
% 68.49/10.19 inference(superposition,[],[f7371,f3749])).
% 68.49/10.19 thf(f25921,plain,(
% 68.49/10.19 spl93_602 | ~spl93_22 | ~spl93_149),
% 68.49/10.19 inference(avatar_split_clause,[],[f2924,f2908,f1832,f25919])).
% 68.49/10.19 thf(f25919,plain,(
% 68.49/10.19 spl93_602 <=> ! [X2 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_602])])).
% 68.49/10.19 thf(f2908,plain,(
% 68.49/10.19 spl93_149 <=> ! [X1 : $tType,X0 : $tType,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_149])])).
% 68.49/10.19 thf(f2924,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : ((vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_149)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2923])).
% 68.49/10.19 thf(f2923,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : $tType,X3 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X3),X1)) = X1) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X3)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X3)))) ) | (~spl93_22 | ~spl93_149)),
% 68.49/10.19 inference(superposition,[],[f2909,f1833])).
% 68.49/10.19 thf(f2909,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) ) | ~spl93_149),
% 68.49/10.19 inference(avatar_component_clause,[],[f2908])).
% 68.49/10.19 thf(f25881,plain,(
% 68.49/10.19 spl93_601 | ~spl93_345 | ~spl93_440 | ~spl93_600),
% 68.49/10.19 inference(avatar_split_clause,[],[f25877,f25872,f13821,f6456,f25879])).
% 68.49/10.19 thf(f25879,plain,(
% 68.49/10.19 spl93_601 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_601])])).
% 68.49/10.19 thf(f25872,plain,(
% 68.49/10.19 spl93_600 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_600])])).
% 68.49/10.19 thf(f25877,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (sK6 = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_440 | ~spl93_600)),
% 68.49/10.19 inference(forward_demodulation,[],[f25876,f6458])).
% 68.49/10.19 thf(f25876,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((sK6 = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_440 | ~spl93_600)),
% 68.49/10.19 inference(forward_demodulation,[],[f25875,f13823])).
% 68.49/10.19 thf(f25875,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_600)),
% 68.49/10.19 inference(forward_demodulation,[],[f25873,f6458])).
% 68.49/10.19 thf(f25873,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_600),
% 68.49/10.19 inference(avatar_component_clause,[],[f25872])).
% 68.49/10.19 thf(f25874,plain,(
% 68.49/10.19 spl93_600 | ~spl93_22 | ~spl93_146),
% 68.49/10.19 inference(avatar_split_clause,[],[f2915,f2895,f1832,f25872])).
% 68.49/10.19 thf(f2895,plain,(
% 68.49/10.19 spl93_146 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_146])])).
% 68.49/10.19 thf(f2915,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_146)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2914])).
% 68.49/10.19 thf(f2914,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_146)),
% 68.49/10.19 inference(superposition,[],[f2896,f1833])).
% 68.49/10.19 thf(f2896,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0)) ) | ~spl93_146),
% 68.49/10.19 inference(avatar_component_clause,[],[f2895])).
% 68.49/10.19 thf(f25870,plain,(
% 68.49/10.19 spl93_599 | ~spl93_75 | ~spl93_102),
% 68.49/10.19 inference(avatar_split_clause,[],[f2521,f2492,f2256,f25868])).
% 68.49/10.19 thf(f25868,plain,(
% 68.49/10.19 spl93_599 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,X1),X2 : X0 > X1 > $o] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2)))) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2),X3)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_599])])).
% 68.49/10.19 thf(f2521,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X0,X1)] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2)))) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2),X3))) ) | (~spl93_75 | ~spl93_102)),
% 68.49/10.19 inference(superposition,[],[f2493,f2257])).
% 68.49/10.19 thf(f25866,plain,(
% 68.49/10.19 spl93_598 | ~spl93_75 | ~spl93_101),
% 68.49/10.19 inference(avatar_split_clause,[],[f2508,f2488,f2256,f25864])).
% 68.49/10.19 thf(f25864,plain,(
% 68.49/10.19 spl93_598 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,X1),X2 : X0 > X1 > $o] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2)))) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2),X3)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_598])])).
% 68.49/10.19 thf(f2508,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : product_prod(X0,X1)] : (($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2)))) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2),X3))) ) | (~spl93_75 | ~spl93_101)),
% 68.49/10.19 inference(superposition,[],[f2489,f2257])).
% 68.49/10.19 thf(f25775,plain,(
% 68.49/10.19 spl93_597 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_197),
% 68.49/10.19 inference(avatar_split_clause,[],[f6241,f3537,f2247,f2243,f2074,f1873,f25773])).
% 68.49/10.19 thf(f25773,plain,(
% 68.49/10.19 spl93_597 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_597])])).
% 68.49/10.19 thf(f6241,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),X0))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_197)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f6240])).
% 68.49/10.19 thf(f6240,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),X0))) ) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_197)),
% 68.49/10.19 inference(forward_demodulation,[],[f6239,f1875])).
% 68.49/10.19 thf(f6239,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),X0)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_197)),
% 68.49/10.19 inference(forward_demodulation,[],[f3553,f5934])).
% 68.49/10.19 thf(f3553,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_197)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3550])).
% 68.49/10.19 thf(f3550,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true)) ) | (~spl93_73 | ~spl93_197)),
% 68.49/10.19 inference(superposition,[],[f3538,f2245])).
% 68.49/10.19 thf(f25693,plain,(
% 68.49/10.19 spl93_596 | ~spl93_235 | ~spl93_330),
% 68.49/10.19 inference(avatar_split_clause,[],[f16528,f5399,f3960,f25691])).
% 68.49/10.19 thf(f25691,plain,(
% 68.49/10.19 spl93_596 <=> ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_596])])).
% 68.49/10.19 thf(f5399,plain,(
% 68.49/10.19 spl93_330 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_330])])).
% 68.49/10.19 thf(f16528,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X0))) ) | (~spl93_235 | ~spl93_330)),
% 68.49/10.19 inference(superposition,[],[f5400,f3961])).
% 68.49/10.19 thf(f5400,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2)) ) | ~spl93_330),
% 68.49/10.19 inference(avatar_component_clause,[],[f5399])).
% 68.49/10.19 thf(f25689,plain,(
% 68.49/10.19 spl93_595 | ~spl93_345 | ~spl93_594),
% 68.49/10.19 inference(avatar_split_clause,[],[f25685,f25682,f6456,f25687])).
% 68.49/10.19 thf(f25687,plain,(
% 68.49/10.19 spl93_595 <=> ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0)),X1)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_595])])).
% 68.49/10.19 thf(f25682,plain,(
% 68.49/10.19 spl93_594 <=> ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_594])])).
% 68.49/10.19 thf(f25685,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0)),X1))) ) | (~spl93_345 | ~spl93_594)),
% 68.49/10.19 inference(forward_demodulation,[],[f25683,f6458])).
% 68.49/10.19 thf(f25683,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_594),
% 68.49/10.19 inference(avatar_component_clause,[],[f25682])).
% 68.49/10.19 thf(f25684,plain,(
% 68.49/10.19 spl93_594 | ~spl93_204),
% 68.49/10.19 inference(avatar_split_clause,[],[f3643,f3622,f25682])).
% 68.49/10.19 thf(f3622,plain,(
% 68.49/10.19 spl93_204 <=> ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0)) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_204])])).
% 68.49/10.19 thf(f3643,plain,(
% 68.49/10.19 ( ! [X0 : nat,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_204),
% 68.49/10.19 inference(equality_resolution,[],[f3623])).
% 68.49/10.19 thf(f3623,plain,(
% 68.49/10.19 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_204),
% 68.49/10.19 inference(avatar_component_clause,[],[f3622])).
% 68.49/10.19 thf(f25680,plain,(
% 68.49/10.19 spl93_593 | ~spl93_22 | ~spl93_145),
% 68.49/10.19 inference(avatar_split_clause,[],[f2893,f2885,f1832,f25678])).
% 68.49/10.19 thf(f25678,plain,(
% 68.49/10.19 spl93_593 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK14(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK15(X1,X0),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_593])])).
% 68.49/10.19 thf(f2893,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK14(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK15(X1,X0),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2)))) ) | (~spl93_22 | ~spl93_145)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2892])).
% 68.49/10.19 thf(f2892,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),sTfun(X0,sTfun(X0,X0)),mult(X0,X1),X2),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK14(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK15(X1,X0),X2))),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2)))) ) | (~spl93_22 | ~spl93_145)),
% 68.49/10.19 inference(superposition,[],[f2886,f1833])).
% 68.49/10.19 thf(f25672,plain,(
% 68.49/10.19 spl93_592 | ~spl93_22 | spl93_144),
% 68.49/10.19 inference(avatar_split_clause,[],[f2883,f2878,f1832,f25669])).
% 68.49/10.19 thf(f2878,plain,(
% 68.49/10.19 spl93_144 <=> ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_144])])).
% 68.49/10.19 thf(f2883,plain,(
% 68.49/10.19 ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | (~spl93_22 | spl93_144)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2882])).
% 68.49/10.19 thf(f2882,plain,(
% 68.49/10.19 ($true != $true) | ($false = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | (~spl93_22 | spl93_144)),
% 68.49/10.19 inference(superposition,[],[f2880,f1833])).
% 68.49/10.19 thf(f2880,plain,(
% 68.49/10.19 ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | spl93_144),
% 68.49/10.19 inference(avatar_component_clause,[],[f2878])).
% 68.49/10.19 thf(f25524,plain,(
% 68.49/10.19 spl93_591 | ~spl93_21 | ~spl93_311 | ~spl93_404),
% 68.49/10.19 inference(avatar_split_clause,[],[f10046,f9257,f5036,f1827,f25522])).
% 68.49/10.19 thf(f25522,plain,(
% 68.49/10.19 spl93_591 <=> ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_591])])).
% 68.49/10.19 thf(f5036,plain,(
% 68.49/10.19 spl93_311 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) != X1) | (group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_311])])).
% 68.49/10.19 thf(f9257,plain,(
% 68.49/10.19 spl93_404 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_404])])).
% 68.49/10.19 thf(f10046,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_21 | ~spl93_311 | ~spl93_404)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f10045])).
% 68.49/10.19 thf(f10045,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (X0 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_21 | ~spl93_311 | ~spl93_404)),
% 68.49/10.19 inference(forward_demodulation,[],[f10011,f1829])).
% 68.49/10.19 thf(f10011,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((X0 != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_311 | ~spl93_404)),
% 68.49/10.19 inference(superposition,[],[f5037,f9258])).
% 68.49/10.19 thf(f9258,plain,(
% 68.49/10.19 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | ~spl93_404),
% 68.49/10.19 inference(avatar_component_clause,[],[f9257])).
% 68.49/10.19 thf(f5037,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) != X1) | (group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2)) ) | ~spl93_311),
% 68.49/10.19 inference(avatar_component_clause,[],[f5036])).
% 68.49/10.19 thf(f25520,plain,(
% 68.49/10.19 spl93_590 | ~spl93_73 | ~spl93_180 | ~spl93_192),
% 68.49/10.19 inference(avatar_split_clause,[],[f6249,f3483,f3357,f2243,f25518])).
% 68.49/10.19 thf(f25518,plain,(
% 68.49/10.19 spl93_590 <=> ! [X0 : nat] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_590])])).
% 68.49/10.19 thf(f6249,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_180 | ~spl93_192)),
% 68.49/10.19 inference(forward_demodulation,[],[f3503,f3509])).
% 68.49/10.19 thf(f3509,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),sK6) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_73 | ~spl93_180 | ~spl93_192)),
% 68.49/10.19 inference(forward_demodulation,[],[f3503,f3369])).
% 68.49/10.19 thf(f3369,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_180)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3366])).
% 68.49/10.19 thf(f3366,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),sK6) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)))) ) | (~spl93_73 | ~spl93_180)),
% 68.49/10.19 inference(superposition,[],[f3358,f2245])).
% 68.49/10.19 thf(f3503,plain,(
% 68.49/10.19 ( ! [X0 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_73 | ~spl93_192)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3500])).
% 68.49/10.19 thf(f3500,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_73 | ~spl93_192)),
% 68.49/10.19 inference(superposition,[],[f3484,f2245])).
% 68.49/10.19 thf(f25516,plain,(
% 68.49/10.19 spl93_589 | ~spl93_73 | ~spl93_180 | ~spl93_192),
% 68.49/10.19 inference(avatar_split_clause,[],[f3509,f3483,f3357,f2243,f25514])).
% 68.49/10.19 thf(f25514,plain,(
% 68.49/10.19 spl93_589 <=> ! [X0 : nat] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X0))),sK6) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_589])])).
% 68.49/10.19 thf(f25481,plain,(
% 68.49/10.19 spl93_588 | ~spl93_345 | ~spl93_587),
% 68.49/10.19 inference(avatar_split_clause,[],[f25477,f25473,f6456,f25479])).
% 68.49/10.19 thf(f25479,plain,(
% 68.49/10.19 spl93_588 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_588])])).
% 68.49/10.19 thf(f25473,plain,(
% 68.49/10.19 spl93_587 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_587])])).
% 68.49/10.19 thf(f25477,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)) ) | (~spl93_345 | ~spl93_587)),
% 68.49/10.19 inference(forward_demodulation,[],[f25476,f6458])).
% 68.49/10.19 thf(f25476,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_587)),
% 68.49/10.19 inference(forward_demodulation,[],[f25474,f6458])).
% 68.49/10.19 thf(f25474,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_587),
% 68.49/10.19 inference(avatar_component_clause,[],[f25473])).
% 68.49/10.19 thf(f25475,plain,(
% 68.49/10.19 spl93_587 | ~spl93_22 | ~spl93_141),
% 68.49/10.19 inference(avatar_split_clause,[],[f2868,f2857,f1832,f25473])).
% 68.49/10.19 thf(f2857,plain,(
% 68.49/10.19 spl93_141 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_141])])).
% 68.49/10.19 thf(f2868,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_141)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2867])).
% 68.49/10.19 thf(f2867,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_141)),
% 68.49/10.19 inference(superposition,[],[f2858,f1833])).
% 68.49/10.19 thf(f2858,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)) ) | ~spl93_141),
% 68.49/10.19 inference(avatar_component_clause,[],[f2857])).
% 68.49/10.19 thf(f25471,plain,(
% 68.49/10.19 spl93_586 | ~spl93_22 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2836,f2831,f1832,f25469])).
% 68.49/10.19 thf(f25469,plain,(
% 68.49/10.19 spl93_586 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,product_prod(X1,$o))] : ((vAPP(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o)),vAPP(X0,sTfun(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o))),product_Pair(X0,product_prod(X1,$o)),vAPP(product_prod(X0,product_prod(X1,$o)),X0,sK43(X0,X1,$o),X2)),vAPP($o,product_prod(X1,$o),vAPP(X1,sTfun($o,product_prod(X1,$o)),product_Pair(X1,$o),vAPP(product_prod(X0,product_prod(X1,$o)),X1,sK44(X0,X1,$o),X2)),$true)) = X2) | ($false = vAPP(product_prod(X0,product_prod(X1,$o)),$o,sK45(X0,X1,$o),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_586])])).
% 68.49/10.19 thf(f2836,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,product_prod(X1,$o))] : ((vAPP(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o)),vAPP(X0,sTfun(product_prod(X1,$o),product_prod(X0,product_prod(X1,$o))),product_Pair(X0,product_prod(X1,$o)),vAPP(product_prod(X0,product_prod(X1,$o)),X0,sK43(X0,X1,$o),X2)),vAPP($o,product_prod(X1,$o),vAPP(X1,sTfun($o,product_prod(X1,$o)),product_Pair(X1,$o),vAPP(product_prod(X0,product_prod(X1,$o)),X1,sK44(X0,X1,$o),X2)),$true)) = X2) | ($false = vAPP(product_prod(X0,product_prod(X1,$o)),$o,sK45(X0,X1,$o),X2))) ) | (~spl93_22 | ~spl93_139)),
% 68.49/10.19 inference(superposition,[],[f2832,f1833])).
% 68.49/10.19 thf(f25467,plain,(
% 68.49/10.19 spl93_585 | ~spl93_22 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2835,f2831,f1832,f25465])).
% 68.49/10.19 thf(f25465,plain,(
% 68.49/10.19 spl93_585 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,product_prod($o,X1))] : ((vAPP(product_prod($o,X1),product_prod(X0,product_prod($o,X1)),vAPP(X0,sTfun(product_prod($o,X1),product_prod(X0,product_prod($o,X1))),product_Pair(X0,product_prod($o,X1)),vAPP(product_prod(X0,product_prod($o,X1)),X0,sK43(X0,$o,X1),X2)),vAPP(X1,product_prod($o,X1),vAPP($o,sTfun(X1,product_prod($o,X1)),product_Pair($o,X1),$true),vAPP(product_prod(X0,product_prod($o,X1)),X1,sK45(X0,$o,X1),X2))) = X2) | ($false = vAPP(product_prod(X0,product_prod($o,X1)),$o,sK44(X0,$o,X1),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_585])])).
% 68.49/10.19 thf(f2835,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,product_prod($o,X1))] : ((vAPP(product_prod($o,X1),product_prod(X0,product_prod($o,X1)),vAPP(X0,sTfun(product_prod($o,X1),product_prod(X0,product_prod($o,X1))),product_Pair(X0,product_prod($o,X1)),vAPP(product_prod(X0,product_prod($o,X1)),X0,sK43(X0,$o,X1),X2)),vAPP(X1,product_prod($o,X1),vAPP($o,sTfun(X1,product_prod($o,X1)),product_Pair($o,X1),$true),vAPP(product_prod(X0,product_prod($o,X1)),X1,sK45(X0,$o,X1),X2))) = X2) | ($false = vAPP(product_prod(X0,product_prod($o,X1)),$o,sK44(X0,$o,X1),X2))) ) | (~spl93_22 | ~spl93_139)),
% 68.49/10.19 inference(superposition,[],[f2832,f1833])).
% 68.49/10.19 thf(f25463,plain,(
% 68.49/10.19 spl93_584 | ~spl93_22 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2834,f2831,f1832,f25461])).
% 68.49/10.19 thf(f25461,plain,(
% 68.49/10.19 spl93_584 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod($o,product_prod(X0,X1))] : ((vAPP(product_prod(X0,X1),product_prod($o,product_prod(X0,X1)),vAPP($o,sTfun(product_prod(X0,X1),product_prod($o,product_prod(X0,X1))),product_Pair($o,product_prod(X0,X1)),$true),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod($o,product_prod(X0,X1)),X0,sK44($o,X0,X1),X2)),vAPP(product_prod($o,product_prod(X0,X1)),X1,sK45($o,X0,X1),X2))) = X2) | ($false = vAPP(product_prod($o,product_prod(X0,X1)),$o,sK43($o,X0,X1),X2)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_584])])).
% 68.49/10.19 thf(f2834,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod($o,product_prod(X0,X1))] : ((vAPP(product_prod(X0,X1),product_prod($o,product_prod(X0,X1)),vAPP($o,sTfun(product_prod(X0,X1),product_prod($o,product_prod(X0,X1))),product_Pair($o,product_prod(X0,X1)),$true),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod($o,product_prod(X0,X1)),X0,sK44($o,X0,X1),X2)),vAPP(product_prod($o,product_prod(X0,X1)),X1,sK45($o,X0,X1),X2))) = X2) | ($false = vAPP(product_prod($o,product_prod(X0,X1)),$o,sK43($o,X0,X1),X2))) ) | (~spl93_22 | ~spl93_139)),
% 68.49/10.19 inference(superposition,[],[f2832,f1833])).
% 68.49/10.19 thf(f25423,plain,(
% 68.49/10.19 spl93_583 | ~spl93_345 | ~spl93_582),
% 68.49/10.19 inference(avatar_split_clause,[],[f25413,f25409,f6456,f25421])).
% 68.49/10.19 thf(f25421,plain,(
% 68.49/10.19 spl93_583 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_583])])).
% 68.49/10.19 thf(f25409,plain,(
% 68.49/10.19 spl93_582 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_582])])).
% 68.49/10.19 thf(f25413,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_582)),
% 68.49/10.19 inference(forward_demodulation,[],[f25412,f6458])).
% 68.49/10.19 thf(f25412,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_582)),
% 68.49/10.19 inference(forward_demodulation,[],[f25410,f6458])).
% 68.49/10.19 thf(f25410,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_582),
% 68.49/10.19 inference(avatar_component_clause,[],[f25409])).
% 68.49/10.19 thf(f25411,plain,(
% 68.49/10.19 spl93_582 | ~spl93_22 | ~spl93_140),
% 68.49/10.19 inference(avatar_split_clause,[],[f2849,f2842,f1832,f25409])).
% 68.49/10.19 thf(f2842,plain,(
% 68.49/10.19 spl93_140 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_140])])).
% 68.49/10.19 thf(f2849,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_140)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2848])).
% 68.49/10.19 thf(f2848,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_140)),
% 68.49/10.19 inference(superposition,[],[f2843,f1833])).
% 68.49/10.19 thf(f2843,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_140),
% 68.49/10.19 inference(avatar_component_clause,[],[f2842])).
% 68.49/10.19 thf(f25388,plain,(
% 68.49/10.19 spl93_581 | ~spl93_139),
% 68.49/10.19 inference(avatar_split_clause,[],[f2839,f2831,f25386])).
% 68.49/10.19 thf(f25386,plain,(
% 68.49/10.19 spl93_581 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X4 : product_prod(X2,product_prod(X0,X1)),X3 : product_prod(X2,product_prod(X0,X1))] : ((X3 = X4) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X4)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_581])])).
% 68.49/10.19 thf(f2839,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X0,X1)),X4 : product_prod(X2,product_prod(X0,X1))] : ((X3 = X4) | (vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X3) != vAPP(product_prod(X2,product_prod(X0,X1)),X1,sK45(X2,X0,X1),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X3) != vAPP(product_prod(X2,product_prod(X0,X1)),X0,sK44(X2,X0,X1),X4)) | (vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X3) != vAPP(product_prod(X2,product_prod(X0,X1)),X2,sK43(X2,X0,X1),X4))) ) | ~spl93_139),
% 68.49/10.19 inference(constrained_superposition,[],[f2832,f2832])).
% 68.49/10.19 thf(f25282,plain,(
% 68.49/10.19 spl93_580 | ~spl93_345 | ~spl93_579),
% 68.49/10.19 inference(avatar_split_clause,[],[f25278,f25275,f6456,f25280])).
% 68.49/10.19 thf(f25280,plain,(
% 68.49/10.19 spl93_580 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_580])])).
% 68.49/10.19 thf(f25275,plain,(
% 68.49/10.19 spl93_579 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_579])])).
% 68.49/10.19 thf(f25278,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0)) ) | (~spl93_345 | ~spl93_579)),
% 68.49/10.19 inference(forward_demodulation,[],[f25276,f6458])).
% 68.49/10.19 thf(f25276,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0)) ) | ~spl93_579),
% 68.49/10.19 inference(avatar_component_clause,[],[f25275])).
% 68.49/10.19 thf(f25277,plain,(
% 68.49/10.19 spl93_579),
% 68.49/10.19 inference(avatar_split_clause,[],[f1653,f25275])).
% 68.49/10.19 thf(f1653,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1652])).
% 68.49/10.19 thf(f1652,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1648])).
% 68.49/10.19 thf(f1648,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1257])).
% 68.49/10.19 thf(f1257,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.19 inference(cnf_transformation,[],[f834])).
% 68.49/10.19 thf(f834,plain,(
% 68.49/10.19 ! [X0 : a] : ((vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 inference(ennf_transformation,[],[f399])).
% 68.49/10.19 thf(f399,plain,(
% 68.49/10.19 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)))),
% 68.49/10.19 inference(fool_elimination,[],[f398])).
% 68.49/10.19 thf(f398,plain,(
% 68.49/10.19 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)))),
% 68.49/10.19 inference(rectify,[],[f219])).
% 68.49/10.19 thf(f219,axiom,(
% 68.49/10.19 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)) = (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X13)))),
% 68.49/10.19 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_218_add_Oinv__eq__1__iff)).
% 68.49/10.19 thf(f25269,plain,(
% 68.49/10.19 spl93_578 | ~spl93_345 | ~spl93_577),
% 68.49/10.19 inference(avatar_split_clause,[],[f25265,f25262,f6456,f25267])).
% 68.49/10.19 thf(f25267,plain,(
% 68.49/10.19 spl93_578 <=> ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_578])])).
% 68.49/10.19 thf(f25262,plain,(
% 68.49/10.19 spl93_577 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_577])])).
% 68.49/10.19 thf(f25265,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)) ) | (~spl93_345 | ~spl93_577)),
% 68.49/10.19 inference(forward_demodulation,[],[f25263,f6458])).
% 68.49/10.19 thf(f25263,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)) ) | ~spl93_577),
% 68.49/10.19 inference(avatar_component_clause,[],[f25262])).
% 68.49/10.19 thf(f25264,plain,(
% 68.49/10.19 spl93_577),
% 68.49/10.19 inference(avatar_split_clause,[],[f1651,f25262])).
% 68.49/10.19 thf(f1651,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1650])).
% 68.49/10.19 thf(f1650,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) )),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f1649])).
% 68.49/10.19 thf(f1649,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(a,$o,vAPP(a,sTfun(a,$o),vEQ(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0))) )),
% 68.49/10.19 inference(binary_proxy_clausification,[],[f1257])).
% 68.49/10.19 thf(f25259,plain,(
% 68.49/10.19 spl93_576 | ~spl93_344 | ~spl93_556 | ~spl93_560),
% 68.49/10.19 inference(avatar_split_clause,[],[f25021,f24881,f24708,f6363,f25256])).
% 68.49/10.19 thf(f25256,plain,(
% 68.49/10.19 spl93_576 <=> (sK6 = vAPP(a,a,sK8,sK6))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_576])])).
% 68.49/10.19 thf(f6363,plain,(
% 68.49/10.19 spl93_344 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_344])])).
% 68.49/10.19 thf(f24708,plain,(
% 68.49/10.19 spl93_556 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_556])])).
% 68.49/10.19 thf(f24881,plain,(
% 68.49/10.19 spl93_560 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_560])])).
% 68.49/10.19 thf(f25021,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,sK8,sK6)) | (~spl93_344 | ~spl93_556 | ~spl93_560)),
% 68.49/10.19 inference(forward_demodulation,[],[f24998,f24710])).
% 68.49/10.19 thf(f24710,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6))) | ~spl93_556),
% 68.49/10.19 inference(avatar_component_clause,[],[f24708])).
% 68.49/10.19 thf(f24998,plain,(
% 68.49/10.19 (vAPP(a,a,sK8,sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6))) | (~spl93_344 | ~spl93_560)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f24904])).
% 68.49/10.19 thf(f24904,plain,(
% 68.49/10.19 ($true = $false) | (vAPP(a,a,sK8,sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6))) | (~spl93_344 | ~spl93_560)),
% 68.49/10.19 inference(superposition,[],[f24882,f6365])).
% 68.49/10.19 thf(f6365,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ~spl93_344),
% 68.49/10.19 inference(avatar_component_clause,[],[f6363])).
% 68.49/10.19 thf(f24882,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0) = X0)) ) | ~spl93_560),
% 68.49/10.19 inference(avatar_component_clause,[],[f24881])).
% 68.49/10.19 thf(f25254,plain,(
% 68.49/10.19 spl93_575 | ~spl93_73 | ~spl93_177 | ~spl93_191),
% 68.49/10.19 inference(avatar_split_clause,[],[f6251,f3479,f3305,f2243,f25252])).
% 68.49/10.19 thf(f25252,plain,(
% 68.49/10.19 spl93_575 <=> ! [X0 : int] : (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),sK6))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_575])])).
% 68.49/10.19 thf(f6251,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),sK6))) ) | (~spl93_73 | ~spl93_177 | ~spl93_191)),
% 68.49/10.19 inference(forward_demodulation,[],[f3491,f3497])).
% 68.49/10.19 thf(f3497,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),sK6) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_73 | ~spl93_177 | ~spl93_191)),
% 68.49/10.19 inference(forward_demodulation,[],[f3491,f3337])).
% 68.49/10.19 thf(f3491,plain,(
% 68.49/10.19 ( ! [X0 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_73 | ~spl93_191)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3488])).
% 68.49/10.19 thf(f3488,plain,(
% 68.49/10.19 ( ! [X0 : int] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))) ) | (~spl93_73 | ~spl93_191)),
% 68.49/10.19 inference(superposition,[],[f3480,f2245])).
% 68.49/10.19 thf(f25250,plain,(
% 68.49/10.19 spl93_574 | ~spl93_73 | ~spl93_177 | ~spl93_191),
% 68.49/10.19 inference(avatar_split_clause,[],[f3497,f3479,f3305,f2243,f25248])).
% 68.49/10.19 thf(f25248,plain,(
% 68.49/10.19 spl93_574 <=> ! [X0 : int] : (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X0)),sK6) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_574])])).
% 68.49/10.19 thf(f25244,plain,(
% 68.49/10.19 spl93_566 | spl93_573 | ~spl93_66 | ~spl93_141),
% 68.49/10.19 inference(avatar_split_clause,[],[f2870,f2857,f2161,f25241,f25119])).
% 68.49/10.19 thf(f25241,plain,(
% 68.49/10.19 spl93_573 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_573])])).
% 68.49/10.19 thf(f2870,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | (~spl93_66 | ~spl93_141)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2865])).
% 68.49/10.19 thf(f2865,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | (~spl93_66 | ~spl93_141)),
% 68.49/10.19 inference(superposition,[],[f2858,f2163])).
% 68.49/10.19 thf(f25215,plain,(
% 68.49/10.19 spl93_572 | ~spl93_440 | ~spl93_571),
% 68.49/10.19 inference(avatar_split_clause,[],[f25211,f25208,f13821,f25213])).
% 68.49/10.19 thf(f25213,plain,(
% 68.49/10.19 spl93_572 <=> ! [X0 : a] : ((sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_572])])).
% 68.49/10.19 thf(f25208,plain,(
% 68.49/10.19 spl93_571 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_571])])).
% 68.49/10.19 thf(f25211,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_440 | ~spl93_571)),
% 68.49/10.19 inference(forward_demodulation,[],[f25209,f13823])).
% 68.49/10.19 thf(f25209,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | ~spl93_571),
% 68.49/10.19 inference(avatar_component_clause,[],[f25208])).
% 68.49/10.19 thf(f25210,plain,(
% 68.49/10.19 spl93_571 | ~spl93_22 | ~spl93_138),
% 68.49/10.19 inference(avatar_split_clause,[],[f2827,f2815,f1832,f25208])).
% 68.49/10.19 thf(f2827,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_138)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2826])).
% 68.49/10.19 thf(f2826,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_138)),
% 68.49/10.19 inference(superposition,[],[f2816,f1833])).
% 68.49/10.19 thf(f25176,plain,(
% 68.49/10.19 spl93_570 | ~spl93_440 | ~spl93_569),
% 68.49/10.19 inference(avatar_split_clause,[],[f25172,f25169,f13821,f25174])).
% 68.49/10.19 thf(f25174,plain,(
% 68.49/10.19 spl93_570 <=> ! [X0 : a] : ((sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_570])])).
% 68.49/10.19 thf(f25169,plain,(
% 68.49/10.19 spl93_569 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_569])])).
% 68.49/10.19 thf(f25172,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_440 | ~spl93_569)),
% 68.49/10.19 inference(forward_demodulation,[],[f25170,f13823])).
% 68.49/10.19 thf(f25170,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | ~spl93_569),
% 68.49/10.19 inference(avatar_component_clause,[],[f25169])).
% 68.49/10.19 thf(f25171,plain,(
% 68.49/10.19 spl93_569 | ~spl93_22 | ~spl93_137),
% 68.49/10.19 inference(avatar_split_clause,[],[f2821,f2811,f1832,f25169])).
% 68.49/10.19 thf(f2821,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_137)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2820])).
% 68.49/10.19 thf(f2820,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_137)),
% 68.49/10.19 inference(superposition,[],[f2812,f1833])).
% 68.49/10.19 thf(f25133,plain,(
% 68.49/10.19 spl93_568 | ~spl93_345 | ~spl93_567),
% 68.49/10.19 inference(avatar_split_clause,[],[f25127,f25123,f6456,f25130])).
% 68.49/10.19 thf(f25130,plain,(
% 68.49/10.19 spl93_568 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_568])])).
% 68.49/10.19 thf(f25123,plain,(
% 68.49/10.19 spl93_567 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_567])])).
% 68.49/10.19 thf(f25127,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | ~spl93_567)),
% 68.49/10.19 inference(forward_demodulation,[],[f25125,f6458])).
% 68.49/10.19 thf(f25125,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_567),
% 68.49/10.19 inference(avatar_component_clause,[],[f25123])).
% 68.49/10.19 thf(f25126,plain,(
% 68.49/10.19 spl93_566 | spl93_567 | ~spl93_61 | ~spl93_146),
% 68.49/10.19 inference(avatar_split_clause,[],[f2917,f2895,f2136,f25123,f25119])).
% 68.49/10.19 thf(f2917,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | (~spl93_61 | ~spl93_146)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2911])).
% 68.49/10.19 thf(f2911,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) | (~spl93_61 | ~spl93_146)),
% 68.49/10.19 inference(superposition,[],[f2896,f2138])).
% 68.49/10.19 thf(f25080,plain,(
% 68.49/10.19 spl93_565 | ~spl93_345 | ~spl93_564),
% 68.49/10.19 inference(avatar_split_clause,[],[f25076,f25073,f6456,f25078])).
% 68.49/10.19 thf(f25078,plain,(
% 68.49/10.19 spl93_565 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_565])])).
% 68.49/10.19 thf(f25073,plain,(
% 68.49/10.19 spl93_564 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_564])])).
% 68.49/10.19 thf(f25076,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0))) ) | (~spl93_345 | ~spl93_564)),
% 68.49/10.19 inference(forward_demodulation,[],[f25074,f6458])).
% 68.49/10.19 thf(f25074,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_564),
% 68.49/10.19 inference(avatar_component_clause,[],[f25073])).
% 68.49/10.19 thf(f25075,plain,(
% 68.49/10.19 spl93_564 | ~spl93_22 | ~spl93_134),
% 68.49/10.19 inference(avatar_split_clause,[],[f2806,f2767,f1832,f25073])).
% 68.49/10.19 thf(f2767,plain,(
% 68.49/10.19 spl93_134 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_134])])).
% 68.49/10.19 thf(f2806,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_134)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2805])).
% 68.49/10.19 thf(f2805,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_134)),
% 68.49/10.19 inference(superposition,[],[f2768,f1833])).
% 68.49/10.19 thf(f2768,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0))) ) | ~spl93_134),
% 68.49/10.19 inference(avatar_component_clause,[],[f2767])).
% 68.49/10.19 thf(f25046,plain,(
% 68.49/10.19 spl93_563 | ~spl93_345 | ~spl93_562),
% 68.49/10.19 inference(avatar_split_clause,[],[f25042,f25039,f6456,f25044])).
% 68.49/10.19 thf(f25044,plain,(
% 68.49/10.19 spl93_563 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_563])])).
% 68.49/10.19 thf(f25039,plain,(
% 68.49/10.19 spl93_562 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_562])])).
% 68.49/10.19 thf(f25042,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0)))) ) | (~spl93_345 | ~spl93_562)),
% 68.49/10.19 inference(forward_demodulation,[],[f25040,f6458])).
% 68.49/10.19 thf(f25040,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_562),
% 68.49/10.19 inference(avatar_component_clause,[],[f25039])).
% 68.49/10.19 thf(f25041,plain,(
% 68.49/10.19 spl93_562 | ~spl93_22 | ~spl93_133),
% 68.49/10.19 inference(avatar_split_clause,[],[f2798,f2763,f1832,f25039])).
% 68.49/10.19 thf(f2763,plain,(
% 68.49/10.19 spl93_133 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_133])])).
% 68.49/10.19 thf(f2798,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_133)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2797])).
% 68.49/10.19 thf(f2797,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_133)),
% 68.49/10.19 inference(superposition,[],[f2764,f1833])).
% 68.49/10.19 thf(f2764,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0)))) ) | ~spl93_133),
% 68.49/10.19 inference(avatar_component_clause,[],[f2763])).
% 68.49/10.19 thf(f24888,plain,(
% 68.49/10.19 spl93_561 | ~spl93_343 | ~spl93_554 | ~spl93_558),
% 68.49/10.19 inference(avatar_split_clause,[],[f24859,f24728,f24674,f6358,f24885])).
% 68.49/10.19 thf(f24885,plain,(
% 68.49/10.19 spl93_561 <=> (sK6 = vAPP(a,a,sK7,sK6))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_561])])).
% 68.49/10.19 thf(f6358,plain,(
% 68.49/10.19 spl93_343 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_343])])).
% 68.49/10.19 thf(f24674,plain,(
% 68.49/10.19 spl93_554 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_554])])).
% 68.49/10.19 thf(f24728,plain,(
% 68.49/10.19 spl93_558 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_558])])).
% 68.49/10.19 thf(f24859,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,sK7,sK6)) | (~spl93_343 | ~spl93_554 | ~spl93_558)),
% 68.49/10.19 inference(forward_demodulation,[],[f24843,f24676])).
% 68.49/10.19 thf(f24676,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6)) | ~spl93_554),
% 68.49/10.19 inference(avatar_component_clause,[],[f24674])).
% 68.49/10.19 thf(f24843,plain,(
% 68.49/10.19 (vAPP(a,a,sK7,sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6)) | (~spl93_343 | ~spl93_558)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f24743])).
% 68.49/10.19 thf(f24743,plain,(
% 68.49/10.19 ($true = $false) | (vAPP(a,a,sK7,sK6) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6)) | (~spl93_343 | ~spl93_558)),
% 68.49/10.19 inference(superposition,[],[f24729,f6360])).
% 68.49/10.19 thf(f6360,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ~spl93_343),
% 68.49/10.19 inference(avatar_component_clause,[],[f6358])).
% 68.49/10.19 thf(f24729,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = X0)) ) | ~spl93_558),
% 68.49/10.19 inference(avatar_component_clause,[],[f24728])).
% 68.49/10.19 thf(f24883,plain,(
% 68.49/10.19 spl93_560 | ~spl93_345 | ~spl93_440 | ~spl93_559),
% 68.49/10.19 inference(avatar_split_clause,[],[f24879,f24875,f13821,f6456,f24881])).
% 68.49/10.19 thf(f24875,plain,(
% 68.49/10.19 spl93_559 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_559])])).
% 68.49/10.19 thf(f24879,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0) = X0)) ) | (~spl93_345 | ~spl93_440 | ~spl93_559)),
% 68.49/10.19 inference(forward_demodulation,[],[f24878,f6458])).
% 68.49/10.19 thf(f24878,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_440 | ~spl93_559)),
% 68.49/10.19 inference(forward_demodulation,[],[f24876,f13823])).
% 68.49/10.19 thf(f24876,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_559),
% 68.49/10.19 inference(avatar_component_clause,[],[f24875])).
% 68.49/10.19 thf(f24877,plain,(
% 68.49/10.19 spl93_559 | ~spl93_22 | ~spl93_132),
% 68.49/10.19 inference(avatar_split_clause,[],[f2782,f2759,f1832,f24875])).
% 68.49/10.19 thf(f2759,plain,(
% 68.49/10.19 spl93_132 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_132])])).
% 68.49/10.19 thf(f2782,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_132)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2781])).
% 68.49/10.19 thf(f2781,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_132)),
% 68.49/10.19 inference(superposition,[],[f2760,f1833])).
% 68.49/10.19 thf(f2760,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0)) ) | ~spl93_132),
% 68.49/10.19 inference(avatar_component_clause,[],[f2759])).
% 68.49/10.19 thf(f24730,plain,(
% 68.49/10.19 spl93_558 | ~spl93_345 | ~spl93_440 | ~spl93_557),
% 68.49/10.19 inference(avatar_split_clause,[],[f24726,f24722,f13821,f6456,f24728])).
% 68.49/10.19 thf(f24722,plain,(
% 68.49/10.19 spl93_557 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_557])])).
% 68.49/10.19 thf(f24726,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = X0)) ) | (~spl93_345 | ~spl93_440 | ~spl93_557)),
% 68.49/10.19 inference(forward_demodulation,[],[f24725,f6458])).
% 68.49/10.19 thf(f24725,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),sK6) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_440 | ~spl93_557)),
% 68.49/10.19 inference(forward_demodulation,[],[f24723,f13823])).
% 68.49/10.19 thf(f24723,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_557),
% 68.49/10.19 inference(avatar_component_clause,[],[f24722])).
% 68.49/10.19 thf(f24724,plain,(
% 68.49/10.19 spl93_557 | ~spl93_22 | ~spl93_131),
% 68.49/10.19 inference(avatar_split_clause,[],[f2774,f2755,f1832,f24722])).
% 68.49/10.19 thf(f2755,plain,(
% 68.49/10.19 spl93_131 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_131])])).
% 68.49/10.19 thf(f2774,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_131)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2773])).
% 68.49/10.19 thf(f2773,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_131)),
% 68.49/10.19 inference(superposition,[],[f2756,f1833])).
% 68.49/10.19 thf(f2756,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0)) ) | ~spl93_131),
% 68.49/10.19 inference(avatar_component_clause,[],[f2755])).
% 68.49/10.19 thf(f24711,plain,(
% 68.49/10.19 spl93_556 | ~spl93_440 | ~spl93_555),
% 68.49/10.19 inference(avatar_split_clause,[],[f24706,f24702,f13821,f24708])).
% 68.49/10.19 thf(f24702,plain,(
% 68.49/10.19 spl93_555 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_555])])).
% 68.49/10.19 thf(f24706,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6))) | (~spl93_440 | ~spl93_555)),
% 68.49/10.19 inference(forward_demodulation,[],[f24704,f13823])).
% 68.49/10.19 thf(f24704,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | ~spl93_555),
% 68.49/10.19 inference(avatar_component_clause,[],[f24702])).
% 68.49/10.19 thf(f24705,plain,(
% 68.49/10.19 spl93_555 | ~spl93_62 | ~spl93_138),
% 68.49/10.19 inference(avatar_split_clause,[],[f2829,f2815,f2141,f24702])).
% 68.49/10.19 thf(f2829,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_62 | ~spl93_138)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2824])).
% 68.49/10.19 thf(f2824,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_62 | ~spl93_138)),
% 68.49/10.19 inference(superposition,[],[f2816,f2143])).
% 68.49/10.19 thf(f24677,plain,(
% 68.49/10.19 spl93_554 | ~spl93_440 | ~spl93_552),
% 68.49/10.19 inference(avatar_split_clause,[],[f24668,f24664,f13821,f24674])).
% 68.49/10.19 thf(f24664,plain,(
% 68.49/10.19 spl93_552 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_552])])).
% 68.49/10.19 thf(f24668,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6)) | (~spl93_440 | ~spl93_552)),
% 68.49/10.19 inference(forward_demodulation,[],[f24666,f13823])).
% 68.49/10.19 thf(f24666,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | ~spl93_552),
% 68.49/10.19 inference(avatar_component_clause,[],[f24664])).
% 68.49/10.19 thf(f24672,plain,(
% 68.49/10.19 spl93_553 | ~spl93_317 | ~spl93_404),
% 68.49/10.19 inference(avatar_split_clause,[],[f9996,f9257,f5217,f24670])).
% 68.49/10.19 thf(f24670,plain,(
% 68.49/10.19 spl93_553 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = X2))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_553])])).
% 68.49/10.19 thf(f9996,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = X2)) ) | (~spl93_317 | ~spl93_404)),
% 68.49/10.19 inference(superposition,[],[f5218,f9258])).
% 68.49/10.19 thf(f24667,plain,(
% 68.49/10.19 spl93_552 | ~spl93_62 | ~spl93_137),
% 68.49/10.19 inference(avatar_split_clause,[],[f2823,f2811,f2141,f24664])).
% 68.49/10.19 thf(f2823,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_62 | ~spl93_137)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2818])).
% 68.49/10.19 thf(f2818,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_62 | ~spl93_137)),
% 68.49/10.19 inference(superposition,[],[f2812,f2143])).
% 68.49/10.19 thf(f24660,plain,(
% 68.49/10.19 spl93_551 | ~spl93_66 | ~spl93_161),
% 68.49/10.19 inference(avatar_split_clause,[],[f3082,f3060,f2161,f24658])).
% 68.49/10.19 thf(f24658,plain,(
% 68.49/10.19 spl93_551 <=> ! [X0 : nat] : ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_551])])).
% 68.49/10.19 thf(f3082,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_161)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3077])).
% 68.49/10.19 thf(f3077,plain,(
% 68.49/10.19 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_161)),
% 68.49/10.19 inference(superposition,[],[f3061,f2163])).
% 68.49/10.19 thf(f24654,plain,(
% 68.49/10.19 spl93_550 | ~spl93_66 | ~spl93_160),
% 68.49/10.19 inference(avatar_split_clause,[],[f3073,f3056,f2161,f24652])).
% 68.49/10.19 thf(f24652,plain,(
% 68.49/10.19 spl93_550 <=> ! [X0 : int] : ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_550])])).
% 68.49/10.19 thf(f3073,plain,(
% 68.49/10.19 ( ! [X0 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_160)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3068])).
% 68.49/10.19 thf(f3068,plain,(
% 68.49/10.19 ( ! [X0 : int] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_66 | ~spl93_160)),
% 68.49/10.19 inference(superposition,[],[f3057,f2163])).
% 68.49/10.19 thf(f24616,plain,(
% 68.49/10.19 spl93_549 | ~spl93_345 | ~spl93_548),
% 68.49/10.19 inference(avatar_split_clause,[],[f24612,f24609,f6456,f24614])).
% 68.49/10.19 thf(f24614,plain,(
% 68.49/10.19 spl93_549 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_549])])).
% 68.49/10.19 thf(f24609,plain,(
% 68.49/10.19 spl93_548 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_548])])).
% 68.49/10.19 thf(f24612,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0)) ) | (~spl93_345 | ~spl93_548)),
% 68.49/10.19 inference(forward_demodulation,[],[f24610,f6458])).
% 68.49/10.19 thf(f24610,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_548),
% 68.49/10.19 inference(avatar_component_clause,[],[f24609])).
% 68.49/10.19 thf(f24611,plain,(
% 68.49/10.19 spl93_548 | ~spl93_22 | ~spl93_130),
% 68.49/10.19 inference(avatar_split_clause,[],[f2750,f2735,f1832,f24609])).
% 68.49/10.19 thf(f2735,plain,(
% 68.49/10.19 spl93_130 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_130])])).
% 68.49/10.19 thf(f2750,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_130)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2749])).
% 68.49/10.19 thf(f2749,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_130)),
% 68.49/10.19 inference(superposition,[],[f2736,f1833])).
% 68.49/10.19 thf(f2736,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0)) ) | ~spl93_130),
% 68.49/10.19 inference(avatar_component_clause,[],[f2735])).
% 68.49/10.19 thf(f24572,plain,(
% 68.49/10.19 spl93_547 | ~spl93_345 | ~spl93_546),
% 68.49/10.19 inference(avatar_split_clause,[],[f24568,f24565,f6456,f24570])).
% 68.49/10.19 thf(f24570,plain,(
% 68.49/10.19 spl93_547 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_547])])).
% 68.49/10.19 thf(f24565,plain,(
% 68.49/10.19 spl93_546 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_546])])).
% 68.49/10.19 thf(f24568,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0)) ) | (~spl93_345 | ~spl93_546)),
% 68.49/10.19 inference(forward_demodulation,[],[f24566,f6458])).
% 68.49/10.19 thf(f24566,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_546),
% 68.49/10.19 inference(avatar_component_clause,[],[f24565])).
% 68.49/10.19 thf(f24567,plain,(
% 68.49/10.19 spl93_546 | ~spl93_22 | ~spl93_129),
% 68.49/10.19 inference(avatar_split_clause,[],[f2742,f2731,f1832,f24565])).
% 68.49/10.19 thf(f2731,plain,(
% 68.49/10.19 spl93_129 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_129])])).
% 68.49/10.19 thf(f2742,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_129)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2741])).
% 68.49/10.19 thf(f2741,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_129)),
% 68.49/10.19 inference(superposition,[],[f2732,f1833])).
% 68.49/10.19 thf(f2732,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0)) ) | ~spl93_129),
% 68.49/10.19 inference(avatar_component_clause,[],[f2731])).
% 68.49/10.19 thf(f24562,plain,(
% 68.49/10.19 spl93_545 | ~spl93_66 | ~spl93_134),
% 68.49/10.19 inference(avatar_split_clause,[],[f2808,f2767,f2161,f24559])).
% 68.49/10.19 thf(f24559,plain,(
% 68.49/10.19 spl93_545 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_545])])).
% 68.49/10.19 thf(f2808,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_134)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2803])).
% 68.49/10.19 thf(f2803,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_134)),
% 68.49/10.19 inference(superposition,[],[f2768,f2163])).
% 68.49/10.19 thf(f24557,plain,(
% 68.49/10.19 spl93_544 | ~spl93_21 | ~spl93_311 | ~spl93_396),
% 68.49/10.19 inference(avatar_split_clause,[],[f9457,f9070,f5036,f1827,f24555])).
% 68.49/10.19 thf(f24555,plain,(
% 68.49/10.19 spl93_544 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_544])])).
% 68.49/10.19 thf(f9457,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) = X0)) ) | (~spl93_21 | ~spl93_311 | ~spl93_396)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f9456])).
% 68.49/10.19 thf(f9456,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) = X0)) ) | (~spl93_21 | ~spl93_311 | ~spl93_396)),
% 68.49/10.19 inference(forward_demodulation,[],[f9409,f1829])).
% 68.49/10.19 thf(f9409,plain,(
% 68.49/10.19 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0) = X0)) ) | (~spl93_311 | ~spl93_396)),
% 68.49/10.19 inference(superposition,[],[f5037,f9071])).
% 68.49/10.19 thf(f24552,plain,(
% 68.49/10.19 spl93_543 | ~spl93_66 | ~spl93_133),
% 68.49/10.19 inference(avatar_split_clause,[],[f2800,f2763,f2161,f24549])).
% 68.49/10.19 thf(f24549,plain,(
% 68.49/10.19 spl93_543 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_543])])).
% 68.49/10.19 thf(f2800,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_66 | ~spl93_133)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2795])).
% 68.49/10.19 thf(f2795,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_66 | ~spl93_133)),
% 68.49/10.19 inference(superposition,[],[f2764,f2163])).
% 68.49/10.19 thf(f24546,plain,(
% 68.49/10.19 spl93_542 | ~spl93_66 | ~spl93_131),
% 68.49/10.19 inference(avatar_split_clause,[],[f2776,f2755,f2161,f24543])).
% 68.49/10.19 thf(f24543,plain,(
% 68.49/10.19 spl93_542 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_542])])).
% 68.49/10.19 thf(f2776,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_131)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2771])).
% 68.49/10.19 thf(f2771,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_131)),
% 68.49/10.19 inference(superposition,[],[f2756,f2163])).
% 68.49/10.19 thf(f24504,plain,(
% 68.49/10.19 spl93_541 | ~spl93_345 | ~spl93_540),
% 68.49/10.19 inference(avatar_split_clause,[],[f24500,f24497,f6456,f24502])).
% 68.49/10.19 thf(f24502,plain,(
% 68.49/10.19 spl93_541 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_541])])).
% 68.49/10.19 thf(f24497,plain,(
% 68.49/10.19 spl93_540 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_540])])).
% 68.49/10.19 thf(f24500,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0)) ) | (~spl93_345 | ~spl93_540)),
% 68.49/10.19 inference(forward_demodulation,[],[f24498,f6458])).
% 68.49/10.19 thf(f24498,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_540),
% 68.49/10.19 inference(avatar_component_clause,[],[f24497])).
% 68.49/10.19 thf(f24499,plain,(
% 68.49/10.19 spl93_540 | ~spl93_22 | ~spl93_128),
% 68.49/10.19 inference(avatar_split_clause,[],[f2724,f2717,f1832,f24497])).
% 68.49/10.19 thf(f2717,plain,(
% 68.49/10.19 spl93_128 <=> ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_128])])).
% 68.49/10.19 thf(f2724,plain,(
% 68.49/10.19 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_128)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2723])).
% 68.49/10.19 thf(f2723,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != $true) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_128)),
% 68.49/10.19 inference(superposition,[],[f2718,f1833])).
% 68.49/10.19 thf(f2718,plain,(
% 68.49/10.19 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0)) ) | ~spl93_128),
% 68.49/10.19 inference(avatar_component_clause,[],[f2717])).
% 68.49/10.19 thf(f24495,plain,(
% 68.49/10.19 spl93_539 | ~spl93_102),
% 68.49/10.19 inference(avatar_split_clause,[],[f2524,f2492,f24493])).
% 68.49/10.19 thf(f24493,plain,(
% 68.49/10.19 spl93_539 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,X1),X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))) != X2) | (X2 = X3))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_539])])).
% 68.49/10.19 thf(f2524,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1),X3 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))) != X2) | (X2 = X3)) ) | ~spl93_102),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f2523])).
% 68.49/10.19 thf(f2523,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1),X3 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))) != X2) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2),X3))) ) | ~spl93_102),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f2515])).
% 68.49/10.19 thf(f2515,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1),X3 : product_prod(X0,X1)] : (($true != vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))))) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2),X3))) ) | ~spl93_102),
% 68.49/10.19 inference(primitive_instantiation,[],[f2493])).
% 68.49/10.19 thf(f24491,plain,(
% 68.49/10.19 spl93_538 | ~spl93_101),
% 68.49/10.19 inference(avatar_split_clause,[],[f2511,f2488,f24489])).
% 68.49/10.19 thf(f24489,plain,(
% 68.49/10.19 spl93_538 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,X1),X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))) != X2) | (X2 = X3))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_538])])).
% 68.49/10.19 thf(f2511,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1),X3 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))) != X2) | (X2 = X3)) ) | ~spl93_101),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f2510])).
% 68.49/10.19 thf(f2510,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1),X3 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))) != X2) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2),X3))) ) | ~spl93_101),
% 68.49/10.19 inference(equality_proxy_clausification,[],[f2502])).
% 68.49/10.19 thf(f2502,plain,(
% 68.49/10.19 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1),X3 : product_prod(X0,X1)] : (($true != vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2))))) | ($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),X2),X3))) ) | ~spl93_101),
% 68.49/10.19 inference(primitive_instantiation,[],[f2489])).
% 68.49/10.19 thf(f24485,plain,(
% 68.49/10.19 spl93_537 | ~spl93_25 | ~spl93_66 | ~spl93_171),
% 68.49/10.19 inference(avatar_split_clause,[],[f3318,f3236,f2161,f1873,f24482])).
% 68.49/10.19 thf(f24482,plain,(
% 68.49/10.19 spl93_537 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_537])])).
% 68.49/10.19 thf(f3318,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_25 | ~spl93_66 | ~spl93_171)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3317])).
% 68.49/10.19 thf(f3317,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_25 | ~spl93_66 | ~spl93_171)),
% 68.49/10.19 inference(forward_demodulation,[],[f3245,f1875])).
% 68.49/10.19 thf(f3245,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_66 | ~spl93_171)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3240])).
% 68.49/10.19 thf(f3240,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_66 | ~spl93_171)),
% 68.49/10.19 inference(superposition,[],[f3237,f2163])).
% 68.49/10.19 thf(f24480,plain,(
% 68.49/10.19 spl93_536 | ~spl93_21 | ~spl93_331 | ~spl93_396),
% 68.49/10.19 inference(avatar_split_clause,[],[f9455,f9070,f5749,f1827,f24478])).
% 68.49/10.19 thf(f5749,plain,(
% 68.49/10.19 spl93_331 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : ((X1 = X2) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) | (group_add(X0) != $true) | (X3 != X4))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_331])])).
% 68.49/10.19 thf(f9455,plain,(
% 68.49/10.19 ( ! [X2 : int,X3 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X3)) | (X2 = X3)) ) | (~spl93_21 | ~spl93_331 | ~spl93_396)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f9454])).
% 68.49/10.19 thf(f9454,plain,(
% 68.49/10.19 ( ! [X2 : int,X3 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X3)) | (X2 = X3)) ) | (~spl93_21 | ~spl93_331 | ~spl93_396)),
% 68.49/10.19 inference(forward_demodulation,[],[f9435,f1829])).
% 68.49/10.19 thf(f9435,plain,(
% 68.49/10.19 ( ! [X2 : int,X3 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X3)) | (X2 = X3) | (group_add(int) != $true)) ) | (~spl93_331 | ~spl93_396)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f9406])).
% 68.49/10.19 thf(f9406,plain,(
% 68.49/10.19 ( ! [X2 : int,X3 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X3)) | (X2 = X3) | (group_add(int) != $true) | (X0 != X0)) ) | (~spl93_331 | ~spl93_396)),
% 68.49/10.19 inference(superposition,[],[f5750,f9071])).
% 68.49/10.19 thf(f5750,plain,(
% 68.49/10.19 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) | (X1 = X2) | (group_add(X0) != $true) | (X3 != X4)) ) | ~spl93_331),
% 68.49/10.19 inference(avatar_component_clause,[],[f5749])).
% 68.49/10.19 thf(f24463,plain,(
% 68.49/10.19 spl93_535 | ~spl93_440 | ~spl93_534),
% 68.49/10.19 inference(avatar_split_clause,[],[f24458,f24454,f13821,f24460])).
% 68.49/10.19 thf(f24460,plain,(
% 68.49/10.19 spl93_535 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_535])])).
% 68.49/10.19 thf(f24454,plain,(
% 68.49/10.19 spl93_534 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_534])])).
% 68.49/10.19 thf(f24458,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r))) | (~spl93_440 | ~spl93_534)),
% 68.49/10.19 inference(forward_demodulation,[],[f24456,f13823])).
% 68.49/10.19 thf(f24456,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r))) | ~spl93_534),
% 68.49/10.19 inference(avatar_component_clause,[],[f24454])).
% 68.49/10.19 thf(f24457,plain,(
% 68.49/10.19 spl93_534 | ~spl93_73 | ~spl93_74 | ~spl93_166),
% 68.49/10.19 inference(avatar_split_clause,[],[f3179,f3143,f2247,f2243,f24454])).
% 68.49/10.19 thf(f3179,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r))) | (~spl93_73 | ~spl93_74 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3178])).
% 68.49/10.19 thf(f3178,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r))) | (~spl93_73 | ~spl93_74 | ~spl93_166)),
% 68.49/10.19 inference(forward_demodulation,[],[f3171,f2249])).
% 68.49/10.19 thf(f3171,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_166)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3168])).
% 68.49/10.19 thf(f3168,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_166)),
% 68.49/10.19 inference(superposition,[],[f3144,f2245])).
% 68.49/10.19 thf(f24431,plain,(
% 68.49/10.19 spl93_533 | ~spl93_440 | ~spl93_532),
% 68.49/10.19 inference(avatar_split_clause,[],[f24426,f24422,f13821,f24428])).
% 68.49/10.19 thf(f24428,plain,(
% 68.49/10.19 spl93_533 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_533])])).
% 68.49/10.19 thf(f24422,plain,(
% 68.49/10.19 spl93_532 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_532])])).
% 68.49/10.19 thf(f24426,plain,(
% 68.49/10.19 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6)) | (~spl93_440 | ~spl93_532)),
% 68.49/10.19 inference(forward_demodulation,[],[f24424,f13823])).
% 68.49/10.19 thf(f24424,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6)) | ~spl93_532),
% 68.49/10.19 inference(avatar_component_clause,[],[f24422])).
% 68.49/10.19 thf(f24425,plain,(
% 68.49/10.19 spl93_532 | ~spl93_73 | ~spl93_74 | ~spl93_165),
% 68.49/10.19 inference(avatar_split_clause,[],[f3163,f3139,f2247,f2243,f24422])).
% 68.49/10.19 thf(f3163,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6)) | (~spl93_73 | ~spl93_74 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3162])).
% 68.49/10.19 thf(f3162,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6)) | (~spl93_73 | ~spl93_74 | ~spl93_165)),
% 68.49/10.19 inference(forward_demodulation,[],[f3155,f2249])).
% 68.49/10.19 thf(f3155,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_165)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3152])).
% 68.49/10.19 thf(f3152,plain,(
% 68.49/10.19 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_165)),
% 68.49/10.19 inference(superposition,[],[f3140,f2245])).
% 68.49/10.19 thf(f24419,plain,(
% 68.49/10.19 spl93_531 | ~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_156),
% 68.49/10.19 inference(avatar_split_clause,[],[f3117,f2998,f2247,f2161,f2074,f24416])).
% 68.49/10.19 thf(f24416,plain,(
% 68.49/10.19 spl93_531 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.19 introduced(avatar_definition,[new_symbols(naming,[spl93_531])])).
% 68.49/10.19 thf(f3117,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_156)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f3116])).
% 68.49/10.19 thf(f3116,plain,(
% 68.49/10.19 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_156)),
% 68.49/10.19 inference(forward_demodulation,[],[f3115,f2249])).
% 68.49/10.19 thf(f3115,plain,(
% 68.49/10.19 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_156)),
% 68.49/10.19 inference(forward_demodulation,[],[f3011,f2300])).
% 68.49/10.19 thf(f2300,plain,(
% 68.49/10.19 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) | (~spl93_53 | ~spl93_74)),
% 68.49/10.19 inference(trivial_inequality_removal,[],[f2299])).
% 68.49/10.20 thf(f2299,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) | (~spl93_53 | ~spl93_74)),
% 68.49/10.20 inference(superposition,[],[f2075,f2249])).
% 68.49/10.20 thf(f24413,plain,(
% 68.49/10.20 spl93_530 | ~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_157),
% 68.49/10.20 inference(avatar_split_clause,[],[f3108,f3002,f2247,f2161,f2074,f24410])).
% 68.49/10.20 thf(f24410,plain,(
% 68.49/10.20 spl93_530 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_530])])).
% 68.49/10.20 thf(f3108,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3107])).
% 68.49/10.20 thf(f3107,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(forward_demodulation,[],[f3106,f2249])).
% 68.49/10.20 thf(f3106,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(forward_demodulation,[],[f3024,f2300])).
% 68.49/10.20 thf(f24387,plain,(
% 68.49/10.20 spl93_529 | ~spl93_345 | ~spl93_527),
% 68.49/10.20 inference(avatar_split_clause,[],[f24379,f24375,f6456,f24385])).
% 68.49/10.20 thf(f24385,plain,(
% 68.49/10.20 spl93_529 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_529])])).
% 68.49/10.20 thf(f24375,plain,(
% 68.49/10.20 spl93_527 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_527])])).
% 68.49/10.20 thf(f24379,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_527)),
% 68.49/10.20 inference(forward_demodulation,[],[f24378,f6458])).
% 68.49/10.20 thf(f24378,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_527)),
% 68.49/10.20 inference(forward_demodulation,[],[f24376,f6458])).
% 68.49/10.20 thf(f24376,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_527),
% 68.49/10.20 inference(avatar_component_clause,[],[f24375])).
% 68.49/10.20 thf(f24383,plain,(
% 68.49/10.20 spl93_528 | ~spl93_317 | ~spl93_396),
% 68.49/10.20 inference(avatar_split_clause,[],[f9395,f9070,f5217,f24381])).
% 68.49/10.20 thf(f9395,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) != X0) | (X0 = X2)) ) | (~spl93_317 | ~spl93_396)),
% 68.49/10.20 inference(superposition,[],[f5218,f9071])).
% 68.49/10.20 thf(f24377,plain,(
% 68.49/10.20 spl93_527 | ~spl93_22 | ~spl93_127),
% 68.49/10.20 inference(avatar_split_clause,[],[f2712,f2697,f1832,f24375])).
% 68.49/10.20 thf(f2697,plain,(
% 68.49/10.20 spl93_127 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_127])])).
% 68.49/10.20 thf(f2712,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_127)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2711])).
% 68.49/10.20 thf(f2711,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_127)),
% 68.49/10.20 inference(superposition,[],[f2698,f1833])).
% 68.49/10.20 thf(f2698,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_127),
% 68.49/10.20 inference(avatar_component_clause,[],[f2697])).
% 68.49/10.20 thf(f24352,plain,(
% 68.49/10.20 spl93_526 | ~spl93_345 | ~spl93_525),
% 68.49/10.20 inference(avatar_split_clause,[],[f24348,f24344,f6456,f24350])).
% 68.49/10.20 thf(f24350,plain,(
% 68.49/10.20 spl93_526 <=> ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_526])])).
% 68.49/10.20 thf(f24344,plain,(
% 68.49/10.20 spl93_525 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_525])])).
% 68.49/10.20 thf(f24348,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_525)),
% 68.49/10.20 inference(forward_demodulation,[],[f24347,f6458])).
% 68.49/10.20 thf(f24347,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_345 | ~spl93_525)),
% 68.49/10.20 inference(forward_demodulation,[],[f24345,f6458])).
% 68.49/10.20 thf(f24345,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_525),
% 68.49/10.20 inference(avatar_component_clause,[],[f24344])).
% 68.49/10.20 thf(f24346,plain,(
% 68.49/10.20 spl93_525 | ~spl93_22 | ~spl93_126),
% 68.49/10.20 inference(avatar_split_clause,[],[f2704,f2693,f1832,f24344])).
% 68.49/10.20 thf(f2693,plain,(
% 68.49/10.20 spl93_126 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_126])])).
% 68.49/10.20 thf(f2704,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_126)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2703])).
% 68.49/10.20 thf(f2703,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_22 | ~spl93_126)),
% 68.49/10.20 inference(superposition,[],[f2694,f1833])).
% 68.49/10.20 thf(f2694,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_126),
% 68.49/10.20 inference(avatar_component_clause,[],[f2693])).
% 68.49/10.20 thf(f23760,plain,(
% 68.49/10.20 spl93_524 | ~spl93_317 | ~spl93_394),
% 68.49/10.20 inference(avatar_split_clause,[],[f8992,f7816,f5217,f23758])).
% 68.49/10.20 thf(f7816,plain,(
% 68.49/10.20 spl93_394 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_394])])).
% 68.49/10.20 thf(f8992,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) != X1) | (X0 = X2)) ) | (~spl93_317 | ~spl93_394)),
% 68.49/10.20 inference(superposition,[],[f5218,f7817])).
% 68.49/10.20 thf(f7817,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)))) ) | ~spl93_394),
% 68.49/10.20 inference(avatar_component_clause,[],[f7816])).
% 68.49/10.20 thf(f23019,plain,(
% 68.49/10.20 spl93_523 | ~spl93_25 | ~spl93_61 | ~spl93_171),
% 68.49/10.20 inference(avatar_split_clause,[],[f3320,f3236,f2136,f1873,f23016])).
% 68.49/10.20 thf(f23016,plain,(
% 68.49/10.20 spl93_523 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_523])])).
% 68.49/10.20 thf(f3320,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_25 | ~spl93_61 | ~spl93_171)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3319])).
% 68.49/10.20 thf(f3319,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_25 | ~spl93_61 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3246,f1875])).
% 68.49/10.20 thf(f3246,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_61 | ~spl93_171)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3239])).
% 68.49/10.20 thf(f3239,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_61 | ~spl93_171)),
% 68.49/10.20 inference(superposition,[],[f3237,f2138])).
% 68.49/10.20 thf(f23013,plain,(
% 68.49/10.20 spl93_522 | ~spl93_25 | ~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_171),
% 68.49/10.20 inference(avatar_split_clause,[],[f3252,f3236,f2247,f2161,f2074,f1873,f23010])).
% 68.49/10.20 thf(f23010,plain,(
% 68.49/10.20 spl93_522 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_522])])).
% 68.49/10.20 thf(f3252,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3251])).
% 68.49/10.20 thf(f3251,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3250,f1875])).
% 68.49/10.20 thf(f3250,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_53 | ~spl93_66 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3245,f2300])).
% 68.49/10.20 thf(f23008,plain,(
% 68.49/10.20 spl93_521 | ~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_156),
% 68.49/10.20 inference(avatar_split_clause,[],[f3120,f2998,f2247,f2136,f2074,f23005])).
% 68.49/10.20 thf(f23005,plain,(
% 68.49/10.20 spl93_521 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_521])])).
% 68.49/10.20 thf(f3120,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_156)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3119])).
% 68.49/10.20 thf(f3119,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_156)),
% 68.49/10.20 inference(forward_demodulation,[],[f3118,f2249])).
% 68.49/10.20 thf(f3118,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_156)),
% 68.49/10.20 inference(forward_demodulation,[],[f3012,f2300])).
% 68.49/10.20 thf(f23003,plain,(
% 68.49/10.20 spl93_520 | ~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_157),
% 68.49/10.20 inference(avatar_split_clause,[],[f3111,f3002,f2247,f2136,f2074,f23000])).
% 68.49/10.20 thf(f3111,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3110])).
% 68.49/10.20 thf(f3110,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(forward_demodulation,[],[f3109,f2249])).
% 68.49/10.20 thf(f3109,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(forward_demodulation,[],[f3025,f2300])).
% 68.49/10.20 thf(f22998,plain,(
% 68.49/10.20 spl93_519 | ~spl93_61 | ~spl93_134),
% 68.49/10.20 inference(avatar_split_clause,[],[f2809,f2767,f2136,f22995])).
% 68.49/10.20 thf(f22995,plain,(
% 68.49/10.20 spl93_519 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_519])])).
% 68.49/10.20 thf(f2809,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_134)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2802])).
% 68.49/10.20 thf(f2802,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_134)),
% 68.49/10.20 inference(superposition,[],[f2768,f2138])).
% 68.49/10.20 thf(f22993,plain,(
% 68.49/10.20 spl93_518 | ~spl93_61 | ~spl93_133),
% 68.49/10.20 inference(avatar_split_clause,[],[f2801,f2763,f2136,f22990])).
% 68.49/10.20 thf(f22990,plain,(
% 68.49/10.20 spl93_518 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_518])])).
% 68.49/10.20 thf(f2801,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | (~spl93_61 | ~spl93_133)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2794])).
% 68.49/10.20 thf(f2794,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) | (~spl93_61 | ~spl93_133)),
% 68.49/10.20 inference(superposition,[],[f2764,f2138])).
% 68.49/10.20 thf(f22988,plain,(
% 68.49/10.20 spl93_517 | ~spl93_221 | ~spl93_317),
% 68.49/10.20 inference(avatar_split_clause,[],[f7112,f5217,f3826,f22986])).
% 68.49/10.20 thf(f22986,plain,(
% 68.49/10.20 spl93_517 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 = X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_517])])).
% 68.49/10.20 thf(f7112,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 = X2)) ) | (~spl93_221 | ~spl93_317)),
% 68.49/10.20 inference(superposition,[],[f5218,f3827])).
% 68.49/10.20 thf(f22983,plain,(
% 68.49/10.20 spl93_516 | ~spl93_61 | ~spl93_131),
% 68.49/10.20 inference(avatar_split_clause,[],[f2777,f2755,f2136,f22980])).
% 68.49/10.20 thf(f22980,plain,(
% 68.49/10.20 spl93_516 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_516])])).
% 68.49/10.20 thf(f2777,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_61 | ~spl93_131)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2770])).
% 68.49/10.20 thf(f2770,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_61 | ~spl93_131)),
% 68.49/10.20 inference(superposition,[],[f2756,f2138])).
% 68.49/10.20 thf(f22977,plain,(
% 68.49/10.20 spl93_515 | ~spl93_66 | ~spl93_130),
% 68.49/10.20 inference(avatar_split_clause,[],[f2752,f2735,f2161,f22974])).
% 68.49/10.20 thf(f22974,plain,(
% 68.49/10.20 spl93_515 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_515])])).
% 68.49/10.20 thf(f2752,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_130)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2747])).
% 68.49/10.20 thf(f2747,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_66 | ~spl93_130)),
% 68.49/10.20 inference(superposition,[],[f2736,f2163])).
% 68.49/10.20 thf(f22971,plain,(
% 68.49/10.20 spl93_514 | ~spl93_66 | ~spl93_129),
% 68.49/10.20 inference(avatar_split_clause,[],[f2744,f2731,f2161,f22968])).
% 68.49/10.20 thf(f22968,plain,(
% 68.49/10.20 spl93_514 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_514])])).
% 68.49/10.20 thf(f2744,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_66 | ~spl93_129)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2739])).
% 68.49/10.20 thf(f2739,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_66 | ~spl93_129)),
% 68.49/10.20 inference(superposition,[],[f2732,f2163])).
% 68.49/10.20 thf(f22964,plain,(
% 68.49/10.20 spl93_513 | ~spl93_116 | ~spl93_124),
% 68.49/10.20 inference(avatar_split_clause,[],[f2685,f2669,f2623,f22961])).
% 68.49/10.20 thf(f22961,plain,(
% 68.49/10.20 spl93_513 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_513])])).
% 68.49/10.20 thf(f2669,plain,(
% 68.49/10.20 spl93_124 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_124])])).
% 68.49/10.20 thf(f2685,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_116 | ~spl93_124)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2682])).
% 68.49/10.20 thf(f2682,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_116 | ~spl93_124)),
% 68.49/10.20 inference(superposition,[],[f2670,f2625])).
% 68.49/10.20 thf(f2670,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_124),
% 68.49/10.20 inference(avatar_component_clause,[],[f2669])).
% 68.49/10.20 thf(f22957,plain,(
% 68.49/10.20 spl93_512 | ~spl93_116 | ~spl93_122),
% 68.49/10.20 inference(avatar_split_clause,[],[f2679,f2652,f2623,f22954])).
% 68.49/10.20 thf(f22954,plain,(
% 68.49/10.20 spl93_512 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_512])])).
% 68.49/10.20 thf(f2652,plain,(
% 68.49/10.20 spl93_122 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_122])])).
% 68.49/10.20 thf(f2679,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_116 | ~spl93_122)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2676])).
% 68.49/10.20 thf(f2676,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_116 | ~spl93_122)),
% 68.49/10.20 inference(superposition,[],[f2653,f2625])).
% 68.49/10.20 thf(f2653,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_122),
% 68.49/10.20 inference(avatar_component_clause,[],[f2652])).
% 68.49/10.20 thf(f22952,plain,(
% 68.49/10.20 spl93_511 | ~spl93_39 | ~spl93_65 | ~spl93_104),
% 68.49/10.20 inference(avatar_split_clause,[],[f2543,f2526,f2157,f1964,f22950])).
% 68.49/10.20 thf(f22950,plain,(
% 68.49/10.20 spl93_511 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_511])])).
% 68.49/10.20 thf(f2526,plain,(
% 68.49/10.20 spl93_104 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_104])])).
% 68.49/10.20 thf(f2543,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3))))) ) | (~spl93_39 | ~spl93_65 | ~spl93_104)),
% 68.49/10.20 inference(forward_demodulation,[],[f2542,f2527])).
% 68.49/10.20 thf(f2527,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)))) ) | ~spl93_104),
% 68.49/10.20 inference(avatar_component_clause,[],[f2526])).
% 68.49/10.20 thf(f2542,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3))))) ) | (~spl93_39 | ~spl93_65 | ~spl93_104)),
% 68.49/10.20 inference(forward_demodulation,[],[f2533,f1965])).
% 68.49/10.20 thf(f2533,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X2)),X3)))) ) | (~spl93_65 | ~spl93_104)),
% 68.49/10.20 inference(superposition,[],[f2158,f2527])).
% 68.49/10.20 thf(f22948,plain,(
% 68.49/10.20 spl93_510 | ~spl93_65 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2237,f2181,f2157,f22946])).
% 68.49/10.20 thf(f22946,plain,(
% 68.49/10.20 spl93_510 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_510])])).
% 68.49/10.20 thf(f2237,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2236,f2216])).
% 68.49/10.20 thf(f2216,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3))))) ) | ~spl93_65),
% 68.49/10.20 inference(forward_demodulation,[],[f2215,f2158])).
% 68.49/10.20 thf(f2215,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X3)))) ) | ~spl93_65),
% 68.49/10.20 inference(forward_demodulation,[],[f2211,f2158])).
% 68.49/10.20 thf(f2211,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3))) ) | ~spl93_65),
% 68.49/10.20 inference(superposition,[],[f2158,f2158])).
% 68.49/10.20 thf(f2236,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X3)))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2227,f2158])).
% 68.49/10.20 thf(f2227,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))),X3))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(superposition,[],[f2158,f2182])).
% 68.49/10.20 thf(f22944,plain,(
% 68.49/10.20 spl93_509 | ~spl93_65 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2233,f2181,f2157,f22942])).
% 68.49/10.20 thf(f22942,plain,(
% 68.49/10.20 spl93_509 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_509])])).
% 68.49/10.20 thf(f2233,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2))))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2224,f2158])).
% 68.49/10.20 thf(f2224,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2)))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(superposition,[],[f2182,f2158])).
% 68.49/10.20 thf(f22940,plain,(
% 68.49/10.20 spl93_508 | ~spl93_65 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2232,f2181,f2157,f22938])).
% 68.49/10.20 thf(f22938,plain,(
% 68.49/10.20 spl93_508 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_508])])).
% 68.49/10.20 thf(f2232,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2231,f2216])).
% 68.49/10.20 thf(f2231,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X3)))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2223,f2158])).
% 68.49/10.20 thf(f2223,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))),X3))) ) | ~spl93_70),
% 68.49/10.20 inference(superposition,[],[f2182,f2182])).
% 68.49/10.20 thf(f22936,plain,(
% 68.49/10.20 spl93_507 | ~spl93_64 | ~spl93_65 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2230,f2181,f2157,f2153,f22934])).
% 68.49/10.20 thf(f22934,plain,(
% 68.49/10.20 spl93_507 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_507])])).
% 68.49/10.20 thf(f2153,plain,(
% 68.49/10.20 spl93_64 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_64])])).
% 68.49/10.20 thf(f2230,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))) ) | (~spl93_64 | ~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2222,f2158])).
% 68.49/10.20 thf(f2222,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))) ) | (~spl93_64 | ~spl93_70)),
% 68.49/10.20 inference(superposition,[],[f2182,f2154])).
% 68.49/10.20 thf(f2154,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) ) | ~spl93_64),
% 68.49/10.20 inference(avatar_component_clause,[],[f2153])).
% 68.49/10.20 thf(f22932,plain,(
% 68.49/10.20 spl93_506 | ~spl93_21 | ~spl93_276 | ~spl93_311),
% 68.49/10.20 inference(avatar_split_clause,[],[f5190,f5036,f4534,f1827,f22930])).
% 68.49/10.20 thf(f22930,plain,(
% 68.49/10.20 spl93_506 <=> ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X0))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_506])])).
% 68.49/10.20 thf(f5190,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X0)) ) | (~spl93_21 | ~spl93_276 | ~spl93_311)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5189])).
% 68.49/10.20 thf(f5189,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X0)) ) | (~spl93_21 | ~spl93_276 | ~spl93_311)),
% 68.49/10.20 inference(forward_demodulation,[],[f5173,f1829])).
% 68.49/10.20 thf(f5173,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X0)) ) | (~spl93_276 | ~spl93_311)),
% 68.49/10.20 inference(superposition,[],[f5037,f4535])).
% 68.49/10.20 thf(f22928,plain,(
% 68.49/10.20 spl93_505 | ~spl93_63 | ~spl93_65 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2229,f2181,f2157,f2149,f22926])).
% 68.49/10.20 thf(f22926,plain,(
% 68.49/10.20 spl93_505 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_505])])).
% 68.49/10.20 thf(f2149,plain,(
% 68.49/10.20 spl93_63 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_63])])).
% 68.49/10.20 thf(f2229,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))) ) | (~spl93_63 | ~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(forward_demodulation,[],[f2221,f2158])).
% 68.49/10.20 thf(f2221,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))) ) | (~spl93_63 | ~spl93_70)),
% 68.49/10.20 inference(superposition,[],[f2182,f2150])).
% 68.49/10.20 thf(f2150,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) ) | ~spl93_63),
% 68.49/10.20 inference(avatar_component_clause,[],[f2149])).
% 68.49/10.20 thf(f22924,plain,(
% 68.49/10.20 spl93_504 | ~spl93_65),
% 68.49/10.20 inference(avatar_split_clause,[],[f2216,f2157,f22922])).
% 68.49/10.20 thf(f22922,plain,(
% 68.49/10.20 spl93_504 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_504])])).
% 68.49/10.20 thf(f22919,plain,(
% 68.49/10.20 spl93_503 | ~spl93_64 | ~spl93_65),
% 68.49/10.20 inference(avatar_split_clause,[],[f2214,f2157,f2153,f22917])).
% 68.49/10.20 thf(f22917,plain,(
% 68.49/10.20 spl93_503 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_503])])).
% 68.49/10.20 thf(f2214,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)))) ) | (~spl93_64 | ~spl93_65)),
% 68.49/10.20 inference(forward_demodulation,[],[f2210,f2158])).
% 68.49/10.20 thf(f2210,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X3))) ) | (~spl93_64 | ~spl93_65)),
% 68.49/10.20 inference(superposition,[],[f2158,f2154])).
% 68.49/10.20 thf(f22914,plain,(
% 68.49/10.20 spl93_502 | ~spl93_63 | ~spl93_65),
% 68.49/10.20 inference(avatar_split_clause,[],[f2213,f2157,f2149,f22912])).
% 68.49/10.20 thf(f22912,plain,(
% 68.49/10.20 spl93_502 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_502])])).
% 68.49/10.20 thf(f2213,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)))) ) | (~spl93_63 | ~spl93_65)),
% 68.49/10.20 inference(forward_demodulation,[],[f2209,f2158])).
% 68.49/10.20 thf(f2209,plain,(
% 68.49/10.20 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),X3)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X3))) ) | (~spl93_63 | ~spl93_65)),
% 68.49/10.20 inference(superposition,[],[f2158,f2150])).
% 68.49/10.20 thf(f20451,plain,(
% 68.49/10.20 spl93_501 | ~spl93_345 | ~spl93_500),
% 68.49/10.20 inference(avatar_split_clause,[],[f20447,f20444,f6456,f20449])).
% 68.49/10.20 thf(f20449,plain,(
% 68.49/10.20 spl93_501 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_501])])).
% 68.49/10.20 thf(f20444,plain,(
% 68.49/10.20 spl93_500 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_500])])).
% 68.49/10.20 thf(f20447,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_345 | ~spl93_500)),
% 68.49/10.20 inference(forward_demodulation,[],[f20445,f6458])).
% 68.49/10.20 thf(f20445,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | ~spl93_500),
% 68.49/10.20 inference(avatar_component_clause,[],[f20444])).
% 68.49/10.20 thf(f20446,plain,(
% 68.49/10.20 spl93_500 | ~spl93_22 | ~spl93_124),
% 68.49/10.20 inference(avatar_split_clause,[],[f2684,f2669,f1832,f20444])).
% 68.49/10.20 thf(f2684,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_124)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2683])).
% 68.49/10.20 thf(f2683,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_124)),
% 68.49/10.20 inference(superposition,[],[f2670,f1833])).
% 68.49/10.20 thf(f20441,plain,(
% 68.49/10.20 spl93_499 | ~spl93_22 | ~spl93_122),
% 68.49/10.20 inference(avatar_split_clause,[],[f2678,f2652,f1832,f20439])).
% 68.49/10.20 thf(f20439,plain,(
% 68.49/10.20 spl93_499 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_499])])).
% 68.49/10.20 thf(f2678,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_122)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2677])).
% 68.49/10.20 thf(f2677,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_122)),
% 68.49/10.20 inference(superposition,[],[f2653,f1833])).
% 68.49/10.20 thf(f20437,plain,(
% 68.49/10.20 spl93_498 | ~spl93_21 | ~spl93_270 | ~spl93_307),
% 68.49/10.20 inference(avatar_split_clause,[],[f5106,f5020,f4444,f1827,f20435])).
% 68.49/10.20 thf(f20435,plain,(
% 68.49/10.20 spl93_498 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 = X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_498])])).
% 68.49/10.20 thf(f5020,plain,(
% 68.49/10.20 spl93_307 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | (X1 = X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_307])])).
% 68.49/10.20 thf(f5106,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 = X2)) ) | (~spl93_21 | ~spl93_270 | ~spl93_307)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5105])).
% 68.49/10.20 thf(f5105,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 = X2)) ) | (~spl93_21 | ~spl93_270 | ~spl93_307)),
% 68.49/10.20 inference(forward_demodulation,[],[f5080,f1829])).
% 68.49/10.20 thf(f5080,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0) != vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (group_add(int) != $true) | (X0 = X2)) ) | (~spl93_270 | ~spl93_307)),
% 68.49/10.20 inference(superposition,[],[f5021,f4445])).
% 68.49/10.20 thf(f5021,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | (X1 = X3)) ) | ~spl93_307),
% 68.49/10.20 inference(avatar_component_clause,[],[f5020])).
% 68.49/10.20 thf(f20433,plain,(
% 68.49/10.20 spl93_497),
% 68.49/10.20 inference(avatar_split_clause,[],[f1609,f20431])).
% 68.49/10.20 thf(f20431,plain,(
% 68.49/10.20 spl93_497 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))) | ($false = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_497])])).
% 68.49/10.20 thf(f1609,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))) | ($false = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1326])).
% 68.49/10.20 thf(f1326,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | (vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)) != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))) )),
% 68.49/10.20 inference(cnf_transformation,[],[f1104])).
% 68.49/10.20 thf(f1104,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | (vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)) != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))),
% 68.49/10.20 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f909,f1103])).
% 68.49/10.20 thf(f1103,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (vAPP(X0,$o,X1,X3) != vAPP(X0,$o,X2,X3)) => (vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)) != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))),
% 68.49/10.20 introduced(choice_axiom,[])).
% 68.49/10.20 thf(f909,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | ? [X3 : X0] : (vAPP(X0,$o,X1,X3) != vAPP(X0,$o,X2,X3)))),
% 68.49/10.20 inference(ennf_transformation,[],[f762])).
% 68.49/10.20 thf(f762,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) = vAPP(X0,$o,X2,X3)) => (vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)))),
% 68.49/10.20 inference(rectify,[],[f48])).
% 68.49/10.20 thf(f48,axiom,(
% 68.49/10.20 ! [X0 : $tType,X26 : X0 > $o,X29 : X0 > $o] : (! [X23 : X0] : (vAPP(X0,$o,X26,X23) = vAPP(X0,$o,X29,X23)) => (vAPP(sTfun(X0,$o),set(X0),collect(X0),X26) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X29)))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_Collect__cong)).
% 68.49/10.20 thf(f20429,plain,(
% 68.49/10.20 spl93_496),
% 68.49/10.20 inference(avatar_split_clause,[],[f1608,f20427])).
% 68.49/10.20 thf(f20427,plain,(
% 68.49/10.20 spl93_496 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_496])])).
% 68.49/10.20 thf(f1608,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),X2) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK13(X0),X2),X1)))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1326])).
% 68.49/10.20 thf(f20397,plain,(
% 68.49/10.20 spl93_495 | ~spl93_25 | ~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_171),
% 68.49/10.20 inference(avatar_split_clause,[],[f5940,f3236,f2247,f2136,f2074,f1873,f20394])).
% 68.49/10.20 thf(f20394,plain,(
% 68.49/10.20 spl93_495 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_495])])).
% 68.49/10.20 thf(f5940,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3248])).
% 68.49/10.20 thf(f3248,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3247,f1875])).
% 68.49/10.20 thf(f3247,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3246,f2300])).
% 68.49/10.20 thf(f20391,plain,(
% 68.49/10.20 spl93_494 | ~spl93_116 | ~spl93_123),
% 68.49/10.20 inference(avatar_split_clause,[],[f3127,f2657,f2623,f20388])).
% 68.49/10.20 thf(f20388,plain,(
% 68.49/10.20 spl93_494 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_494])])).
% 68.49/10.20 thf(f2657,plain,(
% 68.49/10.20 spl93_123 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_123])])).
% 68.49/10.20 thf(f3127,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_116 | ~spl93_123)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3124])).
% 68.49/10.20 thf(f3124,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_116 | ~spl93_123)),
% 68.49/10.20 inference(superposition,[],[f2658,f2625])).
% 68.49/10.20 thf(f2658,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | ~spl93_123),
% 68.49/10.20 inference(avatar_component_clause,[],[f2657])).
% 68.49/10.20 thf(f20386,plain,(
% 68.49/10.20 spl93_493 | ~spl93_61 | ~spl93_150),
% 68.49/10.20 inference(avatar_split_clause,[],[f2944,f2930,f2136,f20383])).
% 68.49/10.20 thf(f20383,plain,(
% 68.49/10.20 spl93_493 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_493])])).
% 68.49/10.20 thf(f2944,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_150)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2937])).
% 68.49/10.20 thf(f2937,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_150)),
% 68.49/10.20 inference(superposition,[],[f2931,f2138])).
% 68.49/10.20 thf(f20380,plain,(
% 68.49/10.20 spl93_492 | ~spl93_66 | ~spl93_128),
% 68.49/10.20 inference(avatar_split_clause,[],[f2726,f2717,f2161,f20377])).
% 68.49/10.20 thf(f20377,plain,(
% 68.49/10.20 spl93_492 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_492])])).
% 68.49/10.20 thf(f2726,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_66 | ~spl93_128)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2721])).
% 68.49/10.20 thf(f2721,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))) | (~spl93_66 | ~spl93_128)),
% 68.49/10.20 inference(superposition,[],[f2718,f2163])).
% 68.49/10.20 thf(f20355,plain,(
% 68.49/10.20 spl93_491 | ~spl93_22 | ~spl93_123),
% 68.49/10.20 inference(avatar_split_clause,[],[f3126,f2657,f1832,f20353])).
% 68.49/10.20 thf(f20353,plain,(
% 68.49/10.20 spl93_491 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_491])])).
% 68.49/10.20 thf(f3126,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_123)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3125])).
% 68.49/10.20 thf(f3125,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_123)),
% 68.49/10.20 inference(superposition,[],[f2658,f1833])).
% 68.49/10.20 thf(f20294,plain,(
% 68.49/10.20 spl93_490 | ~spl93_25 | ~spl93_73 | ~spl93_179),
% 68.49/10.20 inference(avatar_split_clause,[],[f3355,f3329,f2243,f1873,f20291])).
% 68.49/10.20 thf(f20291,plain,(
% 68.49/10.20 spl93_490 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_490])])).
% 68.49/10.20 thf(f3355,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),sK6)) | (~spl93_25 | ~spl93_73 | ~spl93_179)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3354])).
% 68.49/10.20 thf(f3354,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),sK6)) | (~spl93_25 | ~spl93_73 | ~spl93_179)),
% 68.49/10.20 inference(forward_demodulation,[],[f3347,f1875])).
% 68.49/10.20 thf(f3347,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_179)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3344])).
% 68.49/10.20 thf(f3344,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_179)),
% 68.49/10.20 inference(superposition,[],[f3330,f2245])).
% 68.49/10.20 thf(f20289,plain,(
% 68.49/10.20 spl93_489 | ~spl93_61 | ~spl93_129),
% 68.49/10.20 inference(avatar_split_clause,[],[f2745,f2731,f2136,f20286])).
% 68.49/10.20 thf(f20286,plain,(
% 68.49/10.20 spl93_489 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_489])])).
% 68.49/10.20 thf(f2745,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_129)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2738])).
% 68.49/10.20 thf(f2738,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_61 | ~spl93_129)),
% 68.49/10.20 inference(superposition,[],[f2732,f2138])).
% 68.49/10.20 thf(f20283,plain,(
% 68.49/10.20 spl93_488 | ~spl93_116 | ~spl93_121),
% 68.49/10.20 inference(avatar_split_clause,[],[f2666,f2647,f2623,f20280])).
% 68.49/10.20 thf(f20280,plain,(
% 68.49/10.20 spl93_488 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_488])])).
% 68.49/10.20 thf(f2647,plain,(
% 68.49/10.20 spl93_121 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_121])])).
% 68.49/10.20 thf(f2666,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_116 | ~spl93_121)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2663])).
% 68.49/10.20 thf(f2663,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_116 | ~spl93_121)),
% 68.49/10.20 inference(superposition,[],[f2648,f2625])).
% 68.49/10.20 thf(f2648,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | ~spl93_121),
% 68.49/10.20 inference(avatar_component_clause,[],[f2647])).
% 68.49/10.20 thf(f20250,plain,(
% 68.49/10.20 spl93_487 | ~spl93_22 | ~spl93_121),
% 68.49/10.20 inference(avatar_split_clause,[],[f2665,f2647,f1832,f20248])).
% 68.49/10.20 thf(f20248,plain,(
% 68.49/10.20 spl93_487 <=> ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_487])])).
% 68.49/10.20 thf(f2665,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_121)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2664])).
% 68.49/10.20 thf(f2664,plain,(
% 68.49/10.20 ( ! [X0 : a] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_22 | ~spl93_121)),
% 68.49/10.20 inference(superposition,[],[f2648,f1833])).
% 68.49/10.20 thf(f20246,plain,(
% 68.49/10.20 spl93_486 | ~spl93_37 | ~spl93_53),
% 68.49/10.20 inference(avatar_split_clause,[],[f2080,f2074,f1955,f20243])).
% 68.49/10.20 thf(f20243,plain,(
% 68.49/10.20 spl93_486 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),partial_carrier(a,monoid_ext(a,product_unit)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_486])])).
% 68.49/10.20 thf(f1955,plain,(
% 68.49/10.20 spl93_37 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_37])])).
% 68.49/10.20 thf(f2080,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),partial_carrier(a,monoid_ext(a,product_unit)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))) | (~spl93_37 | ~spl93_53)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2077])).
% 68.49/10.20 thf(f2077,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),partial_carrier(a,monoid_ext(a,product_unit)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))) | (~spl93_37 | ~spl93_53)),
% 68.49/10.20 inference(superposition,[],[f2075,f1957])).
% 68.49/10.20 thf(f1957,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true) | ~spl93_37),
% 68.49/10.20 inference(avatar_component_clause,[],[f1955])).
% 68.49/10.20 thf(f20011,plain,(
% 68.49/10.20 spl93_485 | ~spl93_22 | ~spl93_115),
% 68.49/10.20 inference(avatar_split_clause,[],[f2620,f2615,f1832,f20009])).
% 68.49/10.20 thf(f20009,plain,(
% 68.49/10.20 spl93_485 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,one(X0,ring_ext(X0,X1)),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,semiring(X0,X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_485])])).
% 68.49/10.20 thf(f2615,plain,(
% 68.49/10.20 spl93_115 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_115])])).
% 68.49/10.20 thf(f2620,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,one(X0,ring_ext(X0,X1)),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,semiring(X0,X1),X2))) ) | (~spl93_22 | ~spl93_115)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2619])).
% 68.49/10.20 thf(f2619,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,one(X0,ring_ext(X0,X1)),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,semiring(X0,X1),X2))) ) | (~spl93_22 | ~spl93_115)),
% 68.49/10.20 inference(superposition,[],[f2616,f1833])).
% 68.49/10.20 thf(f2616,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) ) | ~spl93_115),
% 68.49/10.20 inference(avatar_component_clause,[],[f2615])).
% 68.49/10.20 thf(f19967,plain,(
% 68.49/10.20 spl93_484 | ~spl93_49),
% 68.49/10.20 inference(avatar_split_clause,[],[f2051,f2044,f19965])).
% 68.49/10.20 thf(f19965,plain,(
% 68.49/10.20 spl93_484 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | (vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1) != vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_484])])).
% 68.49/10.20 thf(f2051,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | (vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1) != vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X2))) ) | ~spl93_49),
% 68.49/10.20 inference(constrained_superposition,[],[f2045,f2045])).
% 68.49/10.20 thf(f17683,plain,(
% 68.49/10.20 spl93_483 | ~spl93_22 | ~spl93_114),
% 68.49/10.20 inference(avatar_split_clause,[],[f2612,f2588,f1832,f17681])).
% 68.49/10.20 thf(f17681,plain,(
% 68.49/10.20 spl93_483 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,abelian_group(X0,X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_483])])).
% 68.49/10.20 thf(f2588,plain,(
% 68.49/10.20 spl93_114 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_114])])).
% 68.49/10.20 thf(f2612,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,abelian_group(X0,X1),X2))) ) | (~spl93_22 | ~spl93_114)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2611])).
% 68.49/10.20 thf(f2611,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,abelian_group(X0,X1),X2))) ) | (~spl93_22 | ~spl93_114)),
% 68.49/10.20 inference(superposition,[],[f2589,f1833])).
% 68.49/10.20 thf(f2589,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) ) | ~spl93_114),
% 68.49/10.20 inference(avatar_component_clause,[],[f2588])).
% 68.49/10.20 thf(f17679,plain,(
% 68.49/10.20 spl93_482 | ~spl93_22 | ~spl93_113),
% 68.49/10.20 inference(avatar_split_clause,[],[f2608,f2584,f1832,f17677])).
% 68.49/10.20 thf(f17677,plain,(
% 68.49/10.20 spl93_482 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,semiring(X0,X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_482])])).
% 68.49/10.20 thf(f2584,plain,(
% 68.49/10.20 spl93_113 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_113])])).
% 68.49/10.20 thf(f2608,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,semiring(X0,X1),X2))) ) | (~spl93_22 | ~spl93_113)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2607])).
% 68.49/10.20 thf(f2607,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,semiring(X0,X1),X2))) ) | (~spl93_22 | ~spl93_113)),
% 68.49/10.20 inference(superposition,[],[f2585,f1833])).
% 68.49/10.20 thf(f2585,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) ) | ~spl93_113),
% 68.49/10.20 inference(avatar_component_clause,[],[f2584])).
% 68.49/10.20 thf(f17675,plain,(
% 68.49/10.20 spl93_481 | ~spl93_22 | ~spl93_112),
% 68.49/10.20 inference(avatar_split_clause,[],[f2605,f2580,f1832,f17673])).
% 68.49/10.20 thf(f17673,plain,(
% 68.49/10.20 spl93_481 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK27(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_481])])).
% 68.49/10.20 thf(f2580,plain,(
% 68.49/10.20 spl93_112 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_112])])).
% 68.49/10.20 thf(f2605,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK27(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2))) ) | (~spl93_22 | ~spl93_112)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2604])).
% 68.49/10.20 thf(f2604,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK27(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2))) ) | (~spl93_22 | ~spl93_112)),
% 68.49/10.20 inference(superposition,[],[f2581,f1833])).
% 68.49/10.20 thf(f2581,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_112),
% 68.49/10.20 inference(avatar_component_clause,[],[f2580])).
% 68.49/10.20 thf(f17671,plain,(
% 68.49/10.20 spl93_480 | ~spl93_22 | ~spl93_111),
% 68.49/10.20 inference(avatar_split_clause,[],[f2603,f2576,f1832,f17669])).
% 68.49/10.20 thf(f17669,plain,(
% 68.49/10.20 spl93_480 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK26(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_480])])).
% 68.49/10.20 thf(f2576,plain,(
% 68.49/10.20 spl93_111 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_111])])).
% 68.49/10.20 thf(f2603,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK26(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2))) ) | (~spl93_22 | ~spl93_111)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2602])).
% 68.49/10.20 thf(f2602,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK26(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2))) ) | (~spl93_22 | ~spl93_111)),
% 68.49/10.20 inference(superposition,[],[f2577,f1833])).
% 68.49/10.20 thf(f2577,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_111),
% 68.49/10.20 inference(avatar_component_clause,[],[f2576])).
% 68.49/10.20 thf(f17667,plain,(
% 68.49/10.20 spl93_479 | ~spl93_22 | ~spl93_110),
% 68.49/10.20 inference(avatar_split_clause,[],[f2601,f2572,f1832,f17665])).
% 68.49/10.20 thf(f17665,plain,(
% 68.49/10.20 spl93_479 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK25(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_479])])).
% 68.49/10.20 thf(f2572,plain,(
% 68.49/10.20 spl93_110 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_110])])).
% 68.49/10.20 thf(f2601,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK25(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2))) ) | (~spl93_22 | ~spl93_110)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2600])).
% 68.49/10.20 thf(f2600,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK25(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP2(X1,X0),X2))) ) | (~spl93_22 | ~spl93_110)),
% 68.49/10.20 inference(superposition,[],[f2573,f1833])).
% 68.49/10.20 thf(f2573,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_110),
% 68.49/10.20 inference(avatar_component_clause,[],[f2572])).
% 68.49/10.20 thf(f17596,plain,(
% 68.49/10.20 spl93_478 | ~spl93_22 | ~spl93_109),
% 68.49/10.20 inference(avatar_split_clause,[],[f2598,f2568,f1832,f17594])).
% 68.49/10.20 thf(f17594,plain,(
% 68.49/10.20 spl93_478 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK24(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_478])])).
% 68.49/10.20 thf(f2568,plain,(
% 68.49/10.20 spl93_109 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_109])])).
% 68.49/10.20 thf(f2598,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK24(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2))) ) | (~spl93_22 | ~spl93_109)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2597])).
% 68.49/10.20 thf(f2597,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK24(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2))) ) | (~spl93_22 | ~spl93_109)),
% 68.49/10.20 inference(superposition,[],[f2569,f1833])).
% 68.49/10.20 thf(f2569,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_109),
% 68.49/10.20 inference(avatar_component_clause,[],[f2568])).
% 68.49/10.20 thf(f17592,plain,(
% 68.49/10.20 spl93_477 | ~spl93_22 | ~spl93_108),
% 68.49/10.20 inference(avatar_split_clause,[],[f2596,f2563,f1832,f17590])).
% 68.49/10.20 thf(f17590,plain,(
% 68.49/10.20 spl93_477 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK23(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_477])])).
% 68.49/10.20 thf(f2563,plain,(
% 68.49/10.20 spl93_108 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_108])])).
% 68.49/10.20 thf(f2596,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK23(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2))) ) | (~spl93_22 | ~spl93_108)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2595])).
% 68.49/10.20 thf(f2595,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK23(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP3(X1,X0),X2))) ) | (~spl93_22 | ~spl93_108)),
% 68.49/10.20 inference(superposition,[],[f2564,f1833])).
% 68.49/10.20 thf(f2564,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_108),
% 68.49/10.20 inference(avatar_component_clause,[],[f2563])).
% 68.49/10.20 thf(f17588,plain,(
% 68.49/10.20 spl93_476 | ~spl93_22 | ~spl93_107),
% 68.49/10.20 inference(avatar_split_clause,[],[f2594,f2559,f1832,f17586])).
% 68.49/10.20 thf(f17586,plain,(
% 68.49/10.20 spl93_476 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK22(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_476])])).
% 68.49/10.20 thf(f2559,plain,(
% 68.49/10.20 spl93_107 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_107])])).
% 68.49/10.20 thf(f2594,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK22(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2))) ) | (~spl93_22 | ~spl93_107)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2593])).
% 68.49/10.20 thf(f2593,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK22(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2))) ) | (~spl93_22 | ~spl93_107)),
% 68.49/10.20 inference(superposition,[],[f2560,f1833])).
% 68.49/10.20 thf(f2560,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_107),
% 68.49/10.20 inference(avatar_component_clause,[],[f2559])).
% 68.49/10.20 thf(f17584,plain,(
% 68.49/10.20 spl93_475 | ~spl93_22 | ~spl93_106),
% 68.49/10.20 inference(avatar_split_clause,[],[f2592,f2555,f1832,f17582])).
% 68.49/10.20 thf(f17582,plain,(
% 68.49/10.20 spl93_475 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK21(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_475])])).
% 68.49/10.20 thf(f2555,plain,(
% 68.49/10.20 spl93_106 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_106])])).
% 68.49/10.20 thf(f2592,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK21(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2))) ) | (~spl93_22 | ~spl93_106)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2591])).
% 68.49/10.20 thf(f2591,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,sK21(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),$o,sP4(X1,X0),X2))) ) | (~spl93_22 | ~spl93_106)),
% 68.49/10.20 inference(superposition,[],[f2556,f1833])).
% 68.49/10.20 thf(f2556,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) ) | ~spl93_106),
% 68.49/10.20 inference(avatar_component_clause,[],[f2555])).
% 68.49/10.20 thf(f17580,plain,(
% 68.49/10.20 spl93_474 | ~spl93_48 | ~spl93_102),
% 68.49/10.20 inference(avatar_split_clause,[],[f2519,f2492,f2031,f17578])).
% 68.49/10.20 thf(f17578,plain,(
% 68.49/10.20 spl93_474 <=> ! [X1 : $tType,X0 : $tType,X4 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_474])])).
% 68.49/10.20 thf(f2519,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X4 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X3))) ) | (~spl93_48 | ~spl93_102)),
% 68.49/10.20 inference(constrained_superposition,[],[f2493,f2032])).
% 68.49/10.20 thf(f17576,plain,(
% 68.49/10.20 spl93_473 | ~spl93_47 | ~spl93_102),
% 68.49/10.20 inference(avatar_split_clause,[],[f2518,f2492,f2027,f17574])).
% 68.49/10.20 thf(f17574,plain,(
% 68.49/10.20 spl93_473 <=> ! [X1 : $tType,X0 : $tType,X4 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_473])])).
% 68.49/10.20 thf(f2518,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X4 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X3))) ) | (~spl93_47 | ~spl93_102)),
% 68.49/10.20 inference(constrained_superposition,[],[f2493,f2028])).
% 68.49/10.20 thf(f17572,plain,(
% 68.49/10.20 spl93_472 | ~spl93_48 | ~spl93_101),
% 68.49/10.20 inference(avatar_split_clause,[],[f2506,f2488,f2031,f17570])).
% 68.49/10.20 thf(f17570,plain,(
% 68.49/10.20 spl93_472 <=> ! [X1 : $tType,X0 : $tType,X4 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_472])])).
% 68.49/10.20 thf(f2506,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X4 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X3))) ) | (~spl93_48 | ~spl93_101)),
% 68.49/10.20 inference(constrained_superposition,[],[f2489,f2032])).
% 68.49/10.20 thf(f17568,plain,(
% 68.49/10.20 spl93_471 | ~spl93_47 | ~spl93_101),
% 68.49/10.20 inference(avatar_split_clause,[],[f2505,f2488,f2027,f17566])).
% 68.49/10.20 thf(f17566,plain,(
% 68.49/10.20 spl93_471 <=> ! [X1 : $tType,X0 : $tType,X4 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X2 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_471])])).
% 68.49/10.20 thf(f2505,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0) > $o,X4 : product_prod(X1,X0)] : (($true != vAPP(product_prod(X1,X0),$o,X3,X2)) | ($true = vAPP(product_prod(X1,X0),$o,X3,X4)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X3)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X3))) ) | (~spl93_47 | ~spl93_101)),
% 68.49/10.20 inference(constrained_superposition,[],[f2489,f2028])).
% 68.49/10.20 thf(f17530,plain,(
% 68.49/10.20 spl93_470 | ~spl93_25 | ~spl93_73 | ~spl93_173),
% 68.49/10.20 inference(avatar_split_clause,[],[f6272,f3263,f2243,f1873,f17527])).
% 68.49/10.20 thf(f17527,plain,(
% 68.49/10.20 spl93_470 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_470])])).
% 68.49/10.20 thf(f6272,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (~spl93_25 | ~spl93_73 | ~spl93_173)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6271])).
% 68.49/10.20 thf(f6271,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (~spl93_25 | ~spl93_73 | ~spl93_173)),
% 68.49/10.20 inference(forward_demodulation,[],[f3275,f1875])).
% 68.49/10.20 thf(f3275,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_173)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3272])).
% 68.49/10.20 thf(f3272,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_173)),
% 68.49/10.20 inference(superposition,[],[f3264,f2245])).
% 68.49/10.20 thf(f17525,plain,(
% 68.49/10.20 spl93_469 | ~spl93_25 | ~spl93_73 | ~spl93_174),
% 68.49/10.20 inference(avatar_split_clause,[],[f6270,f3267,f2243,f1873,f17522])).
% 68.49/10.20 thf(f17522,plain,(
% 68.49/10.20 spl93_469 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_469])])).
% 68.49/10.20 thf(f6270,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),sK6)) | (~spl93_25 | ~spl93_73 | ~spl93_174)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6269])).
% 68.49/10.20 thf(f6269,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),sK6)) | (~spl93_25 | ~spl93_73 | ~spl93_174)),
% 68.49/10.20 inference(forward_demodulation,[],[f3284,f1875])).
% 68.49/10.20 thf(f3284,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_174)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3281])).
% 68.49/10.20 thf(f3281,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_174)),
% 68.49/10.20 inference(superposition,[],[f3268,f2245])).
% 68.49/10.20 thf(f17520,plain,(
% 68.49/10.20 spl93_468 | ~spl93_440 | ~spl93_467),
% 68.49/10.20 inference(avatar_split_clause,[],[f17515,f17511,f13821,f17517])).
% 68.49/10.20 thf(f17517,plain,(
% 68.49/10.20 spl93_468 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_468])])).
% 68.49/10.20 thf(f17511,plain,(
% 68.49/10.20 spl93_467 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_467])])).
% 68.49/10.20 thf(f17515,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))) | (~spl93_440 | ~spl93_467)),
% 68.49/10.20 inference(forward_demodulation,[],[f17513,f13823])).
% 68.49/10.20 thf(f17513,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))) | ~spl93_467),
% 68.49/10.20 inference(avatar_component_clause,[],[f17511])).
% 68.49/10.20 thf(f17514,plain,(
% 68.49/10.20 spl93_467 | ~spl93_36 | ~spl93_37 | ~spl93_46 | ~spl93_53 | ~spl93_96),
% 68.49/10.20 inference(avatar_split_clause,[],[f2458,f2432,f2074,f2023,f1955,f1950,f17511])).
% 68.49/10.20 thf(f1950,plain,(
% 68.49/10.20 spl93_36 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,comm_group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_36])])).
% 68.49/10.20 thf(f2432,plain,(
% 68.49/10.20 spl93_96 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_96])])).
% 68.49/10.20 thf(f2458,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))) | (~spl93_36 | ~spl93_37 | ~spl93_46 | ~spl93_53 | ~spl93_96)),
% 68.49/10.20 inference(forward_demodulation,[],[f2457,f2024])).
% 68.49/10.20 thf(f2457,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),a,one(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),units(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))) | (~spl93_36 | ~spl93_37 | ~spl93_53 | ~spl93_96)),
% 68.49/10.20 inference(forward_demodulation,[],[f2456,f2080])).
% 68.49/10.20 thf(f2456,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),a,one(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),partial_carrier(a,monoid_ext(a,product_unit)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))) | (~spl93_36 | ~spl93_96)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2453])).
% 68.49/10.20 thf(f2453,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),a,one(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),set(a),partial_carrier(a,monoid_ext(a,product_unit)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)))) | (~spl93_36 | ~spl93_96)),
% 68.49/10.20 inference(superposition,[],[f2433,f1952])).
% 68.49/10.20 thf(f1952,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,comm_group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true) | ~spl93_36),
% 68.49/10.20 inference(avatar_component_clause,[],[f1950])).
% 68.49/10.20 thf(f2433,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) ) | ~spl93_96),
% 68.49/10.20 inference(avatar_component_clause,[],[f2432])).
% 68.49/10.20 thf(f17467,plain,(
% 68.49/10.20 spl93_466 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_160),
% 68.49/10.20 inference(avatar_split_clause,[],[f6299,f3056,f2247,f2243,f2074,f17465])).
% 68.49/10.20 thf(f17465,plain,(
% 68.49/10.20 spl93_466 <=> ! [X0 : int] : ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_466])])).
% 68.49/10.20 thf(f6299,plain,(
% 68.49/10.20 ( ! [X0 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_160)),
% 68.49/10.20 inference(forward_demodulation,[],[f3072,f5934])).
% 68.49/10.20 thf(f3072,plain,(
% 68.49/10.20 ( ! [X0 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_160)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3069])).
% 68.49/10.20 thf(f3069,plain,(
% 68.49/10.20 ( ! [X0 : int] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_160)),
% 68.49/10.20 inference(superposition,[],[f3057,f2245])).
% 68.49/10.20 thf(f17463,plain,(
% 68.49/10.20 spl93_465 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_161),
% 68.49/10.20 inference(avatar_split_clause,[],[f6297,f3060,f2247,f2243,f2074,f17461])).
% 68.49/10.20 thf(f17461,plain,(
% 68.49/10.20 spl93_465 <=> ! [X0 : nat] : ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_465])])).
% 68.49/10.20 thf(f6297,plain,(
% 68.49/10.20 ( ! [X0 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_161)),
% 68.49/10.20 inference(forward_demodulation,[],[f3081,f5934])).
% 68.49/10.20 thf(f3081,plain,(
% 68.49/10.20 ( ! [X0 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_161)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3078])).
% 68.49/10.20 thf(f3078,plain,(
% 68.49/10.20 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) ) | (~spl93_73 | ~spl93_161)),
% 68.49/10.20 inference(superposition,[],[f3061,f2245])).
% 68.49/10.20 thf(f17276,plain,(
% 68.49/10.20 spl93_464 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_156),
% 68.49/10.20 inference(avatar_split_clause,[],[f3114,f2998,f2247,f2243,f2074,f17273])).
% 68.49/10.20 thf(f17273,plain,(
% 68.49/10.20 spl93_464 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_464])])).
% 68.49/10.20 thf(f3114,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_156)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3113])).
% 68.49/10.20 thf(f3113,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_156)),
% 68.49/10.20 inference(forward_demodulation,[],[f3112,f2249])).
% 68.49/10.20 thf(f3112,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_156)),
% 68.49/10.20 inference(forward_demodulation,[],[f3010,f2300])).
% 68.49/10.20 thf(f3010,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_156)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3007])).
% 68.49/10.20 thf(f3007,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK40(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_156)),
% 68.49/10.20 inference(superposition,[],[f2999,f2245])).
% 68.49/10.20 thf(f17271,plain,(
% 68.49/10.20 spl93_463 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_157),
% 68.49/10.20 inference(avatar_split_clause,[],[f3105,f3002,f2247,f2243,f2074,f17268])).
% 68.49/10.20 thf(f17268,plain,(
% 68.49/10.20 spl93_463 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_463])])).
% 68.49/10.20 thf(f3105,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3104])).
% 68.49/10.20 thf(f3104,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(forward_demodulation,[],[f3103,f2249])).
% 68.49/10.20 thf(f3103,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_157)),
% 68.49/10.20 inference(forward_demodulation,[],[f3023,f2300])).
% 68.49/10.20 thf(f3023,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_157)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3020])).
% 68.49/10.20 thf(f3020,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK41(ring_ext(a,b),a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | (~spl93_73 | ~spl93_157)),
% 68.49/10.20 inference(superposition,[],[f3003,f2245])).
% 68.49/10.20 thf(f17266,plain,(
% 68.49/10.20 spl93_462 | ~spl93_22 | ~spl93_102),
% 68.49/10.20 inference(avatar_split_clause,[],[f2517,f2492,f1832,f17264])).
% 68.49/10.20 thf(f17264,plain,(
% 68.49/10.20 spl93_462 <=> ! [X0 : $tType,X2 : product_prod(X0,$o),X1 : product_prod(X0,$o) > $o] : (($true != vAPP(product_prod(X0,$o),$o,X1,vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(sTfun(product_prod(X0,$o),$o),X0,sK38($o,X0),X1)),$true))) | ($true = vAPP(product_prod(X0,$o),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod(X0,$o),$o),$o,sK39($o,X0),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_462])])).
% 68.49/10.20 thf(f2517,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : product_prod(X0,$o),X1 : product_prod(X0,$o) > $o] : (($true != vAPP(product_prod(X0,$o),$o,X1,vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(sTfun(product_prod(X0,$o),$o),X0,sK38($o,X0),X1)),$true))) | ($true = vAPP(product_prod(X0,$o),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod(X0,$o),$o),$o,sK39($o,X0),X1))) ) | (~spl93_22 | ~spl93_102)),
% 68.49/10.20 inference(superposition,[],[f2493,f1833])).
% 68.49/10.20 thf(f17262,plain,(
% 68.49/10.20 spl93_461 | ~spl93_22 | ~spl93_102),
% 68.49/10.20 inference(avatar_split_clause,[],[f2516,f2492,f1832,f17260])).
% 68.49/10.20 thf(f17260,plain,(
% 68.49/10.20 spl93_461 <=> ! [X0 : $tType,X2 : product_prod($o,X0),X1 : product_prod($o,X0) > $o] : (($true != vAPP(product_prod($o,X0),$o,X1,vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(sTfun(product_prod($o,X0),$o),X0,sK39(X0,$o),X1)))) | ($true = vAPP(product_prod($o,X0),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod($o,X0),$o),$o,sK38(X0,$o),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_461])])).
% 68.49/10.20 thf(f2516,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : product_prod($o,X0),X1 : product_prod($o,X0) > $o] : (($true != vAPP(product_prod($o,X0),$o,X1,vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(sTfun(product_prod($o,X0),$o),X0,sK39(X0,$o),X1)))) | ($true = vAPP(product_prod($o,X0),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod($o,X0),$o),$o,sK38(X0,$o),X1))) ) | (~spl93_22 | ~spl93_102)),
% 68.49/10.20 inference(superposition,[],[f2493,f1833])).
% 68.49/10.20 thf(f17258,plain,(
% 68.49/10.20 spl93_460 | ~spl93_22 | ~spl93_101),
% 68.49/10.20 inference(avatar_split_clause,[],[f2504,f2488,f1832,f17256])).
% 68.49/10.20 thf(f17256,plain,(
% 68.49/10.20 spl93_460 <=> ! [X0 : $tType,X2 : product_prod(X0,$o),X1 : product_prod(X0,$o) > $o] : (($true != vAPP(product_prod(X0,$o),$o,X1,vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(sTfun(product_prod(X0,$o),$o),X0,sK36($o,X0),X1)),$true))) | ($true = vAPP(product_prod(X0,$o),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod(X0,$o),$o),$o,sK37($o,X0),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_460])])).
% 68.49/10.20 thf(f2504,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : product_prod(X0,$o),X1 : product_prod(X0,$o) > $o] : (($true != vAPP(product_prod(X0,$o),$o,X1,vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(sTfun(product_prod(X0,$o),$o),X0,sK36($o,X0),X1)),$true))) | ($true = vAPP(product_prod(X0,$o),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod(X0,$o),$o),$o,sK37($o,X0),X1))) ) | (~spl93_22 | ~spl93_101)),
% 68.49/10.20 inference(superposition,[],[f2489,f1833])).
% 68.49/10.20 thf(f17253,plain,(
% 68.49/10.20 spl93_459 | ~spl93_22 | ~spl93_101),
% 68.49/10.20 inference(avatar_split_clause,[],[f2503,f2488,f1832,f17251])).
% 68.49/10.20 thf(f17251,plain,(
% 68.49/10.20 spl93_459 <=> ! [X0 : $tType,X2 : product_prod($o,X0),X1 : product_prod($o,X0) > $o] : (($true != vAPP(product_prod($o,X0),$o,X1,vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(sTfun(product_prod($o,X0),$o),X0,sK37(X0,$o),X1)))) | ($true = vAPP(product_prod($o,X0),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod($o,X0),$o),$o,sK36(X0,$o),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_459])])).
% 68.49/10.20 thf(f2503,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : product_prod($o,X0),X1 : product_prod($o,X0) > $o] : (($true != vAPP(product_prod($o,X0),$o,X1,vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(sTfun(product_prod($o,X0),$o),X0,sK37(X0,$o),X1)))) | ($true = vAPP(product_prod($o,X0),$o,X1,X2)) | ($false = vAPP(sTfun(product_prod($o,X0),$o),$o,sK36(X0,$o),X1))) ) | (~spl93_22 | ~spl93_101)),
% 68.49/10.20 inference(superposition,[],[f2489,f1833])).
% 68.49/10.20 thf(f16958,plain,(
% 68.49/10.20 spl93_458 | ~spl93_22 | ~spl93_105),
% 68.49/10.20 inference(avatar_split_clause,[],[f2552,f2547,f1832,f16956])).
% 68.49/10.20 thf(f16956,plain,(
% 68.49/10.20 spl93_458 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_458])])).
% 68.49/10.20 thf(f2547,plain,(
% 68.49/10.20 spl93_105 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (ab_group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_105])])).
% 68.49/10.20 thf(f2552,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_105)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2551])).
% 68.49/10.20 thf(f2551,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_105)),
% 68.49/10.20 inference(superposition,[],[f2548,f1833])).
% 68.49/10.20 thf(f2548,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((ab_group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)))) ) | ~spl93_105),
% 68.49/10.20 inference(avatar_component_clause,[],[f2547])).
% 68.49/10.20 thf(f16025,plain,(
% 68.49/10.20 spl93_457 | ~spl93_24 | ~spl93_73 | ~spl93_168),
% 68.49/10.20 inference(avatar_split_clause,[],[f6278,f3193,f2243,f1868,f16022])).
% 68.49/10.20 thf(f16022,plain,(
% 68.49/10.20 spl93_457 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_457])])).
% 68.49/10.20 thf(f6278,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_24 | ~spl93_73 | ~spl93_168)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6277])).
% 68.49/10.20 thf(f6277,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_24 | ~spl93_73 | ~spl93_168)),
% 68.49/10.20 inference(forward_demodulation,[],[f3209,f1870])).
% 68.49/10.20 thf(f3209,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_168)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3206])).
% 68.49/10.20 thf(f3206,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_168)),
% 68.49/10.20 inference(superposition,[],[f3194,f2245])).
% 68.49/10.20 thf(f16020,plain,(
% 68.49/10.20 spl93_456 | ~spl93_24 | ~spl93_73 | ~spl93_169),
% 68.49/10.20 inference(avatar_split_clause,[],[f6276,f3197,f2243,f1868,f16017])).
% 68.49/10.20 thf(f16017,plain,(
% 68.49/10.20 spl93_456 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_456])])).
% 68.49/10.20 thf(f6276,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (~spl93_24 | ~spl93_73 | ~spl93_169)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6275])).
% 68.49/10.20 thf(f6275,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (~spl93_24 | ~spl93_73 | ~spl93_169)),
% 68.49/10.20 inference(forward_demodulation,[],[f3217,f1870])).
% 68.49/10.20 thf(f3217,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_169)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3214])).
% 68.49/10.20 thf(f3214,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_169)),
% 68.49/10.20 inference(superposition,[],[f3198,f2245])).
% 68.49/10.20 thf(f16015,plain,(
% 68.49/10.20 spl93_455 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_171),
% 68.49/10.20 inference(avatar_split_clause,[],[f6267,f3236,f2247,f2243,f2074,f1873,f16012])).
% 68.49/10.20 thf(f16012,plain,(
% 68.49/10.20 spl93_455 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_455])])).
% 68.49/10.20 thf(f6267,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3316,f5934])).
% 68.49/10.20 thf(f3316,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_25 | ~spl93_73 | ~spl93_171)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3315])).
% 68.49/10.20 thf(f3315,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_25 | ~spl93_73 | ~spl93_171)),
% 68.49/10.20 inference(forward_demodulation,[],[f3244,f1875])).
% 68.49/10.20 thf(f3244,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_171)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3241])).
% 68.49/10.20 thf(f3241,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,vAPP(a,sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a),sK42(b,a),sK6),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_171)),
% 68.49/10.20 inference(superposition,[],[f3237,f2245])).
% 68.49/10.20 thf(f16010,plain,(
% 68.49/10.20 spl93_454 | ~spl93_39 | ~spl93_70 | ~spl93_104),
% 68.49/10.20 inference(avatar_split_clause,[],[f2538,f2526,f2181,f1964,f16008])).
% 68.49/10.20 thf(f16008,plain,(
% 68.49/10.20 spl93_454 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_454])])).
% 68.49/10.20 thf(f2538,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))) ) | (~spl93_39 | ~spl93_70 | ~spl93_104)),
% 68.49/10.20 inference(forward_demodulation,[],[f2530,f1965])).
% 68.49/10.20 thf(f2530,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X2)),X1)))) ) | (~spl93_70 | ~spl93_104)),
% 68.49/10.20 inference(superposition,[],[f2527,f2182])).
% 68.49/10.20 thf(f16006,plain,(
% 68.49/10.20 spl93_453 | ~spl93_22 | ~spl93_97),
% 68.49/10.20 inference(avatar_split_clause,[],[f2467,f2436,f1832,f16004])).
% 68.49/10.20 thf(f16004,plain,(
% 68.49/10.20 spl93_453 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X1),X2))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X1),X2))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_453])])).
% 68.49/10.20 thf(f2467,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X1),X2))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X1),X2)))) ) | (~spl93_22 | ~spl93_97)),
% 68.49/10.20 inference(superposition,[],[f2437,f1833])).
% 68.49/10.20 thf(f15848,plain,(
% 68.49/10.20 spl93_452 | ~spl93_22 | ~spl93_97),
% 68.49/10.20 inference(avatar_split_clause,[],[f2459,f2436,f1832,f15846])).
% 68.49/10.20 thf(f15846,plain,(
% 68.49/10.20 spl93_452 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X2),X1))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X2),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_452])])).
% 68.49/10.20 thf(f2459,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X2),X1))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK35($o,X0),X2),X1)))) ) | (~spl93_22 | ~spl93_97)),
% 68.49/10.20 inference(superposition,[],[f2437,f1833])).
% 68.49/10.20 thf(f15844,plain,(
% 68.49/10.20 spl93_451 | ~spl93_40 | ~spl93_64),
% 68.49/10.20 inference(avatar_split_clause,[],[f2205,f2153,f1968,f15842])).
% 68.49/10.20 thf(f15842,plain,(
% 68.49/10.20 spl93_451 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_451])])).
% 68.49/10.20 thf(f1968,plain,(
% 68.49/10.20 spl93_40 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_40])])).
% 68.49/10.20 thf(f2205,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))) ) | (~spl93_40 | ~spl93_64)),
% 68.49/10.20 inference(forward_demodulation,[],[f2198,f1969])).
% 68.49/10.20 thf(f1969,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)))) ) | ~spl93_40),
% 68.49/10.20 inference(avatar_component_clause,[],[f1968])).
% 68.49/10.20 thf(f2198,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,suc,X1))))) ) | (~spl93_40 | ~spl93_64)),
% 68.49/10.20 inference(superposition,[],[f2154,f1969])).
% 68.49/10.20 thf(f15840,plain,(
% 68.49/10.20 spl93_450 | ~spl93_39 | ~spl93_64),
% 68.49/10.20 inference(avatar_split_clause,[],[f2199,f2153,f1964,f15838])).
% 68.49/10.20 thf(f15838,plain,(
% 68.49/10.20 spl93_450 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_450])])).
% 68.49/10.20 thf(f2199,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,suc,X0)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))) ) | (~spl93_39 | ~spl93_64)),
% 68.49/10.20 inference(superposition,[],[f2154,f1965])).
% 68.49/10.20 thf(f15836,plain,(
% 68.49/10.20 spl93_449 | ~spl93_39 | ~spl93_64),
% 68.49/10.20 inference(avatar_split_clause,[],[f2197,f2153,f1964,f15834])).
% 68.49/10.20 thf(f15834,plain,(
% 68.49/10.20 spl93_449 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_449])])).
% 68.49/10.20 thf(f2197,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) ) | (~spl93_39 | ~spl93_64)),
% 68.49/10.20 inference(superposition,[],[f2154,f1965])).
% 68.49/10.20 thf(f15832,plain,(
% 68.49/10.20 spl93_448 | ~spl93_39 | ~spl93_63),
% 68.49/10.20 inference(avatar_split_clause,[],[f2190,f2149,f1964,f15830])).
% 68.49/10.20 thf(f15830,plain,(
% 68.49/10.20 spl93_448 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_448])])).
% 68.49/10.20 thf(f2190,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))) ) | (~spl93_39 | ~spl93_63)),
% 68.49/10.20 inference(forward_demodulation,[],[f2184,f1965])).
% 68.49/10.20 thf(f2184,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X2)))) ) | (~spl93_39 | ~spl93_63)),
% 68.49/10.20 inference(superposition,[],[f2150,f1965])).
% 68.49/10.20 thf(f15828,plain,(
% 68.49/10.20 spl93_447 | ~spl93_40 | ~spl93_63),
% 68.49/10.20 inference(avatar_split_clause,[],[f2187,f2149,f1968,f15826])).
% 68.49/10.20 thf(f15826,plain,(
% 68.49/10.20 spl93_447 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,suc,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_447])])).
% 68.49/10.20 thf(f2187,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X2),vAPP(nat,nat,suc,X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))) ) | (~spl93_40 | ~spl93_63)),
% 68.49/10.20 inference(superposition,[],[f2150,f1969])).
% 68.49/10.20 thf(f15824,plain,(
% 68.49/10.20 spl93_446 | ~spl93_40 | ~spl93_63),
% 68.49/10.20 inference(avatar_split_clause,[],[f2185,f2149,f1968,f15822])).
% 68.49/10.20 thf(f15822,plain,(
% 68.49/10.20 spl93_446 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_446])])).
% 68.49/10.20 thf(f2185,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) ) | (~spl93_40 | ~spl93_63)),
% 68.49/10.20 inference(superposition,[],[f2150,f1969])).
% 68.49/10.20 thf(f15517,plain,(
% 68.49/10.20 spl93_445 | ~spl93_22 | ~spl93_102),
% 68.49/10.20 inference(avatar_split_clause,[],[f2522,f2492,f1832,f15515])).
% 68.49/10.20 thf(f15515,plain,(
% 68.49/10.20 spl93_445 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,X1),X2 : product_prod(X0,X1) > $o] : (($true = vAPP(product_prod(X0,X1),$o,X2,X3)) | ($false = vAPP(product_prod(X0,X1),$o,X2,vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),X2)),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),X2)))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_445])])).
% 68.49/10.20 thf(f2522,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1) > $o,X3 : product_prod(X0,X1)] : (($true = vAPP(product_prod(X0,X1),$o,X2,X3)) | ($false = vAPP(product_prod(X0,X1),$o,X2,vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),X2)),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),X2))))) ) | (~spl93_22 | ~spl93_102)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2520])).
% 68.49/10.20 thf(f2520,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1) > $o,X3 : product_prod(X0,X1)] : (($true != $true) | ($true = vAPP(product_prod(X0,X1),$o,X2,X3)) | ($false = vAPP(product_prod(X0,X1),$o,X2,vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK38(X1,X0),X2)),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK39(X1,X0),X2))))) ) | (~spl93_22 | ~spl93_102)),
% 68.49/10.20 inference(superposition,[],[f2493,f1833])).
% 68.49/10.20 thf(f15513,plain,(
% 68.49/10.20 spl93_444 | ~spl93_22 | ~spl93_101),
% 68.49/10.20 inference(avatar_split_clause,[],[f2509,f2488,f1832,f15511])).
% 68.49/10.20 thf(f15511,plain,(
% 68.49/10.20 spl93_444 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X0,X1),X2 : product_prod(X0,X1) > $o] : (($true = vAPP(product_prod(X0,X1),$o,X2,X3)) | ($false = vAPP(product_prod(X0,X1),$o,X2,vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),X2)),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),X2)))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_444])])).
% 68.49/10.20 thf(f2509,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1) > $o,X3 : product_prod(X0,X1)] : (($true = vAPP(product_prod(X0,X1),$o,X2,X3)) | ($false = vAPP(product_prod(X0,X1),$o,X2,vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),X2)),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),X2))))) ) | (~spl93_22 | ~spl93_101)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2507])).
% 68.49/10.20 thf(f2507,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1) > $o,X3 : product_prod(X0,X1)] : (($true != $true) | ($true = vAPP(product_prod(X0,X1),$o,X2,X3)) | ($false = vAPP(product_prod(X0,X1),$o,X2,vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(sTfun(product_prod(X0,X1),$o),X0,sK36(X1,X0),X2)),vAPP(sTfun(product_prod(X0,X1),$o),X1,sK37(X1,X0),X2))))) ) | (~spl93_22 | ~spl93_101)),
% 68.49/10.20 inference(superposition,[],[f2489,f1833])).
% 68.49/10.20 thf(f15485,plain,(
% 68.49/10.20 spl93_443 | ~spl93_22 | ~spl93_75),
% 68.49/10.20 inference(avatar_split_clause,[],[f2261,f2256,f1832,f15483])).
% 68.49/10.20 thf(f15483,plain,(
% 68.49/10.20 spl93_443 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X0,X2 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) | ($false = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_443])])).
% 68.49/10.20 thf(f2261,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) | ($false = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_rec_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4)))) ) | (~spl93_22 | ~spl93_75)),
% 68.49/10.20 inference(superposition,[],[f2257,f1833])).
% 68.49/10.20 thf(f13851,plain,(
% 68.49/10.20 ~spl93_442 | spl93_67 | ~spl93_440),
% 68.49/10.20 inference(avatar_split_clause,[],[f13831,f13821,f2166,f13848])).
% 68.49/10.20 thf(f13848,plain,(
% 68.49/10.20 spl93_442 <=> (sK5 = sK6)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_442])])).
% 68.49/10.20 thf(f2166,plain,(
% 68.49/10.20 spl93_67 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK5)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_67])])).
% 68.49/10.20 thf(f13831,plain,(
% 68.49/10.20 (sK5 != sK6) | (spl93_67 | ~spl93_440)),
% 68.49/10.20 inference(superposition,[],[f2167,f13823])).
% 68.49/10.20 thf(f2167,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != sK5) | spl93_67),
% 68.49/10.20 inference(avatar_component_clause,[],[f2166])).
% 68.49/10.20 thf(f13828,plain,(
% 68.49/10.20 spl93_440 | spl93_441 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_146),
% 68.49/10.20 inference(avatar_split_clause,[],[f6311,f2895,f2247,f2243,f2074,f13825,f13821])).
% 68.49/10.20 thf(f13825,plain,(
% 68.49/10.20 spl93_441 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_441])])).
% 68.49/10.20 thf(f6311,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK6) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_146)),
% 68.49/10.20 inference(forward_demodulation,[],[f2916,f5934])).
% 68.49/10.20 thf(f2916,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK6) | (~spl93_73 | ~spl93_146)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2913])).
% 68.49/10.20 thf(f2913,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK6) | (~spl93_73 | ~spl93_146)),
% 68.49/10.20 inference(superposition,[],[f2896,f2245])).
% 68.49/10.20 thf(f13819,plain,(
% 68.49/10.20 spl93_439 | ~spl93_20 | ~spl93_105),
% 68.49/10.20 inference(avatar_split_clause,[],[f2553,f2547,f1822,f13817])).
% 68.49/10.20 thf(f13817,plain,(
% 68.49/10.20 spl93_439 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_439])])).
% 68.49/10.20 thf(f2553,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)))) ) | (~spl93_20 | ~spl93_105)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2550])).
% 68.49/10.20 thf(f2550,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)))) ) | (~spl93_20 | ~spl93_105)),
% 68.49/10.20 inference(superposition,[],[f2548,f1824])).
% 68.49/10.20 thf(f13815,plain,(
% 68.49/10.20 spl93_438 | ~spl93_22 | ~spl93_96),
% 68.49/10.20 inference(avatar_split_clause,[],[f2455,f2432,f1832,f13813])).
% 68.49/10.20 thf(f13813,plain,(
% 68.49/10.20 spl93_438 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,comm_group(X0,X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_438])])).
% 68.49/10.20 thf(f2455,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,comm_group(X0,X1),X2))) ) | (~spl93_22 | ~spl93_96)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2454])).
% 68.49/10.20 thf(f2454,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,one(X0,X1),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,comm_group(X0,X1),X2))) ) | (~spl93_22 | ~spl93_96)),
% 68.49/10.20 inference(superposition,[],[f2433,f1833])).
% 68.49/10.20 thf(f13811,plain,(
% 68.49/10.20 spl93_437 | ~spl93_22 | ~spl93_95),
% 68.49/10.20 inference(avatar_split_clause,[],[f2452,f2428,f1832,f13809])).
% 68.49/10.20 thf(f13809,plain,(
% 68.49/10.20 spl93_437 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK18(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_437])])).
% 68.49/10.20 thf(f2428,plain,(
% 68.49/10.20 spl93_95 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_95])])).
% 68.49/10.20 thf(f2452,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK18(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2))) ) | (~spl93_22 | ~spl93_95)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2451])).
% 68.49/10.20 thf(f2451,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK18(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2))) ) | (~spl93_22 | ~spl93_95)),
% 68.49/10.20 inference(superposition,[],[f2429,f1833])).
% 68.49/10.20 thf(f2429,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) ) | ~spl93_95),
% 68.49/10.20 inference(avatar_component_clause,[],[f2428])).
% 68.49/10.20 thf(f13807,plain,(
% 68.49/10.20 spl93_436 | ~spl93_22 | ~spl93_94),
% 68.49/10.20 inference(avatar_split_clause,[],[f2450,f2424,f1832,f13805])).
% 68.49/10.20 thf(f13805,plain,(
% 68.49/10.20 spl93_436 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK17(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_436])])).
% 68.49/10.20 thf(f2424,plain,(
% 68.49/10.20 spl93_94 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_94])])).
% 68.49/10.20 thf(f2450,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK17(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2))) ) | (~spl93_22 | ~spl93_94)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2449])).
% 68.49/10.20 thf(f2449,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK17(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2))) ) | (~spl93_22 | ~spl93_94)),
% 68.49/10.20 inference(superposition,[],[f2425,f1833])).
% 68.49/10.20 thf(f2425,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) ) | ~spl93_94),
% 68.49/10.20 inference(avatar_component_clause,[],[f2424])).
% 68.49/10.20 thf(f13803,plain,(
% 68.49/10.20 spl93_435 | ~spl93_22 | ~spl93_93),
% 68.49/10.20 inference(avatar_split_clause,[],[f2448,f2420,f1832,f13801])).
% 68.49/10.20 thf(f13801,plain,(
% 68.49/10.20 spl93_435 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK16(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_435])])).
% 68.49/10.20 thf(f2420,plain,(
% 68.49/10.20 spl93_93 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_93])])).
% 68.49/10.20 thf(f2448,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK16(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2))) ) | (~spl93_22 | ~spl93_93)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2447])).
% 68.49/10.20 thf(f2447,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK16(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP0(X1,X0),X2))) ) | (~spl93_22 | ~spl93_93)),
% 68.49/10.20 inference(superposition,[],[f2421,f1833])).
% 68.49/10.20 thf(f2421,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) ) | ~spl93_93),
% 68.49/10.20 inference(avatar_component_clause,[],[f2420])).
% 68.49/10.20 thf(f13799,plain,(
% 68.49/10.20 spl93_434 | ~spl93_22 | ~spl93_92),
% 68.49/10.20 inference(avatar_split_clause,[],[f2442,f2416,f1832,f13797])).
% 68.49/10.20 thf(f13797,plain,(
% 68.49/10.20 spl93_434 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK15(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_434])])).
% 68.49/10.20 thf(f2416,plain,(
% 68.49/10.20 spl93_92 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_92])])).
% 68.49/10.20 thf(f2442,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK15(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2))) ) | (~spl93_22 | ~spl93_92)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2441])).
% 68.49/10.20 thf(f2441,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK15(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2))) ) | (~spl93_22 | ~spl93_92)),
% 68.49/10.20 inference(superposition,[],[f2417,f1833])).
% 68.49/10.20 thf(f2417,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) ) | ~spl93_92),
% 68.49/10.20 inference(avatar_component_clause,[],[f2416])).
% 68.49/10.20 thf(f13795,plain,(
% 68.49/10.20 spl93_433 | ~spl93_22 | ~spl93_91),
% 68.49/10.20 inference(avatar_split_clause,[],[f2440,f2412,f1832,f13793])).
% 68.49/10.20 thf(f13793,plain,(
% 68.49/10.20 spl93_433 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK14(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_433])])).
% 68.49/10.20 thf(f2412,plain,(
% 68.49/10.20 spl93_91 <=> ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_91])])).
% 68.49/10.20 thf(f2440,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK14(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2))) ) | (~spl93_22 | ~spl93_91)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2439])).
% 68.49/10.20 thf(f2439,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),X0,sK14(X1,X0),X2)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2))) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,sP1(X1,X0),X2))) ) | (~spl93_22 | ~spl93_91)),
% 68.49/10.20 inference(superposition,[],[f2413,f1833])).
% 68.49/10.20 thf(f2413,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)) | ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) ) | ~spl93_91),
% 68.49/10.20 inference(avatar_component_clause,[],[f2412])).
% 68.49/10.20 thf(f11068,plain,(
% 68.49/10.20 spl93_432 | ~spl93_235 | ~spl93_396),
% 68.49/10.20 inference(avatar_split_clause,[],[f9392,f9070,f3960,f11066])).
% 68.49/10.20 thf(f9392,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_235 | ~spl93_396)),
% 68.49/10.20 inference(superposition,[],[f3961,f9071])).
% 68.49/10.20 thf(f10153,plain,(
% 68.49/10.20 spl93_431 | ~spl93_345 | ~spl93_430),
% 68.49/10.20 inference(avatar_split_clause,[],[f10148,f10144,f6456,f10150])).
% 68.49/10.20 thf(f10150,plain,(
% 68.49/10.20 spl93_431 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_431])])).
% 68.49/10.20 thf(f10144,plain,(
% 68.49/10.20 spl93_430 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_430])])).
% 68.49/10.20 thf(f10148,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | ~spl93_430)),
% 68.49/10.20 inference(forward_demodulation,[],[f10146,f6458])).
% 68.49/10.20 thf(f10146,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_430),
% 68.49/10.20 inference(avatar_component_clause,[],[f10144])).
% 68.49/10.20 thf(f10147,plain,(
% 68.49/10.20 spl93_430 | ~spl93_66 | ~spl93_127),
% 68.49/10.20 inference(avatar_split_clause,[],[f2714,f2697,f2161,f10144])).
% 68.49/10.20 thf(f2714,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_66 | ~spl93_127)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2709])).
% 68.49/10.20 thf(f2709,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_66 | ~spl93_127)),
% 68.49/10.20 inference(superposition,[],[f2698,f2163])).
% 68.49/10.20 thf(f10123,plain,(
% 68.49/10.20 spl93_429 | ~spl93_345 | ~spl93_428),
% 68.49/10.20 inference(avatar_split_clause,[],[f10118,f10114,f6456,f10120])).
% 68.49/10.20 thf(f10120,plain,(
% 68.49/10.20 spl93_429 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_429])])).
% 68.49/10.20 thf(f10114,plain,(
% 68.49/10.20 spl93_428 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_428])])).
% 68.49/10.20 thf(f10118,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | ~spl93_428)),
% 68.49/10.20 inference(forward_demodulation,[],[f10116,f6458])).
% 68.49/10.20 thf(f10116,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_428),
% 68.49/10.20 inference(avatar_component_clause,[],[f10114])).
% 68.49/10.20 thf(f10117,plain,(
% 68.49/10.20 spl93_428 | ~spl93_66 | ~spl93_126),
% 68.49/10.20 inference(avatar_split_clause,[],[f2706,f2693,f2161,f10114])).
% 68.49/10.20 thf(f2706,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_66 | ~spl93_126)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2701])).
% 68.49/10.20 thf(f2701,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_66 | ~spl93_126)),
% 68.49/10.20 inference(superposition,[],[f2694,f2163])).
% 68.49/10.20 thf(f10112,plain,(
% 68.49/10.20 spl93_427 | ~spl93_227 | ~spl93_396),
% 68.49/10.20 inference(avatar_split_clause,[],[f9391,f9070,f3899,f10110])).
% 68.49/10.20 thf(f9391,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)),X0) = X0)) ) | (~spl93_227 | ~spl93_396)),
% 68.49/10.20 inference(superposition,[],[f3900,f9071])).
% 68.49/10.20 thf(f10089,plain,(
% 68.49/10.20 spl93_426 | ~spl93_345 | ~spl93_425),
% 68.49/10.20 inference(avatar_split_clause,[],[f10084,f10080,f6456,f10086])).
% 68.49/10.20 thf(f10086,plain,(
% 68.49/10.20 spl93_426 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_426])])).
% 68.49/10.20 thf(f10080,plain,(
% 68.49/10.20 spl93_425 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_425])])).
% 68.49/10.20 thf(f10084,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | ~spl93_425)),
% 68.49/10.20 inference(forward_demodulation,[],[f10082,f6458])).
% 68.49/10.20 thf(f10082,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_425),
% 68.49/10.20 inference(avatar_component_clause,[],[f10080])).
% 68.49/10.20 thf(f10083,plain,(
% 68.49/10.20 spl93_425 | ~spl93_62 | ~spl93_124),
% 68.49/10.20 inference(avatar_split_clause,[],[f2686,f2669,f2141,f10080])).
% 68.49/10.20 thf(f2686,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_62 | ~spl93_124)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2681])).
% 68.49/10.20 thf(f2681,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_62 | ~spl93_124)),
% 68.49/10.20 inference(superposition,[],[f2670,f2143])).
% 68.49/10.20 thf(f10077,plain,(
% 68.49/10.20 spl93_424 | ~spl93_62 | ~spl93_122),
% 68.49/10.20 inference(avatar_split_clause,[],[f2680,f2652,f2141,f10074])).
% 68.49/10.20 thf(f10074,plain,(
% 68.49/10.20 spl93_424 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_424])])).
% 68.49/10.20 thf(f2680,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_62 | ~spl93_122)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2675])).
% 68.49/10.20 thf(f2675,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_62 | ~spl93_122)),
% 68.49/10.20 inference(superposition,[],[f2653,f2143])).
% 68.49/10.20 thf(f10072,plain,(
% 68.49/10.20 spl93_423 | ~spl93_22 | ~spl93_90),
% 68.49/10.20 inference(avatar_split_clause,[],[f2408,f2322,f1832,f10070])).
% 68.49/10.20 thf(f10070,plain,(
% 68.49/10.20 spl93_423 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_423])])).
% 68.49/10.20 thf(f2322,plain,(
% 68.49/10.20 spl93_90 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (ab_group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_90])])).
% 68.49/10.20 thf(f2408,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_90)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2407])).
% 68.49/10.20 thf(f2407,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_90)),
% 68.49/10.20 inference(superposition,[],[f2323,f1833])).
% 68.49/10.20 thf(f2323,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((ab_group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4))) ) | ~spl93_90),
% 68.49/10.20 inference(avatar_component_clause,[],[f2322])).
% 68.49/10.20 thf(f10068,plain,(
% 68.49/10.20 spl93_422 | ~spl93_22 | ~spl93_89),
% 68.49/10.20 inference(avatar_split_clause,[],[f2397,f2318,f1832,f10066])).
% 68.49/10.20 thf(f10066,plain,(
% 68.49/10.20 spl93_422 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (comm_monoid_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_422])])).
% 68.49/10.20 thf(f2318,plain,(
% 68.49/10.20 spl93_89 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (comm_monoid_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_89])])).
% 68.49/10.20 thf(f2397,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (comm_monoid_add(X0) = $false)) ) | (~spl93_22 | ~spl93_89)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2396])).
% 68.49/10.20 thf(f2396,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (comm_monoid_add(X0) = $false)) ) | (~spl93_22 | ~spl93_89)),
% 68.49/10.20 inference(superposition,[],[f2319,f1833])).
% 68.49/10.20 thf(f2319,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((comm_monoid_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4))) ) | ~spl93_89),
% 68.49/10.20 inference(avatar_component_clause,[],[f2318])).
% 68.49/10.20 thf(f10064,plain,(
% 68.49/10.20 spl93_421 | ~spl93_22 | ~spl93_88),
% 68.49/10.20 inference(avatar_split_clause,[],[f2391,f2314,f1832,f10062])).
% 68.49/10.20 thf(f10062,plain,(
% 68.49/10.20 spl93_421 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (comm_monoid_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_421])])).
% 68.49/10.20 thf(f2314,plain,(
% 68.49/10.20 spl93_88 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (comm_monoid_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_88])])).
% 68.49/10.20 thf(f2391,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (comm_monoid_add(X0) = $false)) ) | (~spl93_22 | ~spl93_88)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2390])).
% 68.49/10.20 thf(f2390,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (comm_monoid_add(X0) = $false)) ) | (~spl93_22 | ~spl93_88)),
% 68.49/10.20 inference(superposition,[],[f2315,f1833])).
% 68.49/10.20 thf(f2315,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((comm_monoid_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)))) ) | ~spl93_88),
% 68.49/10.20 inference(avatar_component_clause,[],[f2314])).
% 68.49/10.20 thf(f10060,plain,(
% 68.49/10.20 spl93_420 | ~spl93_22 | ~spl93_87),
% 68.49/10.20 inference(avatar_split_clause,[],[f2386,f2310,f1832,f10058])).
% 68.49/10.20 thf(f10058,plain,(
% 68.49/10.20 spl93_420 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_420])])).
% 68.49/10.20 thf(f2310,plain,(
% 68.49/10.20 spl93_87 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_87])])).
% 68.49/10.20 thf(f2386,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_87)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2385])).
% 68.49/10.20 thf(f2385,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_87)),
% 68.49/10.20 inference(superposition,[],[f2311,f1833])).
% 68.49/10.20 thf(f2311,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2))) ) | ~spl93_87),
% 68.49/10.20 inference(avatar_component_clause,[],[f2310])).
% 68.49/10.20 thf(f10056,plain,(
% 68.49/10.20 spl93_419 | ~spl93_22 | ~spl93_86),
% 68.49/10.20 inference(avatar_split_clause,[],[f2381,f2306,f1832,f10054])).
% 68.49/10.20 thf(f10054,plain,(
% 68.49/10.20 spl93_419 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_419])])).
% 68.49/10.20 thf(f2381,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_86)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2380])).
% 68.49/10.20 thf(f2380,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_86)),
% 68.49/10.20 inference(superposition,[],[f2307,f1833])).
% 68.49/10.20 thf(f10052,plain,(
% 68.49/10.20 spl93_418 | ~spl93_22 | ~spl93_85),
% 68.49/10.20 inference(avatar_split_clause,[],[f2377,f2302,f1832,f10050])).
% 68.49/10.20 thf(f10050,plain,(
% 68.49/10.20 spl93_418 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2))) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_418])])).
% 68.49/10.20 thf(f2377,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_85)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2376])).
% 68.49/10.20 thf(f2376,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_85)),
% 68.49/10.20 inference(superposition,[],[f2303,f1833])).
% 68.49/10.20 thf(f9959,plain,(
% 68.49/10.20 spl93_417 | ~spl93_22 | ~spl93_83),
% 68.49/10.20 inference(avatar_split_clause,[],[f2373,f2291,f1832,f9957])).
% 68.49/10.20 thf(f2291,plain,(
% 68.49/10.20 spl93_83 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3)) | (ab_group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_83])])).
% 68.49/10.20 thf(f2373,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_83)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2372])).
% 68.49/10.20 thf(f2372,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_83)),
% 68.49/10.20 inference(superposition,[],[f2292,f1833])).
% 68.49/10.20 thf(f2292,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((ab_group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3))) ) | ~spl93_83),
% 68.49/10.20 inference(avatar_component_clause,[],[f2291])).
% 68.49/10.20 thf(f9955,plain,(
% 68.49/10.20 spl93_416 | ~spl93_22 | ~spl93_82),
% 68.49/10.20 inference(avatar_split_clause,[],[f2368,f2287,f1832,f9953])).
% 68.49/10.20 thf(f9953,plain,(
% 68.49/10.20 spl93_416 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_416])])).
% 68.49/10.20 thf(f2287,plain,(
% 68.49/10.20 spl93_82 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_82])])).
% 68.49/10.20 thf(f2368,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_82)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2367])).
% 68.49/10.20 thf(f2367,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_82)),
% 68.49/10.20 inference(superposition,[],[f2288,f1833])).
% 68.49/10.20 thf(f2288,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((cancel146912293up_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)))) ) | ~spl93_82),
% 68.49/10.20 inference(avatar_component_clause,[],[f2287])).
% 68.49/10.20 thf(f9951,plain,(
% 68.49/10.20 spl93_415 | ~spl93_22 | ~spl93_81),
% 68.49/10.20 inference(avatar_split_clause,[],[f2360,f2283,f1832,f9949])).
% 68.49/10.20 thf(f9949,plain,(
% 68.49/10.20 spl93_415 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_415])])).
% 68.49/10.20 thf(f2283,plain,(
% 68.49/10.20 spl93_81 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_81])])).
% 68.49/10.20 thf(f2360,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_81)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2359])).
% 68.49/10.20 thf(f2359,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_81)),
% 68.49/10.20 inference(superposition,[],[f2284,f1833])).
% 68.49/10.20 thf(f2284,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((cancel146912293up_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2))) ) | ~spl93_81),
% 68.49/10.20 inference(avatar_component_clause,[],[f2283])).
% 68.49/10.20 thf(f9947,plain,(
% 68.49/10.20 spl93_414 | ~spl93_22 | ~spl93_80),
% 68.49/10.20 inference(avatar_split_clause,[],[f2354,f2279,f1832,f9945])).
% 68.49/10.20 thf(f9945,plain,(
% 68.49/10.20 spl93_414 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_414])])).
% 68.49/10.20 thf(f2279,plain,(
% 68.49/10.20 spl93_80 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_80])])).
% 68.49/10.20 thf(f2354,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_80)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2353])).
% 68.49/10.20 thf(f2353,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_80)),
% 68.49/10.20 inference(superposition,[],[f2280,f1833])).
% 68.49/10.20 thf(f2280,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((cancel146912293up_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)))) ) | ~spl93_80),
% 68.49/10.20 inference(avatar_component_clause,[],[f2279])).
% 68.49/10.20 thf(f9943,plain,(
% 68.49/10.20 spl93_413 | ~spl93_22 | ~spl93_79),
% 68.49/10.20 inference(avatar_split_clause,[],[f2348,f2275,f1832,f9941])).
% 68.49/10.20 thf(f9941,plain,(
% 68.49/10.20 spl93_413 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_413])])).
% 68.49/10.20 thf(f2275,plain,(
% 68.49/10.20 spl93_79 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_79])])).
% 68.49/10.20 thf(f2348,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_79)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2347])).
% 68.49/10.20 thf(f2347,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_79)),
% 68.49/10.20 inference(superposition,[],[f2276,f1833])).
% 68.49/10.20 thf(f2276,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((cancel146912293up_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)))) ) | ~spl93_79),
% 68.49/10.20 inference(avatar_component_clause,[],[f2275])).
% 68.49/10.20 thf(f9939,plain,(
% 68.49/10.20 spl93_412 | ~spl93_22 | ~spl93_78),
% 68.49/10.20 inference(avatar_split_clause,[],[f2340,f2271,f1832,f9937])).
% 68.49/10.20 thf(f9937,plain,(
% 68.49/10.20 spl93_412 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_412])])).
% 68.49/10.20 thf(f2271,plain,(
% 68.49/10.20 spl93_78 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_78])])).
% 68.49/10.20 thf(f2340,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_78)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2339])).
% 68.49/10.20 thf(f2339,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_78)),
% 68.49/10.20 inference(superposition,[],[f2272,f1833])).
% 68.49/10.20 thf(f2272,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((ab_semigroup_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3))) ) | ~spl93_78),
% 68.49/10.20 inference(avatar_component_clause,[],[f2271])).
% 68.49/10.20 thf(f9935,plain,(
% 68.49/10.20 spl93_411 | ~spl93_22 | ~spl93_77),
% 68.49/10.20 inference(avatar_split_clause,[],[f2334,f2267,f1832,f9933])).
% 68.49/10.20 thf(f9933,plain,(
% 68.49/10.20 spl93_411 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_411])])).
% 68.49/10.20 thf(f2267,plain,(
% 68.49/10.20 spl93_77 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_77])])).
% 68.49/10.20 thf(f2334,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_77)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2333])).
% 68.49/10.20 thf(f2333,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_77)),
% 68.49/10.20 inference(superposition,[],[f2268,f1833])).
% 68.49/10.20 thf(f2268,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((ab_semigroup_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)))) ) | ~spl93_77),
% 68.49/10.20 inference(avatar_component_clause,[],[f2267])).
% 68.49/10.20 thf(f9931,plain,(
% 68.49/10.20 spl93_410 | ~spl93_22 | ~spl93_76),
% 68.49/10.20 inference(avatar_split_clause,[],[f2328,f2263,f1832,f9929])).
% 68.49/10.20 thf(f9929,plain,(
% 68.49/10.20 spl93_410 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_410])])).
% 68.49/10.20 thf(f2263,plain,(
% 68.49/10.20 spl93_76 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_76])])).
% 68.49/10.20 thf(f2328,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_76)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2327])).
% 68.49/10.20 thf(f2327,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_76)),
% 68.49/10.20 inference(superposition,[],[f2264,f1833])).
% 68.49/10.20 thf(f2264,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((semigroup_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3))) ) | ~spl93_76),
% 68.49/10.20 inference(avatar_component_clause,[],[f2263])).
% 68.49/10.20 thf(f9350,plain,(
% 68.49/10.20 spl93_408 | spl93_409 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_141),
% 68.49/10.20 inference(avatar_split_clause,[],[f6313,f2857,f2247,f2243,f2074,f9347,f9343])).
% 68.49/10.20 thf(f9343,plain,(
% 68.49/10.20 spl93_408 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = sK6)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_408])])).
% 68.49/10.20 thf(f9347,plain,(
% 68.49/10.20 spl93_409 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_409])])).
% 68.49/10.20 thf(f6313,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = sK6) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_141)),
% 68.49/10.20 inference(forward_demodulation,[],[f2869,f5934])).
% 68.49/10.20 thf(f2869,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = sK6) | (~spl93_73 | ~spl93_141)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2866])).
% 68.49/10.20 thf(f2866,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = sK6) | (~spl93_73 | ~spl93_141)),
% 68.49/10.20 inference(superposition,[],[f2858,f2245])).
% 68.49/10.20 thf(f9341,plain,(
% 68.49/10.20 spl93_407 | ~spl93_48 | ~spl93_75),
% 68.49/10.20 inference(avatar_split_clause,[],[f2260,f2256,f2031,f9339])).
% 68.49/10.20 thf(f9339,plain,(
% 68.49/10.20 spl93_407 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X4 : X1 > X0 > X3,X2 : product_prod(X1,X0)] : (vAPP(product_prod(X1,X0),X3,vAPP(sTfun(X1,sTfun(X0,X3)),sTfun(product_prod(X1,X0),X3),product_rec_prod(X1,X0,X3),X4),X2) = vAPP(X0,X3,vAPP(X1,sTfun(X0,X3),X4,vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_407])])).
% 68.49/10.20 thf(f2260,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X4 : X1 > X0 > X3] : ((vAPP(product_prod(X1,X0),X3,vAPP(sTfun(X1,sTfun(X0,X3)),sTfun(product_prod(X1,X0),X3),product_rec_prod(X1,X0,X3),X4),X2) = vAPP(X0,X3,vAPP(X1,sTfun(X0,X3),X4,vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2)))) ) | (~spl93_48 | ~spl93_75)),
% 68.49/10.20 inference(superposition,[],[f2257,f2032])).
% 68.49/10.20 thf(f9337,plain,(
% 68.49/10.20 spl93_406 | ~spl93_47 | ~spl93_75),
% 68.49/10.20 inference(avatar_split_clause,[],[f2259,f2256,f2027,f9335])).
% 68.49/10.20 thf(f9335,plain,(
% 68.49/10.20 spl93_406 <=> ! [X1 : $tType,X3 : $tType,X0 : $tType,X4 : X1 > X0 > X3,X2 : product_prod(X1,X0)] : (vAPP(X0,X3,vAPP(X1,sTfun(X0,X3),X4,vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2)) = vAPP(product_prod(X1,X0),X3,vAPP(sTfun(X1,sTfun(X0,X3)),sTfun(product_prod(X1,X0),X3),product_rec_prod(X1,X0,X3),X4),X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_406])])).
% 68.49/10.20 thf(f2259,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : product_prod(X1,X0),X4 : X1 > X0 > X3] : ((vAPP(X0,X3,vAPP(X1,sTfun(X0,X3),X4,vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2)),vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2)) = vAPP(product_prod(X1,X0),X3,vAPP(sTfun(X1,sTfun(X0,X3)),sTfun(product_prod(X1,X0),X3),product_rec_prod(X1,X0,X3),X4),X2))) ) | (~spl93_47 | ~spl93_75)),
% 68.49/10.20 inference(superposition,[],[f2257,f2028])).
% 68.49/10.20 thf(f9264,plain,(
% 68.49/10.20 spl93_405 | ~spl93_137 | ~spl93_338),
% 68.49/10.20 inference(avatar_split_clause,[],[f6337,f5946,f2811,f9261])).
% 68.49/10.20 thf(f9261,plain,(
% 68.49/10.20 spl93_405 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_405])])).
% 68.49/10.20 thf(f5946,plain,(
% 68.49/10.20 spl93_338 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_338])])).
% 68.49/10.20 thf(f6337,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6)) | (~spl93_137 | ~spl93_338)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6330])).
% 68.49/10.20 thf(f6330,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,sK6)),sK6)) | (~spl93_137 | ~spl93_338)),
% 68.49/10.20 inference(superposition,[],[f2812,f5947])).
% 68.49/10.20 thf(f5947,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ~spl93_338),
% 68.49/10.20 inference(avatar_component_clause,[],[f5946])).
% 68.49/10.20 thf(f9259,plain,(
% 68.49/10.20 spl93_404 | ~spl93_216 | ~spl93_393),
% 68.49/10.20 inference(avatar_split_clause,[],[f8890,f7812,f3748,f9257])).
% 68.49/10.20 thf(f7812,plain,(
% 68.49/10.20 spl93_393 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_393])])).
% 68.49/10.20 thf(f8890,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1)) = X0)) ) | (~spl93_216 | ~spl93_393)),
% 68.49/10.20 inference(superposition,[],[f7813,f3749])).
% 68.49/10.20 thf(f7813,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))) ) | ~spl93_393),
% 68.49/10.20 inference(avatar_component_clause,[],[f7812])).
% 68.49/10.20 thf(f9255,plain,(
% 68.49/10.20 spl93_403 | ~spl93_138 | ~spl93_338),
% 68.49/10.20 inference(avatar_split_clause,[],[f6336,f5946,f2815,f9252])).
% 68.49/10.20 thf(f9252,plain,(
% 68.49/10.20 spl93_403 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_403])])).
% 68.49/10.20 thf(f6336,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6))) | (~spl93_138 | ~spl93_338)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6331])).
% 68.49/10.20 thf(f6331,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(a,a,sK8,sK6))) | (~spl93_138 | ~spl93_338)),
% 68.49/10.20 inference(superposition,[],[f2816,f5947])).
% 68.49/10.20 thf(f9250,plain,(
% 68.49/10.20 spl93_402 | ~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_167),
% 68.49/10.20 inference(avatar_split_clause,[],[f6281,f3147,f2247,f2243,f2074,f1873,f9247])).
% 68.49/10.20 thf(f9247,plain,(
% 68.49/10.20 spl93_402 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_402])])).
% 68.49/10.20 thf(f6281,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6280])).
% 68.49/10.20 thf(f6280,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(forward_demodulation,[],[f6279,f1875])).
% 68.49/10.20 thf(f6279,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(forward_demodulation,[],[f3185,f5934])).
% 68.49/10.20 thf(f3185,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_167)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3182])).
% 68.49/10.20 thf(f3182,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_167)),
% 68.49/10.20 inference(superposition,[],[f3148,f2245])).
% 68.49/10.20 thf(f9245,plain,(
% 68.49/10.20 spl93_401 | ~spl93_62 | ~spl93_123),
% 68.49/10.20 inference(avatar_split_clause,[],[f3128,f2657,f2141,f9242])).
% 68.49/10.20 thf(f9242,plain,(
% 68.49/10.20 spl93_401 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_401])])).
% 68.49/10.20 thf(f3128,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_62 | ~spl93_123)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3123])).
% 68.49/10.20 thf(f3123,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_62 | ~spl93_123)),
% 68.49/10.20 inference(superposition,[],[f2658,f2143])).
% 68.49/10.20 thf(f9221,plain,(
% 68.49/10.20 spl93_400 | ~spl93_345 | ~spl93_399),
% 68.49/10.20 inference(avatar_split_clause,[],[f9216,f9212,f6456,f9218])).
% 68.49/10.20 thf(f9218,plain,(
% 68.49/10.20 spl93_400 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_400])])).
% 68.49/10.20 thf(f9212,plain,(
% 68.49/10.20 spl93_399 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_399])])).
% 68.49/10.20 thf(f9216,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | ~spl93_399)),
% 68.49/10.20 inference(forward_demodulation,[],[f9214,f6458])).
% 68.49/10.20 thf(f9214,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_399),
% 68.49/10.20 inference(avatar_component_clause,[],[f9212])).
% 68.49/10.20 thf(f9215,plain,(
% 68.49/10.20 spl93_399 | ~spl93_61 | ~spl93_127),
% 68.49/10.20 inference(avatar_split_clause,[],[f2715,f2697,f2136,f9212])).
% 68.49/10.20 thf(f2715,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_61 | ~spl93_127)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2708])).
% 68.49/10.20 thf(f2708,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_61 | ~spl93_127)),
% 68.49/10.20 inference(superposition,[],[f2698,f2138])).
% 68.49/10.20 thf(f9191,plain,(
% 68.49/10.20 spl93_398 | ~spl93_345 | ~spl93_397),
% 68.49/10.20 inference(avatar_split_clause,[],[f9186,f9182,f6456,f9188])).
% 68.49/10.20 thf(f9188,plain,(
% 68.49/10.20 spl93_398 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_398])])).
% 68.49/10.20 thf(f9182,plain,(
% 68.49/10.20 spl93_397 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_397])])).
% 68.49/10.20 thf(f9186,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_345 | ~spl93_397)),
% 68.49/10.20 inference(forward_demodulation,[],[f9184,f6458])).
% 68.49/10.20 thf(f9184,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_397),
% 68.49/10.20 inference(avatar_component_clause,[],[f9182])).
% 68.49/10.20 thf(f9185,plain,(
% 68.49/10.20 spl93_397 | ~spl93_61 | ~spl93_126),
% 68.49/10.20 inference(avatar_split_clause,[],[f2707,f2693,f2136,f9182])).
% 68.49/10.20 thf(f2707,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_61 | ~spl93_126)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2700])).
% 68.49/10.20 thf(f2700,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_61 | ~spl93_126)),
% 68.49/10.20 inference(superposition,[],[f2694,f2138])).
% 68.49/10.20 thf(f9072,plain,(
% 68.49/10.20 spl93_396 | ~spl93_387 | ~spl93_391),
% 68.49/10.20 inference(avatar_split_clause,[],[f8806,f7803,f7787,f9070])).
% 68.49/10.20 thf(f7787,plain,(
% 68.49/10.20 spl93_387 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_387])])).
% 68.49/10.20 thf(f7803,plain,(
% 68.49/10.20 spl93_391 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_391])])).
% 68.49/10.20 thf(f8806,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X0))) ) | (~spl93_387 | ~spl93_391)),
% 68.49/10.20 inference(superposition,[],[f7804,f7788])).
% 68.49/10.20 thf(f7788,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)))) ) | ~spl93_387),
% 68.49/10.20 inference(avatar_component_clause,[],[f7787])).
% 68.49/10.20 thf(f7804,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))) ) | ~spl93_391),
% 68.49/10.20 inference(avatar_component_clause,[],[f7803])).
% 68.49/10.20 thf(f8869,plain,(
% 68.49/10.20 spl93_395 | ~spl93_21 | ~spl93_85 | ~spl93_392),
% 68.49/10.20 inference(avatar_split_clause,[],[f7810,f7807,f2302,f1827,f8867])).
% 68.49/10.20 thf(f7807,plain,(
% 68.49/10.20 spl93_392 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_392])])).
% 68.49/10.20 thf(f7810,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),X1)))) ) | (~spl93_21 | ~spl93_85 | ~spl93_392)),
% 68.49/10.20 inference(forward_demodulation,[],[f7808,f2378])).
% 68.49/10.20 thf(f7808,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1))) ) | ~spl93_392),
% 68.49/10.20 inference(avatar_component_clause,[],[f7807])).
% 68.49/10.20 thf(f7818,plain,(
% 68.49/10.20 spl93_394 | ~spl93_21 | ~spl93_85 | ~spl93_86),
% 68.49/10.20 inference(avatar_split_clause,[],[f2383,f2306,f2302,f1827,f7816])).
% 68.49/10.20 thf(f7814,plain,(
% 68.49/10.20 spl93_393 | ~spl93_21 | ~spl93_85),
% 68.49/10.20 inference(avatar_split_clause,[],[f2378,f2302,f1827,f7812])).
% 68.49/10.20 thf(f7809,plain,(
% 68.49/10.20 spl93_392 | ~spl93_20 | ~spl93_83),
% 68.49/10.20 inference(avatar_split_clause,[],[f2374,f2291,f1822,f7807])).
% 68.49/10.20 thf(f2374,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1))) ) | (~spl93_20 | ~spl93_83)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2371])).
% 68.49/10.20 thf(f2371,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1))) ) | (~spl93_20 | ~spl93_83)),
% 68.49/10.20 inference(superposition,[],[f2292,f1824])).
% 68.49/10.20 thf(f7805,plain,(
% 68.49/10.20 spl93_391 | ~spl93_18 | ~spl93_82),
% 68.49/10.20 inference(avatar_split_clause,[],[f2370,f2287,f1812,f7803])).
% 68.49/10.20 thf(f1812,plain,(
% 68.49/10.20 spl93_18 <=> (cancel146912293up_add(int) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_18])])).
% 68.49/10.20 thf(f2370,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))) ) | (~spl93_18 | ~spl93_82)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2365])).
% 68.49/10.20 thf(f2365,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))) ) | (~spl93_18 | ~spl93_82)),
% 68.49/10.20 inference(superposition,[],[f2288,f1814])).
% 68.49/10.20 thf(f1814,plain,(
% 68.49/10.20 (cancel146912293up_add(int) = $true) | ~spl93_18),
% 68.49/10.20 inference(avatar_component_clause,[],[f1812])).
% 68.49/10.20 thf(f7801,plain,(
% 68.49/10.20 spl93_390 | ~spl93_18 | ~spl93_80 | ~spl93_81),
% 68.49/10.20 inference(avatar_split_clause,[],[f2363,f2283,f2279,f1812,f7799])).
% 68.49/10.20 thf(f7799,plain,(
% 68.49/10.20 spl93_390 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_390])])).
% 68.49/10.20 thf(f2363,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)))) ) | (~spl93_18 | ~spl93_80 | ~spl93_81)),
% 68.49/10.20 inference(forward_demodulation,[],[f2362,f2356])).
% 68.49/10.20 thf(f2356,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))) ) | (~spl93_18 | ~spl93_80)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2351])).
% 68.49/10.20 thf(f2351,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))) ) | (~spl93_18 | ~spl93_80)),
% 68.49/10.20 inference(superposition,[],[f2280,f1814])).
% 68.49/10.20 thf(f2362,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1))) ) | (~spl93_18 | ~spl93_81)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2357])).
% 68.49/10.20 thf(f2357,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X2)),X1))) ) | (~spl93_18 | ~spl93_81)),
% 68.49/10.20 inference(superposition,[],[f2284,f1814])).
% 68.49/10.20 thf(f7797,plain,(
% 68.49/10.20 spl93_389 | ~spl93_17 | ~spl93_316),
% 68.49/10.20 inference(avatar_split_clause,[],[f5292,f5069,f1807,f7795])).
% 68.49/10.20 thf(f7795,plain,(
% 68.49/10.20 spl93_389 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)) | (X0 != X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_389])])).
% 68.49/10.20 thf(f1807,plain,(
% 68.49/10.20 spl93_17 <=> (cancel_semigroup_add(nat) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_17])])).
% 68.49/10.20 thf(f5069,plain,(
% 68.49/10.20 spl93_316 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | (X1 != X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_316])])).
% 68.49/10.20 thf(f5292,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)) | (X0 != X2)) ) | (~spl93_17 | ~spl93_316)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5289])).
% 68.49/10.20 thf(f5289,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)) | (X0 != X2)) ) | (~spl93_17 | ~spl93_316)),
% 68.49/10.20 inference(superposition,[],[f5070,f1809])).
% 68.49/10.20 thf(f1809,plain,(
% 68.49/10.20 (cancel_semigroup_add(nat) = $true) | ~spl93_17),
% 68.49/10.20 inference(avatar_component_clause,[],[f1807])).
% 68.49/10.20 thf(f5070,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((cancel_semigroup_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (X1 != X3)) ) | ~spl93_316),
% 68.49/10.20 inference(avatar_component_clause,[],[f5069])).
% 68.49/10.20 thf(f7793,plain,(
% 68.49/10.20 spl93_388 | ~spl93_18 | ~spl93_80),
% 68.49/10.20 inference(avatar_split_clause,[],[f2356,f2279,f1812,f7791])).
% 68.49/10.20 thf(f7791,plain,(
% 68.49/10.20 spl93_388 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_388])])).
% 68.49/10.20 thf(f7789,plain,(
% 68.49/10.20 spl93_387 | ~spl93_18 | ~spl93_79),
% 68.49/10.20 inference(avatar_split_clause,[],[f2350,f2275,f1812,f7787])).
% 68.49/10.20 thf(f2350,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)))) ) | (~spl93_18 | ~spl93_79)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2345])).
% 68.49/10.20 thf(f2345,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)))) ) | (~spl93_18 | ~spl93_79)),
% 68.49/10.20 inference(superposition,[],[f2276,f1814])).
% 68.49/10.20 thf(f7785,plain,(
% 68.49/10.20 spl93_386 | ~spl93_14 | ~spl93_77),
% 68.49/10.20 inference(avatar_split_clause,[],[f2336,f2267,f1792,f7783])).
% 68.49/10.20 thf(f7783,plain,(
% 68.49/10.20 spl93_386 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_386])])).
% 68.49/10.20 thf(f1792,plain,(
% 68.49/10.20 spl93_14 <=> (ab_semigroup_add(int) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_14])])).
% 68.49/10.20 thf(f2336,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)))) ) | (~spl93_14 | ~spl93_77)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2331])).
% 68.49/10.20 thf(f2331,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)))) ) | (~spl93_14 | ~spl93_77)),
% 68.49/10.20 inference(superposition,[],[f2268,f1794])).
% 68.49/10.20 thf(f1794,plain,(
% 68.49/10.20 (ab_semigroup_add(int) = $true) | ~spl93_14),
% 68.49/10.20 inference(avatar_component_clause,[],[f1792])).
% 68.49/10.20 thf(f7781,plain,(
% 68.49/10.20 spl93_385 | ~spl93_15 | ~spl93_77),
% 68.49/10.20 inference(avatar_split_clause,[],[f2335,f2267,f1797,f7779])).
% 68.49/10.20 thf(f7779,plain,(
% 68.49/10.20 spl93_385 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_385])])).
% 68.49/10.20 thf(f1797,plain,(
% 68.49/10.20 spl93_15 <=> (ab_semigroup_add(nat) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_15])])).
% 68.49/10.20 thf(f2335,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) ) | (~spl93_15 | ~spl93_77)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2332])).
% 68.49/10.20 thf(f2332,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) ) | (~spl93_15 | ~spl93_77)),
% 68.49/10.20 inference(superposition,[],[f2268,f1799])).
% 68.49/10.20 thf(f1799,plain,(
% 68.49/10.20 (ab_semigroup_add(nat) = $true) | ~spl93_15),
% 68.49/10.20 inference(avatar_component_clause,[],[f1797])).
% 68.49/10.20 thf(f7777,plain,(
% 68.49/10.20 spl93_384 | ~spl93_2 | ~spl93_76),
% 68.49/10.20 inference(avatar_split_clause,[],[f2330,f2263,f1732,f7775])).
% 68.49/10.20 thf(f7775,plain,(
% 68.49/10.20 spl93_384 <=> ! [X2 : int,X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_384])])).
% 68.49/10.20 thf(f1732,plain,(
% 68.49/10.20 spl93_2 <=> (semigroup_add(int) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_2])])).
% 68.49/10.20 thf(f2330,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2))) ) | (~spl93_2 | ~spl93_76)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2325])).
% 68.49/10.20 thf(f2325,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X2))) ) | (~spl93_2 | ~spl93_76)),
% 68.49/10.20 inference(superposition,[],[f2264,f1734])).
% 68.49/10.20 thf(f1734,plain,(
% 68.49/10.20 (semigroup_add(int) = $true) | ~spl93_2),
% 68.49/10.20 inference(avatar_component_clause,[],[f1732])).
% 68.49/10.20 thf(f7773,plain,(
% 68.49/10.20 spl93_383 | ~spl93_11 | ~spl93_76),
% 68.49/10.20 inference(avatar_split_clause,[],[f2329,f2263,f1777,f7771])).
% 68.49/10.20 thf(f7771,plain,(
% 68.49/10.20 spl93_383 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_383])])).
% 68.49/10.20 thf(f1777,plain,(
% 68.49/10.20 spl93_11 <=> (semigroup_add(nat) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_11])])).
% 68.49/10.20 thf(f2329,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl93_11 | ~spl93_76)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2326])).
% 68.49/10.20 thf(f2326,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl93_11 | ~spl93_76)),
% 68.49/10.20 inference(superposition,[],[f2264,f1779])).
% 68.49/10.20 thf(f1779,plain,(
% 68.49/10.20 (semigroup_add(nat) = $true) | ~spl93_11),
% 68.49/10.20 inference(avatar_component_clause,[],[f1777])).
% 68.49/10.20 thf(f7769,plain,(
% 68.49/10.20 spl93_382 | ~spl93_65 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2226,f2181,f2157,f7767])).
% 68.49/10.20 thf(f7767,plain,(
% 68.49/10.20 spl93_382 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_382])])).
% 68.49/10.20 thf(f2226,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) ) | (~spl93_65 | ~spl93_70)),
% 68.49/10.20 inference(superposition,[],[f2182,f2158])).
% 68.49/10.20 thf(f7765,plain,(
% 68.49/10.20 spl93_381 | ~spl93_27 | ~spl93_70),
% 68.49/10.20 inference(avatar_split_clause,[],[f2220,f2181,f1882,f7763])).
% 68.49/10.20 thf(f7763,plain,(
% 68.49/10.20 spl93_381 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_381])])).
% 68.49/10.20 thf(f1882,plain,(
% 68.49/10.20 spl93_27 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_27])])).
% 68.49/10.20 thf(f2220,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)))) ) | (~spl93_27 | ~spl93_70)),
% 68.49/10.20 inference(superposition,[],[f2182,f1883])).
% 68.49/10.20 thf(f1883,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)) ) | ~spl93_27),
% 68.49/10.20 inference(avatar_component_clause,[],[f1882])).
% 68.49/10.20 thf(f7761,plain,(
% 68.49/10.20 spl93_380 | ~spl93_26 | ~spl93_65),
% 68.49/10.20 inference(avatar_split_clause,[],[f2207,f2157,f1878,f7759])).
% 68.49/10.20 thf(f7759,plain,(
% 68.49/10.20 spl93_380 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_380])])).
% 68.49/10.20 thf(f1878,plain,(
% 68.49/10.20 spl93_26 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_26])])).
% 68.49/10.20 thf(f2207,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | (~spl93_26 | ~spl93_65)),
% 68.49/10.20 inference(superposition,[],[f2158,f1879])).
% 68.49/10.20 thf(f1879,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)) ) | ~spl93_26),
% 68.49/10.20 inference(avatar_component_clause,[],[f1878])).
% 68.49/10.20 thf(f7757,plain,(
% 68.49/10.20 spl93_379 | ~spl93_22 | ~spl93_58),
% 68.49/10.20 inference(avatar_split_clause,[],[f2129,f2108,f1832,f7755])).
% 68.49/10.20 thf(f7755,plain,(
% 68.49/10.20 spl93_379 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,field($o,X0),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,one($o,ring_ext($o,X0)),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_379])])).
% 68.49/10.20 thf(f2108,plain,(
% 68.49/10.20 spl93_58 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_58])])).
% 68.49/10.20 thf(f2129,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0)))] : (($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,zero($o,X0),X1)) | ($true != vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,field($o,X0),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,ring_ext($o,X0))),$o,one($o,ring_ext($o,X0)),X1))) ) | (~spl93_22 | ~spl93_58)),
% 68.49/10.20 inference(superposition,[],[f2109,f1833])).
% 68.49/10.20 thf(f2109,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2))) ) | ~spl93_58),
% 68.49/10.20 inference(avatar_component_clause,[],[f2108])).
% 68.49/10.20 thf(f7753,plain,(
% 68.49/10.20 spl93_378 | ~spl93_16 | ~spl93_227 | ~spl93_315),
% 68.49/10.20 inference(avatar_split_clause,[],[f5287,f5065,f3899,f1802,f7751])).
% 68.49/10.20 thf(f7751,plain,(
% 68.49/10.20 spl93_378 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_378])])).
% 68.49/10.20 thf(f1802,plain,(
% 68.49/10.20 spl93_16 <=> (cancel_semigroup_add(int) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_16])])).
% 68.49/10.20 thf(f5065,plain,(
% 68.49/10.20 spl93_315 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | (X1 = X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_315])])).
% 68.49/10.20 thf(f5287,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X2)) ) | (~spl93_16 | ~spl93_227 | ~spl93_315)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5286])).
% 68.49/10.20 thf(f5286,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1) != X0) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X2)) ) | (~spl93_16 | ~spl93_227 | ~spl93_315)),
% 68.49/10.20 inference(forward_demodulation,[],[f5261,f1804])).
% 68.49/10.20 thf(f1804,plain,(
% 68.49/10.20 (cancel_semigroup_add(int) = $true) | ~spl93_16),
% 68.49/10.20 inference(avatar_component_clause,[],[f1802])).
% 68.49/10.20 thf(f5261,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1) != X0) | (cancel_semigroup_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = X2)) ) | (~spl93_227 | ~spl93_315)),
% 68.49/10.20 inference(superposition,[],[f5066,f3900])).
% 68.49/10.20 thf(f5066,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | (X1 = X3)) ) | ~spl93_315),
% 68.49/10.20 inference(avatar_component_clause,[],[f5065])).
% 68.49/10.20 thf(f7673,plain,(
% 68.49/10.20 spl93_377 | ~spl93_24 | ~spl93_73 | ~spl93_162),
% 68.49/10.20 inference(avatar_split_clause,[],[f6296,f3064,f2243,f1868,f7670])).
% 68.49/10.20 thf(f7670,plain,(
% 68.49/10.20 spl93_377 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_377])])).
% 68.49/10.20 thf(f6296,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),sK6)) | (~spl93_24 | ~spl93_73 | ~spl93_162)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6295])).
% 68.49/10.20 thf(f6295,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),sK6)) | (~spl93_24 | ~spl93_73 | ~spl93_162)),
% 68.49/10.20 inference(forward_demodulation,[],[f3092,f1870])).
% 68.49/10.20 thf(f3092,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_162)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3089])).
% 68.49/10.20 thf(f3089,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_162)),
% 68.49/10.20 inference(superposition,[],[f3065,f2245])).
% 68.49/10.20 thf(f7668,plain,(
% 68.49/10.20 spl93_376 | ~spl93_73 | ~spl93_134),
% 68.49/10.20 inference(avatar_split_clause,[],[f2807,f2767,f2243,f7665])).
% 68.49/10.20 thf(f7665,plain,(
% 68.49/10.20 spl93_376 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,sK6)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_376])])).
% 68.49/10.20 thf(f2807,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,sK6)),sK6)) | (~spl93_73 | ~spl93_134)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2804])).
% 68.49/10.20 thf(f2804,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,sK6)),sK6)) | (~spl93_73 | ~spl93_134)),
% 68.49/10.20 inference(superposition,[],[f2768,f2245])).
% 68.49/10.20 thf(f7663,plain,(
% 68.49/10.20 spl93_375 | ~spl93_73 | ~spl93_133),
% 68.49/10.20 inference(avatar_split_clause,[],[f2799,f2763,f2243,f7660])).
% 68.49/10.20 thf(f7660,plain,(
% 68.49/10.20 spl93_375 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,sK11,sK6)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_375])])).
% 68.49/10.20 thf(f2799,plain,(
% 68.49/10.20 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,sK11,sK6))) | (~spl93_73 | ~spl93_133)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2796])).
% 68.49/10.20 thf(f2796,plain,(
% 68.49/10.20 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(a,a,sK11,sK6))) | (~spl93_73 | ~spl93_133)),
% 68.49/10.20 inference(superposition,[],[f2764,f2245])).
% 68.49/10.20 thf(f7658,plain,(
% 68.49/10.20 spl93_374 | ~spl93_73 | ~spl93_131),
% 68.49/10.20 inference(avatar_split_clause,[],[f2775,f2755,f2243,f7655])).
% 68.49/10.20 thf(f7655,plain,(
% 68.49/10.20 spl93_374 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_374])])).
% 68.49/10.20 thf(f2775,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_73 | ~spl93_131)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2772])).
% 68.49/10.20 thf(f2772,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))) | (~spl93_73 | ~spl93_131)),
% 68.49/10.20 inference(superposition,[],[f2756,f2245])).
% 68.49/10.20 thf(f7481,plain,(
% 68.49/10.20 spl93_373 | ~spl93_17 | ~spl93_314),
% 68.49/10.20 inference(avatar_split_clause,[],[f5255,f5061,f1807,f7479])).
% 68.49/10.20 thf(f7479,plain,(
% 68.49/10.20 spl93_373 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)) | (X1 != X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_373])])).
% 68.49/10.20 thf(f5061,plain,(
% 68.49/10.20 spl93_314 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | (X2 != X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_314])])).
% 68.49/10.20 thf(f5255,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)) | (X1 != X2)) ) | (~spl93_17 | ~spl93_314)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5252])).
% 68.49/10.20 thf(f5252,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)) | (X1 != X2)) ) | (~spl93_17 | ~spl93_314)),
% 68.49/10.20 inference(superposition,[],[f5062,f1809])).
% 68.49/10.20 thf(f5062,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((cancel_semigroup_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (X2 != X3)) ) | ~spl93_314),
% 68.49/10.20 inference(avatar_component_clause,[],[f5061])).
% 68.49/10.20 thf(f7418,plain,(
% 68.49/10.20 spl93_372 | ~spl93_22 | ~spl93_57),
% 68.49/10.20 inference(avatar_split_clause,[],[f2127,f2104,f1832,f7416])).
% 68.49/10.20 thf(f7416,plain,(
% 68.49/10.20 spl93_372 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_372])])).
% 68.49/10.20 thf(f2104,plain,(
% 68.49/10.20 spl93_57 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))) | (group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_57])])).
% 68.49/10.20 thf(f2127,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_57)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2126])).
% 68.49/10.20 thf(f2126,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_57)),
% 68.49/10.20 inference(superposition,[],[f2105,f1833])).
% 68.49/10.20 thf(f2105,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1)))) ) | ~spl93_57),
% 68.49/10.20 inference(avatar_component_clause,[],[f2104])).
% 68.49/10.20 thf(f7414,plain,(
% 68.49/10.20 spl93_371 | ~spl93_22 | ~spl93_56),
% 68.49/10.20 inference(avatar_split_clause,[],[f2123,f2100,f1832,f7412])).
% 68.49/10.20 thf(f7412,plain,(
% 68.49/10.20 spl93_371 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))) | (ab_group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_371])])).
% 68.49/10.20 thf(f2100,plain,(
% 68.49/10.20 spl93_56 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))) | (ab_group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_56])])).
% 68.49/10.20 thf(f2123,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_56)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2122])).
% 68.49/10.20 thf(f2122,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_56)),
% 68.49/10.20 inference(superposition,[],[f2101,f1833])).
% 68.49/10.20 thf(f2101,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((ab_group_add(X0) != $true) | (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2)))) ) | ~spl93_56),
% 68.49/10.20 inference(avatar_component_clause,[],[f2100])).
% 68.49/10.20 thf(f7410,plain,(
% 68.49/10.20 spl93_370 | ~spl93_22 | ~spl93_55),
% 68.49/10.20 inference(avatar_split_clause,[],[f2118,f2096,f1832,f7408])).
% 68.49/10.20 thf(f7408,plain,(
% 68.49/10.20 spl93_370 <=> ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_1(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_370])])).
% 68.49/10.20 thf(f2096,plain,(
% 68.49/10.20 spl93_55 <=> ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_1(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_55])])).
% 68.49/10.20 thf(f2118,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_1(X0) = $false)) ) | (~spl93_22 | ~spl93_55)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2117])).
% 68.49/10.20 thf(f2117,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_1(X0) = $false)) ) | (~spl93_22 | ~spl93_55)),
% 68.49/10.20 inference(superposition,[],[f2097,f1833])).
% 68.49/10.20 thf(f2097,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((semiring_1(X0) != $true) | (vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2)))) ) | ~spl93_55),
% 68.49/10.20 inference(avatar_component_clause,[],[f2096])).
% 68.49/10.20 thf(f7377,plain,(
% 68.49/10.20 spl93_369 | ~spl93_25 | ~spl93_53 | ~spl93_60 | ~spl93_61 | ~spl93_74 | ~spl93_167),
% 68.49/10.20 inference(avatar_split_clause,[],[f3191,f3147,f2247,f2136,f2131,f2074,f1873,f7374])).
% 68.49/10.20 thf(f3191,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_60 | ~spl93_61 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3190])).
% 68.49/10.20 thf(f3190,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_25 | ~spl93_53 | ~spl93_60 | ~spl93_61 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(forward_demodulation,[],[f3189,f1875])).
% 68.49/10.20 thf(f3189,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_53 | ~spl93_60 | ~spl93_61 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(forward_demodulation,[],[f3188,f2133])).
% 68.49/10.20 thf(f3188,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_53 | ~spl93_61 | ~spl93_74 | ~spl93_167)),
% 68.49/10.20 inference(forward_demodulation,[],[f3187,f2300])).
% 68.49/10.20 thf(f3187,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_61 | ~spl93_167)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f3180])).
% 68.49/10.20 thf(f3180,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_61 | ~spl93_167)),
% 68.49/10.20 inference(superposition,[],[f3148,f2138])).
% 68.49/10.20 thf(f7372,plain,(
% 68.49/10.20 spl93_368 | ~spl93_16 | ~spl93_227 | ~spl93_313),
% 68.49/10.20 inference(avatar_split_clause,[],[f5250,f5057,f3899,f1802,f7370])).
% 68.49/10.20 thf(f5057,plain,(
% 68.49/10.20 spl93_313 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | (X2 = X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_313])])).
% 68.49/10.20 thf(f5250,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X0) | (X1 = X2)) ) | (~spl93_16 | ~spl93_227 | ~spl93_313)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5249])).
% 68.49/10.20 thf(f5249,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X0) | (X1 = X2)) ) | (~spl93_16 | ~spl93_227 | ~spl93_313)),
% 68.49/10.20 inference(forward_demodulation,[],[f5224,f1804])).
% 68.49/10.20 thf(f5224,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X2) != X0) | (cancel_semigroup_add(int) != $true) | (X1 = X2)) ) | (~spl93_227 | ~spl93_313)),
% 68.49/10.20 inference(superposition,[],[f5058,f3900])).
% 68.49/10.20 thf(f5058,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | (X2 = X3)) ) | ~spl93_313),
% 68.49/10.20 inference(avatar_component_clause,[],[f5057])).
% 68.49/10.20 thf(f7368,plain,(
% 68.49/10.20 spl93_367 | ~spl93_48),
% 68.49/10.20 inference(avatar_split_clause,[],[f2041,f2031,f7366])).
% 68.49/10.20 thf(f7366,plain,(
% 68.49/10.20 spl93_367 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_367])])).
% 68.49/10.20 thf(f2041,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X3))) ) | ~spl93_48),
% 68.49/10.20 inference(constrained_superposition,[],[f2032,f2032])).
% 68.49/10.20 thf(f7364,plain,(
% 68.49/10.20 spl93_366 | ~spl93_47 | ~spl93_48),
% 68.49/10.20 inference(avatar_split_clause,[],[f2040,f2031,f2027,f7362])).
% 68.49/10.20 thf(f7362,plain,(
% 68.49/10.20 spl93_366 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_366])])).
% 68.49/10.20 thf(f2040,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,sK33(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,sK34(X1,X0),X3))) ) | (~spl93_47 | ~spl93_48)),
% 68.49/10.20 inference(constrained_superposition,[],[f2032,f2028])).
% 68.49/10.20 thf(f7360,plain,(
% 68.49/10.20 spl93_365 | ~spl93_47),
% 68.49/10.20 inference(avatar_split_clause,[],[f2037,f2027,f7358])).
% 68.49/10.20 thf(f7358,plain,(
% 68.49/10.20 spl93_365 <=> ! [X1 : $tType,X0 : $tType,X3 : product_prod(X1,X0),X2 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X3)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_365])])).
% 68.49/10.20 thf(f2037,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0),X3 : product_prod(X1,X0)] : ((X2 = X3) | (vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X2) != vAPP(product_prod(X1,X0),X0,sK32(X1,X0),X3)) | (vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X2) != vAPP(product_prod(X1,X0),X1,sK31(X1,X0),X3))) ) | ~spl93_47),
% 68.49/10.20 inference(constrained_superposition,[],[f2028,f2028])).
% 68.49/10.20 thf(f7356,plain,(
% 68.49/10.20 spl93_364),
% 68.49/10.20 inference(avatar_split_clause,[],[f1546,f7354])).
% 68.49/10.20 thf(f7354,plain,(
% 68.49/10.20 spl93_364 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) | (X3 != X5) | (X2 != X4))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_364])])).
% 68.49/10.20 thf(f1546,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) | (X3 != X5) | (X2 != X4)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1545])).
% 68.49/10.20 thf(f1545,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) | (X3 != X5) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X4))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1544])).
% 68.49/10.20 thf(f1544,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) | ($false = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X3),X5)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X4))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1543])).
% 68.49/10.20 thf(f1543,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X4)),vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X3),X5)))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1536])).
% 68.49/10.20 thf(f1536,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X4)),vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X3),X5)))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1433])).
% 68.49/10.20 thf(f1433,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X4)),vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X3),X5)))) )),
% 68.49/10.20 inference(cnf_transformation,[],[f633])).
% 68.49/10.20 thf(f633,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : (vAPP(product_prod(X0,X1),$o,vAPP(product_prod(X0,X1),sTfun(product_prod(X0,X1),$o),vEQ(product_prod(X0,X1)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3)),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X4)),vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),vEQ(X1),X3),X5)))),
% 68.49/10.20 inference(fool_elimination,[],[f632])).
% 68.49/10.20 thf(f632,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1,X4 : X0,X5 : X1] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X2),X3) = vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X4),X5)) = (X3 = X5) & (X2 = X4))),
% 68.49/10.20 inference(rectify,[],[f21])).
% 68.49/10.20 thf(f21,axiom,(
% 68.49/10.20 ! [X0 : $tType,X2 : $tType,X16 : X0,X17 : X2,X18 : X0,X19 : X2] : ((vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X16),X17) = vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X18),X19)) = (X17 = X19) & (X16 = X18))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_prod_Oinject)).
% 68.49/10.20 thf(f7296,plain,(
% 68.49/10.20 spl93_363 | ~spl93_22 | ~spl93_54),
% 68.49/10.20 inference(avatar_split_clause,[],[f2090,f2082,f1832,f7294])).
% 68.49/10.20 thf(f7294,plain,(
% 68.49/10.20 spl93_363 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0)))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($false = vAPP(nat,$o,X0,X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_363])])).
% 68.49/10.20 thf(f2082,plain,(
% 68.49/10.20 spl93_54 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_54])])).
% 68.49/10.20 thf(f2090,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0)))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl93_22 | ~spl93_54)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2089])).
% 68.49/10.20 thf(f2089,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0)))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl93_22 | ~spl93_54)),
% 68.49/10.20 inference(superposition,[],[f2083,f1833])).
% 68.49/10.20 thf(f2083,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0)))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))) ) | ~spl93_54),
% 68.49/10.20 inference(avatar_component_clause,[],[f2082])).
% 68.49/10.20 thf(f7136,plain,(
% 68.49/10.20 spl93_362 | ~spl93_24 | ~spl93_73 | ~spl93_153),
% 68.49/10.20 inference(avatar_split_clause,[],[f6308,f2962,f2243,f1868,f7133])).
% 68.49/10.20 thf(f7133,plain,(
% 68.49/10.20 spl93_362 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_362])])).
% 68.49/10.20 thf(f6308,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_24 | ~spl93_73 | ~spl93_153)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6307])).
% 68.49/10.20 thf(f6307,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (~spl93_24 | ~spl93_73 | ~spl93_153)),
% 68.49/10.20 inference(forward_demodulation,[],[f2978,f1870])).
% 68.49/10.20 thf(f2978,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_153)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2975])).
% 68.49/10.20 thf(f2975,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) != $true) | (~spl93_73 | ~spl93_153)),
% 68.49/10.20 inference(superposition,[],[f2963,f2245])).
% 68.49/10.20 thf(f7110,plain,(
% 68.49/10.20 spl93_361 | ~spl93_25 | ~spl93_73 | ~spl93_155),
% 68.49/10.20 inference(avatar_split_clause,[],[f6306,f2970,f2243,f1873,f7107])).
% 68.49/10.20 thf(f7107,plain,(
% 68.49/10.20 spl93_361 <=> (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_361])])).
% 68.49/10.20 thf(f6306,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (~spl93_25 | ~spl93_73 | ~spl93_155)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6305])).
% 68.49/10.20 thf(f6305,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (~spl93_25 | ~spl93_73 | ~spl93_155)),
% 68.49/10.20 inference(forward_demodulation,[],[f2994,f1875])).
% 68.49/10.20 thf(f2994,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_155)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2991])).
% 68.49/10.20 thf(f2991,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),sK6)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_155)),
% 68.49/10.20 inference(superposition,[],[f2971,f2245])).
% 68.49/10.20 thf(f7105,plain,(
% 68.49/10.20 spl93_360 | ~spl93_22 | ~spl93_53),
% 68.49/10.20 inference(avatar_split_clause,[],[f2079,f2074,f1832,f7103])).
% 68.49/10.20 thf(f7103,plain,(
% 68.49/10.20 spl93_360 <=> ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),units(X0,X1),X2)) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,group(X0,X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_360])])).
% 68.49/10.20 thf(f2079,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),units(X0,X1),X2)) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,group(X0,X1),X2))) ) | (~spl93_22 | ~spl93_53)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2078])).
% 68.49/10.20 thf(f2078,plain,(
% 68.49/10.20 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X0,monoid_ext(X0,X1))] : (($true != $true) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),partial_carrier(X0,monoid_ext(X0,X1)),X2) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),set(X0),units(X0,X1),X2)) | ($false = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X1)),$o,group(X0,X1),X2))) ) | (~spl93_22 | ~spl93_53)),
% 68.49/10.20 inference(superposition,[],[f2075,f1833])).
% 68.49/10.20 thf(f6825,plain,(
% 68.49/10.20 spl93_359 | ~spl93_21 | ~spl93_235 | ~spl93_312),
% 68.49/10.20 inference(avatar_split_clause,[],[f5215,f5040,f3960,f1827,f6823])).
% 68.49/10.20 thf(f6823,plain,(
% 68.49/10.20 spl93_359 <=> ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X0))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_359])])).
% 68.49/10.20 thf(f5215,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X0)) ) | (~spl93_21 | ~spl93_235 | ~spl93_312)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5214])).
% 68.49/10.20 thf(f5214,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X0)) ) | (~spl93_21 | ~spl93_235 | ~spl93_312)),
% 68.49/10.20 inference(forward_demodulation,[],[f5200,f1829])).
% 68.49/10.20 thf(f5200,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X0)) ) | (~spl93_235 | ~spl93_312)),
% 68.49/10.20 inference(superposition,[],[f5041,f3961])).
% 68.49/10.20 thf(f6804,plain,(
% 68.49/10.20 spl93_358 | ~spl93_21 | ~spl93_57),
% 68.49/10.20 inference(avatar_split_clause,[],[f2128,f2104,f1827,f6802])).
% 68.49/10.20 thf(f6802,plain,(
% 68.49/10.20 spl93_358 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X1)),vAPP(int,int,uminus_uminus(int),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_358])])).
% 68.49/10.20 thf(f2128,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X1)),vAPP(int,int,uminus_uminus(int),X0)))) ) | (~spl93_21 | ~spl93_57)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2125])).
% 68.49/10.20 thf(f2125,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X1)),vAPP(int,int,uminus_uminus(int),X0)))) ) | (~spl93_21 | ~spl93_57)),
% 68.49/10.20 inference(superposition,[],[f2105,f1829])).
% 68.49/10.20 thf(f6800,plain,(
% 68.49/10.20 spl93_357 | ~spl93_20 | ~spl93_56),
% 68.49/10.20 inference(avatar_split_clause,[],[f2124,f2100,f1822,f6798])).
% 68.49/10.20 thf(f6798,plain,(
% 68.49/10.20 spl93_357 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,uminus_uminus(int),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_357])])).
% 68.49/10.20 thf(f2124,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,uminus_uminus(int),X1)))) ) | (~spl93_20 | ~spl93_56)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2121])).
% 68.49/10.20 thf(f2121,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,uminus_uminus(int),X1)))) ) | (~spl93_20 | ~spl93_56)),
% 68.49/10.20 inference(superposition,[],[f2101,f1824])).
% 68.49/10.20 thf(f6796,plain,(
% 68.49/10.20 spl93_356 | ~spl93_6 | ~spl93_55),
% 68.49/10.20 inference(avatar_split_clause,[],[f2120,f2096,f1752,f6794])).
% 68.49/10.20 thf(f6794,plain,(
% 68.49/10.20 spl93_356 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,int,semiring_1_of_nat(int),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(nat,int,semiring_1_of_nat(int),X0)),vAPP(nat,int,semiring_1_of_nat(int),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_356])])).
% 68.49/10.20 thf(f1752,plain,(
% 68.49/10.20 spl93_6 <=> (semiring_1(int) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_6])])).
% 68.49/10.20 thf(f2120,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,int,semiring_1_of_nat(int),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(nat,int,semiring_1_of_nat(int),X0)),vAPP(nat,int,semiring_1_of_nat(int),X1)))) ) | (~spl93_6 | ~spl93_55)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2115])).
% 68.49/10.20 thf(f2115,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,int,semiring_1_of_nat(int),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(nat,int,semiring_1_of_nat(int),X0)),vAPP(nat,int,semiring_1_of_nat(int),X1)))) ) | (~spl93_6 | ~spl93_55)),
% 68.49/10.20 inference(superposition,[],[f2097,f1754])).
% 68.49/10.20 thf(f1754,plain,(
% 68.49/10.20 (semiring_1(int) = $true) | ~spl93_6),
% 68.49/10.20 inference(avatar_component_clause,[],[f1752])).
% 68.49/10.20 thf(f6792,plain,(
% 68.49/10.20 spl93_355 | ~spl93_8 | ~spl93_55),
% 68.49/10.20 inference(avatar_split_clause,[],[f2119,f2096,f1762,f6790])).
% 68.49/10.20 thf(f6790,plain,(
% 68.49/10.20 spl93_355 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,semiring_1_of_nat(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,semiring_1_of_nat(nat),X0)),vAPP(nat,nat,semiring_1_of_nat(nat),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_355])])).
% 68.49/10.20 thf(f1762,plain,(
% 68.49/10.20 spl93_8 <=> (semiring_1(nat) = $true)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_8])])).
% 68.49/10.20 thf(f2119,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,semiring_1_of_nat(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,semiring_1_of_nat(nat),X0)),vAPP(nat,nat,semiring_1_of_nat(nat),X1)))) ) | (~spl93_8 | ~spl93_55)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2116])).
% 68.49/10.20 thf(f2116,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,semiring_1_of_nat(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,semiring_1_of_nat(nat),X0)),vAPP(nat,nat,semiring_1_of_nat(nat),X1)))) ) | (~spl93_8 | ~spl93_55)),
% 68.49/10.20 inference(superposition,[],[f2097,f1764])).
% 68.49/10.20 thf(f1764,plain,(
% 68.49/10.20 (semiring_1(nat) = $true) | ~spl93_8),
% 68.49/10.20 inference(avatar_component_clause,[],[f1762])).
% 68.49/10.20 thf(f6788,plain,(
% 68.49/10.20 spl93_354 | ~spl93_22 | ~spl93_48),
% 68.49/10.20 inference(avatar_split_clause,[],[f2039,f2031,f1832,f6786])).
% 68.49/10.20 thf(f6786,plain,(
% 68.49/10.20 spl93_354 <=> ! [X0 : $tType,X1 : product_prod(X0,$o)] : ((vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(product_prod(X0,$o),X0,sK33(X0,$o),X1)),$true) = X1) | ($false = vAPP(product_prod(X0,$o),$o,sK34(X0,$o),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_354])])).
% 68.49/10.20 thf(f2039,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X1 : product_prod(X0,$o)] : ((vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(product_prod(X0,$o),X0,sK33(X0,$o),X1)),$true) = X1) | ($false = vAPP(product_prod(X0,$o),$o,sK34(X0,$o),X1))) ) | (~spl93_22 | ~spl93_48)),
% 68.49/10.20 inference(superposition,[],[f2032,f1833])).
% 68.49/10.20 thf(f6784,plain,(
% 68.49/10.20 spl93_353 | ~spl93_22 | ~spl93_48),
% 68.49/10.20 inference(avatar_split_clause,[],[f2038,f2031,f1832,f6782])).
% 68.49/10.20 thf(f6782,plain,(
% 68.49/10.20 spl93_353 <=> ! [X0 : $tType,X1 : product_prod($o,X0)] : ((vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(product_prod($o,X0),X0,sK34($o,X0),X1)) = X1) | ($false = vAPP(product_prod($o,X0),$o,sK33($o,X0),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_353])])).
% 68.49/10.20 thf(f2038,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X1 : product_prod($o,X0)] : ((vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(product_prod($o,X0),X0,sK34($o,X0),X1)) = X1) | ($false = vAPP(product_prod($o,X0),$o,sK33($o,X0),X1))) ) | (~spl93_22 | ~spl93_48)),
% 68.49/10.20 inference(superposition,[],[f2032,f1833])).
% 68.49/10.20 thf(f6780,plain,(
% 68.49/10.20 spl93_352 | ~spl93_22 | ~spl93_47),
% 68.49/10.20 inference(avatar_split_clause,[],[f2036,f2027,f1832,f6778])).
% 68.49/10.20 thf(f6778,plain,(
% 68.49/10.20 spl93_352 <=> ! [X0 : $tType,X1 : product_prod(X0,$o)] : ((vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(product_prod(X0,$o),X0,sK31(X0,$o),X1)),$true) = X1) | ($false = vAPP(product_prod(X0,$o),$o,sK32(X0,$o),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_352])])).
% 68.49/10.20 thf(f2036,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X1 : product_prod(X0,$o)] : ((vAPP($o,product_prod(X0,$o),vAPP(X0,sTfun($o,product_prod(X0,$o)),product_Pair(X0,$o),vAPP(product_prod(X0,$o),X0,sK31(X0,$o),X1)),$true) = X1) | ($false = vAPP(product_prod(X0,$o),$o,sK32(X0,$o),X1))) ) | (~spl93_22 | ~spl93_47)),
% 68.49/10.20 inference(superposition,[],[f2028,f1833])).
% 68.49/10.20 thf(f6776,plain,(
% 68.49/10.20 spl93_351 | ~spl93_22 | ~spl93_47),
% 68.49/10.20 inference(avatar_split_clause,[],[f2035,f2027,f1832,f6774])).
% 68.49/10.20 thf(f6774,plain,(
% 68.49/10.20 spl93_351 <=> ! [X0 : $tType,X1 : product_prod($o,X0)] : ((vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(product_prod($o,X0),X0,sK32($o,X0),X1)) = X1) | ($false = vAPP(product_prod($o,X0),$o,sK31($o,X0),X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_351])])).
% 68.49/10.20 thf(f2035,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X1 : product_prod($o,X0)] : ((vAPP(X0,product_prod($o,X0),vAPP($o,sTfun(X0,product_prod($o,X0)),product_Pair($o,X0),$true),vAPP(product_prod($o,X0),X0,sK32($o,X0),X1)) = X1) | ($false = vAPP(product_prod($o,X0),$o,sK31($o,X0),X1))) ) | (~spl93_22 | ~spl93_47)),
% 68.49/10.20 inference(superposition,[],[f2028,f1833])).
% 68.49/10.20 thf(f6772,plain,(
% 68.49/10.20 spl93_350 | ~spl93_22 | ~spl93_46),
% 68.49/10.20 inference(avatar_split_clause,[],[f2034,f2023,f1832,f6770])).
% 68.49/10.20 thf(f6770,plain,(
% 68.49/10.20 spl93_350 <=> ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,product_unit)),$o,one($o,product_unit),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),partia1265057091ct_ext($o,monoid_ext($o,product_unit)),units_of($o,X0),X1))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_350])])).
% 68.49/10.20 thf(f2034,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X1 : partia1265057091ct_ext($o,monoid_ext($o,X0))] : (($true = vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),$o,one($o,X0),X1)) | ($false = vAPP(partia1265057091ct_ext($o,monoid_ext($o,product_unit)),$o,one($o,product_unit),vAPP(partia1265057091ct_ext($o,monoid_ext($o,X0)),partia1265057091ct_ext($o,monoid_ext($o,product_unit)),units_of($o,X0),X1)))) ) | (~spl93_22 | ~spl93_46)),
% 68.49/10.20 inference(superposition,[],[f2024,f1833])).
% 68.49/10.20 thf(f6768,plain,(
% 68.49/10.20 spl93_349 | ~spl93_21 | ~spl93_221 | ~spl93_311),
% 68.49/10.20 inference(avatar_split_clause,[],[f5188,f5036,f3826,f1827,f6766])).
% 68.49/10.20 thf(f6766,plain,(
% 68.49/10.20 spl93_349 <=> ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_349])])).
% 68.49/10.20 thf(f5188,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0))) ) | (~spl93_21 | ~spl93_221 | ~spl93_311)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5187])).
% 68.49/10.20 thf(f5187,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (X1 != X2) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0))) ) | (~spl93_21 | ~spl93_221 | ~spl93_311)),
% 68.49/10.20 inference(forward_demodulation,[],[f5172,f1829])).
% 68.49/10.20 thf(f5172,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((X1 != X2) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X0))) ) | (~spl93_221 | ~spl93_311)),
% 68.49/10.20 inference(superposition,[],[f5037,f3827])).
% 68.49/10.20 thf(f6656,plain,(
% 68.49/10.20 spl93_348 | ~spl93_25 | ~spl93_73 | ~spl93_149),
% 68.49/10.20 inference(avatar_split_clause,[],[f6310,f2908,f2243,f1873,f6653])).
% 68.49/10.20 thf(f6653,plain,(
% 68.49/10.20 spl93_348 <=> (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_348])])).
% 68.49/10.20 thf(f6310,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (~spl93_25 | ~spl93_73 | ~spl93_149)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6309])).
% 68.49/10.20 thf(f6309,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (~spl93_25 | ~spl93_73 | ~spl93_149)),
% 68.49/10.20 inference(forward_demodulation,[],[f2925,f1875])).
% 68.49/10.20 thf(f2925,plain,(
% 68.49/10.20 (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_149)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2922])).
% 68.49/10.20 thf(f2922,plain,(
% 68.49/10.20 ($true != $true) | (sK6 = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),sK6))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) != $true) | (~spl93_73 | ~spl93_149)),
% 68.49/10.20 inference(superposition,[],[f2909,f2245])).
% 68.49/10.20 thf(f6651,plain,(
% 68.49/10.20 spl93_347 | ~spl93_22 | ~spl93_52),
% 68.49/10.20 inference(avatar_split_clause,[],[f2071,f2066,f1832,f6649])).
% 68.49/10.20 thf(f6649,plain,(
% 68.49/10.20 spl93_347 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)) | (ab_group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_347])])).
% 68.49/10.20 thf(f2066,plain,(
% 68.49/10.20 spl93_52 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)) | (ab_group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_52])])).
% 68.49/10.20 thf(f2071,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_52)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2070])).
% 68.49/10.20 thf(f2070,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_52)),
% 68.49/10.20 inference(superposition,[],[f2067,f1833])).
% 68.49/10.20 thf(f2067,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((ab_group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1))) ) | ~spl93_52),
% 68.49/10.20 inference(avatar_component_clause,[],[f2066])).
% 68.49/10.20 thf(f6636,plain,(
% 68.49/10.20 spl93_346 | ~spl93_22 | ~spl93_50),
% 68.49/10.20 inference(avatar_split_clause,[],[f2057,f2048,f1832,f6634])).
% 68.49/10.20 thf(f6634,plain,(
% 68.49/10.20 spl93_346 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0))))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_346])])).
% 68.49/10.20 thf(f2057,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0)))) ) | (~spl93_22 | ~spl93_50)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2056])).
% 68.49/10.20 thf(f2056,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0)))) ) | (~spl93_22 | ~spl93_50)),
% 68.49/10.20 inference(superposition,[],[f2049,f1833])).
% 68.49/10.20 thf(f6459,plain,(
% 68.49/10.20 spl93_345 | ~spl93_53 | ~spl93_74),
% 68.49/10.20 inference(avatar_split_clause,[],[f5934,f2247,f2074,f6456])).
% 68.49/10.20 thf(f6366,plain,(
% 68.49/10.20 spl93_344 | ~spl93_53 | ~spl93_74 | ~spl93_124 | ~spl93_338),
% 68.49/10.20 inference(avatar_split_clause,[],[f6344,f5946,f2669,f2247,f2074,f6363])).
% 68.49/10.20 thf(f6344,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_74 | ~spl93_124 | ~spl93_338)),
% 68.49/10.20 inference(forward_demodulation,[],[f6338,f5934])).
% 68.49/10.20 thf(f6338,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_124 | ~spl93_338)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6329])).
% 68.49/10.20 thf(f6329,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_124 | ~spl93_338)),
% 68.49/10.20 inference(superposition,[],[f2670,f5947])).
% 68.49/10.20 thf(f6361,plain,(
% 68.49/10.20 spl93_343 | ~spl93_53 | ~spl93_74 | ~spl93_122 | ~spl93_338),
% 68.49/10.20 inference(avatar_split_clause,[],[f6343,f5946,f2652,f2247,f2074,f6358])).
% 68.49/10.20 thf(f6343,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_74 | ~spl93_122 | ~spl93_338)),
% 68.49/10.20 inference(forward_demodulation,[],[f6340,f5934])).
% 68.49/10.20 thf(f6340,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_122 | ~spl93_338)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f6327])).
% 68.49/10.20 thf(f6327,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_122 | ~spl93_338)),
% 68.49/10.20 inference(superposition,[],[f2653,f5947])).
% 68.49/10.20 thf(f6356,plain,(
% 68.49/10.20 spl93_342 | ~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_127),
% 68.49/10.20 inference(avatar_split_clause,[],[f6317,f2697,f2247,f2243,f2074,f6353])).
% 68.49/10.20 thf(f6353,plain,(
% 68.49/10.20 spl93_342 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_342])])).
% 68.49/10.20 thf(f6317,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_73 | ~spl93_74 | ~spl93_127)),
% 68.49/10.20 inference(forward_demodulation,[],[f2713,f5934])).
% 68.49/10.20 thf(f2713,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_73 | ~spl93_127)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2710])).
% 68.49/10.20 thf(f2710,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_73 | ~spl93_127)),
% 68.49/10.20 inference(superposition,[],[f2698,f2245])).
% 68.49/10.20 thf(f6351,plain,(
% 68.49/10.20 spl93_341 | ~spl93_53 | ~spl93_74 | ~spl93_337),
% 68.49/10.20 inference(avatar_split_clause,[],[f6067,f5924,f2247,f2074,f6348])).
% 68.49/10.20 thf(f6348,plain,(
% 68.49/10.20 spl93_341 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_341])])).
% 68.49/10.20 thf(f5924,plain,(
% 68.49/10.20 spl93_337 <=> ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_337])])).
% 68.49/10.20 thf(f6067,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | ~spl93_74 | ~spl93_337)),
% 68.49/10.20 inference(forward_demodulation,[],[f5926,f5934])).
% 68.49/10.20 thf(f5926,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ~spl93_337),
% 68.49/10.20 inference(avatar_component_clause,[],[f5924])).
% 68.49/10.20 thf(f6325,plain,(
% 68.49/10.20 spl93_340 | ~spl93_21 | ~spl93_85 | ~spl93_86 | ~spl93_216 | ~spl93_276 | ~spl93_300 | ~spl93_301 | ~spl93_333),
% 68.49/10.20 inference(avatar_split_clause,[],[f5895,f5865,f4916,f4912,f4534,f3748,f2306,f2302,f1827,f6323])).
% 68.49/10.20 thf(f6323,plain,(
% 68.49/10.20 spl93_340 <=> ! [X1 : int] : (vAPP(int,int,uminus_uminus(int),vAPP(int,int,uminus_uminus(int),X1)) = X1)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_340])])).
% 68.49/10.20 thf(f5967,plain,(
% 68.49/10.20 spl93_339 | ~spl93_22 | spl93_338),
% 68.49/10.20 inference(avatar_split_clause,[],[f5951,f5946,f1832,f5964])).
% 68.49/10.20 thf(f5964,plain,(
% 68.49/10.20 spl93_339 <=> ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_339])])).
% 68.49/10.20 thf(f5951,plain,(
% 68.49/10.20 ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_22 | spl93_338)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5950])).
% 68.49/10.20 thf(f5950,plain,(
% 68.49/10.20 ($true != $true) | ($false = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_22 | spl93_338)),
% 68.49/10.20 inference(superposition,[],[f5948,f1833])).
% 68.49/10.20 thf(f5948,plain,(
% 68.49/10.20 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | spl93_338),
% 68.49/10.20 inference(avatar_component_clause,[],[f5946])).
% 68.49/10.20 thf(f5949,plain,(
% 68.49/10.20 ~spl93_338 | ~spl93_53 | spl93_73 | ~spl93_74),
% 68.49/10.20 inference(avatar_split_clause,[],[f5942,f2247,f2243,f2074,f5946])).
% 68.49/10.20 thf(f5942,plain,(
% 68.49/10.20 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (~spl93_53 | spl93_73 | ~spl93_74)),
% 68.49/10.20 inference(forward_demodulation,[],[f2244,f5934])).
% 68.49/10.20 thf(f2244,plain,(
% 68.49/10.20 ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | spl93_73),
% 68.49/10.20 inference(avatar_component_clause,[],[f2243])).
% 68.49/10.20 thf(f5927,plain,(
% 68.49/10.20 spl93_337 | ~spl93_73 | ~spl93_126),
% 68.49/10.20 inference(avatar_split_clause,[],[f2705,f2693,f2243,f5924])).
% 68.49/10.20 thf(f2705,plain,(
% 68.49/10.20 ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_73 | ~spl93_126)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2702])).
% 68.49/10.20 thf(f2702,plain,(
% 68.49/10.20 ($true != $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,sK6)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (~spl93_73 | ~spl93_126)),
% 68.49/10.20 inference(superposition,[],[f2694,f2245])).
% 68.49/10.20 thf(f5922,plain,(
% 68.49/10.20 spl93_336 | ~spl93_22 | ~spl93_97),
% 68.49/10.20 inference(avatar_split_clause,[],[f2466,f2436,f1832,f5920])).
% 68.49/10.20 thf(f5920,plain,(
% 68.49/10.20 spl93_336 <=> ! [X0 : $tType,X2 : $o > X0,X1 : $o > X0] : ((vAPP($o,X0,X2,$true) != vAPP($o,X0,X1,$true)) | (X1 = X2) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),sK35(X0,$o),X1),X2)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_336])])).
% 68.49/10.20 thf(f2466,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : $o > X0,X1 : $o > X0] : ((vAPP($o,X0,X2,$true) != vAPP($o,X0,X1,$true)) | (X1 = X2) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),sK35(X0,$o),X1),X2))) ) | (~spl93_22 | ~spl93_97)),
% 68.49/10.20 inference(superposition,[],[f2437,f1833])).
% 68.49/10.20 thf(f5918,plain,(
% 68.49/10.20 spl93_335 | ~spl93_54),
% 68.49/10.20 inference(avatar_split_clause,[],[f2093,f2082,f5916])).
% 68.49/10.20 thf(f5916,plain,(
% 68.49/10.20 spl93_335 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((X0 != X1) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = X0))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_335])])).
% 68.49/10.20 thf(f2093,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X0 != X1) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = X0)) ) | ~spl93_54),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2092])).
% 68.49/10.20 thf(f2092,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X0 != X1) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))) ) | ~spl93_54),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2091])).
% 68.49/10.20 thf(f2091,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((X0 != X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))) ) | ~spl93_54),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2088])).
% 68.49/10.20 thf(f2088,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))) ) | ~spl93_54),
% 68.49/10.20 inference(primitive_instantiation,[],[f2083])).
% 68.49/10.20 thf(f5871,plain,(
% 68.49/10.20 spl93_334 | ~spl93_21 | ~spl93_310),
% 68.49/10.20 inference(avatar_split_clause,[],[f5155,f5032,f1827,f5869])).
% 68.49/10.20 thf(f5869,plain,(
% 68.49/10.20 spl93_334 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)) | (X1 != X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_334])])).
% 68.49/10.20 thf(f5032,plain,(
% 68.49/10.20 spl93_310 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | (X2 != X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_310])])).
% 68.49/10.20 thf(f5155,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)) | (X1 != X2)) ) | (~spl93_21 | ~spl93_310)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5151])).
% 68.49/10.20 thf(f5151,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2)) | (X1 != X2)) ) | (~spl93_21 | ~spl93_310)),
% 68.49/10.20 inference(superposition,[],[f5033,f1829])).
% 68.49/10.20 thf(f5033,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (X2 != X3)) ) | ~spl93_310),
% 68.49/10.20 inference(avatar_component_clause,[],[f5032])).
% 68.49/10.20 thf(f5867,plain,(
% 68.49/10.20 spl93_333 | ~spl93_300 | ~spl93_301 | ~spl93_332),
% 68.49/10.20 inference(avatar_split_clause,[],[f5756,f5753,f4916,f4912,f5865])).
% 68.49/10.20 thf(f5753,plain,(
% 68.49/10.20 spl93_332 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X1)),X0))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_332])])).
% 68.49/10.20 thf(f5756,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)))) ) | (~spl93_300 | ~spl93_301 | ~spl93_332)),
% 68.49/10.20 inference(forward_demodulation,[],[f5754,f4970])).
% 68.49/10.20 thf(f4970,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X1)),X0) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)))) ) | (~spl93_300 | ~spl93_301)),
% 68.49/10.20 inference(superposition,[],[f4917,f4913])).
% 68.49/10.20 thf(f5754,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X1)),X0))) ) | ~spl93_332),
% 68.49/10.20 inference(avatar_component_clause,[],[f5753])).
% 68.49/10.20 thf(f5755,plain,(
% 68.49/10.20 spl93_332 | ~spl93_20 | ~spl93_52),
% 68.49/10.20 inference(avatar_split_clause,[],[f2072,f2066,f1822,f5753])).
% 68.49/10.20 thf(f2072,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X1)),X0))) ) | (~spl93_20 | ~spl93_52)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2069])).
% 68.49/10.20 thf(f2069,plain,(
% 68.49/10.20 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,uminus_uminus(int),X1)),X0))) ) | (~spl93_20 | ~spl93_52)),
% 68.49/10.20 inference(superposition,[],[f2067,f1824])).
% 68.49/10.20 thf(f5751,plain,(
% 68.49/10.20 spl93_331),
% 68.49/10.20 inference(avatar_split_clause,[],[f1659,f5749])).
% 68.49/10.20 thf(f1659,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((X1 = X2) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) | (group_add(X0) != $true) | (X3 != X4)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1658])).
% 68.49/10.20 thf(f1658,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((X1 = X2) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X3),X4))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1654])).
% 68.49/10.20 thf(f1654,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X3),X4))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1242])).
% 68.49/10.20 thf(f1242,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X3),X4)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) | (group_add(X0) != $true)) )),
% 68.49/10.20 inference(cnf_transformation,[],[f821])).
% 68.49/10.20 thf(f821,plain,(
% 68.49/10.20 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X3),X4)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4))) | (group_add(X0) != $true))),
% 68.49/10.20 inference(ennf_transformation,[],[f373])).
% 68.49/10.20 thf(f373,plain,(
% 68.49/10.20 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X3),X4))))),
% 68.49/10.20 inference(fool_elimination,[],[f372])).
% 68.49/10.20 thf(f372,plain,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) => ((X1 = X2) = (X3 = X4))))),
% 68.49/10.20 inference(rectify,[],[f167])).
% 68.49/10.20 thf(f167,axiom,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0,X25 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X25)) => ((X6 = X7) = (X8 = X25))))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_diff__eq__diff__eq)).
% 68.49/10.20 thf(f5401,plain,(
% 68.49/10.20 spl93_330 | ~spl93_21 | ~spl93_235 | ~spl93_309),
% 68.49/10.20 inference(avatar_split_clause,[],[f5148,f5028,f3960,f1827,f5399])).
% 68.49/10.20 thf(f5148,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2)) ) | (~spl93_21 | ~spl93_235 | ~spl93_309)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5147])).
% 68.49/10.20 thf(f5147,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X1) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2)) ) | (~spl93_21 | ~spl93_235 | ~spl93_309)),
% 68.49/10.20 inference(forward_demodulation,[],[f5121,f1829])).
% 68.49/10.20 thf(f5121,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X2) != X1) | (group_add(int) != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0) = X2)) ) | (~spl93_235 | ~spl93_309)),
% 68.49/10.20 inference(superposition,[],[f5029,f3961])).
% 68.49/10.20 thf(f5397,plain,(
% 68.49/10.20 spl93_329 | ~spl93_54),
% 68.49/10.20 inference(avatar_split_clause,[],[f2094,f2082,f5395])).
% 68.49/10.20 thf(f5395,plain,(
% 68.49/10.20 spl93_329 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = X0) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_329])])).
% 68.49/10.20 thf(f2094,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = X0) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl93_54),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2085])).
% 68.49/10.20 thf(f2085,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1))) | (vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl93_54),
% 68.49/10.20 inference(leibniz_equality_elimination,[],[f2083])).
% 68.49/10.20 thf(f5393,plain,(
% 68.49/10.20 spl93_328 | ~spl93_22 | ~spl93_45),
% 68.49/10.20 inference(avatar_split_clause,[],[f2019,f1997,f1832,f5391])).
% 68.49/10.20 thf(f5391,plain,(
% 68.49/10.20 spl93_328 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_328])])).
% 68.49/10.20 thf(f1997,plain,(
% 68.49/10.20 spl93_45 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2) | (group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_45])])).
% 68.49/10.20 thf(f2019,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_45)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2018])).
% 68.49/10.20 thf(f2018,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_45)),
% 68.49/10.20 inference(superposition,[],[f1998,f1833])).
% 68.49/10.20 thf(f1998,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2)) ) | ~spl93_45),
% 68.49/10.20 inference(avatar_component_clause,[],[f1997])).
% 68.49/10.20 thf(f5389,plain,(
% 68.49/10.20 spl93_327 | ~spl93_22 | ~spl93_44),
% 68.49/10.20 inference(avatar_split_clause,[],[f2014,f1993,f1832,f5387])).
% 68.49/10.20 thf(f1993,plain,(
% 68.49/10.20 spl93_44 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_44])])).
% 68.49/10.20 thf(f2014,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_44)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2013])).
% 68.49/10.20 thf(f2013,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_44)),
% 68.49/10.20 inference(superposition,[],[f1994,f1833])).
% 68.49/10.20 thf(f1994,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2)) ) | ~spl93_44),
% 68.49/10.20 inference(avatar_component_clause,[],[f1993])).
% 68.49/10.20 thf(f5385,plain,(
% 68.49/10.20 spl93_326 | ~spl93_22 | ~spl93_43),
% 68.49/10.20 inference(avatar_split_clause,[],[f2010,f1989,f1832,f5383])).
% 68.49/10.20 thf(f5383,plain,(
% 68.49/10.20 spl93_326 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_326])])).
% 68.49/10.20 thf(f1989,plain,(
% 68.49/10.20 spl93_43 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2))) | (group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_43])])).
% 68.49/10.20 thf(f2010,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_43)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2009])).
% 68.49/10.20 thf(f2009,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_43)),
% 68.49/10.20 inference(superposition,[],[f1990,f1833])).
% 68.49/10.20 thf(f1990,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)))) ) | ~spl93_43),
% 68.49/10.20 inference(avatar_component_clause,[],[f1989])).
% 68.49/10.20 thf(f5381,plain,(
% 68.49/10.20 spl93_325 | ~spl93_22 | ~spl93_42),
% 68.49/10.20 inference(avatar_split_clause,[],[f2006,f1985,f1832,f5379])).
% 68.49/10.20 thf(f5379,plain,(
% 68.49/10.20 spl93_325 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))) | (group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_325])])).
% 68.49/10.20 thf(f1985,plain,(
% 68.49/10.20 spl93_42 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))) | (group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_42])])).
% 68.49/10.20 thf(f2006,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_42)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2005])).
% 68.49/10.20 thf(f2005,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_42)),
% 68.49/10.20 inference(superposition,[],[f1986,f1833])).
% 68.49/10.20 thf(f1986,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2)))) ) | ~spl93_42),
% 68.49/10.20 inference(avatar_component_clause,[],[f1985])).
% 68.49/10.20 thf(f5377,plain,(
% 68.49/10.20 spl93_324 | ~spl93_22 | ~spl93_41),
% 68.49/10.20 inference(avatar_split_clause,[],[f2002,f1981,f1832,f5375])).
% 68.49/10.20 thf(f5375,plain,(
% 68.49/10.20 spl93_324 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) | (ab_group_add(X0) = $false))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_324])])).
% 68.49/10.20 thf(f1981,plain,(
% 68.49/10.20 spl93_41 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) | (ab_group_add(X0) != $true))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_41])])).
% 68.49/10.20 thf(f2002,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_41)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f2001])).
% 68.49/10.20 thf(f2001,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) | (ab_group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_41)),
% 68.49/10.20 inference(superposition,[],[f1982,f1833])).
% 68.49/10.20 thf(f1982,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((ab_group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1))) ) | ~spl93_41),
% 68.49/10.20 inference(avatar_component_clause,[],[f1981])).
% 68.49/10.20 thf(f5331,plain,(
% 68.49/10.20 spl93_323 | ~spl93_21 | ~spl93_308),
% 68.49/10.20 inference(avatar_split_clause,[],[f5113,f5024,f1827,f5329])).
% 68.49/10.20 thf(f5329,plain,(
% 68.49/10.20 spl93_323 <=> ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 != X2))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_323])])).
% 68.49/10.20 thf(f5024,plain,(
% 68.49/10.20 spl93_308 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | (X1 != X3))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_308])])).
% 68.49/10.20 thf(f5113,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 != X2)) ) | (~spl93_21 | ~spl93_308)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5109])).
% 68.49/10.20 thf(f5109,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),X1)) | (X0 != X2)) ) | (~spl93_21 | ~spl93_308)),
% 68.49/10.20 inference(superposition,[],[f5025,f1829])).
% 68.49/10.20 thf(f5025,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (X1 != X3)) ) | ~spl93_308),
% 68.49/10.20 inference(avatar_component_clause,[],[f5024])).
% 68.49/10.20 thf(f5313,plain,(
% 68.49/10.20 spl93_322 | ~spl93_50),
% 68.49/10.20 inference(avatar_split_clause,[],[f2060,f2048,f5311])).
% 68.49/10.20 thf(f5311,plain,(
% 68.49/10.20 spl93_322 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = X0) | (X0 != X1))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_322])])).
% 68.49/10.20 thf(f2060,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = X0) | (X0 != X1)) ) | ~spl93_50),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2059])).
% 68.49/10.20 thf(f2059,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl93_50),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2058])).
% 68.49/10.20 thf(f2058,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl93_50),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f2055])).
% 68.49/10.20 thf(f2055,plain,(
% 68.49/10.20 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK30,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl93_50),
% 68.49/10.20 inference(primitive_instantiation,[],[f2049])).
% 68.49/10.20 thf(f5309,plain,(
% 68.49/10.20 spl93_321 | ~spl93_26 | ~spl93_40),
% 68.49/10.20 inference(avatar_split_clause,[],[f1975,f1968,f1878,f5307])).
% 68.49/10.20 thf(f5307,plain,(
% 68.49/10.20 spl93_321 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,X1)) = X0)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_321])])).
% 68.49/10.20 thf(f1975,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,X1)) = X0)) ) | (~spl93_26 | ~spl93_40)),
% 68.49/10.20 inference(superposition,[],[f1879,f1969])).
% 68.49/10.20 thf(f5305,plain,(
% 68.49/10.20 spl93_320 | ~spl93_27 | ~spl93_40),
% 68.49/10.20 inference(avatar_split_clause,[],[f1974,f1968,f1882,f5303])).
% 68.49/10.20 thf(f5303,plain,(
% 68.49/10.20 spl93_320 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,suc,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),X0))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_320])])).
% 68.49/10.20 thf(f1974,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),X0))) ) | (~spl93_27 | ~spl93_40)),
% 68.49/10.20 inference(superposition,[],[f1883,f1969])).
% 68.49/10.20 thf(f5301,plain,(
% 68.49/10.20 spl93_319 | ~spl93_26 | ~spl93_39),
% 68.49/10.20 inference(avatar_split_clause,[],[f1972,f1964,f1878,f5299])).
% 68.49/10.20 thf(f5299,plain,(
% 68.49/10.20 spl93_319 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,suc,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),X1))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_319])])).
% 68.49/10.20 thf(f1972,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),X1))) ) | (~spl93_26 | ~spl93_39)),
% 68.49/10.20 inference(superposition,[],[f1879,f1965])).
% 68.49/10.20 thf(f5297,plain,(
% 68.49/10.20 spl93_318 | ~spl93_27 | ~spl93_39),
% 68.49/10.20 inference(avatar_split_clause,[],[f1971,f1964,f1882,f5295])).
% 68.49/10.20 thf(f5295,plain,(
% 68.49/10.20 spl93_318 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,X0)) = X1)),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_318])])).
% 68.49/10.20 thf(f1971,plain,(
% 68.49/10.20 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),vAPP(nat,nat,suc,X0)) = X1)) ) | (~spl93_27 | ~spl93_39)),
% 68.49/10.20 inference(superposition,[],[f1883,f1965])).
% 68.49/10.20 thf(f5219,plain,(
% 68.49/10.20 spl93_317 | ~spl93_21 | ~spl93_235 | ~spl93_307),
% 68.49/10.20 inference(avatar_split_clause,[],[f5104,f5020,f3960,f1827,f5217])).
% 68.49/10.20 thf(f5104,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) != X1) | (X0 = X2)) ) | (~spl93_21 | ~spl93_235 | ~spl93_307)),
% 68.49/10.20 inference(trivial_inequality_removal,[],[f5103])).
% 68.49/10.20 thf(f5103,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) != X1) | (X0 = X2)) ) | (~spl93_21 | ~spl93_235 | ~spl93_307)),
% 68.49/10.20 inference(forward_demodulation,[],[f5079,f1829])).
% 68.49/10.20 thf(f5079,plain,(
% 68.49/10.20 ( ! [X2 : int,X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X2),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) != X1) | (group_add(int) != $true) | (X0 = X2)) ) | (~spl93_235 | ~spl93_307)),
% 68.49/10.20 inference(superposition,[],[f5021,f3961])).
% 68.49/10.20 thf(f5071,plain,(
% 68.49/10.20 spl93_316),
% 68.49/10.20 inference(avatar_split_clause,[],[f1695,f5069])).
% 68.49/10.20 thf(f1695,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | (X1 != X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1694])).
% 68.49/10.20 thf(f1694,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1690])).
% 68.49/10.20 thf(f1690,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel_semigroup_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1209])).
% 68.49/10.20 thf(f1209,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true)) )),
% 68.49/10.20 inference(cnf_transformation,[],[f788])).
% 68.49/10.20 thf(f788,plain,(
% 68.49/10.20 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true))),
% 68.49/10.20 inference(ennf_transformation,[],[f307])).
% 68.49/10.20 thf(f307,plain,(
% 68.49/10.20 ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)))),
% 68.49/10.20 inference(fool_elimination,[],[f306])).
% 68.49/10.20 thf(f306,plain,(
% 68.49/10.20 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = (X1 = X3)))),
% 68.49/10.20 inference(rectify,[],[f151])).
% 68.49/10.20 thf(f151,axiom,(
% 68.49/10.20 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X7 : X0,X6 : X0,X8 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X6) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X6)) = (X7 = X8)))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_150_add__right__cancel)).
% 68.49/10.20 thf(f5067,plain,(
% 68.49/10.20 spl93_315),
% 68.49/10.20 inference(avatar_split_clause,[],[f1693,f5065])).
% 68.49/10.20 thf(f1693,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | (X1 = X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1692])).
% 68.49/10.20 thf(f1692,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (cancel_semigroup_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1691])).
% 68.49/10.20 thf(f1691,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel_semigroup_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1209])).
% 68.49/10.20 thf(f5063,plain,(
% 68.49/10.20 spl93_314),
% 68.49/10.20 inference(avatar_split_clause,[],[f1689,f5061])).
% 68.49/10.20 thf(f1689,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | (X2 != X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1688])).
% 68.49/10.20 thf(f1688,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1684])).
% 68.49/10.20 thf(f1684,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel_semigroup_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1210])).
% 68.49/10.20 thf(f1210,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (cancel_semigroup_add(X0) != $true)) )),
% 68.49/10.20 inference(cnf_transformation,[],[f789])).
% 68.49/10.20 thf(f789,plain,(
% 68.49/10.20 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (cancel_semigroup_add(X0) != $true))),
% 68.49/10.20 inference(ennf_transformation,[],[f309])).
% 68.49/10.20 thf(f309,plain,(
% 68.49/10.20 ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))),
% 68.49/10.20 inference(fool_elimination,[],[f308])).
% 68.49/10.20 thf(f308,plain,(
% 68.49/10.20 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = (X2 = X3)))),
% 68.49/10.20 inference(rectify,[],[f152])).
% 68.49/10.20 thf(f152,axiom,(
% 68.49/10.20 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8)) = (X7 = X8)))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_151_add__left__cancel)).
% 68.49/10.20 thf(f5059,plain,(
% 68.49/10.20 spl93_313),
% 68.49/10.20 inference(avatar_split_clause,[],[f1687,f5057])).
% 68.49/10.20 thf(f1687,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | (X2 = X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1686])).
% 68.49/10.20 thf(f1686,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (cancel_semigroup_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1685])).
% 68.49/10.20 thf(f1685,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel_semigroup_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1210])).
% 68.49/10.20 thf(f5042,plain,(
% 68.49/10.20 spl93_312),
% 68.49/10.20 inference(avatar_split_clause,[],[f1683,f5040])).
% 68.49/10.20 thf(f1683,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = X1) | (group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1682])).
% 68.49/10.20 thf(f1682,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = X1) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1678])).
% 68.49/10.20 thf(f1678,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)),X1)) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1238])).
% 68.49/10.20 thf(f1238,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)),X1) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)) | (group_add(X0) != $true)) )),
% 68.49/10.20 inference(cnf_transformation,[],[f817])).
% 68.49/10.20 thf(f817,plain,(
% 68.49/10.20 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)),X1) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)) | (group_add(X0) != $true))),
% 68.49/10.20 inference(ennf_transformation,[],[f365])).
% 68.49/10.20 thf(f365,plain,(
% 68.49/10.20 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)),X1) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2)))),
% 68.49/10.20 inference(fool_elimination,[],[f364])).
% 68.49/10.20 thf(f364,plain,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = X1) = (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2)))),
% 68.49/10.20 inference(rectify,[],[f170])).
% 68.49/10.20 thf(f170,axiom,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X8 : X0,X7 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X8),X7) = X6) = (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7) = X8)))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_eq__diff__eq)).
% 68.49/10.20 thf(f5038,plain,(
% 68.49/10.20 spl93_311),
% 68.49/10.20 inference(avatar_split_clause,[],[f1681,f5036])).
% 68.49/10.20 thf(f1681,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) != X1) | (group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1680])).
% 68.49/10.20 thf(f1680,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) != X1) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1679])).
% 68.49/10.20 thf(f1679,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)),X1)) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1238])).
% 68.49/10.20 thf(f5034,plain,(
% 68.49/10.20 spl93_310),
% 68.49/10.20 inference(avatar_split_clause,[],[f1671,f5032])).
% 68.49/10.20 thf(f1671,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | (X2 != X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1670])).
% 68.49/10.20 thf(f1670,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1666])).
% 68.49/10.20 thf(f1666,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1240])).
% 68.49/10.20 thf(f1240,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (group_add(X0) != $true)) )),
% 68.49/10.20 inference(cnf_transformation,[],[f819])).
% 68.49/10.20 thf(f819,plain,(
% 68.49/10.20 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (group_add(X0) != $true))),
% 68.49/10.20 inference(ennf_transformation,[],[f369])).
% 68.49/10.20 thf(f369,plain,(
% 68.49/10.20 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))),
% 68.49/10.20 inference(fool_elimination,[],[f368])).
% 68.49/10.20 thf(f368,plain,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = (X2 = X3)))),
% 68.49/10.20 inference(rectify,[],[f160])).
% 68.49/10.20 thf(f160,axiom,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8)) = (X7 = X8)))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_159_add_Oleft__cancel)).
% 68.49/10.20 thf(f5030,plain,(
% 68.49/10.20 spl93_309),
% 68.49/10.20 inference(avatar_split_clause,[],[f1669,f5028])).
% 68.49/10.20 thf(f1669,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | (X2 = X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1668])).
% 68.49/10.20 thf(f1668,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1667])).
% 68.49/10.20 thf(f1667,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1240])).
% 68.49/10.20 thf(f5026,plain,(
% 68.49/10.20 spl93_308),
% 68.49/10.20 inference(avatar_split_clause,[],[f1665,f5024])).
% 68.49/10.20 thf(f1665,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | (X1 != X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1664])).
% 68.49/10.20 thf(f1664,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1660])).
% 68.49/10.20 thf(f1660,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1241])).
% 68.49/10.20 thf(f1241,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) | (group_add(X0) != $true)) )),
% 68.49/10.20 inference(cnf_transformation,[],[f820])).
% 68.49/10.20 thf(f820,plain,(
% 68.49/10.20 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)) | (group_add(X0) != $true))),
% 68.49/10.20 inference(ennf_transformation,[],[f371])).
% 68.49/10.20 thf(f371,plain,(
% 68.49/10.20 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3)))),
% 68.49/10.20 inference(fool_elimination,[],[f370])).
% 68.49/10.20 thf(f370,plain,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = (X1 = X3)))),
% 68.49/10.20 inference(rectify,[],[f159])).
% 68.49/10.20 thf(f159,axiom,(
% 68.49/10.20 ! [X0 : $tType] : (group_add(X0) => ! [X7 : X0,X6 : X0,X8 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X6) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X6)) = (X7 = X8)))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_158_group__add__class_Oadd_Oright__cancel)).
% 68.49/10.20 thf(f5022,plain,(
% 68.49/10.20 spl93_307),
% 68.49/10.20 inference(avatar_split_clause,[],[f1663,f5020])).
% 68.49/10.20 thf(f1663,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | (X1 = X3)) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1662])).
% 68.49/10.20 thf(f1662,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(equality_proxy_clausification,[],[f1661])).
% 68.49/10.20 thf(f1661,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1241])).
% 68.49/10.20 thf(f5010,plain,(
% 68.49/10.20 spl93_306),
% 68.49/10.20 inference(avatar_split_clause,[],[f1611,f5008])).
% 68.49/10.20 thf(f5008,plain,(
% 68.49/10.20 spl93_306 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true = vAPP(X0,$o,X2,X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_306])])).
% 68.49/10.20 thf(f1611,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true = vAPP(X0,$o,X2,X1))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1309])).
% 68.49/10.20 thf(f1309,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)) = vAPP(X0,$o,X2,X1))) )),
% 68.49/10.20 inference(cnf_transformation,[],[f751])).
% 68.49/10.20 thf(f751,plain,(
% 68.49/10.20 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)) = vAPP(X0,$o,X2,X1))),
% 68.49/10.20 inference(rectify,[],[f46])).
% 68.49/10.20 thf(f46,axiom,(
% 68.49/10.20 ! [X0 : $tType,X6 : X0,X26 : X0 > $o] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(sTfun(X0,$o),set(X0),collect(X0),X26)) = vAPP(X0,$o,X26,X6))),
% 68.49/10.20 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_mem__Collect__eq)).
% 68.49/10.20 thf(f5006,plain,(
% 68.49/10.20 spl93_305),
% 68.49/10.20 inference(avatar_split_clause,[],[f1610,f5004])).
% 68.49/10.20 thf(f5004,plain,(
% 68.49/10.20 spl93_305 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($false = vAPP(X0,$o,X2,X1)))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_305])])).
% 68.49/10.20 thf(f1610,plain,(
% 68.49/10.20 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($false = vAPP(X0,$o,X2,X1))) )),
% 68.49/10.20 inference(binary_proxy_clausification,[],[f1309])).
% 68.49/10.20 thf(f5002,plain,(
% 68.49/10.20 spl93_303 | spl93_304 | ~spl93_27 | ~spl93_297),
% 68.49/10.20 inference(avatar_split_clause,[],[f4855,f4787,f1882,f5000,f4996])).
% 68.49/10.20 thf(f4996,plain,(
% 68.49/10.20 spl93_303 <=> ($false = group_add(nat))),
% 68.49/10.20 introduced(avatar_definition,[new_symbols(naming,[spl93_303])])).
% 68.49/10.20 thf(f5000,plain,(
% 68.49/10.20 spl93_304 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_304])])).
% 68.49/10.21 thf(f4787,plain,(
% 68.49/10.21 spl93_297 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_297])])).
% 68.49/10.21 thf(f4855,plain,(
% 68.49/10.21 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)) | ($false = group_add(nat))) ) | (~spl93_27 | ~spl93_297)),
% 68.49/10.21 inference(superposition,[],[f4788,f1883])).
% 68.49/10.21 thf(f4788,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false)) ) | ~spl93_297),
% 68.49/10.21 inference(avatar_component_clause,[],[f4787])).
% 68.49/10.21 thf(f4922,plain,(
% 68.49/10.21 spl93_302 | ~spl93_21 | ~spl93_45),
% 68.49/10.21 inference(avatar_split_clause,[],[f2020,f1997,f1827,f4920])).
% 68.49/10.21 thf(f4920,plain,(
% 68.49/10.21 spl93_302 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = X1)),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_302])])).
% 68.49/10.21 thf(f2020,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = X1)) ) | (~spl93_21 | ~spl93_45)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f2017])).
% 68.49/10.21 thf(f2017,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)) = X1)) ) | (~spl93_21 | ~spl93_45)),
% 68.49/10.21 inference(superposition,[],[f1998,f1829])).
% 68.49/10.21 thf(f4918,plain,(
% 68.49/10.21 spl93_301 | ~spl93_21 | ~spl93_43),
% 68.49/10.21 inference(avatar_split_clause,[],[f2011,f1989,f1827,f4916])).
% 68.49/10.21 thf(f2011,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)))) ) | (~spl93_21 | ~spl93_43)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f2008])).
% 68.49/10.21 thf(f2008,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1) = vAPP(int,int,uminus_uminus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)))) ) | (~spl93_21 | ~spl93_43)),
% 68.49/10.21 inference(superposition,[],[f1990,f1829])).
% 68.49/10.21 thf(f4914,plain,(
% 68.49/10.21 spl93_300 | ~spl93_21 | ~spl93_42),
% 68.49/10.21 inference(avatar_split_clause,[],[f2007,f1985,f1827,f4912])).
% 68.49/10.21 thf(f2007,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,uminus_uminus(int),X1)))) ) | (~spl93_21 | ~spl93_42)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f2004])).
% 68.49/10.21 thf(f2004,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,uminus_uminus(int),X1)))) ) | (~spl93_21 | ~spl93_42)),
% 68.49/10.21 inference(superposition,[],[f1986,f1829])).
% 68.49/10.21 thf(f4910,plain,(
% 68.49/10.21 spl93_299 | ~spl93_20 | ~spl93_41),
% 68.49/10.21 inference(avatar_split_clause,[],[f2003,f1981,f1822,f4908])).
% 68.49/10.21 thf(f4908,plain,(
% 68.49/10.21 spl93_299 <=> ! [X0 : int,X1 : int] : (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_299])])).
% 68.49/10.21 thf(f2003,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0))) ) | (~spl93_20 | ~spl93_41)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f2000])).
% 68.49/10.21 thf(f2000,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0))) ) | (~spl93_20 | ~spl93_41)),
% 68.49/10.21 inference(superposition,[],[f1982,f1824])).
% 68.49/10.21 thf(f4793,plain,(
% 68.49/10.21 spl93_298 | ~spl93_22 | ~spl93_34),
% 68.49/10.21 inference(avatar_split_clause,[],[f1942,f1916,f1832,f4791])).
% 68.49/10.21 thf(f4791,plain,(
% 68.49/10.21 spl93_298 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) = $false))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_298])])).
% 68.49/10.21 thf(f1916,plain,(
% 68.49/10.21 spl93_34 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) != $true))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_34])])).
% 68.49/10.21 thf(f1942,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) = $false)) ) | (~spl93_22 | ~spl93_34)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1941])).
% 68.49/10.21 thf(f1941,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) = $false)) ) | (~spl93_22 | ~spl93_34)),
% 68.49/10.21 inference(superposition,[],[f1917,f1833])).
% 68.49/10.21 thf(f1917,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((cancel1352612707id_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1)) ) | ~spl93_34),
% 68.49/10.21 inference(avatar_component_clause,[],[f1916])).
% 68.49/10.21 thf(f4789,plain,(
% 68.49/10.21 spl93_297 | ~spl93_22 | ~spl93_33),
% 68.49/10.21 inference(avatar_split_clause,[],[f1937,f1912,f1832,f4787])).
% 68.49/10.21 thf(f1912,plain,(
% 68.49/10.21 spl93_33 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_33])])).
% 68.49/10.21 thf(f1937,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_33)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1936])).
% 68.49/10.21 thf(f1936,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_33)),
% 68.49/10.21 inference(superposition,[],[f1913,f1833])).
% 68.49/10.21 thf(f1913,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1)) ) | ~spl93_33),
% 68.49/10.21 inference(avatar_component_clause,[],[f1912])).
% 68.49/10.21 thf(f4785,plain,(
% 68.49/10.21 spl93_296 | ~spl93_22 | ~spl93_32),
% 68.49/10.21 inference(avatar_split_clause,[],[f1933,f1908,f1832,f4783])).
% 68.49/10.21 thf(f4783,plain,(
% 68.49/10.21 spl93_296 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_296])])).
% 68.49/10.21 thf(f1908,plain,(
% 68.49/10.21 spl93_32 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_32])])).
% 68.49/10.21 thf(f1933,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_32)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1932])).
% 68.49/10.21 thf(f1932,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) = $false)) ) | (~spl93_22 | ~spl93_32)),
% 68.49/10.21 inference(superposition,[],[f1909,f1833])).
% 68.49/10.21 thf(f1909,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((group_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1)) ) | ~spl93_32),
% 68.49/10.21 inference(avatar_component_clause,[],[f1908])).
% 68.49/10.21 thf(f4781,plain,(
% 68.49/10.21 spl93_295 | ~spl93_22 | ~spl93_31),
% 68.49/10.21 inference(avatar_split_clause,[],[f1928,f1904,f1832,f4779])).
% 68.49/10.21 thf(f4779,plain,(
% 68.49/10.21 spl93_295 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) = $false))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_295])])).
% 68.49/10.21 thf(f1904,plain,(
% 68.49/10.21 spl93_31 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_31])])).
% 68.49/10.21 thf(f1928,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_31)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1927])).
% 68.49/10.21 thf(f1927,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_31)),
% 68.49/10.21 inference(superposition,[],[f1905,f1833])).
% 68.49/10.21 thf(f1905,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((cancel146912293up_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2)) ) | ~spl93_31),
% 68.49/10.21 inference(avatar_component_clause,[],[f1904])).
% 68.49/10.21 thf(f4777,plain,(
% 68.49/10.21 spl93_294 | ~spl93_22 | ~spl93_30),
% 68.49/10.21 inference(avatar_split_clause,[],[f1922,f1900,f1832,f4775])).
% 68.49/10.21 thf(f4775,plain,(
% 68.49/10.21 spl93_294 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) = $false))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_294])])).
% 68.49/10.21 thf(f1900,plain,(
% 68.49/10.21 spl93_30 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_30])])).
% 68.49/10.21 thf(f1922,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_30)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1921])).
% 68.49/10.21 thf(f1921,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) = $false)) ) | (~spl93_22 | ~spl93_30)),
% 68.49/10.21 inference(superposition,[],[f1901,f1833])).
% 68.49/10.21 thf(f1901,plain,(
% 68.49/10.21 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((cancel146912293up_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1)) ) | ~spl93_30),
% 68.49/10.21 inference(avatar_component_clause,[],[f1900])).
% 68.49/10.21 thf(f4751,plain,(
% 68.49/10.21 spl93_293),
% 68.49/10.21 inference(avatar_split_clause,[],[f1505,f4749])).
% 68.49/10.21 thf(f4749,plain,(
% 68.49/10.21 spl93_293 <=> ! [X1 : $tType,X0 : $tType,X5 : X1,X4 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X6 : X1,X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_293])])).
% 68.49/10.21 thf(f1505,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X6 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1452,f1277,f1277,f1277,f1277])).
% 68.49/10.21 thf(f1277,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType] : ((a_minus(X1,X0) = vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f415])).
% 68.49/10.21 thf(f415,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType] : (a_minus(X1,X0) = vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)))),
% 68.49/10.21 inference(fool_elimination,[],[f414])).
% 68.49/10.21 thf(f414,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType] : (a_minus(X1,X0) = (^[X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))), X3 : X1, X4 : X1] : (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)))))),
% 68.49/10.21 inference(rectify,[],[f224])).
% 68.49/10.21 thf(f224,axiom,(
% 68.49/10.21 ! [X4 : $tType,X0 : $tType] : (a_minus(X0,X4) = (^[X64 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X4))), X28 : X0, X65 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X4))),sTfun(X0,sTfun(X0,X0)),add(X0,X4),X64),X28),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X4))),sTfun(X0,X0),a_inv(X0,X4),X64),X65)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_223_a__minus__def)).
% 68.49/10.21 thf(f1452,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X6 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1075])).
% 68.49/10.21 thf(f1075,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1,X6 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1074])).
% 68.49/10.21 thf(f1074,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1,X6 : X1] : ((((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f665])).
% 68.49/10.21 thf(f665,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1,X6 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f664])).
% 68.49/10.21 thf(f664,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1,X6 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X5)),X4)),X6) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)),X6)))))))),
% 68.49/10.21 inference(rectify,[],[f127])).
% 68.49/10.21 thf(f127,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X6 : X0,X7 : X0,X8 : X0,X25 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X7),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X8),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X25),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),X6),X8)),X7)),X25) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X6),X7)),X8)),X25)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_abelian__group_Ofour__elem__comm)).
% 68.49/10.21 thf(f4747,plain,(
% 68.49/10.21 spl93_292 | ~spl93_22 | ~spl93_28),
% 68.49/10.21 inference(avatar_split_clause,[],[f1892,f1886,f1832,f4745])).
% 68.49/10.21 thf(f4745,plain,(
% 68.49/10.21 spl93_292 <=> ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) = $false))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_292])])).
% 68.49/10.21 thf(f1886,plain,(
% 68.49/10.21 spl93_28 <=> ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) != $true))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_28])])).
% 68.49/10.21 thf(f1892,plain,(
% 68.49/10.21 ( ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_28)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1891])).
% 68.49/10.21 thf(f1891,plain,(
% 68.49/10.21 ( ! [X0 : $tType] : (($true != $true) | (plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) = $false)) ) | (~spl93_22 | ~spl93_28)),
% 68.49/10.21 inference(superposition,[],[f1887,f1833])).
% 68.49/10.21 thf(f1887,plain,(
% 68.49/10.21 ( ! [X0 : $tType] : ((ab_semigroup_add(X0) != $true) | (plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0)))) ) | ~spl93_28),
% 68.49/10.21 inference(avatar_component_clause,[],[f1886])).
% 68.49/10.21 thf(f4729,plain,(
% 68.49/10.21 spl93_291),
% 68.49/10.21 inference(avatar_split_clause,[],[f1504,f4727])).
% 68.49/10.21 thf(f4727,plain,(
% 68.49/10.21 spl93_291 <=> ! [X1 : $tType,X0 : $tType,X5 : X1,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_291])])).
% 68.49/10.21 thf(f1504,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1448,f1277,f1277,f1277])).
% 68.49/10.21 thf(f1448,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1069])).
% 68.49/10.21 thf(f1069,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1068])).
% 68.49/10.21 thf(f1068,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f659])).
% 68.49/10.21 thf(f659,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f658])).
% 68.49/10.21 thf(f658,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),X3)),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)))))))),
% 68.49/10.21 inference(rectify,[],[f128])).
% 68.49/10.21 thf(f128,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X6 : X0,X7 : X0,X8 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X7),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X8),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),X8),X6)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),X8),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X6),X7)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_127_abelian__group_Oright__inv__add)).
% 68.49/10.21 thf(f4722,plain,(
% 68.49/10.21 spl93_290),
% 68.49/10.21 inference(avatar_split_clause,[],[f1708,f4719])).
% 68.49/10.21 thf(f4719,plain,(
% 68.49/10.21 spl93_290 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_290])])).
% 68.49/10.21 thf(f1708,plain,(
% 68.49/10.21 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))))),
% 68.49/10.21 inference(forward_demodulation,[],[f1707,f1181])).
% 68.49/10.21 thf(f1181,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),
% 68.49/10.21 inference(cnf_transformation,[],[f7])).
% 68.49/10.21 thf(f7,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_f9)).
% 68.49/10.21 thf(f1707,plain,(
% 68.49/10.21 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))))),
% 68.49/10.21 inference(forward_demodulation,[],[f1491,f1706])).
% 68.49/10.21 thf(f1706,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)))),
% 68.49/10.21 inference(forward_demodulation,[],[f1186,f1181])).
% 68.49/10.21 thf(f1186,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))))),
% 68.49/10.21 inference(cnf_transformation,[],[f14])).
% 68.49/10.21 thf(f14,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062)).
% 68.49/10.21 thf(f1491,plain,(
% 68.49/10.21 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))))))),
% 68.49/10.21 inference(definition_unfolding,[],[f1187,f1277])).
% 68.49/10.21 thf(f1187,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))))) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.21 inference(cnf_transformation,[],[f20])).
% 68.49/10.21 thf(f20,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))))) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_092_060ominus_062_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_A_092_060otimes_062_Ar_H_H_J_A_092_060oplus_062_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_A_061_A_092_060zero_062_092_060close_062)).
% 68.49/10.21 thf(f4708,plain,(
% 68.49/10.21 spl93_289),
% 68.49/10.21 inference(avatar_split_clause,[],[f1725,f4706])).
% 68.49/10.21 thf(f4706,plain,(
% 68.49/10.21 spl93_289 <=> ! [X0 : a,X3 : a,X2 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X1)),X3)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_289])])).
% 68.49/10.21 thf(f1725,plain,(
% 68.49/10.21 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),X1)),X3)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(forward_demodulation,[],[f1724,f1493])).
% 68.49/10.21 thf(f1493,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X1))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1273,f1277])).
% 68.49/10.21 thf(f1273,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f748])).
% 68.49/10.21 thf(f748,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)))),
% 68.49/10.21 inference(rectify,[],[f210])).
% 68.49/10.21 thf(f210,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X13),X14) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X14)))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_minus__eq)).
% 68.49/10.21 thf(f1724,plain,(
% 68.49/10.21 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X2))),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X3))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(forward_demodulation,[],[f1723,f1493])).
% 68.49/10.21 thf(f1723,plain,(
% 68.49/10.21 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X3))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(forward_demodulation,[],[f1499,f1493])).
% 68.49/10.21 thf(f1499,plain,(
% 68.49/10.21 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),X3)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1406,f1277,f1277,f1277,f1277])).
% 68.49/10.21 thf(f1406,plain,(
% 68.49/10.21 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),X3)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f999])).
% 68.49/10.21 thf(f999,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),X3)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f998])).
% 68.49/10.21 thf(f998,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : (((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),X3)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f585])).
% 68.49/10.21 thf(f585,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),X3))))))),
% 68.49/10.21 inference(fool_elimination,[],[f584])).
% 68.49/10.21 thf(f584,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X3),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X2)),X1)),X3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)),X3))))))),
% 68.49/10.21 inference(rectify,[],[f37])).
% 68.49/10.21 thf(f37,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a,X8 : a,X25 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X8),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X25),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X6),X8)),X7)),X25) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X6),X7)),X8)),X25))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_four__elem__comm)).
% 68.49/10.21 thf(f4696,plain,(
% 68.49/10.21 spl93_288),
% 68.49/10.21 inference(avatar_split_clause,[],[f1722,f4694])).
% 68.49/10.21 thf(f4694,plain,(
% 68.49/10.21 spl93_288 <=> ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_288])])).
% 68.49/10.21 thf(f1722,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(forward_demodulation,[],[f1721,f1493])).
% 68.49/10.21 thf(f1721,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X2),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(forward_demodulation,[],[f1498,f1493])).
% 68.49/10.21 thf(f1498,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1373,f1277,f1277,f1277])).
% 68.49/10.21 thf(f1373,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f945])).
% 68.49/10.21 thf(f945,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f944])).
% 68.49/10.21 thf(f944,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f533])).
% 68.49/10.21 thf(f533,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))))))),
% 68.49/10.21 inference(fool_elimination,[],[f532])).
% 68.49/10.21 thf(f532,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))))))),
% 68.49/10.21 inference(rectify,[],[f36])).
% 68.49/10.21 thf(f36,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a,X8 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X8),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X8),X6)),X7) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X8),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X6),X7))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_right__inv__add)).
% 68.49/10.21 thf(f4688,plain,(
% 68.49/10.21 spl93_287),
% 68.49/10.21 inference(avatar_split_clause,[],[f1714,f4685])).
% 68.49/10.21 thf(f4685,plain,(
% 68.49/10.21 spl93_287 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_287])])).
% 68.49/10.21 thf(f1714,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)))),
% 68.49/10.21 inference(forward_demodulation,[],[f1713,f1703])).
% 68.49/10.21 thf(f1703,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)))),
% 68.49/10.21 inference(forward_demodulation,[],[f1183,f1181])).
% 68.49/10.21 thf(f1183,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))))),
% 68.49/10.21 inference(cnf_transformation,[],[f10])).
% 68.49/10.21 thf(f10,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_f10)).
% 68.49/10.21 thf(f1713,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))))),
% 68.49/10.21 inference(forward_demodulation,[],[f1712,f1704])).
% 68.49/10.21 thf(f1704,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4)))),
% 68.49/10.21 inference(forward_demodulation,[],[f1184,f1181])).
% 68.49/10.21 thf(f1184,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))))),
% 68.49/10.21 inference(cnf_transformation,[],[f9])).
% 68.49/10.21 thf(f9,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_J_092_060close_062)).
% 68.49/10.21 thf(f1712,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 inference(forward_demodulation,[],[f1189,f1181])).
% 68.49/10.21 thf(f1189,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 inference(cnf_transformation,[],[f15])).
% 68.49/10.21 thf(f15,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_f7)).
% 68.49/10.21 thf(f4671,plain,(
% 68.49/10.21 spl93_286),
% 68.49/10.21 inference(avatar_split_clause,[],[f1502,f4669])).
% 68.49/10.21 thf(f4669,plain,(
% 68.49/10.21 spl93_286 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_286])])).
% 68.49/10.21 thf(f1502,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1427,f1277])).
% 68.49/10.21 thf(f1427,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1038])).
% 68.49/10.21 thf(f1038,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1037])).
% 68.49/10.21 thf(f1037,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f625])).
% 68.49/10.21 thf(f625,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)))))),
% 68.49/10.21 inference(fool_elimination,[],[f624])).
% 68.49/10.21 thf(f624,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)))))),
% 68.49/10.21 inference(rectify,[],[f233])).
% 68.49/10.21 thf(f233,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X6 : X0,X7 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X7),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X6)),X7)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_232_abelian__group_Oinv__add)).
% 68.49/10.21 thf(f4659,plain,(
% 68.49/10.21 spl93_285),
% 68.49/10.21 inference(avatar_split_clause,[],[f1495,f4657])).
% 68.49/10.21 thf(f4657,plain,(
% 68.49/10.21 spl93_285 <=> ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_285])])).
% 68.49/10.21 thf(f1495,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1294,f1277])).
% 68.49/10.21 thf(f1294,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f867])).
% 68.49/10.21 thf(f867,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f866])).
% 68.49/10.21 thf(f866,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f447])).
% 68.49/10.21 thf(f447,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1))))),
% 68.49/10.21 inference(fool_elimination,[],[f446])).
% 68.49/10.21 thf(f446,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1))))),
% 68.49/10.21 inference(rectify,[],[f196])).
% 68.49/10.21 thf(f196,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X6),X7)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X6)),X7))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_inv__add)).
% 68.49/10.21 thf(f4648,plain,(
% 68.49/10.21 spl93_284),
% 68.49/10.21 inference(avatar_split_clause,[],[f1706,f4645])).
% 68.49/10.21 thf(f4645,plain,(
% 68.49/10.21 spl93_284 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_284])])).
% 68.49/10.21 thf(f4631,plain,(
% 68.49/10.21 spl93_283),
% 68.49/10.21 inference(avatar_split_clause,[],[f1503,f4629])).
% 68.49/10.21 thf(f1503,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1429,f1277])).
% 68.49/10.21 thf(f1429,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1042])).
% 68.49/10.21 thf(f1042,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1041])).
% 68.49/10.21 thf(f1041,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (((($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f629])).
% 68.49/10.21 thf(f629,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f628])).
% 68.49/10.21 thf(f628,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 inference(rectify,[],[f123])).
% 68.49/10.21 thf(f123,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),X13),X14)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_122_abelian__group_Ominus__closed)).
% 68.49/10.21 thf(f4620,plain,(
% 68.49/10.21 spl93_282),
% 68.49/10.21 inference(avatar_split_clause,[],[f1547,f4618])).
% 68.49/10.21 thf(f1547,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((X3 = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(duplicate_literal_removal,[],[f1501])).
% 68.49/10.21 thf(f1501,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((X3 = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1423,f1277])).
% 68.49/10.21 thf(f1423,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((X3 = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1030])).
% 68.49/10.21 thf(f1030,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((X3 = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1029])).
% 68.49/10.21 thf(f1029,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((((X3 = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f617])).
% 68.49/10.21 thf(f617,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)) => (X3 = X4))))))),
% 68.49/10.21 inference(fool_elimination,[],[f616])).
% 68.49/10.21 thf(f616,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)) => (X3 = X4))))))),
% 68.49/10.21 inference(rectify,[],[f129])).
% 68.49/10.21 thf(f129,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),X13),X14) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X54)) => (X13 = X14))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_128_abelian__group_Ominus__to__eq)).
% 68.49/10.21 thf(f4601,plain,(
% 68.49/10.21 spl93_281),
% 68.49/10.21 inference(avatar_split_clause,[],[f1705,f4598])).
% 68.49/10.21 thf(f4598,plain,(
% 68.49/10.21 spl93_281 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_281])])).
% 68.49/10.21 thf(f1705,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 inference(forward_demodulation,[],[f1185,f1181])).
% 68.49/10.21 thf(f1185,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 inference(cnf_transformation,[],[f13])).
% 68.49/10.21 thf(f13,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_I_Is_H_A_092_060otimes_062_Ar_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_J_A_092_060otimes_062_Ar_H_H_J_A_061_As_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_Ar_A_092_060otimes_062_Ar_H_H_A_092_060oplus_062_As_A_092_060otimes_062_Ar_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062)).
% 68.49/10.21 thf(f4573,plain,(
% 68.49/10.21 spl93_280),
% 68.49/10.21 inference(avatar_split_clause,[],[f1456,f4571])).
% 68.49/10.21 thf(f4571,plain,(
% 68.49/10.21 spl93_280 <=> ! [X5 : $tType,X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X8 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o] : (($true = vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,X8)) | ($true != vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X6,sK86(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X5,sK87(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X4,sK88(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X3,sK89(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X2,sK90(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X1,sK91(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X0,sK92(X0,X1,X2,X3,X4,X5,X6),X7))))))))))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_280])])).
% 68.49/10.21 thf(f1456,plain,(
% 68.49/10.21 ( ! [X5 : $tType,X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X8 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o] : (($true = vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,X8)) | ($true != vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X6,sK86(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X5,sK87(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X4,sK88(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X3,sK89(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X2,sK90(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X1,sK91(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X0,sK92(X0,X1,X2,X3,X4,X5,X6),X7)))))))))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1177])).
% 68.49/10.21 thf(f1177,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o,X8 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))] : (($true = vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,X8)) | ($true != vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X6,sK86(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X5,sK87(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X4,sK88(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X3,sK89(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X2,sK90(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X1,sK91(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X0,sK92(X0,X1,X2,X3,X4,X5,X6),X7))))))))))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK86,sK87,sK88,sK89,sK90,sK91,sK92])],[f1079,f1176])).
% 68.49/10.21 thf(f1176,plain,(
% 68.49/10.21 ! [X6 : $tType,X5 : $tType,X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o] : (? [X9 : X6,X10 : X5,X11 : X4,X12 : X3,X13 : X2,X14 : X1,X15 : X0] : ($true != vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),X9),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X10),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X11),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X12),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X13),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X14),X15)))))))) => ($true != vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X6,sK86(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X5,sK87(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X4,sK88(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X3,sK89(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X2,sK90(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X1,sK91(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(sTfun(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o),X0,sK92(X0,X1,X2,X3,X4,X5,X6),X7))))))))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1079,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o,X8 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))] : (($true = vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,X8)) | ? [X9 : X6,X10 : X5,X11 : X4,X12 : X3,X13 : X2,X14 : X1,X15 : X0] : ($true != vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),X9),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X10),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X11),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X12),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X13),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X14),X15)))))))))),
% 68.49/10.21 inference(ennf_transformation,[],[f669])).
% 68.49/10.21 thf(f669,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o,X8 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))] : (! [X9 : X6,X10 : X5,X11 : X4,X12 : X3,X13 : X2,X14 : X1,X15 : X0] : ($true = vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),X9),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X10),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X11),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X12),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X13),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X14),X15)))))))) => ($true = vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,X8)))),
% 68.49/10.21 inference(fool_elimination,[],[f668])).
% 68.49/10.21 thf(f668,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))) > $o,X8 : product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))] : (! [X9 : X6,X10 : X5,X11 : X4,X12 : X3,X13 : X2,X14 : X1,X15 : X0] : vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),vAPP(X6,sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))))),product_Pair(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),X9),vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X10),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X11),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X12),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X13),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X14),X15))))))) => vAPP(product_prod(X6,product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),$o,X7,X8))),
% 68.49/10.21 inference(rectify,[],[f57])).
% 68.49/10.21 thf(f57,axiom,(
% 68.49/10.21 ! [X35 : $tType,X36 : $tType,X37 : $tType,X38 : $tType,X5 : $tType,X2 : $tType,X0 : $tType,X26 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))) > $o,X13 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))))] : (! [X33 : X0,X34 : X2,X39 : X5,X40 : X38,X41 : X37,X42 : X36,X43 : X35] : vAPP(product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),$o,X26,vAPP(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))))),product_Pair(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),X33),vAPP(product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),vAPP(X2,sTfun(product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),product_Pair(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),X34),vAPP(product_prod(X38,product_prod(X37,product_prod(X36,X35))),product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),vAPP(X5,sTfun(product_prod(X38,product_prod(X37,product_prod(X36,X35))),product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),product_Pair(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),X39),vAPP(product_prod(X37,product_prod(X36,X35)),product_prod(X38,product_prod(X37,product_prod(X36,X35))),vAPP(X38,sTfun(product_prod(X37,product_prod(X36,X35)),product_prod(X38,product_prod(X37,product_prod(X36,X35)))),product_Pair(X38,product_prod(X37,product_prod(X36,X35))),X40),vAPP(product_prod(X36,X35),product_prod(X37,product_prod(X36,X35)),vAPP(X37,sTfun(product_prod(X36,X35),product_prod(X37,product_prod(X36,X35))),product_Pair(X37,product_prod(X36,X35)),X41),vAPP(X35,product_prod(X36,X35),vAPP(X36,sTfun(X35,product_prod(X36,X35)),product_Pair(X36,X35),X42),X43))))))) => vAPP(product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),$o,X26,X13))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_prod__induct7)).
% 68.49/10.21 thf(f4565,plain,(
% 68.49/10.21 spl93_279),
% 68.49/10.21 inference(avatar_split_clause,[],[f1500,f4563])).
% 68.49/10.21 thf(f4563,plain,(
% 68.49/10.21 spl93_279 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_279])])).
% 68.49/10.21 thf(f1500,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1)),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(sTfun(X1,X1),sTfun(X1,sTfun(X1,X1))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),vAPP(sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),sTfun(sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1))),sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1))))),bCOMB,vAPP(sTfun(sTfun(X1,X1),sTfun(sTfun(X1,X1),sTfun(X1,X1))),sTfun(sTfun(X1,sTfun(X1,X1)),sTfun(X1,sTfun(sTfun(X1,X1),sTfun(X1,X1)))),bCOMB,bCOMB)),add(X1,X0)))),a_inv(X1,X0)),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1421,f1277])).
% 68.49/10.21 thf(f1421,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1026])).
% 68.49/10.21 thf(f1026,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f613])).
% 68.49/10.21 thf(f613,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)))),
% 68.49/10.21 inference(fool_elimination,[],[f612])).
% 68.49/10.21 thf(f612,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),a_minus(X1,X0),X2),X3),X4)))),
% 68.49/10.21 inference(rectify,[],[f229])).
% 68.49/10.21 thf(f229,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),a_minus(X0,X2),X54),X13),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X13),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X14))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_228_abelian__group_Ominus__eq)).
% 68.49/10.21 thf(f4559,plain,(
% 68.49/10.21 spl93_278),
% 68.49/10.21 inference(avatar_split_clause,[],[f1493,f4557])).
% 68.49/10.21 thf(f4540,plain,(
% 68.49/10.21 spl93_277),
% 68.49/10.21 inference(avatar_split_clause,[],[f1455,f4538])).
% 68.49/10.21 thf(f4538,plain,(
% 68.49/10.21 spl93_277 <=> ! [X1 : $tType,X3 : $tType,X6 : $tType,X0 : $tType,X2 : $tType,X4 : $tType,X5 : $tType,X7 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X0,sK79(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X1,sK80(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X2,sK81(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X3,sK82(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X4,sK83(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X5,sK84(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X6,sK85(X0,X1,X2,X3,X4,X5,X6),X7))))))) = X7)),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_277])])).
% 68.49/10.21 thf(f1455,plain,(
% 68.49/10.21 ( ! [X5 : $tType,X4 : $tType,X6 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X7 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X0,sK79(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X1,sK80(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X2,sK81(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X3,sK82(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X4,sK83(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X5,sK84(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X6,sK85(X0,X1,X2,X3,X4,X5,X6),X7))))))) = X7)) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1175])).
% 68.49/10.21 thf(f1175,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X0,sK79(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X1,sK80(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X2,sK81(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X3,sK82(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X4,sK83(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X5,sK84(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X6,sK85(X0,X1,X2,X3,X4,X5,X6),X7))))))) = X7)),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80,sK81,sK82,sK83,sK84,sK85])],[f1078,f1174])).
% 68.49/10.21 thf(f1174,plain,(
% 68.49/10.21 ! [X6 : $tType,X5 : $tType,X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X7 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))] : (? [X8 : X0,X9 : X1,X10 : X2,X11 : X3,X12 : X4,X13 : X5,X14 : X6] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X8),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),X9),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),X10),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),X11),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),X12),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),X13),X14)))))) = X7) => (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X0,sK79(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X1,sK80(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X2,sK81(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X3,sK82(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X4,sK83(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X5,sK84(X0,X1,X2,X3,X4,X5,X6),X7)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X6,sK85(X0,X1,X2,X3,X4,X5,X6),X7))))))) = X7))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1078,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))] : ? [X8 : X0,X9 : X1,X10 : X2,X11 : X3,X12 : X4,X13 : X5,X14 : X6] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X8),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),X9),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),X10),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),X11),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),X12),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),X13),X14)))))) = X7)),
% 68.49/10.21 inference(ennf_transformation,[],[f773])).
% 68.49/10.21 thf(f773,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : $tType,X7 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))] : ~! [X8 : X0,X9 : X1,X10 : X2,X11 : X3,X12 : X4,X13 : X5,X14 : X6] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),X8),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),X9),vAPP(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,product_prod(X5,X6))),product_prod(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6))))),product_Pair(X2,product_prod(X3,product_prod(X4,product_prod(X5,X6)))),X10),vAPP(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6))),vAPP(X3,sTfun(product_prod(X4,product_prod(X5,X6)),product_prod(X3,product_prod(X4,product_prod(X5,X6)))),product_Pair(X3,product_prod(X4,product_prod(X5,X6))),X11),vAPP(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6)),vAPP(X4,sTfun(product_prod(X5,X6),product_prod(X4,product_prod(X5,X6))),product_Pair(X4,product_prod(X5,X6)),X12),vAPP(X6,product_prod(X5,X6),vAPP(X5,sTfun(X6,product_prod(X5,X6)),product_Pair(X5,X6),X13),X14)))))) != X7)),
% 68.49/10.21 inference(rectify,[],[f62])).
% 68.49/10.21 thf(f62,axiom,(
% 68.49/10.21 ! [X0 : $tType,X2 : $tType,X5 : $tType,X38 : $tType,X37 : $tType,X36 : $tType,X35 : $tType,X14 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))))] : ~! [X33 : X0,X34 : X2,X39 : X5,X40 : X38,X41 : X37,X42 : X36,X43 : X35] : (vAPP(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))))),product_Pair(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),X33),vAPP(product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),vAPP(X2,sTfun(product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))))),product_Pair(X2,product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),X34),vAPP(product_prod(X38,product_prod(X37,product_prod(X36,X35))),product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),vAPP(X5,sTfun(product_prod(X38,product_prod(X37,product_prod(X36,X35))),product_prod(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35))))),product_Pair(X5,product_prod(X38,product_prod(X37,product_prod(X36,X35)))),X39),vAPP(product_prod(X37,product_prod(X36,X35)),product_prod(X38,product_prod(X37,product_prod(X36,X35))),vAPP(X38,sTfun(product_prod(X37,product_prod(X36,X35)),product_prod(X38,product_prod(X37,product_prod(X36,X35)))),product_Pair(X38,product_prod(X37,product_prod(X36,X35))),X40),vAPP(product_prod(X36,X35),product_prod(X37,product_prod(X36,X35)),vAPP(X37,sTfun(product_prod(X36,X35),product_prod(X37,product_prod(X36,X35))),product_Pair(X37,product_prod(X36,X35)),X41),vAPP(X35,product_prod(X36,X35),vAPP(X36,sTfun(X35,product_prod(X36,X35)),product_Pair(X36,X35),X42),X43)))))) != X14)),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_prod__cases7)).
% 68.49/10.21 thf(f4536,plain,(
% 68.49/10.21 spl93_276 | ~spl93_221 | ~spl93_227),
% 68.49/10.21 inference(avatar_split_clause,[],[f4225,f3899,f3826,f4534])).
% 68.49/10.21 thf(f4225,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)) = X1)) ) | (~spl93_221 | ~spl93_227)),
% 68.49/10.21 inference(superposition,[],[f3827,f3900])).
% 68.49/10.21 thf(f4511,plain,(
% 68.49/10.21 spl93_275),
% 68.49/10.21 inference(avatar_split_clause,[],[f1454,f4509])).
% 68.49/10.21 thf(f1454,plain,(
% 68.49/10.21 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7)) | ($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X5,sK73(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X4,sK74(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X3,sK75(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X2,sK76(X0,X1,X2,X3,X4,X5),X6)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X1,sK77(X0,X1,X2,X3,X4,X5),X6)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X0,sK78(X0,X1,X2,X3,X4,X5),X6))))))))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1173])).
% 68.49/10.21 thf(f1173,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7)) | ($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X5,sK73(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X4,sK74(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X3,sK75(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X2,sK76(X0,X1,X2,X3,X4,X5),X6)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X1,sK77(X0,X1,X2,X3,X4,X5),X6)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X0,sK78(X0,X1,X2,X3,X4,X5),X6)))))))))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74,sK75,sK76,sK77,sK78])],[f1077,f1172])).
% 68.49/10.21 thf(f1172,plain,(
% 68.49/10.21 ! [X5 : $tType,X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o] : (? [X8 : X5,X9 : X4,X10 : X3,X11 : X2,X12 : X1,X13 : X0] : ($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13))))))) => ($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X5,sK73(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X4,sK74(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X3,sK75(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X2,sK76(X0,X1,X2,X3,X4,X5),X6)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X1,sK77(X0,X1,X2,X3,X4,X5),X6)),vAPP(sTfun(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o),X0,sK78(X0,X1,X2,X3,X4,X5),X6)))))))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1077,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7)) | ? [X8 : X5,X9 : X4,X10 : X3,X11 : X2,X12 : X1,X13 : X0] : ($true != vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13))))))))),
% 68.49/10.21 inference(ennf_transformation,[],[f667])).
% 68.49/10.21 thf(f667,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (! [X8 : X5,X9 : X4,X10 : X3,X11 : X2,X12 : X1,X13 : X0] : ($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13))))))) => ($true = vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7)))),
% 68.49/10.21 inference(fool_elimination,[],[f666])).
% 68.49/10.21 thf(f666,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))) > $o,X7 : product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))] : (! [X8 : X5,X9 : X4,X10 : X3,X11 : X2,X12 : X1,X13 : X0] : vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),vAPP(X5,sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))))),product_Pair(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),X8),vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X9),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X10),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X11),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X12),X13)))))) => vAPP(product_prod(X5,product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),$o,X6,X7))),
% 68.49/10.21 inference(rectify,[],[f58])).
% 68.49/10.21 thf(f58,axiom,(
% 68.49/10.21 ! [X36 : $tType,X37 : $tType,X38 : $tType,X5 : $tType,X2 : $tType,X0 : $tType,X26 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))) > $o,X13 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))))] : (! [X33 : X0,X34 : X2,X39 : X5,X40 : X38,X41 : X37,X42 : X36] : vAPP(product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),$o,X26,vAPP(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))))),product_Pair(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),X33),vAPP(product_prod(X5,product_prod(X38,product_prod(X37,X36))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),vAPP(X2,sTfun(product_prod(X5,product_prod(X38,product_prod(X37,X36))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),product_Pair(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),X34),vAPP(product_prod(X38,product_prod(X37,X36)),product_prod(X5,product_prod(X38,product_prod(X37,X36))),vAPP(X5,sTfun(product_prod(X38,product_prod(X37,X36)),product_prod(X5,product_prod(X38,product_prod(X37,X36)))),product_Pair(X5,product_prod(X38,product_prod(X37,X36))),X39),vAPP(product_prod(X37,X36),product_prod(X38,product_prod(X37,X36)),vAPP(X38,sTfun(product_prod(X37,X36),product_prod(X38,product_prod(X37,X36))),product_Pair(X38,product_prod(X37,X36)),X40),vAPP(X36,product_prod(X37,X36),vAPP(X37,sTfun(X36,product_prod(X37,X36)),product_Pair(X37,X36),X41),X42)))))) => vAPP(product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),$o,X26,X13))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_prod__induct6)).
% 68.49/10.21 thf(f4493,plain,(
% 68.49/10.21 spl93_274),
% 68.49/10.21 inference(avatar_split_clause,[],[f1704,f4490])).
% 68.49/10.21 thf(f4490,plain,(
% 68.49/10.21 spl93_274 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3)),r4)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_274])])).
% 68.49/10.21 thf(f4488,plain,(
% 68.49/10.21 spl93_273),
% 68.49/10.21 inference(avatar_split_clause,[],[f1703,f4485])).
% 68.49/10.21 thf(f4485,plain,(
% 68.49/10.21 spl93_273 <=> (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),r4)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_273])])).
% 68.49/10.21 thf(f4470,plain,(
% 68.49/10.21 spl93_272),
% 68.49/10.21 inference(avatar_split_clause,[],[f1453,f4468])).
% 68.49/10.21 thf(f1453,plain,(
% 68.49/10.21 ( ! [X5 : $tType,X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X0,sK67(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X1,sK68(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X2,sK69(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X3,sK70(X0,X1,X2,X3,X4,X5),X6)),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X4,sK71(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X5,sK72(X0,X1,X2,X3,X4,X5),X6)))))) = X6)) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1171])).
% 68.49/10.21 thf(f1171,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X0,sK67(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X1,sK68(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X2,sK69(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X3,sK70(X0,X1,X2,X3,X4,X5),X6)),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X4,sK71(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X5,sK72(X0,X1,X2,X3,X4,X5),X6)))))) = X6)),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68,sK69,sK70,sK71,sK72])],[f1076,f1170])).
% 68.49/10.21 thf(f1170,plain,(
% 68.49/10.21 ! [X5 : $tType,X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : (? [X7 : X0,X8 : X1,X9 : X2,X10 : X3,X11 : X4,X12 : X5] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X7),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),X8),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),X9),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),X10),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),X11),X12))))) = X6) => (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X0,sK67(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X1,sK68(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X2,sK69(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X3,sK70(X0,X1,X2,X3,X4,X5),X6)),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X4,sK71(X0,X1,X2,X3,X4,X5),X6)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X5,sK72(X0,X1,X2,X3,X4,X5),X6)))))) = X6))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1076,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ? [X7 : X0,X8 : X1,X9 : X2,X10 : X3,X11 : X4,X12 : X5] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X7),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),X8),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),X9),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),X10),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),X11),X12))))) = X6)),
% 68.49/10.21 inference(ennf_transformation,[],[f772])).
% 68.49/10.21 thf(f772,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : $tType,X6 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))] : ~! [X7 : X0,X8 : X1,X9 : X2,X10 : X3,X11 : X4,X12 : X5] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),X7),vAPP(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,product_prod(X4,X5))),product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))),product_Pair(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5)))),X8),vAPP(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5))),vAPP(X2,sTfun(product_prod(X3,product_prod(X4,X5)),product_prod(X2,product_prod(X3,product_prod(X4,X5)))),product_Pair(X2,product_prod(X3,product_prod(X4,X5))),X9),vAPP(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5)),vAPP(X3,sTfun(product_prod(X4,X5),product_prod(X3,product_prod(X4,X5))),product_Pair(X3,product_prod(X4,X5)),X10),vAPP(X5,product_prod(X4,X5),vAPP(X4,sTfun(X5,product_prod(X4,X5)),product_Pair(X4,X5),X11),X12))))) != X6)),
% 68.49/10.21 inference(rectify,[],[f63])).
% 68.49/10.21 thf(f63,axiom,(
% 68.49/10.21 ! [X0 : $tType,X2 : $tType,X5 : $tType,X38 : $tType,X37 : $tType,X36 : $tType,X14 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))))] : ~! [X33 : X0,X34 : X2,X39 : X5,X40 : X38,X41 : X37,X42 : X36] : (vAPP(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))))),product_Pair(X0,product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),X33),vAPP(product_prod(X5,product_prod(X38,product_prod(X37,X36))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),vAPP(X2,sTfun(product_prod(X5,product_prod(X38,product_prod(X37,X36))),product_prod(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36))))),product_Pair(X2,product_prod(X5,product_prod(X38,product_prod(X37,X36)))),X34),vAPP(product_prod(X38,product_prod(X37,X36)),product_prod(X5,product_prod(X38,product_prod(X37,X36))),vAPP(X5,sTfun(product_prod(X38,product_prod(X37,X36)),product_prod(X5,product_prod(X38,product_prod(X37,X36)))),product_Pair(X5,product_prod(X38,product_prod(X37,X36))),X39),vAPP(product_prod(X37,X36),product_prod(X38,product_prod(X37,X36)),vAPP(X38,sTfun(product_prod(X37,X36),product_prod(X38,product_prod(X37,X36))),product_Pair(X38,product_prod(X37,X36)),X40),vAPP(X36,product_prod(X37,X36),vAPP(X37,sTfun(X36,product_prod(X37,X36)),product_Pair(X37,X36),X41),X42))))) != X14)),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_prod__cases6)).
% 68.49/10.21 thf(f4450,plain,(
% 68.49/10.21 spl93_271),
% 68.49/10.21 inference(avatar_split_clause,[],[f1407,f4448])).
% 68.49/10.21 thf(f1407,plain,(
% 68.49/10.21 ( ! [X2 : a,X3 : a,X0 : a,X1 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1001])).
% 68.49/10.21 thf(f1001,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.21 inference(flattening,[],[f1000])).
% 68.49/10.21 thf(f1000,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : ((($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))) | ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.21 inference(ennf_transformation,[],[f587])).
% 68.49/10.21 thf(f587,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) => (($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) => ($true = vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)))))),
% 68.49/10.21 inference(fool_elimination,[],[f586])).
% 68.49/10.21 thf(f586,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a,X3 : a] : (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X0),X1)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) => (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X2),X3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) => vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X3),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.21 inference(rectify,[],[f5])).
% 68.49/10.21 thf(f5,axiom,(
% 68.49/10.21 ! [X9 : a,X10 : a,X11 : a,X12 : a] : (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X9),X10)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) => (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),X11),X12)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) => vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X12),X9)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X10),X11))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X10),X12))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_closed__rel__add)).
% 68.49/10.21 thf(f4446,plain,(
% 68.49/10.21 spl93_270 | ~spl93_221 | ~spl93_227),
% 68.49/10.21 inference(avatar_split_clause,[],[f4224,f3899,f3826,f4444])).
% 68.49/10.21 thf(f4224,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1) = vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X0))) ) | (~spl93_221 | ~spl93_227)),
% 68.49/10.21 inference(superposition,[],[f3900,f3827])).
% 68.49/10.21 thf(f4431,plain,(
% 68.49/10.21 spl93_269),
% 68.49/10.21 inference(avatar_split_clause,[],[f1351,f4429])).
% 68.49/10.21 thf(f4429,plain,(
% 68.49/10.21 spl93_269 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_269])])).
% 68.49/10.21 thf(f1351,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1139])).
% 68.49/10.21 thf(f1139,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f1136,f1138,f1137])).
% 68.49/10.21 thf(f1137,plain,(
% 68.49/10.21 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (? [X3 : X1] : (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) => (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1138,plain,(
% 68.49/10.21 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (? [X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X5) != X5) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1136,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ? [X3 : X1] : (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ? [X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X5) != X5) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.21 inference(rectify,[],[f1086])).
% 68.49/10.21 thf(f1086,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ? [X11 : X1] : (! [X12 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X12),X11)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X12),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X11),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ? [X10 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X10) != X10) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.21 inference(definition_folding,[],[f913,f1085,f1084,f1083])).
% 68.49/10.21 thf(f1083,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0 : $tType,X1 : $tType] : (? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ~($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)))),
% 68.49/10.21 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 68.49/10.21 thf(f1084,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0 : $tType,X1 : $tType] : (? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ~($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.21 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 68.49/10.21 thf(f1085,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0 : $tType,X1 : $tType] : (? [X8 : X1] : (? [X9 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X8),X9) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X9),X8)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ~($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)))),
% 68.49/10.21 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 68.49/10.21 thf(f913,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ? [X11 : X1] : (! [X12 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X12),X11)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X12),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X11),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ? [X10 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X10) != X10) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ? [X8 : X1] : (? [X9 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X8),X9) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X9),X8)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 inference(flattening,[],[f912])).
% 68.49/10.21 thf(f912,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((((((($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ? [X11 : X1] : (! [X12 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X12),X11)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X12),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X11),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))) | ? [X10 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X10) != X10) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))) | ? [X8 : X1] : (? [X9 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X8),X9) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X9),X8)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))) | ? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 inference(ennf_transformation,[],[f491])).
% 68.49/10.21 thf(f491,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (! [X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ! [X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (! [X5 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ! [X6 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ! [X7 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),X6)),X7) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X6),X7)))))) => (! [X8 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ! [X9 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X8),X9) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X9),X8)))) => (! [X10 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X10) = X10)) => (! [X11 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X11),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ? [X12 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X12),X11)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X12),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))) => ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))))))))),
% 68.49/10.21 inference(fool_elimination,[],[f490])).
% 68.49/10.21 thf(f490,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (! [X3 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ! [X4 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (! [X5 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ! [X6 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ! [X7 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),X6)),X7) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X6),X7)))))) => (! [X8 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ! [X9 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X8),X9) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X9),X8)))) => (! [X10 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X10) = X10)) => (! [X11 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X11),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ? [X12 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X12),X11)) & vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X12),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) => vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))))))),
% 68.49/10.21 inference(rectify,[],[f124])).
% 68.49/10.21 thf(f124,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2)))] : (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ! [X45 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X45),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X23),X45)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ! [X45 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X45),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ! [X55 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X55),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X23),X45)),X55) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X23),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X45),X55)))))) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ! [X45 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X45),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X23),X45) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X45),X23)))) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),X23) = X23)) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ? [X56 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X56),X23)) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X56),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))) => vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_123_abelian__groupI)).
% 68.49/10.21 thf(f4411,plain,(
% 68.49/10.21 spl93_268),
% 68.49/10.21 inference(avatar_split_clause,[],[f1446,f4409])).
% 68.49/10.21 thf(f1446,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1065])).
% 68.49/10.21 thf(f1065,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1064])).
% 68.49/10.21 thf(f1064,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f655])).
% 68.49/10.21 thf(f655,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f654])).
% 68.49/10.21 thf(f654,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X5)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5)))))))),
% 68.49/10.21 inference(rectify,[],[f76])).
% 68.49/10.21 thf(f76,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14)),X15) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X13),X15)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X14),X15)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_semiring_Ol__distr)).
% 68.49/10.21 thf(f4407,plain,(
% 68.49/10.21 spl93_267),
% 68.49/10.21 inference(avatar_split_clause,[],[f1445,f4405])).
% 68.49/10.21 thf(f1445,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1063])).
% 68.49/10.21 thf(f1063,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1062])).
% 68.49/10.21 thf(f1062,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f653])).
% 68.49/10.21 thf(f653,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f652])).
% 68.49/10.21 thf(f652,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X5),X4)))))))),
% 68.49/10.21 inference(rectify,[],[f75])).
% 68.49/10.21 thf(f75,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X15),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X15),X13)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X15),X14)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_semiring_Or__distr)).
% 68.49/10.21 thf(f4384,plain,(
% 68.49/10.21 spl93_266),
% 68.49/10.21 inference(avatar_split_clause,[],[f1451,f4382])).
% 68.49/10.21 thf(f1451,plain,(
% 68.49/10.21 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o] : (($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6)) | ($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X4,sK62(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X3,sK63(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X2,sK64(X0,X1,X2,X3,X4),X5)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X2,X3,X4),X5)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X2,X3,X4),X5)))))))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1169])).
% 68.49/10.21 thf(f1169,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] : (($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6)) | ($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X4,sK62(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X3,sK63(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X2,sK64(X0,X1,X2,X3,X4),X5)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X2,X3,X4),X5)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X2,X3,X4),X5))))))))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63,sK64,sK65,sK66])],[f1073,f1168])).
% 68.49/10.21 thf(f1168,plain,(
% 68.49/10.21 ! [X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o] : (? [X7 : X4,X8 : X3,X9 : X2,X10 : X1,X11 : X0] : ($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11)))))) => ($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X4,sK62(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X3,sK63(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X2,sK64(X0,X1,X2,X3,X4),X5)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X1,sK65(X0,X1,X2,X3,X4),X5)),vAPP(sTfun(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o),X0,sK66(X0,X1,X2,X3,X4),X5))))))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1073,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] : (($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6)) | ? [X7 : X4,X8 : X3,X9 : X2,X10 : X1,X11 : X0] : ($true != vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11)))))))),
% 68.49/10.21 inference(ennf_transformation,[],[f663])).
% 68.49/10.21 thf(f663,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] : (! [X7 : X4,X8 : X3,X9 : X2,X10 : X1,X11 : X0] : ($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11)))))) => ($true = vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6)))),
% 68.49/10.21 inference(fool_elimination,[],[f662])).
% 68.49/10.21 thf(f662,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))) > $o,X6 : product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))] : (! [X7 : X4,X8 : X3,X9 : X2,X10 : X1,X11 : X0] : vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),vAPP(X4,sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0))))),product_Pair(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),X7),vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X8),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X9),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X10),X11))))) => vAPP(product_prod(X4,product_prod(X3,product_prod(X2,product_prod(X1,X0)))),$o,X5,X6))),
% 68.49/10.21 inference(rectify,[],[f59])).
% 68.49/10.21 thf(f59,axiom,(
% 68.49/10.21 ! [X37 : $tType,X38 : $tType,X5 : $tType,X2 : $tType,X0 : $tType,X26 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))) > $o,X13 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37))))] : (! [X33 : X0,X34 : X2,X39 : X5,X40 : X38,X41 : X37] : vAPP(product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))),$o,X26,vAPP(product_prod(X2,product_prod(X5,product_prod(X38,X37))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,product_prod(X38,X37))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37))))),product_Pair(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))),X33),vAPP(product_prod(X5,product_prod(X38,X37)),product_prod(X2,product_prod(X5,product_prod(X38,X37))),vAPP(X2,sTfun(product_prod(X5,product_prod(X38,X37)),product_prod(X2,product_prod(X5,product_prod(X38,X37)))),product_Pair(X2,product_prod(X5,product_prod(X38,X37))),X34),vAPP(product_prod(X38,X37),product_prod(X5,product_prod(X38,X37)),vAPP(X5,sTfun(product_prod(X38,X37),product_prod(X5,product_prod(X38,X37))),product_Pair(X5,product_prod(X38,X37)),X39),vAPP(X37,product_prod(X38,X37),vAPP(X38,sTfun(X37,product_prod(X38,X37)),product_Pair(X38,X37),X40),X41))))) => vAPP(product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))),$o,X26,X13))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_prod__induct5)).
% 68.49/10.21 thf(f4332,plain,(
% 68.49/10.21 spl93_265),
% 68.49/10.21 inference(avatar_split_clause,[],[f1378,f4330])).
% 68.49/10.21 thf(f1378,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f955])).
% 68.49/10.21 thf(f955,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f954])).
% 68.49/10.21 thf(f954,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f543])).
% 68.49/10.21 thf(f543,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f542])).
% 68.49/10.21 thf(f542,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))))))),
% 68.49/10.21 inference(rectify,[],[f18])).
% 68.49/10.21 thf(f18,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X15)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),X15))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_l__distr)).
% 68.49/10.21 thf(f4328,plain,(
% 68.49/10.21 spl93_264),
% 68.49/10.21 inference(avatar_split_clause,[],[f1377,f4326])).
% 68.49/10.21 thf(f1377,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f953])).
% 68.49/10.21 thf(f953,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f952])).
% 68.49/10.21 thf(f952,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f541])).
% 68.49/10.21 thf(f541,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))))))),
% 68.49/10.21 inference(fool_elimination,[],[f540])).
% 68.49/10.21 thf(f540,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X2),X1))))))),
% 68.49/10.21 inference(rectify,[],[f19])).
% 68.49/10.21 thf(f19,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X15),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X15),X13)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X15),X14))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_r__distr)).
% 68.49/10.21 thf(f4318,plain,(
% 68.49/10.21 spl93_263),
% 68.49/10.21 inference(avatar_split_clause,[],[f1350,f4316])).
% 68.49/10.21 thf(f1350,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1139])).
% 68.49/10.21 thf(f4309,plain,(
% 68.49/10.21 spl93_262),
% 68.49/10.21 inference(avatar_split_clause,[],[f1323,f4307])).
% 68.49/10.21 thf(f4307,plain,(
% 68.49/10.21 spl93_262 <=> ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_262])])).
% 68.49/10.21 thf(f1323,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f904])).
% 68.49/10.21 thf(f904,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))),
% 68.49/10.21 inference(flattening,[],[f903])).
% 68.49/10.21 thf(f903,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))),
% 68.49/10.21 inference(ennf_transformation,[],[f483])).
% 68.49/10.21 thf(f483,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))))))),
% 68.49/10.21 inference(fool_elimination,[],[f482])).
% 68.49/10.21 thf(f482,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))))))),
% 68.49/10.21 inference(rectify,[],[f102])).
% 68.49/10.21 thf(f102,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X52 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X13)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13)),X14) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_101_add_Ogroup__commutes__pow)).
% 68.49/10.21 thf(f4297,plain,(
% 68.49/10.21 spl93_261),
% 68.49/10.21 inference(avatar_split_clause,[],[f1490,f4294])).
% 68.49/10.21 thf(f4294,plain,(
% 68.49/10.21 spl93_261 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_261])])).
% 68.49/10.21 thf(f1490,plain,(
% 68.49/10.21 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.21 inference(cnf_transformation,[],[f737])).
% 68.49/10.21 thf(f737,plain,(
% 68.49/10.21 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.21 inference(fool_elimination,[],[f736])).
% 68.49/10.21 thf(f736,plain,(
% 68.49/10.21 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.21 inference(rectify,[],[f17])).
% 68.49/10.21 thf(f17,axiom,(
% 68.49/10.21 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_f12)).
% 68.49/10.21 thf(f4292,plain,(
% 68.49/10.21 spl93_260),
% 68.49/10.21 inference(avatar_split_clause,[],[f1444,f4290])).
% 68.49/10.21 thf(f1444,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1061])).
% 68.49/10.21 thf(f1061,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1060])).
% 68.49/10.21 thf(f1060,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f651])).
% 68.49/10.21 thf(f651,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f650])).
% 68.49/10.21 thf(f650,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X4),X5)))))))),
% 68.49/10.21 inference(rectify,[],[f91])).
% 68.49/10.21 thf(f91,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X13),X14)),X15) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X13),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X14),X15)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_semiring_Osemiring__simprules_I8_J)).
% 68.49/10.21 thf(f4262,plain,(
% 68.49/10.21 spl93_259),
% 68.49/10.21 inference(avatar_split_clause,[],[f1449,f4260])).
% 68.49/10.21 thf(f1449,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1071])).
% 68.49/10.21 thf(f1071,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1070])).
% 68.49/10.21 thf(f1070,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f661])).
% 68.49/10.21 thf(f661,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5))))))),
% 68.49/10.21 inference(fool_elimination,[],[f660])).
% 68.49/10.21 thf(f660,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5))))))),
% 68.49/10.21 inference(rectify,[],[f120])).
% 68.49/10.21 thf(f120,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14)),X15) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X14),X15)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_abelian__groupE_I3_J)).
% 68.49/10.21 thf(f4258,plain,(
% 68.49/10.21 spl93_258),
% 68.49/10.21 inference(avatar_split_clause,[],[f1443,f4256])).
% 68.49/10.21 thf(f1443,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1059])).
% 68.49/10.21 thf(f1059,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1058])).
% 68.49/10.21 thf(f1058,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f649])).
% 68.49/10.21 thf(f649,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5))))))),
% 68.49/10.21 inference(fool_elimination,[],[f648])).
% 68.49/10.21 thf(f648,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),X5))))))),
% 68.49/10.21 inference(rectify,[],[f93])).
% 68.49/10.21 thf(f93,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14)),X15) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X14),X15)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_semiring_Osemiring__simprules_I5_J)).
% 68.49/10.21 thf(f4254,plain,(
% 68.49/10.21 spl93_257),
% 68.49/10.21 inference(avatar_split_clause,[],[f1442,f4252])).
% 68.49/10.21 thf(f1442,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1057])).
% 68.49/10.21 thf(f1057,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1056])).
% 68.49/10.21 thf(f1056,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f647])).
% 68.49/10.21 thf(f647,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f646])).
% 68.49/10.21 thf(f646,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X5)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X5)))))))),
% 68.49/10.21 inference(rectify,[],[f95])).
% 68.49/10.21 thf(f95,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X14),X15)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X14),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X15)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_semiring_Osemiring__simprules_I12_J)).
% 68.49/10.21 thf(f4239,plain,(
% 68.49/10.21 spl93_256),
% 68.49/10.21 inference(avatar_split_clause,[],[f1450,f4237])).
% 68.49/10.21 thf(f1450,plain,(
% 68.49/10.21 ( ! [X4 : $tType,X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ((vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X0,sK57(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X1,sK58(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X2,sK59(X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X3,sK60(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X4,sK61(X0,X1,X2,X3,X4),X5))))) = X5)) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1167])).
% 68.49/10.21 thf(f1167,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X0,sK57(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X1,sK58(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X2,sK59(X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X3,sK60(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X4,sK61(X0,X1,X2,X3,X4),X5))))) = X5)),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60,sK61])],[f1072,f1166])).
% 68.49/10.21 thf(f1166,plain,(
% 68.49/10.21 ! [X4 : $tType,X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : (? [X6 : X0,X7 : X1,X8 : X2,X9 : X3,X10 : X4] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X6),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),X7),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),X8),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),X9),X10)))) = X5) => (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X0,sK57(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X1,sK58(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X2,sK59(X0,X1,X2,X3,X4),X5)),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X3,sK60(X0,X1,X2,X3,X4),X5)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X4,sK61(X0,X1,X2,X3,X4),X5))))) = X5))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1072,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ? [X6 : X0,X7 : X1,X8 : X2,X9 : X3,X10 : X4] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X6),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),X7),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),X8),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),X9),X10)))) = X5)),
% 68.49/10.21 inference(ennf_transformation,[],[f771])).
% 68.49/10.21 thf(f771,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : $tType,X5 : product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))] : ~! [X6 : X0,X7 : X1,X8 : X2,X9 : X3,X10 : X4] : (vAPP(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,product_prod(X3,X4))),product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4))))),product_Pair(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))),X6),vAPP(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4))),vAPP(X1,sTfun(product_prod(X2,product_prod(X3,X4)),product_prod(X1,product_prod(X2,product_prod(X3,X4)))),product_Pair(X1,product_prod(X2,product_prod(X3,X4))),X7),vAPP(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4)),vAPP(X2,sTfun(product_prod(X3,X4),product_prod(X2,product_prod(X3,X4))),product_Pair(X2,product_prod(X3,X4)),X8),vAPP(X4,product_prod(X3,X4),vAPP(X3,sTfun(X4,product_prod(X3,X4)),product_Pair(X3,X4),X9),X10)))) != X5)),
% 68.49/10.21 inference(rectify,[],[f64])).
% 68.49/10.21 thf(f64,axiom,(
% 68.49/10.21 ! [X0 : $tType,X2 : $tType,X5 : $tType,X38 : $tType,X37 : $tType,X14 : product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37))))] : ~! [X33 : X0,X34 : X2,X39 : X5,X40 : X38,X41 : X37] : (vAPP(product_prod(X2,product_prod(X5,product_prod(X38,X37))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,product_prod(X38,X37))),product_prod(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37))))),product_Pair(X0,product_prod(X2,product_prod(X5,product_prod(X38,X37)))),X33),vAPP(product_prod(X5,product_prod(X38,X37)),product_prod(X2,product_prod(X5,product_prod(X38,X37))),vAPP(X2,sTfun(product_prod(X5,product_prod(X38,X37)),product_prod(X2,product_prod(X5,product_prod(X38,X37)))),product_Pair(X2,product_prod(X5,product_prod(X38,X37))),X34),vAPP(product_prod(X38,X37),product_prod(X5,product_prod(X38,X37)),vAPP(X5,sTfun(product_prod(X38,X37),product_prod(X5,product_prod(X38,X37))),product_Pair(X5,product_prod(X38,X37)),X39),vAPP(X37,product_prod(X38,X37),vAPP(X38,sTfun(X37,product_prod(X38,X37)),product_Pair(X38,X37),X40),X41)))) != X14)),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_prod__cases5)).
% 68.49/10.21 thf(f4229,plain,(
% 68.49/10.21 spl93_255),
% 68.49/10.21 inference(avatar_split_clause,[],[f1349,f4227])).
% 68.49/10.21 thf(f1349,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1139])).
% 68.49/10.21 thf(f4206,plain,(
% 68.49/10.21 spl93_254),
% 68.49/10.21 inference(avatar_split_clause,[],[f1386,f4204])).
% 68.49/10.21 thf(f4204,plain,(
% 68.49/10.21 spl93_254 <=> ! [X1 : $tType,X0 : $tType,X3 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((X2 = X3) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X3)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_254])])).
% 68.49/10.21 thf(f1386,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((X2 = X3) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X3))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f968])).
% 68.49/10.21 thf(f968,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((X2 = X3) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X3)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X3)))),
% 68.49/10.21 inference(flattening,[],[f967])).
% 68.49/10.21 thf(f967,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (((((((X2 = X3) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X3))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X3))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X3))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X3))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X3))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X3)))),
% 68.49/10.21 inference(ennf_transformation,[],[f765])).
% 68.49/10.21 thf(f765,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X3)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X3)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X3)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X3)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X3)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0,more(X1,X0),X3)) => (X2 = X3)))))))),
% 68.49/10.21 inference(rectify,[],[f116])).
% 68.49/10.21 thf(f116,axiom,(
% 68.49/10.21 ! [X1 : $tType,X0 : $tType,X9 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X11 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1)))] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X9) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X1))),X11)) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X1)),X9) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X1)),X11)) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,one(X0,ring_ext(X0,X1)),X9) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,one(X0,ring_ext(X0,X1)),X11)) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X9) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X0,zero(X0,X1),X11)) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),add(X0,X1),X9) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),sTfun(X0,sTfun(X0,X0)),add(X0,X1),X11)) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X1,more(X0,X1),X9) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X1))),X1,more(X0,X1),X11)) => (X9 = X11)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_115_ring_Oequality)).
% 68.49/10.21 thf(f4202,plain,(
% 68.49/10.21 spl93_253),
% 68.49/10.21 inference(avatar_split_clause,[],[f1376,f4200])).
% 68.49/10.21 thf(f1376,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f951])).
% 68.49/10.21 thf(f951,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f950])).
% 68.49/10.21 thf(f950,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f539])).
% 68.49/10.21 thf(f539,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)))))),
% 68.49/10.21 inference(fool_elimination,[],[f538])).
% 68.49/10.21 thf(f538,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),X2)))))),
% 68.49/10.21 inference(rectify,[],[f24])).
% 68.49/10.21 thf(f24,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14)),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),X15))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_m__assoc)).
% 68.49/10.21 thf(f4198,plain,(
% 68.49/10.21 spl93_252),
% 68.49/10.21 inference(avatar_split_clause,[],[f1375,f4196])).
% 68.49/10.21 thf(f1375,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f949])).
% 68.49/10.21 thf(f949,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f948])).
% 68.49/10.21 thf(f948,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f537])).
% 68.49/10.21 thf(f537,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f536])).
% 68.49/10.21 thf(f536,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X2))))))),
% 68.49/10.21 inference(rectify,[],[f26])).
% 68.49/10.21 thf(f26,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X15))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_m__lcomm)).
% 68.49/10.21 thf(f4176,plain,(
% 68.49/10.21 spl93_251),
% 68.49/10.21 inference(avatar_split_clause,[],[f1337,f4174])).
% 68.49/10.21 thf(f4174,plain,(
% 68.49/10.21 spl93_251 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_251])])).
% 68.49/10.21 thf(f1337,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1119])).
% 68.49/10.21 thf(f1119,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19,sK20])],[f1116,f1118,f1117])).
% 68.49/10.21 thf(f1117,plain,(
% 68.49/10.21 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (? [X3 : X1] : (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) => (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1118,plain,(
% 68.49/10.21 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (? [X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X5) != X5) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1116,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ? [X3 : X1] : (! [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ? [X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X5) != X5) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.21 inference(rectify,[],[f1082])).
% 68.49/10.21 thf(f1082,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ? [X9 : X1] : (! [X10 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X10),X9)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ? [X8 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X8) != X8) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.21 inference(definition_folding,[],[f911,f1081,f1080])).
% 68.49/10.21 thf(f1080,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X0 : $tType,X1 : $tType] : (? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ~($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)))),
% 68.49/10.21 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 68.49/10.21 thf(f1081,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X0 : $tType,X1 : $tType] : (? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ~($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.21 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 68.49/10.21 thf(f911,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ? [X9 : X1] : (! [X10 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X10),X9)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ? [X8 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X8) != X8) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.21 inference(flattening,[],[f910])).
% 68.49/10.21 thf(f910,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (((((($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ? [X9 : X1] : (! [X10 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X10),X9)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))) | ? [X8 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X8) != X8) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))) | ? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.21 inference(ennf_transformation,[],[f489])).
% 68.49/10.21 thf(f489,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (! [X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ! [X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (! [X5 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ! [X6 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ! [X7 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X6)),X7) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X6),X7)))))) => (! [X8 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X8) = X8)) => (! [X9 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ? [X10 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X10),X9)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))) => ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f488])).
% 68.49/10.21 thf(f488,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (! [X3 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ! [X4 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (! [X5 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ! [X6 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ! [X7 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X6)),X7) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X6),X7)))))) => (! [X8 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),X8) = X8)) => (! [X9 : X1] : (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ? [X10 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X10),X9)) & vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X10),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) => vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))))))),
% 68.49/10.21 inference(rectify,[],[f185])).
% 68.49/10.21 thf(f185,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2))] : (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ! [X45 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X45),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X23),X45)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)))) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ! [X45 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X45),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ! [X55 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X55),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X23),X45)),X55) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X23),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X45),X55)))))) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54)),X23) = X23)) => (! [X23 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ? [X56 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X56),X23)) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X56),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)))) => vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_184_groupI)).
% 68.49/10.21 thf(f4156,plain,(
% 68.49/10.21 spl93_250),
% 68.49/10.21 inference(avatar_split_clause,[],[f1374,f4154])).
% 68.49/10.21 thf(f1374,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f947])).
% 68.49/10.21 thf(f947,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f946])).
% 68.49/10.21 thf(f946,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f535])).
% 68.49/10.21 thf(f535,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)))))),
% 68.49/10.21 inference(fool_elimination,[],[f534])).
% 68.49/10.21 thf(f534,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),X2)))))),
% 68.49/10.21 inference(rectify,[],[f27])).
% 68.49/10.21 thf(f27,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)),X15) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X15))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_add_Om__assoc)).
% 68.49/10.21 thf(f4152,plain,(
% 68.49/10.21 spl93_249),
% 68.49/10.21 inference(avatar_split_clause,[],[f1372,f4150])).
% 68.49/10.21 thf(f1372,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f943])).
% 68.49/10.21 thf(f943,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f942])).
% 68.49/10.21 thf(f942,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f531])).
% 68.49/10.21 thf(f531,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f530])).
% 68.49/10.21 thf(f530,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X2))))))),
% 68.49/10.21 inference(rectify,[],[f29])).
% 68.49/10.21 thf(f29,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X15 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X15)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X15))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_add_Om__lcomm)).
% 68.49/10.21 thf(f4130,plain,(
% 68.49/10.21 spl93_248),
% 68.49/10.21 inference(avatar_split_clause,[],[f1371,f4128])).
% 68.49/10.21 thf(f1371,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f941])).
% 68.49/10.21 thf(f941,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f940])).
% 68.49/10.21 thf(f940,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f529])).
% 68.49/10.21 thf(f529,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1)))))),
% 68.49/10.21 inference(fool_elimination,[],[f528])).
% 68.49/10.21 thf(f528,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1)))))),
% 68.49/10.21 inference(rectify,[],[f104])).
% 68.49/10.21 thf(f104,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X52 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X14)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_add_Onat__pow__distrib)).
% 68.49/10.21 thf(f4126,plain,(
% 68.49/10.21 spl93_247),
% 68.49/10.21 inference(avatar_split_clause,[],[f1370,f4124])).
% 68.49/10.21 thf(f1370,plain,(
% 68.49/10.21 ( ! [X2 : int,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f939])).
% 68.49/10.21 thf(f939,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f938])).
% 68.49/10.21 thf(f938,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f527])).
% 68.49/10.21 thf(f527,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1)))))),
% 68.49/10.21 inference(fool_elimination,[],[f526])).
% 68.49/10.21 thf(f526,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1)))))),
% 68.49/10.21 inference(rectify,[],[f81])).
% 68.49/10.21 thf(f81,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a,X48 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),X13)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),X14)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_add_Oint__pow__distrib)).
% 68.49/10.21 thf(f4114,plain,(
% 68.49/10.21 spl93_246),
% 68.49/10.21 inference(avatar_split_clause,[],[f1438,f4112])).
% 68.49/10.21 thf(f1438,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1049])).
% 68.49/10.21 thf(f1049,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1048])).
% 68.49/10.21 thf(f1048,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f639])).
% 68.49/10.21 thf(f639,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5)))))))),
% 68.49/10.21 inference(fool_elimination,[],[f638])).
% 68.49/10.21 thf(f638,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1,X5 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),X5) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X5)))))))),
% 68.49/10.21 inference(rectify,[],[f253])).
% 68.49/10.21 thf(f253,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X14 : X0,X15 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X15),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),X14)),X15) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X14),X15)))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_252_comm__groupE_I3_J)).
% 68.49/10.21 thf(f4096,plain,(
% 68.49/10.21 spl93_245),
% 68.49/10.21 inference(avatar_split_clause,[],[f1364,f4094])).
% 68.49/10.21 thf(f1364,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f927])).
% 68.49/10.21 thf(f927,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f515])).
% 68.49/10.21 thf(f515,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.21 inference(fool_elimination,[],[f514])).
% 68.49/10.21 thf(f514,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.21 inference(rectify,[],[f105])).
% 68.49/10.21 thf(f105,axiom,(
% 68.49/10.21 ! [X13 : a,X52 : nat,X53 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X53),X13)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X53),X13)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_104_add_Onat__pow__comm)).
% 68.49/10.21 thf(f4087,plain,(
% 68.49/10.21 spl93_244),
% 68.49/10.21 inference(avatar_split_clause,[],[f1348,f4085])).
% 68.49/10.21 thf(f1348,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK28(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,sK29(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1139])).
% 68.49/10.21 thf(f4053,plain,(
% 68.49/10.21 spl93_243),
% 68.49/10.21 inference(avatar_split_clause,[],[f1441,f4051])).
% 68.49/10.21 thf(f1441,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : ((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1055])).
% 68.49/10.21 thf(f1055,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : ((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1054])).
% 68.49/10.21 thf(f1054,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : ((((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f645])).
% 68.49/10.21 thf(f645,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)))))),
% 68.49/10.21 inference(fool_elimination,[],[f644])).
% 68.49/10.21 thf(f644,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X3)),X4)))))),
% 68.49/10.21 inference(rectify,[],[f110])).
% 68.49/10.21 thf(f110,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X6 : X0,X7 : X0,X47 : nat] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X7),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X46),X47),X6)),X7) = vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X46),X47),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X6),X7))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_109_semiring_Oadd__pow__ldistr)).
% 68.49/10.21 thf(f4049,plain,(
% 68.49/10.21 spl93_242),
% 68.49/10.21 inference(avatar_split_clause,[],[f1440,f4047])).
% 68.49/10.21 thf(f1440,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : ((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1053])).
% 68.49/10.21 thf(f1053,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : ((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1052])).
% 68.49/10.21 thf(f1052,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : ((((vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f643])).
% 68.49/10.21 thf(f643,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))))))),
% 68.49/10.21 inference(fool_elimination,[],[f642])).
% 68.49/10.21 thf(f642,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1,X5 : nat] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(X1,X1,vAPP(nat,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(nat,sTfun(X1,X1)),add_pow(X1,X0,nat),X2),X5),X4))))))),
% 68.49/10.21 inference(rectify,[],[f111])).
% 68.49/10.21 thf(f111,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X6 : X0,X7 : X0,X47 : nat] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X7),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X46),X47),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X6),vAPP(X0,X0,vAPP(nat,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(nat,sTfun(X0,X0)),add_pow(X0,X2,nat),X46),X47),X7))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_semiring_Oadd__pow__rdistr)).
% 68.49/10.21 thf(f4045,plain,(
% 68.49/10.21 spl93_241),
% 68.49/10.21 inference(avatar_split_clause,[],[f1347,f4043])).
% 68.49/10.21 thf(f1347,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1135])).
% 68.49/10.21 thf(f1135,plain,(
% 68.49/10.21 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X1 : $tType,X2 : $tType] : (((((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26,sK27])],[f1131,f1134,f1133,f1132])).
% 68.49/10.21 thf(f1132,plain,(
% 68.49/10.21 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X3 : X2] : (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1133,plain,(
% 68.49/10.21 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1134,plain,(
% 68.49/10.21 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1131,plain,(
% 68.49/10.21 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X1 : $tType,X2 : $tType] : (? [X3 : X2] : (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0)))),
% 68.49/10.21 inference(rectify,[],[f1130])).
% 68.49/10.21 thf(f1130,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0 : $tType,X1 : $tType] : (? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP2(X0,X1),X2)))),
% 68.49/10.21 inference(nnf_transformation,[],[f1083])).
% 68.49/10.21 thf(f4033,plain,(
% 68.49/10.21 spl93_240),
% 68.49/10.21 inference(avatar_split_clause,[],[f1336,f4031])).
% 68.49/10.21 thf(f1336,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1119])).
% 68.49/10.21 thf(f4029,plain,(
% 68.49/10.21 spl93_239 | ~spl93_63 | ~spl93_64),
% 68.49/10.21 inference(avatar_split_clause,[],[f2201,f2153,f2149,f4027])).
% 68.49/10.21 thf(f4027,plain,(
% 68.49/10.21 spl93_239 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_239])])).
% 68.49/10.21 thf(f2201,plain,(
% 68.49/10.21 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X0))) ) | (~spl93_63 | ~spl93_64)),
% 68.49/10.21 inference(superposition,[],[f2154,f2150])).
% 68.49/10.21 thf(f4018,plain,(
% 68.49/10.21 spl93_238),
% 68.49/10.21 inference(avatar_split_clause,[],[f1322,f4016])).
% 68.49/10.21 thf(f1322,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f902])).
% 68.49/10.21 thf(f902,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)))),
% 68.49/10.21 inference(flattening,[],[f901])).
% 68.49/10.21 thf(f901,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)))),
% 68.49/10.21 inference(ennf_transformation,[],[f481])).
% 68.49/10.21 thf(f481,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (X0 = X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f480])).
% 68.49/10.21 thf(f480,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X2)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (X0 = X2))))))),
% 68.49/10.21 inference(rectify,[],[f79])).
% 68.49/10.21 thf(f79,axiom,(
% 68.49/10.21 ! [X14 : a,X13 : a,X22 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),X13) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X22)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X22),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (X14 = X22))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_inv__unique)).
% 68.49/10.21 thf(f4005,plain,(
% 68.49/10.21 spl93_237),
% 68.49/10.21 inference(avatar_split_clause,[],[f1428,f4003])).
% 68.49/10.21 thf(f1428,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1040])).
% 68.49/10.21 thf(f1040,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1039])).
% 68.49/10.21 thf(f1039,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f627])).
% 68.49/10.21 thf(f627,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))))))),
% 68.49/10.21 inference(fool_elimination,[],[f626])).
% 68.49/10.21 thf(f626,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4))))))),
% 68.49/10.21 inference(rectify,[],[f226])).
% 68.49/10.21 thf(f226,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X13),X14)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X14))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_abelian__group_Ominus__add)).
% 68.49/10.21 thf(f4000,plain,(
% 68.49/10.21 spl93_236),
% 68.49/10.21 inference(avatar_split_clause,[],[f1321,f3998])).
% 68.49/10.21 thf(f1321,plain,(
% 68.49/10.21 ( ! [X2 : a,X0 : a,X1 : a] : ((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f900])).
% 68.49/10.21 thf(f900,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.21 inference(flattening,[],[f899])).
% 68.49/10.21 thf(f899,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((((((X0 = X2) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.21 inference(ennf_transformation,[],[f479])).
% 68.49/10.21 thf(f479,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (X0 = X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f478])).
% 68.49/10.21 thf(f478,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X2)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X2),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (X0 = X2))))))),
% 68.49/10.21 inference(rectify,[],[f31])).
% 68.49/10.21 thf(f31,axiom,(
% 68.49/10.21 ! [X14 : a,X13 : a,X22 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X13)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X22)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X22),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (X14 = X22))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_local_Ominus__unique)).
% 68.49/10.21 thf(f3962,plain,(
% 68.49/10.21 spl93_235 | ~spl93_20 | ~spl93_21 | ~spl93_41 | ~spl93_44),
% 68.49/10.21 inference(avatar_split_clause,[],[f2016,f1993,f1981,f1827,f1822,f3960])).
% 68.49/10.21 thf(f2016,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X0)) = X1)) ) | (~spl93_20 | ~spl93_21 | ~spl93_41 | ~spl93_44)),
% 68.49/10.21 inference(forward_demodulation,[],[f2015,f2003])).
% 68.49/10.21 thf(f2015,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),X1)) = X1)) ) | (~spl93_21 | ~spl93_44)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f2012])).
% 68.49/10.21 thf(f2012,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,uminus_uminus(int),X0)),X1)) = X1)) ) | (~spl93_21 | ~spl93_44)),
% 68.49/10.21 inference(superposition,[],[f1994,f1829])).
% 68.49/10.21 thf(f3958,plain,(
% 68.49/10.21 spl93_234),
% 68.49/10.21 inference(avatar_split_clause,[],[f1369,f3956])).
% 68.49/10.21 thf(f1369,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f937])).
% 68.49/10.21 thf(f937,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f936])).
% 68.49/10.21 thf(f936,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f525])).
% 68.49/10.21 thf(f525,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1))))),
% 68.49/10.21 inference(fool_elimination,[],[f524])).
% 68.49/10.21 thf(f524,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)),X1))))),
% 68.49/10.21 inference(rectify,[],[f99])).
% 68.49/10.21 thf(f99,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a,X47 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X47),X6)),X7) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X47),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X6),X7)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_add__pow__ldistr)).
% 68.49/10.21 thf(f3954,plain,(
% 68.49/10.21 spl93_233),
% 68.49/10.21 inference(avatar_split_clause,[],[f1368,f3952])).
% 68.49/10.21 thf(f1368,plain,(
% 68.49/10.21 ( ! [X2 : int,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f935])).
% 68.49/10.21 thf(f935,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f934])).
% 68.49/10.21 thf(f934,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f523])).
% 68.49/10.21 thf(f523,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1)))))),
% 68.49/10.21 inference(fool_elimination,[],[f522])).
% 68.49/10.21 thf(f522,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X1)))))),
% 68.49/10.21 inference(rectify,[],[f77])).
% 68.49/10.21 thf(f77,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a,X47 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X6),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X47),X7)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X47),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X6),X7)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__pow__rdistr__int)).
% 68.49/10.21 thf(f3950,plain,(
% 68.49/10.21 spl93_232),
% 68.49/10.21 inference(avatar_split_clause,[],[f1367,f3948])).
% 68.49/10.21 thf(f1367,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f933])).
% 68.49/10.21 thf(f933,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f932])).
% 68.49/10.21 thf(f932,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f521])).
% 68.49/10.21 thf(f521,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1)))))),
% 68.49/10.21 inference(fool_elimination,[],[f520])).
% 68.49/10.21 thf(f520,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X1)))))),
% 68.49/10.21 inference(rectify,[],[f100])).
% 68.49/10.21 thf(f100,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a,X47 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X47),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X6),X7)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X6),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X47),X7)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_99_add__pow__rdistr)).
% 68.49/10.21 thf(f3946,plain,(
% 68.49/10.21 spl93_231),
% 68.49/10.21 inference(avatar_split_clause,[],[f1366,f3944])).
% 68.49/10.21 thf(f1366,plain,(
% 68.49/10.21 ( ! [X2 : int,X0 : a,X1 : a] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f931])).
% 68.49/10.21 thf(f931,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f930])).
% 68.49/10.21 thf(f930,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f519])).
% 68.49/10.21 thf(f519,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1))))),
% 68.49/10.21 inference(fool_elimination,[],[f518])).
% 68.49/10.21 thf(f518,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a,X2 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)),X1))))),
% 68.49/10.21 inference(rectify,[],[f78])).
% 68.49/10.21 thf(f78,axiom,(
% 68.49/10.21 ! [X6 : a,X7 : a,X47 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X7),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X47),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X6),X7)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X47),X6)),X7))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_add__pow__ldistr__int)).
% 68.49/10.21 thf(f3924,plain,(
% 68.49/10.21 spl93_230),
% 68.49/10.21 inference(avatar_split_clause,[],[f1298,f3922])).
% 68.49/10.21 thf(f1298,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f875])).
% 68.49/10.21 thf(f875,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f874])).
% 68.49/10.21 thf(f874,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f455])).
% 68.49/10.21 thf(f455,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)))))),
% 68.49/10.21 inference(fool_elimination,[],[f454])).
% 68.49/10.21 thf(f454,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)))))),
% 68.49/10.21 inference(rectify,[],[f199])).
% 68.49/10.21 thf(f199,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X14)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_local_Ominus__add)).
% 68.49/10.21 thf(f3920,plain,(
% 68.49/10.21 spl93_229),
% 68.49/10.21 inference(avatar_split_clause,[],[f1297,f3918])).
% 68.49/10.21 thf(f1297,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f873])).
% 68.49/10.21 thf(f873,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f872])).
% 68.49/10.21 thf(f872,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f453])).
% 68.49/10.21 thf(f453,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))))),
% 68.49/10.21 inference(fool_elimination,[],[f452])).
% 68.49/10.21 thf(f452,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)))))),
% 68.49/10.21 inference(rectify,[],[f204])).
% 68.49/10.21 thf(f204,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X14)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_add_Oinv__mult__group)).
% 68.49/10.21 thf(f3905,plain,(
% 68.49/10.21 spl93_228),
% 68.49/10.21 inference(avatar_split_clause,[],[f1335,f3903])).
% 68.49/10.21 thf(f1335,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1119])).
% 68.49/10.21 thf(f3901,plain,(
% 68.49/10.21 spl93_227 | ~spl93_21 | ~spl93_33),
% 68.49/10.21 inference(avatar_split_clause,[],[f1938,f1912,f1827,f3899])).
% 68.49/10.21 thf(f1938,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X1) = X0)) ) | (~spl93_21 | ~spl93_33)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1935])).
% 68.49/10.21 thf(f1935,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X0),X1)),X1) = X0)) ) | (~spl93_21 | ~spl93_33)),
% 68.49/10.21 inference(superposition,[],[f1913,f1829])).
% 68.49/10.21 thf(f3869,plain,(
% 68.49/10.21 spl93_226),
% 68.49/10.21 inference(avatar_split_clause,[],[f1363,f3867])).
% 68.49/10.21 thf(f1363,plain,(
% 68.49/10.21 ( ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f926])).
% 68.49/10.21 thf(f926,plain,(
% 68.49/10.21 ! [X0 : a,X1 : int,X2 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f513])).
% 68.49/10.21 thf(f513,plain,(
% 68.49/10.21 ! [X0 : a,X1 : int,X2 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))))),
% 68.49/10.21 inference(fool_elimination,[],[f512])).
% 68.49/10.21 thf(f512,plain,(
% 68.49/10.21 ! [X0 : a,X1 : int,X2 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0)))))),
% 68.49/10.21 inference(rectify,[],[f215])).
% 68.49/10.21 thf(f215,axiom,(
% 68.49/10.21 ! [X13 : a,X52 : int,X53 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),X52),X53)),X13) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X52),X13)),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X53),X13)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_add_Oint__pow__diff)).
% 68.49/10.21 thf(f3865,plain,(
% 68.49/10.21 spl93_225),
% 68.49/10.21 inference(avatar_split_clause,[],[f1333,f3863])).
% 68.49/10.21 thf(f1333,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1115])).
% 68.49/10.21 thf(f1115,plain,(
% 68.49/10.21 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X1 : $tType,X2 : $tType] : (((((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18])],[f1111,f1114,f1113,f1112])).
% 68.49/10.21 thf(f1112,plain,(
% 68.49/10.21 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (? [X3 : X2] : (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X3),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X3),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) => (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1113,plain,(
% 68.49/10.21 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) => (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1114,plain,(
% 68.49/10.21 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) => ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1111,plain,(
% 68.49/10.21 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X1 : $tType,X2 : $tType] : (? [X3 : X2] : (? [X4 : X2] : (? [X5 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X3),X4)),X5) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X3),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X4),X5))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X5),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0)))),
% 68.49/10.21 inference(rectify,[],[f1110])).
% 68.49/10.21 thf(f1110,plain,(
% 68.49/10.21 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X0 : $tType,X1 : $tType] : (? [X5 : X1] : (? [X6 : X1] : (? [X7 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),X6)),X7) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X5),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X6),X7))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X7),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X6),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X5),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)))),
% 68.49/10.21 inference(nnf_transformation,[],[f1080])).
% 68.49/10.21 thf(f3843,plain,(
% 68.49/10.21 spl93_224),
% 68.49/10.21 inference(avatar_split_clause,[],[f1702,f3840])).
% 68.49/10.21 thf(f1702,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),s3) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),
% 68.49/10.21 inference(forward_demodulation,[],[f1182,f1181])).
% 68.49/10.21 thf(f1182,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),s3))),
% 68.49/10.21 inference(cnf_transformation,[],[f6])).
% 68.49/10.21 thf(f6,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s2))),s3))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Is_H_A_092_060otimes_062_As_H_H_J_A_061_As_A_092_060otimes_062_A_Is_H_H_A_092_060otimes_062_As_H_J_A_092_060otimes_062_As_H_H_092_060close_062)).
% 68.49/10.21 thf(f3838,plain,(
% 68.49/10.21 spl93_223),
% 68.49/10.21 inference(avatar_split_clause,[],[f1181,f3835])).
% 68.49/10.21 thf(f3833,plain,(
% 68.49/10.21 spl93_222),
% 68.49/10.21 inference(avatar_split_clause,[],[f1180,f3830])).
% 68.49/10.21 thf(f1180,plain,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),
% 68.49/10.21 inference(cnf_transformation,[],[f8])).
% 68.49/10.21 thf(f8,axiom,(
% 68.49/10.21 (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7__092_060open_062s_A_092_060otimes_062_As_H_H_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_A_061_As_H_H_A_092_060otimes_062_As_A_092_060otimes_062_A_Ir_H_A_092_060otimes_062_Ar_H_H_J_092_060close_062)).
% 68.49/10.21 thf(f3828,plain,(
% 68.49/10.21 spl93_221 | ~spl93_18 | ~spl93_31),
% 68.49/10.21 inference(avatar_split_clause,[],[f1930,f1904,f1812,f3826])).
% 68.49/10.21 thf(f1930,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) = X1)) ) | (~spl93_18 | ~spl93_31)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1925])).
% 68.49/10.21 thf(f1925,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X0) = X1)) ) | (~spl93_18 | ~spl93_31)),
% 68.49/10.21 inference(superposition,[],[f1905,f1814])).
% 68.49/10.21 thf(f3807,plain,(
% 68.49/10.21 spl93_220),
% 68.49/10.21 inference(avatar_split_clause,[],[f1437,f3805])).
% 68.49/10.21 thf(f1437,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5)) | ($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X2,X3),X4)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X2,sK54(X0,X1,X2,X3),X4)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X2,X3),X4)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X2,X3),X4))))))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1165])).
% 68.49/10.21 thf(f1165,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5)) | ($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X2,X3),X4)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X2,sK54(X0,X1,X2,X3),X4)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X2,X3),X4)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X2,X3),X4)))))))),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56])],[f1047,f1164])).
% 68.49/10.21 thf(f1164,plain,(
% 68.49/10.21 ! [X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o] : (? [X6 : X3,X7 : X2,X8 : X1,X9 : X0] : ($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9))))) => ($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X3,sK53(X0,X1,X2,X3),X4)),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X2,sK54(X0,X1,X2,X3),X4)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X1,sK55(X0,X1,X2,X3),X4)),vAPP(sTfun(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o),X0,sK56(X0,X1,X2,X3),X4)))))))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1047,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5)) | ? [X6 : X3,X7 : X2,X8 : X1,X9 : X0] : ($true != vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9))))))),
% 68.49/10.21 inference(ennf_transformation,[],[f637])).
% 68.49/10.21 thf(f637,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (! [X6 : X3,X7 : X2,X8 : X1,X9 : X0] : ($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9))))) => ($true = vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5)))),
% 68.49/10.21 inference(fool_elimination,[],[f636])).
% 68.49/10.21 thf(f636,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X3,product_prod(X2,product_prod(X1,X0))) > $o,X5 : product_prod(X3,product_prod(X2,product_prod(X1,X0)))] : (! [X6 : X3,X7 : X2,X8 : X1,X9 : X0] : vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,vAPP(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0))),vAPP(X3,sTfun(product_prod(X2,product_prod(X1,X0)),product_prod(X3,product_prod(X2,product_prod(X1,X0)))),product_Pair(X3,product_prod(X2,product_prod(X1,X0))),X6),vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X7),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X8),X9)))) => vAPP(product_prod(X3,product_prod(X2,product_prod(X1,X0))),$o,X4,X5))),
% 68.49/10.21 inference(rectify,[],[f60])).
% 68.49/10.21 thf(f60,axiom,(
% 68.49/10.21 ! [X38 : $tType,X5 : $tType,X2 : $tType,X0 : $tType,X26 : product_prod(X0,product_prod(X2,product_prod(X5,X38))) > $o,X13 : product_prod(X0,product_prod(X2,product_prod(X5,X38)))] : (! [X33 : X0,X34 : X2,X39 : X5,X40 : X38] : vAPP(product_prod(X0,product_prod(X2,product_prod(X5,X38))),$o,X26,vAPP(product_prod(X2,product_prod(X5,X38)),product_prod(X0,product_prod(X2,product_prod(X5,X38))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,X38)),product_prod(X0,product_prod(X2,product_prod(X5,X38)))),product_Pair(X0,product_prod(X2,product_prod(X5,X38))),X33),vAPP(product_prod(X5,X38),product_prod(X2,product_prod(X5,X38)),vAPP(X2,sTfun(product_prod(X5,X38),product_prod(X2,product_prod(X5,X38))),product_Pair(X2,product_prod(X5,X38)),X34),vAPP(X38,product_prod(X5,X38),vAPP(X5,sTfun(X38,product_prod(X5,X38)),product_Pair(X5,X38),X39),X40)))) => vAPP(product_prod(X0,product_prod(X2,product_prod(X5,X38))),$o,X26,X13))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_prod__induct4)).
% 68.49/10.21 thf(f3786,plain,(
% 68.49/10.21 spl93_219),
% 68.49/10.21 inference(avatar_split_clause,[],[f1296,f3784])).
% 68.49/10.21 thf(f1296,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f871])).
% 68.49/10.21 thf(f871,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f870])).
% 68.49/10.21 thf(f870,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f451])).
% 68.49/10.21 thf(f451,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)))))),
% 68.49/10.21 inference(fool_elimination,[],[f450])).
% 68.49/10.21 thf(f450,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1)))))),
% 68.49/10.21 inference(rectify,[],[f206])).
% 68.49/10.21 thf(f206,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X14)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_r__minus)).
% 68.49/10.21 thf(f3782,plain,(
% 68.49/10.21 spl93_218),
% 68.49/10.21 inference(avatar_split_clause,[],[f1295,f3780])).
% 68.49/10.21 thf(f1295,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f869])).
% 68.49/10.21 thf(f869,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f868])).
% 68.49/10.21 thf(f868,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f449])).
% 68.49/10.21 thf(f449,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1))))),
% 68.49/10.21 inference(fool_elimination,[],[f448])).
% 68.49/10.21 thf(f448,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1))))),
% 68.49/10.21 inference(rectify,[],[f207])).
% 68.49/10.21 thf(f207,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14)) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)),X14))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_206_l__minus)).
% 68.49/10.21 thf(f3770,plain,(
% 68.49/10.21 spl93_217),
% 68.49/10.21 inference(avatar_split_clause,[],[f1334,f3768])).
% 68.49/10.21 thf(f1334,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK19(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,sK20(X0,X1),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP0(X0,X1),X2)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1119])).
% 68.49/10.21 thf(f3750,plain,(
% 68.49/10.21 spl93_216 | ~spl93_18 | ~spl93_30),
% 68.49/10.21 inference(avatar_split_clause,[],[f1924,f1900,f1812,f3748])).
% 68.49/10.21 thf(f1924,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : ((vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X1) = X0)) ) | (~spl93_18 | ~spl93_30)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1919])).
% 68.49/10.21 thf(f1919,plain,(
% 68.49/10.21 ( ! [X0 : int,X1 : int] : (($true != $true) | (vAPP(int,int,vAPP(int,sTfun(int,int),minus_minus(int),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X0),X1)),X1) = X0)) ) | (~spl93_18 | ~spl93_30)),
% 68.49/10.21 inference(superposition,[],[f1901,f1814])).
% 68.49/10.21 thf(f3715,plain,(
% 68.49/10.21 spl93_215),
% 68.49/10.21 inference(avatar_split_clause,[],[f1426,f3713])).
% 68.49/10.21 thf(f1426,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1036])).
% 68.49/10.21 thf(f1036,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1035])).
% 68.49/10.21 thf(f1035,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f623])).
% 68.49/10.21 thf(f623,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4))))),
% 68.49/10.21 inference(fool_elimination,[],[f622])).
% 68.49/10.21 thf(f622,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)) = X4))))),
% 68.49/10.21 inference(rectify,[],[f228])).
% 68.49/10.21 thf(f228,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X13),X14)) = X14))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_227_abelian__group_Or__neg1)).
% 68.49/10.21 thf(f3711,plain,(
% 68.49/10.21 spl93_214),
% 68.49/10.21 inference(avatar_split_clause,[],[f1425,f3709])).
% 68.49/10.21 thf(f1425,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1034])).
% 68.49/10.21 thf(f1034,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1033])).
% 68.49/10.21 thf(f1033,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f621])).
% 68.49/10.21 thf(f621,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4))))),
% 68.49/10.21 inference(fool_elimination,[],[f620])).
% 68.49/10.21 thf(f620,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X4)) = X4))))),
% 68.49/10.21 inference(rectify,[],[f227])).
% 68.49/10.21 thf(f227,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X13),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)),X14)) = X14))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_226_abelian__group_Or__neg2)).
% 68.49/10.21 thf(f3707,plain,(
% 68.49/10.21 spl93_213),
% 68.49/10.21 inference(avatar_split_clause,[],[f1417,f3705])).
% 68.49/10.21 thf(f1417,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1019])).
% 68.49/10.21 thf(f1019,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1018])).
% 68.49/10.21 thf(f1018,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f605])).
% 68.49/10.21 thf(f605,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3))))))),
% 68.49/10.21 inference(fool_elimination,[],[f604])).
% 68.49/10.21 thf(f604,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X4) | (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = X3))))))),
% 68.49/10.21 inference(rectify,[],[f109])).
% 68.49/10.21 thf(f109,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X6 : X0,X7 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,field(X0,X2),X46) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X6),X7)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X7),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = X7) | (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = X6))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_108_integral)).
% 68.49/10.21 thf(f3703,plain,(
% 68.49/10.21 spl93_212),
% 68.49/10.21 inference(avatar_split_clause,[],[f1362,f3701])).
% 68.49/10.21 thf(f1362,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f925])).
% 68.49/10.21 thf(f925,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f511])).
% 68.49/10.21 thf(f511,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)))),
% 68.49/10.21 inference(fool_elimination,[],[f510])).
% 68.49/10.21 thf(f510,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)),X0)))),
% 68.49/10.21 inference(rectify,[],[f112])).
% 68.49/10.21 thf(f112,axiom,(
% 68.49/10.21 ! [X13 : a,X52 : nat,X53 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13)),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X53),X13)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X52),X53)),X13)))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_111_add_Onat__pow__mult)).
% 68.49/10.21 thf(f3699,plain,(
% 68.49/10.21 spl93_211),
% 68.49/10.21 inference(avatar_split_clause,[],[f1361,f3697])).
% 68.49/10.21 thf(f1361,plain,(
% 68.49/10.21 ( ! [X2 : int,X0 : a,X1 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f924])).
% 68.49/10.21 thf(f924,plain,(
% 68.49/10.21 ! [X0 : a,X1 : int,X2 : int] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f509])).
% 68.49/10.21 thf(f509,plain,(
% 68.49/10.21 ! [X0 : a,X1 : int,X2 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))))),
% 68.49/10.21 inference(fool_elimination,[],[f508])).
% 68.49/10.21 thf(f508,plain,(
% 68.49/10.21 ! [X0 : a,X1 : int,X2 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X1),X2)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X2),X0))))),
% 68.49/10.21 inference(rectify,[],[f98])).
% 68.49/10.21 thf(f98,axiom,(
% 68.49/10.21 ! [X13 : a,X48 : int,X50 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,vAPP(int,sTfun(int,int),plus_plus(int),X48),X50)),X13) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),X13)),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X50),X13))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_add_Oint__pow__mult)).
% 68.49/10.21 thf(f3691,plain,(
% 68.49/10.21 spl93_210),
% 68.49/10.21 inference(avatar_split_clause,[],[f1282,f3689])).
% 68.49/10.21 thf(f1282,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f848])).
% 68.49/10.21 thf(f848,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)))),
% 68.49/10.21 inference(flattening,[],[f847])).
% 68.49/10.21 thf(f847,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)))),
% 68.49/10.21 inference(ennf_transformation,[],[f423])).
% 68.49/10.21 thf(f423,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)))))),
% 68.49/10.21 inference(fool_elimination,[],[f422])).
% 68.49/10.21 thf(f422,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)))))),
% 68.49/10.21 inference(rectify,[],[f181])).
% 68.49/10.21 thf(f181,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),X13) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_Units__inv__comm)).
% 68.49/10.21 thf(f3682,plain,(
% 68.49/10.21 spl93_209),
% 68.49/10.21 inference(avatar_split_clause,[],[f1281,f3680])).
% 68.49/10.21 thf(f1281,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f846])).
% 68.49/10.21 thf(f846,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.21 inference(flattening,[],[f845])).
% 68.49/10.21 thf(f845,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.21 inference(ennf_transformation,[],[f421])).
% 68.49/10.21 thf(f421,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))))),
% 68.49/10.21 inference(fool_elimination,[],[f420])).
% 68.49/10.21 thf(f420,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)))))),
% 68.49/10.21 inference(rectify,[],[f35])).
% 68.49/10.21 thf(f35,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X13)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_add_Oinv__comm)).
% 68.49/10.21 thf(f3669,plain,(
% 68.49/10.21 spl93_208),
% 68.49/10.21 inference(avatar_split_clause,[],[f1412,f3667])).
% 68.49/10.21 thf(f1412,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1009])).
% 68.49/10.21 thf(f1009,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1008])).
% 68.49/10.21 thf(f1008,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (((((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f595])).
% 68.49/10.21 thf(f595,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3))))))),
% 68.49/10.21 inference(fool_elimination,[],[f594])).
% 68.49/10.21 thf(f594,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3))))))),
% 68.49/10.21 inference(rectify,[],[f186])).
% 68.49/10.21 thf(f186,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),X14)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X14),X13))))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_group_Oinv__comm)).
% 68.49/10.21 thf(f3640,plain,(
% 68.49/10.21 spl93_207),
% 68.49/10.21 inference(avatar_split_clause,[],[f1718,f3638])).
% 68.49/10.21 thf(f1718,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(forward_demodulation,[],[f1496,f1493])).
% 68.49/10.21 thf(f1496,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(definition_unfolding,[],[f1304,f1277])).
% 68.49/10.21 thf(f1304,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f887])).
% 68.49/10.21 thf(f887,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f886])).
% 68.49/10.21 thf(f886,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f467])).
% 68.49/10.21 thf(f467,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.21 inference(fool_elimination,[],[f466])).
% 68.49/10.21 thf(f466,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(rectify,[],[f42])).
% 68.49/10.21 thf(f42,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),X13),X14)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_minus__closed)).
% 68.49/10.21 thf(f3636,plain,(
% 68.49/10.21 spl93_206),
% 68.49/10.21 inference(avatar_split_clause,[],[f1431,f3634])).
% 68.49/10.21 thf(f1431,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ((vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK49(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK50(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK51(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK52(X0,X1,X2,X3),X4)))) = X4)) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1163])).
% 68.49/10.21 thf(f1163,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK49(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK50(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK51(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK52(X0,X1,X2,X3),X4)))) = X4)),
% 68.49/10.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52])],[f1045,f1162])).
% 68.49/10.21 thf(f1162,plain,(
% 68.49/10.21 ! [X3 : $tType,X2 : $tType,X1 : $tType,X0 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : (? [X5 : X0,X6 : X1,X7 : X2,X8 : X3] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) = X4) => (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X0,sK49(X0,X1,X2,X3),X4)),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X1,sK50(X0,X1,X2,X3),X4)),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X2,sK51(X0,X1,X2,X3),X4)),vAPP(product_prod(X0,product_prod(X1,product_prod(X2,X3))),X3,sK52(X0,X1,X2,X3),X4)))) = X4))),
% 68.49/10.21 introduced(choice_axiom,[])).
% 68.49/10.21 thf(f1045,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ? [X5 : X0,X6 : X1,X7 : X2,X8 : X3] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) = X4)),
% 68.49/10.21 inference(ennf_transformation,[],[f768])).
% 68.49/10.21 thf(f768,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : $tType,X4 : product_prod(X0,product_prod(X1,product_prod(X2,X3)))] : ~! [X5 : X0,X6 : X1,X7 : X2,X8 : X3] : (vAPP(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3))),vAPP(X0,sTfun(product_prod(X1,product_prod(X2,X3)),product_prod(X0,product_prod(X1,product_prod(X2,X3)))),product_Pair(X0,product_prod(X1,product_prod(X2,X3))),X5),vAPP(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3)),vAPP(X1,sTfun(product_prod(X2,X3),product_prod(X1,product_prod(X2,X3))),product_Pair(X1,product_prod(X2,X3)),X6),vAPP(X3,product_prod(X2,X3),vAPP(X2,sTfun(X3,product_prod(X2,X3)),product_Pair(X2,X3),X7),X8))) != X4)),
% 68.49/10.21 inference(rectify,[],[f65])).
% 68.49/10.21 thf(f65,axiom,(
% 68.49/10.21 ! [X0 : $tType,X2 : $tType,X5 : $tType,X38 : $tType,X14 : product_prod(X0,product_prod(X2,product_prod(X5,X38)))] : ~! [X33 : X0,X34 : X2,X39 : X5,X40 : X38] : (vAPP(product_prod(X2,product_prod(X5,X38)),product_prod(X0,product_prod(X2,product_prod(X5,X38))),vAPP(X0,sTfun(product_prod(X2,product_prod(X5,X38)),product_prod(X0,product_prod(X2,product_prod(X5,X38)))),product_Pair(X0,product_prod(X2,product_prod(X5,X38))),X33),vAPP(product_prod(X5,X38),product_prod(X2,product_prod(X5,X38)),vAPP(X2,sTfun(product_prod(X5,X38),product_prod(X2,product_prod(X5,X38))),product_Pair(X2,product_prod(X5,X38)),X34),vAPP(X38,product_prod(X5,X38),vAPP(X5,sTfun(X38,product_prod(X5,X38)),product_Pair(X5,X38),X39),X40))) != X14)),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_prod__cases4)).
% 68.49/10.21 thf(f3628,plain,(
% 68.49/10.21 spl93_205),
% 68.49/10.21 inference(avatar_split_clause,[],[f1422,f3626])).
% 68.49/10.21 thf(f3626,plain,(
% 68.49/10.21 spl93_205 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_205])])).
% 68.49/10.21 thf(f1422,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1028])).
% 68.49/10.21 thf(f1028,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1027])).
% 68.49/10.21 thf(f1027,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (((((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f615])).
% 68.49/10.21 thf(f615,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4) = X3)))))),
% 68.49/10.21 inference(fool_elimination,[],[f614])).
% 68.49/10.21 thf(f614,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X4) = X3)))))),
% 68.49/10.21 inference(rectify,[],[f232])).
% 68.49/10.21 thf(f232,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X14 : X0,X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X14),X13)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13) = X14)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_abelian__group_Ominus__equality)).
% 68.49/10.21 thf(f3624,plain,(
% 68.49/10.21 spl93_204),
% 68.49/10.21 inference(avatar_split_clause,[],[f1365,f3622])).
% 68.49/10.21 thf(f1365,plain,(
% 68.49/10.21 ( ! [X2 : nat,X0 : a,X1 : nat] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0)) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f929])).
% 68.49/10.21 thf(f929,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0)) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f928])).
% 68.49/10.21 thf(f928,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0)) | (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) != vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f517])).
% 68.49/10.21 thf(f517,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0))))),
% 68.49/10.21 inference(fool_elimination,[],[f516])).
% 68.49/10.21 thf(f516,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat,X2 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X2),X0)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)),X0))))),
% 68.49/10.21 inference(rectify,[],[f114])).
% 68.49/10.21 thf(f114,axiom,(
% 68.49/10.21 ! [X13 : a,X53 : nat,X52 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X53),X13)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X53),X52)),X13))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_113_add_Opow__eq__div2)).
% 68.49/10.21 thf(f3612,plain,(
% 68.49/10.21 spl93_203),
% 68.49/10.21 inference(avatar_split_clause,[],[f1420,f3610])).
% 68.49/10.21 thf(f1420,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1025])).
% 68.49/10.21 thf(f1025,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1024])).
% 68.49/10.21 thf(f1024,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (((($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f611])).
% 68.49/10.21 thf(f611,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f610])).
% 68.49/10.21 thf(f610,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 inference(rectify,[],[f90])).
% 68.49/10.21 thf(f90,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X13),X14)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_semiring_Osemiring__simprules_I3_J)).
% 68.49/10.21 thf(f3592,plain,(
% 68.49/10.21 spl93_202),
% 68.49/10.21 inference(avatar_split_clause,[],[f1430,f3590])).
% 68.49/10.21 thf(f1430,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1044])).
% 68.49/10.21 thf(f1044,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1043])).
% 68.49/10.21 thf(f1043,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (((($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f631])).
% 68.49/10.21 thf(f631,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f630])).
% 68.49/10.21 thf(f630,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 inference(rectify,[],[f119])).
% 68.49/10.21 thf(f119,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_118_abelian__groupE_I1_J)).
% 68.49/10.21 thf(f3588,plain,(
% 68.49/10.21 spl93_201),
% 68.49/10.21 inference(avatar_split_clause,[],[f1419,f3586])).
% 68.49/10.21 thf(f1419,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1023])).
% 68.49/10.21 thf(f1023,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1022])).
% 68.49/10.21 thf(f1022,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (((($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f609])).
% 68.49/10.21 thf(f609,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))))),
% 68.49/10.21 inference(fool_elimination,[],[f608])).
% 68.49/10.21 thf(f608,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.21 inference(rectify,[],[f92])).
% 68.49/10.21 thf(f92,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_semiring_Osemiring__simprules_I1_J)).
% 68.49/10.21 thf(f3568,plain,(
% 68.49/10.21 spl93_200 | ~spl93_14 | ~spl93_28),
% 68.49/10.21 inference(avatar_split_clause,[],[f1894,f1886,f1792,f3565])).
% 68.49/10.21 thf(f3565,plain,(
% 68.49/10.21 spl93_200 <=> (plus_plus(int) = vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(int,int)),cCOMB,plus_plus(int)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_200])])).
% 68.49/10.21 thf(f1894,plain,(
% 68.49/10.21 (plus_plus(int) = vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(int,int)),cCOMB,plus_plus(int))) | (~spl93_14 | ~spl93_28)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1889])).
% 68.49/10.21 thf(f1889,plain,(
% 68.49/10.21 ($true != $true) | (plus_plus(int) = vAPP(sTfun(int,sTfun(int,int)),sTfun(int,sTfun(int,int)),cCOMB,plus_plus(int))) | (~spl93_14 | ~spl93_28)),
% 68.49/10.21 inference(superposition,[],[f1887,f1794])).
% 68.49/10.21 thf(f3563,plain,(
% 68.49/10.21 spl93_199),
% 68.49/10.21 inference(avatar_split_clause,[],[f1293,f3561])).
% 68.49/10.21 thf(f1293,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f865])).
% 68.49/10.21 thf(f865,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f864])).
% 68.49/10.21 thf(f864,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f445])).
% 68.49/10.21 thf(f445,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1)))),
% 68.49/10.21 inference(fool_elimination,[],[f444])).
% 68.49/10.21 thf(f444,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) = X1)))),
% 68.49/10.21 inference(rectify,[],[f198])).
% 68.49/10.21 thf(f198,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)) = X14)))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_r__neg1)).
% 68.49/10.21 thf(f3559,plain,(
% 68.49/10.21 spl93_198),
% 68.49/10.21 inference(avatar_split_clause,[],[f1292,f3557])).
% 68.49/10.21 thf(f1292,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f863])).
% 68.49/10.21 thf(f863,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f862])).
% 68.49/10.21 thf(f862,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f443])).
% 68.49/10.21 thf(f443,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1)))),
% 68.49/10.21 inference(fool_elimination,[],[f442])).
% 68.49/10.21 thf(f442,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X1)) = X1)))),
% 68.49/10.21 inference(rectify,[],[f197])).
% 68.49/10.21 thf(f197,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)),X14)) = X14)))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_r__neg2)).
% 68.49/10.21 thf(f3539,plain,(
% 68.49/10.21 spl93_197),
% 68.49/10.21 inference(avatar_split_clause,[],[f1424,f3537])).
% 68.49/10.21 thf(f1424,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1032])).
% 68.49/10.21 thf(f1032,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1031])).
% 68.49/10.21 thf(f1031,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f619])).
% 68.49/10.21 thf(f619,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)))))),
% 68.49/10.21 inference(fool_elimination,[],[f618])).
% 68.49/10.21 thf(f618,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)))))),
% 68.49/10.21 inference(rectify,[],[f121])).
% 68.49/10.21 thf(f121,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X14),X13)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_abelian__groupE_I4_J)).
% 68.49/10.21 thf(f3535,plain,(
% 68.49/10.21 spl93_196),
% 68.49/10.21 inference(avatar_split_clause,[],[f1418,f3533])).
% 68.49/10.21 thf(f1418,plain,(
% 68.49/10.21 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f1021])).
% 68.49/10.21 thf(f1021,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(flattening,[],[f1020])).
% 68.49/10.21 thf(f1020,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.21 inference(ennf_transformation,[],[f607])).
% 68.49/10.21 thf(f607,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)))))),
% 68.49/10.21 inference(fool_elimination,[],[f606])).
% 68.49/10.21 thf(f606,plain,(
% 68.49/10.21 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)))))),
% 68.49/10.21 inference(rectify,[],[f94])).
% 68.49/10.21 thf(f94,axiom,(
% 68.49/10.21 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X14),X13)))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_semiring_Osemiring__simprules_I7_J)).
% 68.49/10.21 thf(f3530,plain,(
% 68.49/10.21 spl93_195),
% 68.49/10.21 inference(avatar_split_clause,[],[f1280,f3528])).
% 68.49/10.21 thf(f1280,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f844])).
% 68.49/10.21 thf(f844,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.21 inference(flattening,[],[f843])).
% 68.49/10.21 thf(f843,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)))),
% 68.49/10.21 inference(ennf_transformation,[],[f419])).
% 68.49/10.21 thf(f419,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0))))),
% 68.49/10.21 inference(fool_elimination,[],[f418])).
% 68.49/10.21 thf(f418,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X1) = X0))))),
% 68.49/10.21 inference(rectify,[],[f213])).
% 68.49/10.21 thf(f213,axiom,(
% 68.49/10.21 ! [X14 : a,X13 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X13)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13) = X14))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_minus__equality)).
% 68.49/10.21 thf(f3518,plain,(
% 68.49/10.21 spl93_194),
% 68.49/10.21 inference(avatar_split_clause,[],[f1306,f3516])).
% 68.49/10.21 thf(f1306,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f891])).
% 68.49/10.21 thf(f891,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(flattening,[],[f890])).
% 68.49/10.21 thf(f890,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : ((($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f471])).
% 68.49/10.21 thf(f471,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.21 inference(fool_elimination,[],[f470])).
% 68.49/10.21 thf(f470,plain,(
% 68.49/10.21 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(rectify,[],[f41])).
% 68.49/10.21 thf(f41,axiom,(
% 68.49/10.21 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_semiring__simprules_I3_J)).
% 68.49/10.21 thf(f3514,plain,(
% 68.49/10.21 spl93_193 | ~spl93_15 | ~spl93_28),
% 68.49/10.21 inference(avatar_split_clause,[],[f1893,f1886,f1797,f3511])).
% 68.49/10.21 thf(f3511,plain,(
% 68.49/10.21 spl93_193 <=> (plus_plus(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus(nat)))),
% 68.49/10.21 introduced(avatar_definition,[new_symbols(naming,[spl93_193])])).
% 68.49/10.21 thf(f1893,plain,(
% 68.49/10.21 (plus_plus(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus(nat))) | (~spl93_15 | ~spl93_28)),
% 68.49/10.21 inference(trivial_inequality_removal,[],[f1890])).
% 68.49/10.21 thf(f1890,plain,(
% 68.49/10.21 ($true != $true) | (plus_plus(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus(nat))) | (~spl93_15 | ~spl93_28)),
% 68.49/10.21 inference(superposition,[],[f1887,f1799])).
% 68.49/10.21 thf(f3485,plain,(
% 68.49/10.21 spl93_192),
% 68.49/10.21 inference(avatar_split_clause,[],[f1289,f3483])).
% 68.49/10.21 thf(f1289,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.21 inference(cnf_transformation,[],[f857])).
% 68.49/10.21 thf(f857,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.21 inference(ennf_transformation,[],[f437])).
% 68.49/10.21 thf(f437,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.21 inference(fool_elimination,[],[f436])).
% 68.49/10.21 thf(f436,plain,(
% 68.49/10.21 ! [X0 : a,X1 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.21 inference(rectify,[],[f208])).
% 68.49/10.21 thf(f208,axiom,(
% 68.49/10.21 ! [X13 : a,X48 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X48),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X48),X13))))),
% 68.49/10.21 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_207_add_Onat__pow__inv)).
% 68.49/10.21 thf(f3481,plain,(
% 68.49/10.21 spl93_191),
% 68.49/10.21 inference(avatar_split_clause,[],[f1288,f3479])).
% 68.49/10.21 thf(f1288,plain,(
% 68.49/10.21 ( ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f856])).
% 68.49/10.22 thf(f856,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f435])).
% 68.49/10.22 thf(f435,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f434])).
% 68.49/10.22 thf(f434,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.22 inference(rectify,[],[f209])).
% 68.49/10.22 thf(f209,axiom,(
% 68.49/10.22 ! [X13 : a,X48 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_208_add_Oint__pow__inv)).
% 68.49/10.22 thf(f3461,plain,(
% 68.49/10.22 spl93_190),
% 68.49/10.22 inference(avatar_split_clause,[],[f1305,f3459])).
% 68.49/10.22 thf(f1305,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f889])).
% 68.49/10.22 thf(f889,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(flattening,[],[f888])).
% 68.49/10.22 thf(f888,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : ((($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f469])).
% 68.49/10.22 thf(f469,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 inference(fool_elimination,[],[f468])).
% 68.49/10.22 thf(f468,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(rectify,[],[f39])).
% 68.49/10.22 thf(f39,axiom,(
% 68.49/10.22 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_add_Om__closed)).
% 68.49/10.22 thf(f3457,plain,(
% 68.49/10.22 spl93_189),
% 68.49/10.22 inference(avatar_split_clause,[],[f1291,f3455])).
% 68.49/10.22 thf(f1291,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f861])).
% 68.49/10.22 thf(f861,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(flattening,[],[f860])).
% 68.49/10.22 thf(f860,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f441])).
% 68.49/10.22 thf(f441,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f440])).
% 68.49/10.22 thf(f440,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0))))),
% 68.49/10.22 inference(rectify,[],[f25])).
% 68.49/10.22 thf(f25,axiom,(
% 68.49/10.22 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X14),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_m__comm)).
% 68.49/10.22 thf(f3445,plain,(
% 68.49/10.22 spl93_188),
% 68.49/10.22 inference(avatar_split_clause,[],[f1411,f3443])).
% 68.49/10.22 thf(f1411,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1007])).
% 68.49/10.22 thf(f1007,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f1006])).
% 68.49/10.22 thf(f1006,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (((($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f593])).
% 68.49/10.22 thf(f593,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))))),
% 68.49/10.22 inference(fool_elimination,[],[f592])).
% 68.49/10.22 thf(f592,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.22 inference(rectify,[],[f254])).
% 68.49/10.22 thf(f254,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),X14)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_253_comm__groupE_I1_J)).
% 68.49/10.22 thf(f3430,plain,(
% 68.49/10.22 spl93_187),
% 68.49/10.22 inference(avatar_split_clause,[],[f1410,f3428])).
% 68.49/10.22 thf(f1410,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1005])).
% 68.49/10.22 thf(f1005,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f1004])).
% 68.49/10.22 thf(f1004,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : ((((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f591])).
% 68.49/10.22 thf(f591,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)))))),
% 68.49/10.22 inference(fool_elimination,[],[f590])).
% 68.49/10.22 thf(f590,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1,X4 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)))))),
% 68.49/10.22 inference(rectify,[],[f252])).
% 68.49/10.22 thf(f252,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0,X14 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X14),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),X14) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X14),X13)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_251_comm__groupE_I4_J)).
% 68.49/10.22 thf(f3412,plain,(
% 68.49/10.22 spl93_186),
% 68.49/10.22 inference(avatar_split_clause,[],[f1290,f3410])).
% 68.49/10.22 thf(f1290,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f859])).
% 68.49/10.22 thf(f859,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(flattening,[],[f858])).
% 68.49/10.22 thf(f858,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f439])).
% 68.49/10.22 thf(f439,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f438])).
% 68.49/10.22 thf(f438,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0))))),
% 68.49/10.22 inference(rectify,[],[f28])).
% 68.49/10.22 thf(f28,axiom,(
% 68.49/10.22 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X14) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X14),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_add_Om__comm)).
% 68.49/10.22 thf(f3408,plain,(
% 68.49/10.22 spl93_185),
% 68.49/10.22 inference(avatar_split_clause,[],[f1284,f3406])).
% 68.49/10.22 thf(f1284,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f852])).
% 68.49/10.22 thf(f852,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(flattening,[],[f851])).
% 68.49/10.22 thf(f851,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : ((($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f427])).
% 68.49/10.22 thf(f427,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))))),
% 68.49/10.22 inference(fool_elimination,[],[f426])).
% 68.49/10.22 thf(f426,plain,(
% 68.49/10.22 ! [X0 : a,X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(rectify,[],[f182])).
% 68.49/10.22 thf(f182,axiom,(
% 68.49/10.22 ! [X13 : a,X14 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X14),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X14)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_Units__m__closed)).
% 68.49/10.22 thf(f3394,plain,(
% 68.49/10.22 spl93_184),
% 68.49/10.22 inference(avatar_split_clause,[],[f1287,f3392])).
% 68.49/10.22 thf(f1287,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f855])).
% 68.49/10.22 thf(f855,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f433])).
% 68.49/10.22 thf(f433,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f432])).
% 68.49/10.22 thf(f432,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X1)),X0) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.22 inference(rectify,[],[f113])).
% 68.49/10.22 thf(f113,axiom,(
% 68.49/10.22 ! [X13 : a,X52 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X52)),X13) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_add_Onat__pow__Suc2)).
% 68.49/10.22 thf(f3390,plain,(
% 68.49/10.22 spl93_183),
% 68.49/10.22 inference(avatar_split_clause,[],[f1489,f3387])).
% 68.49/10.22 thf(f1489,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f735])).
% 68.49/10.22 thf(f735,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f734])).
% 68.49/10.22 thf(f734,plain,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(rectify,[],[f11])).
% 68.49/10.22 thf(f11,axiom,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_f5)).
% 68.49/10.22 thf(f3385,plain,(
% 68.49/10.22 spl93_182),
% 68.49/10.22 inference(avatar_split_clause,[],[f1488,f3382])).
% 68.49/10.22 thf(f1488,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f733])).
% 68.49/10.22 thf(f733,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f732])).
% 68.49/10.22 thf(f732,plain,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(rectify,[],[f12])).
% 68.49/10.22 thf(f12,axiom,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_f4)).
% 68.49/10.22 thf(f3363,plain,(
% 68.49/10.22 spl93_181),
% 68.49/10.22 inference(avatar_split_clause,[],[f1340,f3361])).
% 68.49/10.22 thf(f1340,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1124])).
% 68.49/10.22 thf(f1124,plain,(
% 68.49/10.22 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X1 : $tType,X2 : $tType] : ((((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21,sK22])],[f1121,f1123,f1122])).
% 68.49/10.22 thf(f1122,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X3 : X2] : (? [X4 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),X4) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),X3)) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => (? [X4 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),X4) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1123,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X4 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),X4) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1121,plain,(
% 68.49/10.22 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X1 : $tType,X2 : $tType] : (? [X3 : X2] : (? [X4 : X2] : ((vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),X4) != vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X4),X3)) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0)))),
% 68.49/10.22 inference(rectify,[],[f1120])).
% 68.49/10.22 thf(f1120,plain,(
% 68.49/10.22 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0 : $tType,X1 : $tType] : (? [X8 : X1] : (? [X9 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X8),X9) != vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X9),X8)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X9),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X8),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP4(X0,X1),X2)))),
% 68.49/10.22 inference(nnf_transformation,[],[f1085])).
% 68.49/10.22 thf(f3359,plain,(
% 68.49/10.22 spl93_180),
% 68.49/10.22 inference(avatar_split_clause,[],[f1286,f3357])).
% 68.49/10.22 thf(f1286,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f854])).
% 68.49/10.22 thf(f854,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : ((vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f431])).
% 68.49/10.22 thf(f431,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f430])).
% 68.49/10.22 thf(f430,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X1))),X0) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0))))),
% 68.49/10.22 inference(rectify,[],[f248])).
% 68.49/10.22 thf(f248,axiom,(
% 68.49/10.22 ! [X13 : a,X52 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),vAPP(nat,int,semiring_1_of_nat(int),X52))),X13) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_247_add_Oint__pow__neg__int)).
% 68.49/10.22 thf(f3331,plain,(
% 68.49/10.22 spl93_179),
% 68.49/10.22 inference(avatar_split_clause,[],[f1404,f3329])).
% 68.49/10.22 thf(f1404,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1157])).
% 68.49/10.22 thf(f1157,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f995,f1156])).
% 68.49/10.22 thf(f1156,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f995,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f994])).
% 68.49/10.22 thf(f994,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f581])).
% 68.49/10.22 thf(f581,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))))),
% 68.49/10.22 inference(fool_elimination,[],[f580])).
% 68.49/10.22 thf(f580,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => ? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X4),X3)) & vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.22 inference(rectify,[],[f126])).
% 68.49/10.22 thf(f126,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => ? [X23 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X23),X13)) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_125_abelian__groupE_I6_J)).
% 68.49/10.22 thf(f3312,plain,(
% 68.49/10.22 spl93_178 | ~spl93_53 | ~spl93_74 | ~spl93_177),
% 68.49/10.22 inference(avatar_split_clause,[],[f3308,f3305,f2247,f2074,f3310])).
% 68.49/10.22 thf(f3308,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : int] : (($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0))) ) | (~spl93_53 | ~spl93_74 | ~spl93_177)),
% 68.49/10.22 inference(forward_demodulation,[],[f3306,f2300])).
% 68.49/10.22 thf(f3307,plain,(
% 68.49/10.22 spl93_177),
% 68.49/10.22 inference(avatar_split_clause,[],[f1285,f3305])).
% 68.49/10.22 thf(f1285,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f853])).
% 68.49/10.22 thf(f853,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f429])).
% 68.49/10.22 thf(f429,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)))),
% 68.49/10.22 inference(fool_elimination,[],[f428])).
% 68.49/10.22 thf(f428,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X1)),X0)))),
% 68.49/10.22 inference(rectify,[],[f235])).
% 68.49/10.22 thf(f235,axiom,(
% 68.49/10.22 ! [X13 : a,X48 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),X13)) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),vAPP(int,int,uminus_uminus(int),X48)),X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_add_Oint__pow__neg)).
% 68.49/10.22 thf(f3295,plain,(
% 68.49/10.22 spl93_176),
% 68.49/10.22 inference(avatar_split_clause,[],[f1227,f3293])).
% 68.49/10.22 thf(f1227,plain,(
% 68.49/10.22 ( ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f806])).
% 68.49/10.22 thf(f806,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f343])).
% 68.49/10.22 thf(f343,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => (minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f342])).
% 68.49/10.22 thf(f342,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => (minus_minus(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))))))),
% 68.49/10.22 inference(rectify,[],[f243])).
% 68.49/10.22 thf(f243,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => (minus_minus(X0) = (^[X60 : X0, X61 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X60),vAPP(X0,X0,uminus_uminus(X0),X61))))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_diff__conv__add__uminus)).
% 68.49/10.22 thf(f3291,plain,(
% 68.49/10.22 spl93_175),
% 68.49/10.22 inference(avatar_split_clause,[],[f1219,f3289])).
% 68.49/10.22 thf(f1219,plain,(
% 68.49/10.22 ( ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f798])).
% 68.49/10.22 thf(f798,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f327])).
% 68.49/10.22 thf(f327,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => (minus_minus(X0) = vAPP(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0)),vAPP(sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,X0))),cCOMB,vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0))),vAPP(sTfun(sTfun(X0,X0),sTfun(sTfun(X0,X0),sTfun(X0,X0))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(sTfun(X0,X0),sTfun(X0,X0)))),bCOMB,bCOMB),plus_plus(X0))),uminus_uminus(X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f326])).
% 68.49/10.22 thf(f326,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => (minus_minus(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))))))),
% 68.49/10.22 inference(rectify,[],[f244])).
% 68.49/10.22 thf(f244,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => (minus_minus(X0) = (^[X60 : X0, X61 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X60),vAPP(X0,X0,uminus_uminus(X0),X61))))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_ab__group__add__class_Oab__diff__conv__add__uminus)).
% 68.49/10.22 thf(f3269,plain,(
% 68.49/10.22 spl93_174),
% 68.49/10.22 inference(avatar_split_clause,[],[f1402,f3267])).
% 68.49/10.22 thf(f1402,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f993])).
% 68.49/10.22 thf(f993,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f992])).
% 68.49/10.22 thf(f992,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f579])).
% 68.49/10.22 thf(f579,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3))))),
% 68.49/10.22 inference(fool_elimination,[],[f578])).
% 68.49/10.22 thf(f578,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),X3))))),
% 68.49/10.22 inference(rectify,[],[f230])).
% 68.49/10.22 thf(f230,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_229_abelian__group_Ol__neg)).
% 68.49/10.22 thf(f3265,plain,(
% 68.49/10.22 spl93_173),
% 68.49/10.22 inference(avatar_split_clause,[],[f1401,f3263])).
% 68.49/10.22 thf(f1401,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f991])).
% 68.49/10.22 thf(f991,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f990])).
% 68.49/10.22 thf(f990,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f577])).
% 68.49/10.22 thf(f577,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)))))),
% 68.49/10.22 inference(fool_elimination,[],[f576])).
% 68.49/10.22 thf(f576,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)))))),
% 68.49/10.22 inference(rectify,[],[f231])).
% 68.49/10.22 thf(f231,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X54),X13),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_230_abelian__group_Or__neg)).
% 68.49/10.22 thf(f3259,plain,(
% 68.49/10.22 spl93_172 | ~spl93_22 | ~spl93_136),
% 68.49/10.22 inference(avatar_split_clause,[],[f3086,f2791,f1832,f3257])).
% 68.49/10.22 thf(f3257,plain,(
% 68.49/10.22 spl93_172 <=> ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,semiring_1_of_nat($o),X1)) | (X0 = X1) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X0)))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_172])])).
% 68.49/10.22 thf(f2791,plain,(
% 68.49/10.22 spl93_136 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,semiring_1_of_nat($o),X1)) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X0)) | (X0 = X1))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_136])])).
% 68.49/10.22 thf(f3086,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,semiring_1_of_nat($o),X1)) | (X0 = X1) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X0))) ) | (~spl93_22 | ~spl93_136)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f3085])).
% 68.49/10.22 thf(f3085,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X1)) | (X0 = X1) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X0))) ) | (~spl93_22 | ~spl93_136)),
% 68.49/10.22 inference(superposition,[],[f2792,f1833])).
% 68.49/10.22 thf(f2792,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,semiring_1_of_nat($o),X1)) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X0)) | (X0 = X1)) ) | ~spl93_136),
% 68.49/10.22 inference(avatar_component_clause,[],[f2791])).
% 68.49/10.22 thf(f3238,plain,(
% 68.49/10.22 spl93_171),
% 68.49/10.22 inference(avatar_split_clause,[],[f1403,f3236])).
% 68.49/10.22 thf(f1403,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1),sK42(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1157])).
% 68.49/10.22 thf(f3203,plain,(
% 68.49/10.22 spl93_170),
% 68.49/10.22 inference(avatar_split_clause,[],[f1409,f3201])).
% 68.49/10.22 thf(f1409,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK46(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X2),X3)))))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1161])).
% 68.49/10.22 thf(f1161,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK46(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X2),X3))))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK46,sK47,sK48])],[f1003,f1160])).
% 68.49/10.22 thf(f1160,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o] : (? [X5 : X2,X6 : X1,X7 : X0] : ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))) => ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X2,sK46(X0,X1,X2),X3)),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X1,sK47(X0,X1,X2),X3)),vAPP(sTfun(product_prod(X2,product_prod(X1,X0)),$o),X0,sK48(X0,X1,X2),X3))))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1003,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)) | ? [X5 : X2,X6 : X1,X7 : X0] : ($true != vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))))),
% 68.49/10.22 inference(ennf_transformation,[],[f589])).
% 68.49/10.22 thf(f589,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (! [X5 : X2,X6 : X1,X7 : X0] : ($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7)))) => ($true = vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4)))),
% 68.49/10.22 inference(fool_elimination,[],[f588])).
% 68.49/10.22 thf(f588,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X2,product_prod(X1,X0)) > $o,X4 : product_prod(X2,product_prod(X1,X0))] : (! [X5 : X2,X6 : X1,X7 : X0] : vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,vAPP(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0)),vAPP(X2,sTfun(product_prod(X1,X0),product_prod(X2,product_prod(X1,X0))),product_Pair(X2,product_prod(X1,X0)),X5),vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X6),X7))) => vAPP(product_prod(X2,product_prod(X1,X0)),$o,X3,X4))),
% 68.49/10.22 inference(rectify,[],[f61])).
% 68.49/10.22 thf(f61,axiom,(
% 68.49/10.22 ! [X5 : $tType,X2 : $tType,X0 : $tType,X26 : product_prod(X0,product_prod(X2,X5)) > $o,X13 : product_prod(X0,product_prod(X2,X5))] : (! [X33 : X0,X34 : X2,X39 : X5] : vAPP(product_prod(X0,product_prod(X2,X5)),$o,X26,vAPP(product_prod(X2,X5),product_prod(X0,product_prod(X2,X5)),vAPP(X0,sTfun(product_prod(X2,X5),product_prod(X0,product_prod(X2,X5))),product_Pair(X0,product_prod(X2,X5)),X33),vAPP(X5,product_prod(X2,X5),vAPP(X2,sTfun(X5,product_prod(X2,X5)),product_Pair(X2,X5),X34),X39))) => vAPP(product_prod(X0,product_prod(X2,X5)),$o,X26,X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_prod__induct3)).
% 68.49/10.22 thf(f3199,plain,(
% 68.49/10.22 spl93_169),
% 68.49/10.22 inference(avatar_split_clause,[],[f1398,f3197])).
% 68.49/10.22 thf(f1398,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f985])).
% 68.49/10.22 thf(f985,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f984])).
% 68.49/10.22 thf(f984,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f571])).
% 68.49/10.22 thf(f571,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3))))),
% 68.49/10.22 inference(fool_elimination,[],[f570])).
% 68.49/10.22 thf(f570,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3))))),
% 68.49/10.22 inference(rectify,[],[f73])).
% 68.49/10.22 thf(f73,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_semiring_Ol__null)).
% 68.49/10.22 thf(f3195,plain,(
% 68.49/10.22 spl93_168),
% 68.49/10.22 inference(avatar_split_clause,[],[f1397,f3193])).
% 68.49/10.22 thf(f1397,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f983])).
% 68.49/10.22 thf(f983,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f982])).
% 68.49/10.22 thf(f982,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f569])).
% 68.49/10.22 thf(f569,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)))))),
% 68.49/10.22 inference(fool_elimination,[],[f568])).
% 68.49/10.22 thf(f568,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)))))),
% 68.49/10.22 inference(rectify,[],[f74])).
% 68.49/10.22 thf(f74,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_semiring_Or__null)).
% 68.49/10.22 thf(f3149,plain,(
% 68.49/10.22 spl93_167),
% 68.49/10.22 inference(avatar_split_clause,[],[f1405,f3147])).
% 68.49/10.22 thf(f1405,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f997])).
% 68.49/10.22 thf(f997,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f996])).
% 68.49/10.22 thf(f996,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f583])).
% 68.49/10.22 thf(f583,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))))),
% 68.49/10.22 inference(fool_elimination,[],[f582])).
% 68.49/10.22 thf(f582,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))),
% 68.49/10.22 inference(rectify,[],[f222])).
% 68.49/10.22 thf(f222,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_221_abelian__group_Oa__inv__closed)).
% 68.49/10.22 thf(f3145,plain,(
% 68.49/10.22 spl93_166),
% 68.49/10.22 inference(avatar_split_clause,[],[f1393,f3143])).
% 68.49/10.22 thf(f1393,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1155])).
% 68.49/10.22 thf(f1155,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f975,f1154])).
% 68.49/10.22 thf(f1154,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (? [X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f975,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (? [X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f974])).
% 68.49/10.22 thf(f974,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : ((? [X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f561])).
% 68.49/10.22 thf(f561,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ? [X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))))),
% 68.49/10.22 inference(fool_elimination,[],[f560])).
% 68.49/10.22 thf(f560,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ? [X4 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)) & vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.22 inference(rectify,[],[f194])).
% 68.49/10.22 thf(f194,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ? [X23 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X13),X23)) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_193_group_Or__inv__ex)).
% 68.49/10.22 thf(f3141,plain,(
% 68.49/10.22 spl93_165),
% 68.49/10.22 inference(avatar_split_clause,[],[f1391,f3139])).
% 68.49/10.22 thf(f1391,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),X3)) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1153])).
% 68.49/10.22 thf(f1153,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f973,f1152])).
% 68.49/10.22 thf(f1152,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) => ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f973,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f972])).
% 68.49/10.22 thf(f972,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : ((? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f559])).
% 68.49/10.22 thf(f559,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) => ? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))))),
% 68.49/10.22 inference(fool_elimination,[],[f558])).
% 68.49/10.22 thf(f558,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)) => ? [X4 : X1] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X4),X3)) & vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))))),
% 68.49/10.22 inference(rectify,[],[f187])).
% 68.49/10.22 thf(f187,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)) => ? [X23 : X0] : ((vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54),X23),X13)) & vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X23),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_186_group_Ol__inv__ex)).
% 68.49/10.22 thf(f3132,plain,(
% 68.49/10.22 spl93_164),
% 68.49/10.22 inference(avatar_split_clause,[],[f1343,f3130])).
% 68.49/10.22 thf(f1343,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1129])).
% 68.49/10.22 thf(f1129,plain,(
% 68.49/10.22 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X1 : $tType,X2 : $tType] : (((($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24])],[f1126,f1128,f1127])).
% 68.49/10.22 thf(f1127,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X3 : X2] : (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1128,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) => (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1126,plain,(
% 68.49/10.22 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X1 : $tType,X2 : $tType] : (? [X3 : X2] : (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),sTfun(X2,sTfun(X2,X2)),add(X2,X1),X0),X3),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0)))),
% 68.49/10.22 inference(rectify,[],[f1125])).
% 68.49/10.22 thf(f1125,plain,(
% 68.49/10.22 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X0 : $tType,X1 : $tType] : (? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,sP3(X0,X1),X2)))),
% 68.49/10.22 inference(nnf_transformation,[],[f1084])).
% 68.49/10.22 thf(f3102,plain,(
% 68.49/10.22 ~spl93_74 | ~spl93_84),
% 68.49/10.22 inference(avatar_contradiction_clause,[],[f3101])).
% 68.49/10.22 thf(f3101,plain,(
% 68.49/10.22 $false | (~spl93_74 | ~spl93_84)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f3100])).
% 68.49/10.22 thf(f3100,plain,(
% 68.49/10.22 ($true = $false) | (~spl93_74 | ~spl93_84)),
% 68.49/10.22 inference(forward_demodulation,[],[f2249,f2297])).
% 68.49/10.22 thf(f2297,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $false) | ~spl93_84),
% 68.49/10.22 inference(avatar_component_clause,[],[f2295])).
% 68.49/10.22 thf(f2295,plain,(
% 68.49/10.22 spl93_84 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $false)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_84])])).
% 68.49/10.22 thf(f3098,plain,(
% 68.49/10.22 spl93_163 | spl93_74),
% 68.49/10.22 inference(avatar_split_clause,[],[f1195,f2247,f3096])).
% 68.49/10.22 thf(f3096,plain,(
% 68.49/10.22 spl93_163 <=> ! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_163])])).
% 68.49/10.22 thf(f1195,plain,(
% 68.49/10.22 ( ! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1090])).
% 68.49/10.22 thf(f1090,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true) | (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f776,f1089])).
% 68.49/10.22 thf(f1089,plain,(
% 68.49/10.22 ? [X0 : a] : (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),sK6)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f776,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true) | ? [X0 : a] : (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f285])).
% 68.49/10.22 thf(f285,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f284])).
% 68.49/10.22 thf(f284,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r)),
% 68.49/10.22 inference(rectify,[],[f179])).
% 68.49/10.22 thf(f179,axiom,(
% 68.49/10.22 ! [X23 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ? [X56 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X56),X23)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X56),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_178_group__l__invI)).
% 68.49/10.22 thf(f3066,plain,(
% 68.49/10.22 spl93_162),
% 68.49/10.22 inference(avatar_split_clause,[],[f1396,f3064])).
% 68.49/10.22 thf(f1396,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f981])).
% 68.49/10.22 thf(f981,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f980])).
% 68.49/10.22 thf(f980,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f567])).
% 68.49/10.22 thf(f567,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f566])).
% 68.49/10.22 thf(f566,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),mult(X1,ring_ext(X1,X0)),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),X3) = X3)))),
% 68.49/10.22 inference(rectify,[],[f89])).
% 68.49/10.22 thf(f89,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),mult(X0,ring_ext(X0,X2)),X46),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,one(X0,ring_ext(X0,X2)),X46)),X13) = X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_semiring_Osemiring__simprules_I9_J)).
% 68.49/10.22 thf(f3062,plain,(
% 68.49/10.22 spl93_161),
% 68.49/10.22 inference(avatar_split_clause,[],[f1308,f3060])).
% 68.49/10.22 thf(f1308,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f893])).
% 68.49/10.22 thf(f893,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f475])).
% 68.49/10.22 thf(f475,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(fool_elimination,[],[f474])).
% 68.49/10.22 thf(f474,plain,(
% 68.49/10.22 ! [X0 : a,X1 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 inference(rectify,[],[f106])).
% 68.49/10.22 thf(f106,axiom,(
% 68.49/10.22 ! [X13 : a,X52 : nat] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_105_add_Onat__pow__closed)).
% 68.49/10.22 thf(f3058,plain,(
% 68.49/10.22 spl93_160),
% 68.49/10.22 inference(avatar_split_clause,[],[f1307,f3056])).
% 68.49/10.22 thf(f1307,plain,(
% 68.49/10.22 ( ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f892])).
% 68.49/10.22 thf(f892,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f473])).
% 68.49/10.22 thf(f473,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(fool_elimination,[],[f472])).
% 68.49/10.22 thf(f472,plain,(
% 68.49/10.22 ! [X0 : a,X1 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X1),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 inference(rectify,[],[f84])).
% 68.49/10.22 thf(f84,axiom,(
% 68.49/10.22 ! [X13 : a,X48 : int] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X48),X13)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_add_Oint__pow__closed)).
% 68.49/10.22 thf(f3036,plain,(
% 68.49/10.22 spl93_159),
% 68.49/10.22 inference(avatar_split_clause,[],[f1256,f3034])).
% 68.49/10.22 thf(f1256,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f833])).
% 68.49/10.22 thf(f833,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f397])).
% 68.49/10.22 thf(f397,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)))),
% 68.49/10.22 inference(fool_elimination,[],[f396])).
% 68.49/10.22 thf(f396,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),X0)))),
% 68.49/10.22 inference(rectify,[],[f214])).
% 68.49/10.22 thf(f214,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)),X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_213_l__neg)).
% 68.49/10.22 thf(f3032,plain,(
% 68.49/10.22 spl93_158),
% 68.49/10.22 inference(avatar_split_clause,[],[f1255,f3030])).
% 68.49/10.22 thf(f1255,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f832])).
% 68.49/10.22 thf(f832,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f395])).
% 68.49/10.22 thf(f395,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f394])).
% 68.49/10.22 thf(f394,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0))))),
% 68.49/10.22 inference(rectify,[],[f212])).
% 68.49/10.22 thf(f212,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_211_r__neg)).
% 68.49/10.22 thf(f3004,plain,(
% 68.49/10.22 spl93_157),
% 68.49/10.22 inference(avatar_split_clause,[],[f1392,f3002])).
% 68.49/10.22 thf(f1392,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK41(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1155])).
% 68.49/10.22 thf(f3000,plain,(
% 68.49/10.22 spl93_156),
% 68.49/10.22 inference(avatar_split_clause,[],[f1390,f2998])).
% 68.49/10.22 thf(f1390,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X3 : X1] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,vAPP(X1,sTfun(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1),sK40(X0,X1),X3),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1153])).
% 68.49/10.22 thf(f2972,plain,(
% 68.49/10.22 spl93_155),
% 68.49/10.22 inference(avatar_split_clause,[],[f1400,f2970])).
% 68.49/10.22 thf(f1400,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f989])).
% 68.49/10.22 thf(f989,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f988])).
% 68.49/10.22 thf(f988,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f575])).
% 68.49/10.22 thf(f575,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f574])).
% 68.49/10.22 thf(f574,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3)))),
% 68.49/10.22 inference(rectify,[],[f125])).
% 68.49/10.22 thf(f125,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),X13) = X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_abelian__groupE_I5_J)).
% 68.49/10.22 thf(f2968,plain,(
% 68.49/10.22 spl93_154),
% 68.49/10.22 inference(avatar_split_clause,[],[f1395,f2966])).
% 68.49/10.22 thf(f1395,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f979])).
% 68.49/10.22 thf(f979,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f978])).
% 68.49/10.22 thf(f978,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f565])).
% 68.49/10.22 thf(f565,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f564])).
% 68.49/10.22 thf(f564,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),X3) = X3)))),
% 68.49/10.22 inference(rectify,[],[f72])).
% 68.49/10.22 thf(f72,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),X13) = X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_semiring_Osemiring__simprules_I6_J)).
% 68.49/10.22 thf(f2964,plain,(
% 68.49/10.22 spl93_153),
% 68.49/10.22 inference(avatar_split_clause,[],[f1394,f2962])).
% 68.49/10.22 thf(f1394,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f977])).
% 68.49/10.22 thf(f977,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f976])).
% 68.49/10.22 thf(f976,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f563])).
% 68.49/10.22 thf(f563,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f562])).
% 68.49/10.22 thf(f562,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,sTfun(X1,X1)),add(X1,X0),X2),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)) = X3)))),
% 68.49/10.22 inference(rectify,[],[f71])).
% 68.49/10.22 thf(f71,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,sTfun(X0,X0)),add(X0,X2),X46),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)) = X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_semiring_Osemiring__simprules_I11_J)).
% 68.49/10.22 thf(f2956,plain,(
% 68.49/10.22 spl93_152),
% 68.49/10.22 inference(avatar_split_clause,[],[f1261,f2954])).
% 68.49/10.22 thf(f2954,plain,(
% 68.49/10.22 spl93_152 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | (vAPP(a,a,sK10,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK10,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_152])])).
% 68.49/10.22 thf(f1261,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | (vAPP(a,a,sK10,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK10,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1098])).
% 68.49/10.22 thf(f1098,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ((vAPP(a,a,sK10,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK10,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f838,f1097])).
% 68.49/10.22 thf(f1097,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != X1) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => ((vAPP(a,a,sK10,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK10,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f838,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ? [X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != X1) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(flattening,[],[f837])).
% 68.49/10.22 thf(f837,plain,(
% 68.49/10.22 ! [X0 : a] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ? [X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) != X1) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f403])).
% 68.49/10.22 thf(f403,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (! [X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = X1)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0)))),
% 68.49/10.22 inference(fool_elimination,[],[f402])).
% 68.49/10.22 thf(f402,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (! [X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1) = X1)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0)))),
% 68.49/10.22 inference(rectify,[],[f80])).
% 68.49/10.22 thf(f80,axiom,(
% 68.49/10.22 ! [X24 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X24),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (! [X23 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X24),X23) = X23)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X24)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_one__unique)).
% 68.49/10.22 thf(f2936,plain,(
% 68.49/10.22 spl93_151),
% 68.49/10.22 inference(avatar_split_clause,[],[f1254,f2934])).
% 68.49/10.22 thf(f1254,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f831])).
% 68.49/10.22 thf(f831,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f393])).
% 68.49/10.22 thf(f393,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)))),
% 68.49/10.22 inference(fool_elimination,[],[f392])).
% 68.49/10.22 thf(f392,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0)))),
% 68.49/10.22 inference(rectify,[],[f54])).
% 68.49/10.22 thf(f54,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_l__null)).
% 68.49/10.22 thf(f2932,plain,(
% 68.49/10.22 spl93_150),
% 68.49/10.22 inference(avatar_split_clause,[],[f1253,f2930])).
% 68.49/10.22 thf(f1253,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f830])).
% 68.49/10.22 thf(f830,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f391])).
% 68.49/10.22 thf(f391,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.22 inference(fool_elimination,[],[f390])).
% 68.49/10.22 thf(f390,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.22 inference(rectify,[],[f53])).
% 68.49/10.22 thf(f53,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_r__null)).
% 68.49/10.22 thf(f2910,plain,(
% 68.49/10.22 spl93_149),
% 68.49/10.22 inference(avatar_split_clause,[],[f1399,f2908])).
% 68.49/10.22 thf(f1399,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f987])).
% 68.49/10.22 thf(f987,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : ((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(flattening,[],[f986])).
% 68.49/10.22 thf(f986,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (((vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3) | ($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f573])).
% 68.49/10.22 thf(f573,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f572])).
% 68.49/10.22 thf(f572,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X3 : X1] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => (vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)) => (vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),vAPP(X1,X1,vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),sTfun(X1,X1),a_inv(X1,X0),X2),X3)) = X3)))),
% 68.49/10.22 inference(rectify,[],[f223])).
% 68.49/10.22 thf(f223,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X13 : X0] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X54) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X13),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X54)) => (vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),vAPP(X0,X0,vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),sTfun(X0,X0),a_inv(X0,X2),X54),X13)) = X13)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_222_abelian__group_Ominus__minus)).
% 68.49/10.22 thf(f2906,plain,(
% 68.49/10.22 spl93_148),
% 68.49/10.22 inference(avatar_split_clause,[],[f1274,f2904])).
% 68.49/10.22 thf(f1274,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : a] : ((vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),X1))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f749])).
% 68.49/10.22 thf(f749,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : a] : (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X0)),X1) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),X1)),X1))),
% 68.49/10.22 inference(rectify,[],[f118])).
% 68.49/10.22 thf(f118,axiom,(
% 68.49/10.22 ! [X52 : nat,X13 : a] : (vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),vAPP(nat,nat,suc,X52)),X13) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),X13)),X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_117_add_Onat__pow__Suc)).
% 68.49/10.22 thf(f2902,plain,(
% 68.49/10.22 spl93_147 | ~spl93_22 | spl93_135),
% 68.49/10.22 inference(avatar_split_clause,[],[f2855,f2787,f1832,f2899])).
% 68.49/10.22 thf(f2899,plain,(
% 68.49/10.22 spl93_147 <=> ($false = semiring_char_0($o))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_147])])).
% 68.49/10.22 thf(f2787,plain,(
% 68.49/10.22 spl93_135 <=> ($true = semiring_char_0($o))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_135])])).
% 68.49/10.22 thf(f2855,plain,(
% 68.49/10.22 ($false = semiring_char_0($o)) | (~spl93_22 | spl93_135)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f2854])).
% 68.49/10.22 thf(f2854,plain,(
% 68.49/10.22 ($true != $true) | ($false = semiring_char_0($o)) | (~spl93_22 | spl93_135)),
% 68.49/10.22 inference(superposition,[],[f2789,f1833])).
% 68.49/10.22 thf(f2789,plain,(
% 68.49/10.22 ($true != semiring_char_0($o)) | spl93_135),
% 68.49/10.22 inference(avatar_component_clause,[],[f2787])).
% 68.49/10.22 thf(f2897,plain,(
% 68.49/10.22 spl93_146),
% 68.49/10.22 inference(avatar_split_clause,[],[f1260,f2895])).
% 68.49/10.22 thf(f1260,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK10,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1098])).
% 68.49/10.22 thf(f2887,plain,(
% 68.49/10.22 spl93_145),
% 68.49/10.22 inference(avatar_split_clause,[],[f1329,f2885])).
% 68.49/10.22 thf(f1329,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1109])).
% 68.49/10.22 thf(f1109,plain,(
% 68.49/10.22 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X1 : $tType,X2 : $tType] : (((($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK14,sK15])],[f1106,f1108,f1107])).
% 68.49/10.22 thf(f1107,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (? [X3 : X2] : (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X3),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) => (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1108,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) => (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0))),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1106,plain,(
% 68.49/10.22 ! [X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X1 : $tType,X2 : $tType] : (? [X3 : X2] : (? [X4 : X2] : (($true != vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(X2,X2,vAPP(X2,sTfun(X2,X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),sTfun(X2,sTfun(X2,X2)),mult(X2,X1),X0),X3),X4)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X4),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) & ($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),X3),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0)))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0)))),
% 68.49/10.22 inference(rectify,[],[f1105])).
% 68.49/10.22 thf(f1105,plain,(
% 68.49/10.22 ! [X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X0 : $tType,X1 : $tType] : (? [X3 : X1] : (? [X4 : X1] : (($true != vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(X1,X1,vAPP(X1,sTfun(X1,X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2),X3),X4)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X4),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) & ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),X3),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,sP1(X0,X1),X2)))),
% 68.49/10.22 inference(nnf_transformation,[],[f1081])).
% 68.49/10.22 thf(f2881,plain,(
% 68.49/10.22 ~spl93_144 | spl93_143),
% 68.49/10.22 inference(avatar_split_clause,[],[f2876,f2872,f2878])).
% 68.49/10.22 thf(f2872,plain,(
% 68.49/10.22 spl93_143 <=> (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_143])])).
% 68.49/10.22 thf(f2876,plain,(
% 68.49/10.22 ($true != vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))) | spl93_143),
% 68.49/10.22 inference(forward_demodulation,[],[f2874,f1181])).
% 68.49/10.22 thf(f2874,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) != $true) | spl93_143),
% 68.49/10.22 inference(avatar_component_clause,[],[f2872])).
% 68.49/10.22 thf(f2875,plain,(
% 68.49/10.22 ~spl93_143),
% 68.49/10.22 inference(avatar_split_clause,[],[f1178,f2872])).
% 68.49/10.22 thf(f1178,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) != $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f738])).
% 68.49/10.22 thf(f738,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) != $true)),
% 68.49/10.22 inference(flattening,[],[f281])).
% 68.49/10.22 thf(f281,plain,(
% 68.49/10.22 ~(vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f280])).
% 68.49/10.22 thf(f280,plain,(
% 68.49/10.22 ~vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(rectify,[],[f277])).
% 68.49/10.22 thf(f277,negated_conjecture,(
% 68.49/10.22 ~vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(negated_conjecture,[],[f276])).
% 68.49/10.22 thf(f276,conjecture,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)))),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 68.49/10.22 thf(f2863,plain,(
% 68.49/10.22 spl93_142),
% 68.49/10.22 inference(avatar_split_clause,[],[f1259,f2861])).
% 68.49/10.22 thf(f2861,plain,(
% 68.49/10.22 spl93_142 <=> ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | (vAPP(a,a,sK9,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK9,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_142])])).
% 68.49/10.22 thf(f1259,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | (vAPP(a,a,sK9,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK9,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1096])).
% 68.49/10.22 thf(f1096,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ((vAPP(a,a,sK9,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK9,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f836,f1095])).
% 68.49/10.22 thf(f1095,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X1) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => ((vAPP(a,a,sK9,X0) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK9,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f836,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ? [X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X1) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(flattening,[],[f835])).
% 68.49/10.22 thf(f835,plain,(
% 68.49/10.22 ! [X0 : a] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ? [X1 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) != X1) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f401])).
% 68.49/10.22 thf(f401,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (! [X1 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X1)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)))),
% 68.49/10.22 inference(fool_elimination,[],[f400])).
% 68.49/10.22 thf(f400,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (! [X1 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1) = X1)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0)))),
% 68.49/10.22 inference(rectify,[],[f33])).
% 68.49/10.22 thf(f33,axiom,(
% 68.49/10.22 ! [X24 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X24),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (! [X23 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X24),X23) = X23)) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X24)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_add_Oone__unique)).
% 68.49/10.22 thf(f2859,plain,(
% 68.49/10.22 spl93_141),
% 68.49/10.22 inference(avatar_split_clause,[],[f1258,f2857])).
% 68.49/10.22 thf(f1258,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = X0) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK9,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1096])).
% 68.49/10.22 thf(f2844,plain,(
% 68.49/10.22 spl93_140),
% 68.49/10.22 inference(avatar_split_clause,[],[f1266,f2842])).
% 68.49/10.22 thf(f1266,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f841])).
% 68.49/10.22 thf(f841,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f409])).
% 68.49/10.22 thf(f409,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(fool_elimination,[],[f408])).
% 68.49/10.22 thf(f408,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 inference(rectify,[],[f217])).
% 68.49/10.22 thf(f217,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_add_Oinv__closed)).
% 68.49/10.22 thf(f2833,plain,(
% 68.49/10.22 spl93_139),
% 68.49/10.22 inference(avatar_split_clause,[],[f1408,f2831])).
% 68.49/10.22 thf(f1408,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ((vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK43(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK44(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK45(X0,X1,X2),X3))) = X3)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1159])).
% 68.49/10.22 thf(f1159,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK43(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK44(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK45(X0,X1,X2),X3))) = X3)),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK43,sK44,sK45])],[f1002,f1158])).
% 68.49/10.22 thf(f1158,plain,(
% 68.49/10.22 ! [X2 : $tType,X1 : $tType,X0 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : (? [X4 : X0,X5 : X1,X6 : X2] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3) => (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),vAPP(product_prod(X0,product_prod(X1,X2)),X0,sK43(X0,X1,X2),X3)),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),vAPP(product_prod(X0,product_prod(X1,X2)),X1,sK44(X0,X1,X2),X3)),vAPP(product_prod(X0,product_prod(X1,X2)),X2,sK45(X0,X1,X2),X3))) = X3))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f1002,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ? [X4 : X0,X5 : X1,X6 : X2] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) = X3)),
% 68.49/10.22 inference(ennf_transformation,[],[f767])).
% 68.49/10.22 thf(f767,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : product_prod(X0,product_prod(X1,X2))] : ~! [X4 : X0,X5 : X1,X6 : X2] : (vAPP(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2)),vAPP(X0,sTfun(product_prod(X1,X2),product_prod(X0,product_prod(X1,X2))),product_Pair(X0,product_prod(X1,X2)),X4),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X5),X6)) != X3)),
% 68.49/10.22 inference(rectify,[],[f66])).
% 68.49/10.22 thf(f66,axiom,(
% 68.49/10.22 ! [X0 : $tType,X2 : $tType,X5 : $tType,X14 : product_prod(X0,product_prod(X2,X5))] : ~! [X33 : X0,X34 : X2,X39 : X5] : (vAPP(product_prod(X2,X5),product_prod(X0,product_prod(X2,X5)),vAPP(X0,sTfun(product_prod(X2,X5),product_prod(X0,product_prod(X2,X5))),product_Pair(X0,product_prod(X2,X5)),X33),vAPP(X5,product_prod(X2,X5),vAPP(X2,sTfun(X5,product_prod(X2,X5)),product_Pair(X2,X5),X34),X39)) != X14)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_prod__cases3)).
% 68.49/10.22 thf(f2817,plain,(
% 68.49/10.22 spl93_138),
% 68.49/10.22 inference(avatar_split_clause,[],[f1246,f2815])).
% 68.49/10.22 thf(f1246,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1094])).
% 68.49/10.22 thf(f1094,plain,(
% 68.49/10.22 ! [X0 : a] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f823,f1093])).
% 68.49/10.22 thf(f1093,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(a,a,sK8,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f823,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f377])).
% 68.49/10.22 thf(f377,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 inference(fool_elimination,[],[f376])).
% 68.49/10.22 thf(f376,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(rectify,[],[f178])).
% 68.49/10.22 thf(f178,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => ? [X23 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),X23)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_Units__r__inv__ex)).
% 68.49/10.22 thf(f2813,plain,(
% 68.49/10.22 spl93_137),
% 68.49/10.22 inference(avatar_split_clause,[],[f1244,f2811])).
% 68.49/10.22 thf(f1244,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1092])).
% 68.49/10.22 thf(f1092,plain,(
% 68.49/10.22 ! [X0 : a] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f822,f1091])).
% 68.49/10.22 thf(f1091,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,sK7,X0)),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f822,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f375])).
% 68.49/10.22 thf(f375,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 inference(fool_elimination,[],[f374])).
% 68.49/10.22 thf(f374,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X1),X0)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(rectify,[],[f177])).
% 68.49/10.22 thf(f177,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => ? [X23 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X23),X13)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_Units__l__inv__ex)).
% 68.49/10.22 thf(f2793,plain,(
% 68.49/10.22 ~spl93_135 | spl93_136 | ~spl93_22 | ~spl93_51),
% 68.49/10.22 inference(avatar_split_clause,[],[f2145,f2062,f1832,f2791,f2787])).
% 68.49/10.22 thf(f2062,plain,(
% 68.49/10.22 spl93_51 <=> ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) != vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | (X1 = X2))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_51])])).
% 68.49/10.22 thf(f2145,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,semiring_1_of_nat($o),X1)) | ($true != semiring_char_0($o)) | (X0 = X1) | ($false = vAPP(nat,$o,semiring_1_of_nat($o),X0))) ) | (~spl93_22 | ~spl93_51)),
% 68.49/10.22 inference(superposition,[],[f2063,f1833])).
% 68.49/10.22 thf(f2063,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) != vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | (X1 = X2)) ) | ~spl93_51),
% 68.49/10.22 inference(avatar_component_clause,[],[f2062])).
% 68.49/10.22 thf(f2769,plain,(
% 68.49/10.22 spl93_134),
% 68.49/10.22 inference(avatar_split_clause,[],[f1265,f2767])).
% 68.49/10.22 thf(f1265,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1102])).
% 68.49/10.22 thf(f1102,plain,(
% 68.49/10.22 ! [X0 : a] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f840,f1101])).
% 68.49/10.22 thf(f1101,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,sK12,X0)),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f840,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f407])).
% 68.49/10.22 thf(f407,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 inference(fool_elimination,[],[f406])).
% 68.49/10.22 thf(f406,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X1),X0)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(rectify,[],[f34])).
% 68.49/10.22 thf(f34,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ? [X23 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X23),X13)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_add_Ol__inv__ex)).
% 68.49/10.22 thf(f2765,plain,(
% 68.49/10.22 spl93_133),
% 68.49/10.22 inference(avatar_split_clause,[],[f1263,f2763])).
% 68.49/10.22 thf(f1263,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1100])).
% 68.49/10.22 thf(f1100,plain,(
% 68.49/10.22 ! [X0 : a] : (((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f839,f1099])).
% 68.49/10.22 thf(f1099,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(a,a,sK11,X0))) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f839,plain,(
% 68.49/10.22 ! [X0 : a] : (? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f405])).
% 68.49/10.22 thf(f405,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))),
% 68.49/10.22 inference(fool_elimination,[],[f404])).
% 68.49/10.22 thf(f404,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),X1)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(rectify,[],[f32])).
% 68.49/10.22 thf(f32,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ? [X23 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),X23)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X23),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_add_Or__inv__ex)).
% 68.49/10.22 thf(f2761,plain,(
% 68.49/10.22 spl93_132),
% 68.49/10.22 inference(avatar_split_clause,[],[f1252,f2759])).
% 68.49/10.22 thf(f1252,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f829])).
% 68.49/10.22 thf(f829,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f389])).
% 68.49/10.22 thf(f389,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0))),
% 68.49/10.22 inference(fool_elimination,[],[f388])).
% 68.49/10.22 thf(f388,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X0) = X0))),
% 68.49/10.22 inference(rectify,[],[f86])).
% 68.49/10.22 thf(f86,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),X13) = X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_l__one)).
% 68.49/10.22 thf(f2757,plain,(
% 68.49/10.22 spl93_131),
% 68.49/10.22 inference(avatar_split_clause,[],[f1251,f2755])).
% 68.49/10.22 thf(f1251,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f828])).
% 68.49/10.22 thf(f828,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f387])).
% 68.49/10.22 thf(f387,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0))),
% 68.49/10.22 inference(fool_elimination,[],[f386])).
% 68.49/10.22 thf(f386,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X0))),
% 68.49/10.22 inference(rectify,[],[f87])).
% 68.49/10.22 thf(f87,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) = X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_r__one)).
% 68.49/10.22 thf(f2737,plain,(
% 68.49/10.22 spl93_130),
% 68.49/10.22 inference(avatar_split_clause,[],[f1250,f2735])).
% 68.49/10.22 thf(f1250,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f827])).
% 68.49/10.22 thf(f827,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f385])).
% 68.49/10.22 thf(f385,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0))),
% 68.49/10.22 inference(fool_elimination,[],[f384])).
% 68.49/10.22 thf(f384,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X0) = X0))),
% 68.49/10.22 inference(rectify,[],[f44])).
% 68.49/10.22 thf(f44,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),X13) = X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_l__zero)).
% 68.49/10.22 thf(f2733,plain,(
% 68.49/10.22 spl93_129),
% 68.49/10.22 inference(avatar_split_clause,[],[f1249,f2731])).
% 68.49/10.22 thf(f1249,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f826])).
% 68.49/10.22 thf(f826,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f383])).
% 68.49/10.22 thf(f383,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0))),
% 68.49/10.22 inference(fool_elimination,[],[f382])).
% 68.49/10.22 thf(f382,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X0))),
% 68.49/10.22 inference(rectify,[],[f43])).
% 68.49/10.22 thf(f43,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)) = X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_r__zero)).
% 68.49/10.22 thf(f2719,plain,(
% 68.49/10.22 spl93_128),
% 68.49/10.22 inference(avatar_split_clause,[],[f1248,f2717])).
% 68.49/10.22 thf(f1248,plain,(
% 68.49/10.22 ( ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f825])).
% 68.49/10.22 thf(f825,plain,(
% 68.49/10.22 ! [X0 : a] : ((vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f381])).
% 68.49/10.22 thf(f381,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0))),
% 68.49/10.22 inference(fool_elimination,[],[f380])).
% 68.49/10.22 thf(f380,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X0)) = X0))),
% 68.49/10.22 inference(rectify,[],[f216])).
% 68.49/10.22 thf(f216,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => (vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),X13)) = X13))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_215_local_Ominus__minus)).
% 68.49/10.22 thf(f2699,plain,(
% 68.49/10.22 spl93_127),
% 68.49/10.22 inference(avatar_split_clause,[],[f1264,f2697])).
% 68.49/10.22 thf(f1264,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK12,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1102])).
% 68.49/10.22 thf(f2695,plain,(
% 68.49/10.22 spl93_126),
% 68.49/10.22 inference(avatar_split_clause,[],[f1262,f2693])).
% 68.49/10.22 thf(f1262,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK11,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1100])).
% 68.49/10.22 thf(f2691,plain,(
% 68.49/10.22 spl93_125),
% 68.49/10.22 inference(avatar_split_clause,[],[f1711,f2688])).
% 68.49/10.22 thf(f1711,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 inference(forward_demodulation,[],[f1710,f1708])).
% 68.49/10.22 thf(f1710,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)))))),
% 68.49/10.22 inference(forward_demodulation,[],[f1709,f1181])).
% 68.49/10.22 thf(f1709,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s3),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4)))))),
% 68.49/10.22 inference(forward_demodulation,[],[f1492,f1706])).
% 68.49/10.22 thf(f1492,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a)),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)))),sCOMB,vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(sTfun(a,a),sTfun(a,sTfun(a,a))))),bCOMB,cCOMB),vAPP(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),vAPP(sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),sTfun(sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a))),sTfun(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a))))),bCOMB,vAPP(sTfun(sTfun(a,a),sTfun(sTfun(a,a),sTfun(a,a))),sTfun(sTfun(a,sTfun(a,a)),sTfun(a,sTfun(sTfun(a,a),sTfun(a,a)))),bCOMB,bCOMB)),add(a,b)))),a_inv(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))))))),
% 68.49/10.22 inference(definition_unfolding,[],[f1188,f1277])).
% 68.49/10.22 thf(f1188,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))))))),
% 68.49/10.22 inference(cnf_transformation,[],[f70])).
% 68.49/10.22 thf(f70,axiom,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),a_minus(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),r2)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),r3))),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s2)),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),add(a,b),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s2),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r2),r4))),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),s),s3)),vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),r3),r4)))))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_f11)).
% 68.49/10.22 thf(f2671,plain,(
% 68.49/10.22 spl93_124),
% 68.49/10.22 inference(avatar_split_clause,[],[f1245,f2669])).
% 68.49/10.22 thf(f1245,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK8,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1094])).
% 68.49/10.22 thf(f2659,plain,(
% 68.49/10.22 spl93_123 | ~spl93_53 | ~spl93_74 | ~spl93_122),
% 68.49/10.22 inference(avatar_split_clause,[],[f2655,f2652,f2247,f2074,f2657])).
% 68.49/10.22 thf(f2655,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) ) | (~spl93_53 | ~spl93_74 | ~spl93_122)),
% 68.49/10.22 inference(forward_demodulation,[],[f2653,f2300])).
% 68.49/10.22 thf(f2654,plain,(
% 68.49/10.22 spl93_122),
% 68.49/10.22 inference(avatar_split_clause,[],[f1243,f2652])).
% 68.49/10.22 thf(f1243,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,sK7,X0)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1092])).
% 68.49/10.22 thf(f2649,plain,(
% 68.49/10.22 spl93_121),
% 68.49/10.22 inference(avatar_split_clause,[],[f1247,f2647])).
% 68.49/10.22 thf(f1247,plain,(
% 68.49/10.22 ( ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f824])).
% 68.49/10.22 thf(f824,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))))),
% 68.49/10.22 inference(ennf_transformation,[],[f379])).
% 68.49/10.22 thf(f379,plain,(
% 68.49/10.22 ! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))) => ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 inference(fool_elimination,[],[f378])).
% 68.49/10.22 thf(f378,plain,(
% 68.49/10.22 ! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 inference(rectify,[],[f180])).
% 68.49/10.22 thf(f180,axiom,(
% 68.49/10.22 ! [X13 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) => vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X13),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_179_Units__closed)).
% 68.49/10.22 thf(f2645,plain,(
% 68.49/10.22 spl93_120),
% 68.49/10.22 inference(avatar_split_clause,[],[f1487,f2642])).
% 68.49/10.22 thf(f1487,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r4),s3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f731])).
% 68.49/10.22 thf(f731,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r4),s3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f730])).
% 68.49/10.22 thf(f730,plain,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r4),s3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(rectify,[],[f2])).
% 68.49/10.22 thf(f2,axiom,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r4),s3)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_assms_I3_J)).
% 68.49/10.22 thf(f2640,plain,(
% 68.49/10.22 spl93_119 | ~spl93_22 | ~spl93_59),
% 68.49/10.22 inference(avatar_split_clause,[],[f2403,f2112,f1832,f2638])).
% 68.49/10.22 thf(f2638,plain,(
% 68.49/10.22 spl93_119 <=> ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (X1 != X2) | (semiring_char_0(X0) = $false))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_119])])).
% 68.49/10.22 thf(f2112,plain,(
% 68.49/10.22 spl93_59 <=> ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | (X1 != X2))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_59])])).
% 68.49/10.22 thf(f2403,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (X1 != X2) | (semiring_char_0(X0) = $false)) ) | (~spl93_22 | ~spl93_59)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f2402])).
% 68.49/10.22 thf(f2402,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (X1 != X2) | (semiring_char_0(X0) = $false)) ) | (~spl93_22 | ~spl93_59)),
% 68.49/10.22 inference(superposition,[],[f2113,f1833])).
% 68.49/10.22 thf(f2113,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((semiring_char_0(X0) != $true) | (vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (X1 != X2)) ) | ~spl93_59),
% 68.49/10.22 inference(avatar_component_clause,[],[f2112])).
% 68.49/10.22 thf(f2636,plain,(
% 68.49/10.22 spl93_118),
% 68.49/10.22 inference(avatar_split_clause,[],[f1486,f2633])).
% 68.49/10.22 thf(f1486,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r3),s2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f729])).
% 68.49/10.22 thf(f729,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r3),s2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f728])).
% 68.49/10.22 thf(f728,plain,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r3),s2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(rectify,[],[f3])).
% 68.49/10.22 thf(f3,axiom,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r3),s2)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_assms_I2_J)).
% 68.49/10.22 thf(f2631,plain,(
% 68.49/10.22 spl93_117),
% 68.49/10.22 inference(avatar_split_clause,[],[f1485,f2628])).
% 68.49/10.22 thf(f1485,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r2),s)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f727])).
% 68.49/10.22 thf(f727,plain,(
% 68.49/10.22 (vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r2),s)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f726])).
% 68.49/10.22 thf(f726,plain,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r2),s)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 inference(rectify,[],[f4])).
% 68.49/10.22 thf(f4,axiom,(
% 68.49/10.22 vAPP(set(product_prod(a,a)),$o,vAPP(product_prod(a,a),sTfun(set(product_prod(a,a)),$o),member(product_prod(a,a)),vAPP(a,product_prod(a,a),vAPP(a,sTfun(a,product_prod(a,a)),product_Pair(a,a),r2),s)),vAPP(partia1265057091ct_ext(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),set(product_prod(a,a)),partial_carrier(product_prod(a,a),eq_eq_object_ext(product_prod(a,a),product_unit)),rel))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_assms_I1_J)).
% 68.49/10.22 thf(f2626,plain,(
% 68.49/10.22 spl93_116),
% 68.49/10.22 inference(avatar_split_clause,[],[f1484,f2623])).
% 68.49/10.22 thf(f1484,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f725])).
% 68.49/10.22 thf(f725,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f724])).
% 68.49/10.22 thf(f724,plain,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(rectify,[],[f220])).
% 68.49/10.22 thf(f220,axiom,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_219_Units__minus__one__closed)).
% 68.49/10.22 thf(f2617,plain,(
% 68.49/10.22 spl93_115),
% 68.49/10.22 inference(avatar_split_clause,[],[f1358,f2615])).
% 68.49/10.22 thf(f1358,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f920])).
% 68.49/10.22 thf(f920,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f503])).
% 68.49/10.22 thf(f503,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f502])).
% 68.49/10.22 thf(f502,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))),
% 68.49/10.22 inference(rectify,[],[f88])).
% 68.49/10.22 thf(f88,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2)))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,one(X0,ring_ext(X0,X2)),X46)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_semiring_Osemiring__simprules_I4_J)).
% 68.49/10.22 thf(f2590,plain,(
% 68.49/10.22 spl93_114),
% 68.49/10.22 inference(avatar_split_clause,[],[f1359,f2588])).
% 68.49/10.22 thf(f1359,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f921])).
% 68.49/10.22 thf(f921,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f505])).
% 68.49/10.22 thf(f505,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2)) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f504])).
% 68.49/10.22 thf(f504,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,abelian_group(X1,X0),X2) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))),
% 68.49/10.22 inference(rectify,[],[f122])).
% 68.49/10.22 thf(f122,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2)))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,abelian_group(X0,X2),X46) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_abelian__groupE_I2_J)).
% 68.49/10.22 thf(f2586,plain,(
% 68.49/10.22 spl93_113),
% 68.49/10.22 inference(avatar_split_clause,[],[f1357,f2584])).
% 68.49/10.22 thf(f1357,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f919])).
% 68.49/10.22 thf(f919,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f501])).
% 68.49/10.22 thf(f501,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2)) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f500])).
% 68.49/10.22 thf(f500,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,semiring(X1,X0),X2) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),set(X1),partial_carrier(X1,monoid_ext(X1,ring_ext(X1,X0))),X2)))),
% 68.49/10.22 inference(rectify,[],[f96])).
% 68.49/10.22 thf(f96,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2)))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,semiring(X0,X2),X46) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),set(X0),partial_carrier(X0,monoid_ext(X0,ring_ext(X0,X2))),X46)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_semiring_Osemiring__simprules_I2_J)).
% 68.49/10.22 thf(f2582,plain,(
% 68.49/10.22 spl93_112),
% 68.49/10.22 inference(avatar_split_clause,[],[f1346,f2580])).
% 68.49/10.22 thf(f1346,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK27(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1135])).
% 68.49/10.22 thf(f2578,plain,(
% 68.49/10.22 spl93_111),
% 68.49/10.22 inference(avatar_split_clause,[],[f1345,f2576])).
% 68.49/10.22 thf(f1345,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK26(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1135])).
% 68.49/10.22 thf(f2574,plain,(
% 68.49/10.22 spl93_110),
% 68.49/10.22 inference(avatar_split_clause,[],[f1344,f2572])).
% 68.49/10.22 thf(f1344,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK25(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP2(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1135])).
% 68.49/10.22 thf(f2570,plain,(
% 68.49/10.22 spl93_109),
% 68.49/10.22 inference(avatar_split_clause,[],[f1342,f2568])).
% 68.49/10.22 thf(f1342,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK24(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1129])).
% 68.49/10.22 thf(f2565,plain,(
% 68.49/10.22 spl93_108),
% 68.49/10.22 inference(avatar_split_clause,[],[f1341,f2563])).
% 68.49/10.22 thf(f1341,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK23(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP3(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1129])).
% 68.49/10.22 thf(f2561,plain,(
% 68.49/10.22 spl93_107),
% 68.49/10.22 inference(avatar_split_clause,[],[f1339,f2559])).
% 68.49/10.22 thf(f1339,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK22(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1124])).
% 68.49/10.22 thf(f2557,plain,(
% 68.49/10.22 spl93_106),
% 68.49/10.22 inference(avatar_split_clause,[],[f1338,f2555])).
% 68.49/10.22 thf(f1338,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1)))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),X2,sK21(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),set(X2),partial_carrier(X2,monoid_ext(X2,ring_ext(X2,X1))),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,ring_ext(X2,X1))),$o,sP4(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1124])).
% 68.49/10.22 thf(f2549,plain,(
% 68.49/10.22 spl93_105),
% 68.49/10.22 inference(avatar_split_clause,[],[f1513,f2547])).
% 68.49/10.22 thf(f1513,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(equality_resolution,[],[f1226])).
% 68.49/10.22 thf(f1226,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f805])).
% 68.49/10.22 thf(f805,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f341])).
% 68.49/10.22 thf(f341,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3)))))),
% 68.49/10.22 inference(fool_elimination,[],[f340])).
% 68.49/10.22 thf(f340,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X4),X3)))))),
% 68.49/10.22 inference(rectify,[],[f242])).
% 68.49/10.22 thf(f242,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X62 : X0,X47 : X0,X7 : X0,X6 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),X7) = X62) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X62) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X47)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_241_group__cancel_Osub2)).
% 68.49/10.22 thf(f2528,plain,(
% 68.49/10.22 spl93_104),
% 68.49/10.22 inference(avatar_split_clause,[],[f1720,f2526])).
% 68.49/10.22 thf(f1720,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)))) )),
% 68.49/10.22 inference(forward_demodulation,[],[f1316,f1313])).
% 68.49/10.22 thf(f1313,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f755])).
% 68.49/10.22 thf(f755,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 68.49/10.22 inference(rectify,[],[f130])).
% 68.49/10.22 thf(f130,axiom,(
% 68.49/10.22 ! [X48 : nat,X50 : nat,X47 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X48),X50)),X47) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X48),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X50),X47)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_129_diff__diff__left)).
% 68.49/10.22 thf(f1316,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f758])).
% 68.49/10.22 thf(f758,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),X1)),vAPP(nat,nat,suc,X2)))),
% 68.49/10.22 inference(rectify,[],[f131])).
% 68.49/10.22 thf(f131,axiom,(
% 68.49/10.22 ! [X53 : nat,X52 : nat,X47 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X53)),X52)),vAPP(nat,nat,suc,X47)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X53),X52)),X47))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_130_Suc__diff__diff)).
% 68.49/10.22 thf(f2498,plain,(
% 68.49/10.22 spl93_103 | ~spl93_3 | ~spl93_59),
% 68.49/10.22 inference(avatar_split_clause,[],[f2405,f2112,f1737,f2496])).
% 68.49/10.22 thf(f2496,plain,(
% 68.49/10.22 spl93_103 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,int,semiring_1_of_nat(int),X1) = vAPP(nat,int,semiring_1_of_nat(int),X0)) | (X0 != X1))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_103])])).
% 68.49/10.22 thf(f1737,plain,(
% 68.49/10.22 spl93_3 <=> (semiring_char_0(int) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_3])])).
% 68.49/10.22 thf(f2405,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,int,semiring_1_of_nat(int),X1) = vAPP(nat,int,semiring_1_of_nat(int),X0)) | (X0 != X1)) ) | (~spl93_3 | ~spl93_59)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f2400])).
% 68.49/10.22 thf(f2400,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,int,semiring_1_of_nat(int),X1) = vAPP(nat,int,semiring_1_of_nat(int),X0)) | (X0 != X1)) ) | (~spl93_3 | ~spl93_59)),
% 68.49/10.22 inference(superposition,[],[f2113,f1739])).
% 68.49/10.22 thf(f1739,plain,(
% 68.49/10.22 (semiring_char_0(int) = $true) | ~spl93_3),
% 68.49/10.22 inference(avatar_component_clause,[],[f1737])).
% 68.49/10.22 thf(f2494,plain,(
% 68.49/10.22 spl93_102),
% 68.49/10.22 inference(avatar_split_clause,[],[f1389,f2492])).
% 68.49/10.22 thf(f1389,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X2))))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1151])).
% 68.49/10.22 thf(f1151,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X2)))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f971,f1150])).
% 68.49/10.22 thf(f1150,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o] : (? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK38(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK39(X0,X1),X2)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f971,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))))),
% 68.49/10.22 inference(ennf_transformation,[],[f557])).
% 68.49/10.22 thf(f557,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : ($true = vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true = vAPP(product_prod(X1,X0),$o,X2,X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f556])).
% 68.49/10.22 thf(f556,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) => vAPP(product_prod(X1,X0),$o,X2,X3))),
% 68.49/10.22 inference(rectify,[],[f55])).
% 68.49/10.22 thf(f55,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X26 : product_prod(X0,X2) > $o,X32 : product_prod(X0,X2)] : (! [X33 : X0,X34 : X2] : vAPP(product_prod(X0,X2),$o,X26,vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X33),X34)) => vAPP(product_prod(X0,X2),$o,X26,X32))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_old_Oprod_Oinducts)).
% 68.49/10.22 thf(f2490,plain,(
% 68.49/10.22 spl93_101),
% 68.49/10.22 inference(avatar_split_clause,[],[f1388,f2488])).
% 68.49/10.22 thf(f1388,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X2))))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1149])).
% 68.49/10.22 thf(f1149,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X2)))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f970,f1148])).
% 68.49/10.22 thf(f1148,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0) > $o] : (? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),vAPP(sTfun(product_prod(X1,X0),$o),X1,sK36(X0,X1),X2)),vAPP(sTfun(product_prod(X1,X0),$o),X0,sK37(X0,X1),X2)))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f970,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,X2,X3)) | ? [X4 : X1,X5 : X0] : ($true != vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))))),
% 68.49/10.22 inference(ennf_transformation,[],[f555])).
% 68.49/10.22 thf(f555,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : ($true = vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5))) => ($true = vAPP(product_prod(X1,X0),$o,X2,X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f554])).
% 68.49/10.22 thf(f554,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0) > $o,X3 : product_prod(X1,X0)] : (! [X4 : X1,X5 : X0] : vAPP(product_prod(X1,X0),$o,X2,vAPP(X0,product_prod(X1,X0),vAPP(X1,sTfun(X0,product_prod(X1,X0)),product_Pair(X1,X0),X4),X5)) => vAPP(product_prod(X1,X0),$o,X2,X3))),
% 68.49/10.22 inference(rectify,[],[f68])).
% 68.49/10.22 thf(f68,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X26 : product_prod(X0,X2) > $o,X44 : product_prod(X0,X2)] : (! [X33 : X0,X34 : X2] : vAPP(product_prod(X0,X2),$o,X26,vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X33),X34)) => vAPP(product_prod(X0,X2),$o,X26,X44))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_prod__cases)).
% 68.49/10.22 thf(f2486,plain,(
% 68.49/10.22 spl93_100),
% 68.49/10.22 inference(avatar_split_clause,[],[f1198,f2484])).
% 68.49/10.22 thf(f1198,plain,(
% 68.49/10.22 ( ! [X0 : nat] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f741])).
% 68.49/10.22 thf(f741,plain,(
% 68.49/10.22 ! [X0 : nat] : (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 inference(rectify,[],[f107])).
% 68.49/10.22 thf(f107,axiom,(
% 68.49/10.22 ! [X52 : nat] : (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(nat,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(nat,sTfun(a,a)),add_pow(a,b,nat),r),X52),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_106_add_Onat__pow__one)).
% 68.49/10.22 thf(f2482,plain,(
% 68.49/10.22 spl93_99),
% 68.49/10.22 inference(avatar_split_clause,[],[f1197,f2480])).
% 68.49/10.22 thf(f1197,plain,(
% 68.49/10.22 ( ! [X0 : int] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f740])).
% 68.49/10.22 thf(f740,plain,(
% 68.49/10.22 ! [X0 : int] : (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 inference(rectify,[],[f85])).
% 68.49/10.22 thf(f85,axiom,(
% 68.49/10.22 ! [X15 : int] : (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(int,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(int,sTfun(a,a)),add_pow(a,b,int),r),X15),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_add_Oint__pow__one)).
% 68.49/10.22 thf(f2446,plain,(
% 68.49/10.22 spl93_98 | ~spl93_9 | ~spl93_59),
% 68.49/10.22 inference(avatar_split_clause,[],[f2404,f2112,f1767,f2444])).
% 68.49/10.22 thf(f2444,plain,(
% 68.49/10.22 spl93_98 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,semiring_1_of_nat(nat),X0) = vAPP(nat,nat,semiring_1_of_nat(nat),X1)) | (X0 != X1))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_98])])).
% 68.49/10.22 thf(f1767,plain,(
% 68.49/10.22 spl93_9 <=> (semiring_char_0(nat) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_9])])).
% 68.49/10.22 thf(f2404,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,semiring_1_of_nat(nat),X0) = vAPP(nat,nat,semiring_1_of_nat(nat),X1)) | (X0 != X1)) ) | (~spl93_9 | ~spl93_59)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f2401])).
% 68.49/10.22 thf(f2401,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,semiring_1_of_nat(nat),X0) = vAPP(nat,nat,semiring_1_of_nat(nat),X1)) | (X0 != X1)) ) | (~spl93_9 | ~spl93_59)),
% 68.49/10.22 inference(superposition,[],[f2113,f1769])).
% 68.49/10.22 thf(f1769,plain,(
% 68.49/10.22 (semiring_char_0(nat) = $true) | ~spl93_9),
% 68.49/10.22 inference(avatar_component_clause,[],[f1767])).
% 68.49/10.22 thf(f2438,plain,(
% 68.49/10.22 spl93_97),
% 68.49/10.22 inference(avatar_split_clause,[],[f1387,f2436])).
% 68.49/10.22 thf(f1387,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1147])).
% 68.49/10.22 thf(f1147,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2))))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK35])],[f969,f1146])).
% 68.49/10.22 thf(f1146,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (? [X4 : X1] : (vAPP(X1,X0,X2,X4) != vAPP(X1,X0,X3,X4)) => (vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2)) != vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK35(X0,X1),X3),X2))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f969,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | ? [X4 : X1] : (vAPP(X1,X0,X2,X4) != vAPP(X1,X0,X3,X4)))),
% 68.49/10.22 inference(ennf_transformation,[],[f766])).
% 68.49/10.22 thf(f766,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : (vAPP(X1,X0,X2,X4) = vAPP(X1,X0,X3,X4)) => (X2 = X3))),
% 68.49/10.22 inference(rectify,[],[f49])).
% 68.49/10.22 thf(f49,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X30 : X0 > X2,X31 : X0 > X2] : (! [X23 : X0] : (vAPP(X0,X2,X30,X23) = vAPP(X0,X2,X31,X23)) => (X30 = X31))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_ext)).
% 68.49/10.22 thf(f2434,plain,(
% 68.49/10.22 spl93_96),
% 68.49/10.22 inference(avatar_split_clause,[],[f1354,f2432])).
% 68.49/10.22 thf(f1354,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f916])).
% 68.49/10.22 thf(f916,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f495])).
% 68.49/10.22 thf(f495,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2)) => ($true = vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f494])).
% 68.49/10.22 thf(f494,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,comm_group(X1,X0),X2) => vAPP(set(X1),$o,vAPP(X1,sTfun(set(X1),$o),member(X1),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2)),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2)))),
% 68.49/10.22 inference(rectify,[],[f255])).
% 68.49/10.22 thf(f255,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,comm_group(X0,X2),X54) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54)),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_comm__groupE_I2_J)).
% 68.49/10.22 thf(f2430,plain,(
% 68.49/10.22 spl93_95),
% 68.49/10.22 inference(avatar_split_clause,[],[f1332,f2428])).
% 68.49/10.22 thf(f1332,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK18(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1115])).
% 68.49/10.22 thf(f2426,plain,(
% 68.49/10.22 spl93_94),
% 68.49/10.22 inference(avatar_split_clause,[],[f1331,f2424])).
% 68.49/10.22 thf(f1331,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK17(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1115])).
% 68.49/10.22 thf(f2422,plain,(
% 68.49/10.22 spl93_93),
% 68.49/10.22 inference(avatar_split_clause,[],[f1330,f2420])).
% 68.49/10.22 thf(f1330,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK16(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP0(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1115])).
% 68.49/10.22 thf(f2418,plain,(
% 68.49/10.22 spl93_92),
% 68.49/10.22 inference(avatar_split_clause,[],[f1328,f2416])).
% 68.49/10.22 thf(f1328,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK15(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1109])).
% 68.49/10.22 thf(f2414,plain,(
% 68.49/10.22 spl93_91),
% 68.49/10.22 inference(avatar_split_clause,[],[f1327,f2412])).
% 68.49/10.22 thf(f1327,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X2 : $tType,X0 : partia1265057091ct_ext(X2,monoid_ext(X2,X1))] : (($true = vAPP(set(X2),$o,vAPP(X2,sTfun(set(X2),$o),member(X2),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),X2,sK14(X1,X2),X0)),vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),set(X2),partial_carrier(X2,monoid_ext(X2,X1)),X0))) | ($true != vAPP(partia1265057091ct_ext(X2,monoid_ext(X2,X1)),$o,sP1(X1,X2),X0))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1109])).
% 68.49/10.22 thf(f2324,plain,(
% 68.49/10.22 spl93_90),
% 68.49/10.22 inference(avatar_split_clause,[],[f1512,f2322])).
% 68.49/10.22 thf(f1512,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(equality_resolution,[],[f1225])).
% 68.49/10.22 thf(f1225,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f804])).
% 68.49/10.22 thf(f804,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f339])).
% 68.49/10.22 thf(f339,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)))))),
% 68.49/10.22 inference(fool_elimination,[],[f338])).
% 68.49/10.22 thf(f338,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X4) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X4)))))),
% 68.49/10.22 inference(rectify,[],[f168])).
% 68.49/10.22 thf(f168,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X27 : X0,X47 : X0,X6 : X0,X7 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),X6) = X27) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X27),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_group__cancel_Osub1)).
% 68.49/10.22 thf(f2320,plain,(
% 68.49/10.22 spl93_89),
% 68.49/10.22 inference(avatar_split_clause,[],[f1510,f2318])).
% 68.49/10.22 thf(f1510,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)),X4)) | (comm_monoid_add(X0) != $true)) )),
% 68.49/10.22 inference(equality_resolution,[],[f1205])).
% 68.49/10.22 thf(f1205,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (comm_monoid_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f784])).
% 68.49/10.22 thf(f784,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (comm_monoid_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f299])).
% 68.49/10.22 thf(f299,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4))))),
% 68.49/10.22 inference(fool_elimination,[],[f298])).
% 68.49/10.22 thf(f298,plain,(
% 68.49/10.22 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X4)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X4))))),
% 68.49/10.22 inference(rectify,[],[f163])).
% 68.49/10.22 thf(f163,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X27 : X0,X47 : X0,X6 : X0,X7 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),X6) = X27) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X27),X7))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_162_group__cancel_Oadd1)).
% 68.49/10.22 thf(f2316,plain,(
% 68.49/10.22 spl93_88),
% 68.49/10.22 inference(avatar_split_clause,[],[f1509,f2314])).
% 68.49/10.22 thf(f1509,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (comm_monoid_add(X0) != $true)) )),
% 68.49/10.22 inference(equality_resolution,[],[f1204])).
% 68.49/10.22 thf(f1204,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1) | (comm_monoid_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f783])).
% 68.49/10.22 thf(f783,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3))) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) != X1)) | (comm_monoid_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f297])).
% 68.49/10.22 thf(f297,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)))))),
% 68.49/10.22 inference(fool_elimination,[],[f296])).
% 68.49/10.22 thf(f296,plain,(
% 68.49/10.22 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3) = X1) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X1) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X4),X3)))))),
% 68.49/10.22 inference(rectify,[],[f162])).
% 68.49/10.22 thf(f162,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X62 : X0,X47 : X0,X7 : X0,X6 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),X7) = X62) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X62) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X47),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_group__cancel_Oadd2)).
% 68.49/10.22 thf(f2312,plain,(
% 68.49/10.22 spl93_87),
% 68.49/10.22 inference(avatar_split_clause,[],[f1237,f2310])).
% 68.49/10.22 thf(f1237,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f816])).
% 68.49/10.22 thf(f816,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f363])).
% 68.49/10.22 thf(f363,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 68.49/10.22 inference(fool_elimination,[],[f362])).
% 68.49/10.22 thf(f362,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 68.49/10.22 inference(rectify,[],[f174])).
% 68.49/10.22 thf(f174,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X8)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X8))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_173_diff__add__eq__diff__diff__swap)).
% 68.49/10.22 thf(f2308,plain,(
% 68.49/10.22 spl93_86),
% 68.49/10.22 inference(avatar_split_clause,[],[f1236,f2306])).
% 68.49/10.22 thf(f1236,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f815])).
% 68.49/10.22 thf(f815,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f361])).
% 68.49/10.22 thf(f361,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f360])).
% 68.49/10.22 thf(f360,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(rectify,[],[f171])).
% 68.49/10.22 thf(f171,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X8)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_add__diff__eq)).
% 68.49/10.22 thf(f2304,plain,(
% 68.49/10.22 spl93_85),
% 68.49/10.22 inference(avatar_split_clause,[],[f1235,f2302])).
% 68.49/10.22 thf(f1235,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f814])).
% 68.49/10.22 thf(f814,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f359])).
% 68.49/10.22 thf(f359,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))),
% 68.49/10.22 inference(fool_elimination,[],[f358])).
% 68.49/10.22 thf(f358,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3))))),
% 68.49/10.22 inference(rectify,[],[f172])).
% 68.49/10.22 thf(f172,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8)),X7)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_171_diff__diff__eq2)).
% 68.49/10.22 thf(f2298,plain,(
% 68.49/10.22 spl93_84 | ~spl93_22 | spl93_74),
% 68.49/10.22 inference(avatar_split_clause,[],[f2252,f2247,f1832,f2295])).
% 68.49/10.22 thf(f2252,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $false) | (~spl93_22 | spl93_74)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f2251])).
% 68.49/10.22 thf(f2251,plain,(
% 68.49/10.22 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $false) | (~spl93_22 | spl93_74)),
% 68.49/10.22 inference(superposition,[],[f2248,f1833])).
% 68.49/10.22 thf(f2248,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) != $true) | spl93_74),
% 68.49/10.22 inference(avatar_component_clause,[],[f2247])).
% 68.49/10.22 thf(f2293,plain,(
% 68.49/10.22 spl93_83),
% 68.49/10.22 inference(avatar_split_clause,[],[f1223,f2291])).
% 68.49/10.22 thf(f1223,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3)) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f802])).
% 68.49/10.22 thf(f802,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3)) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f335])).
% 68.49/10.22 thf(f335,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f334])).
% 68.49/10.22 thf(f334,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(rectify,[],[f173])).
% 68.49/10.22 thf(f173,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)),X8)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_172_diff__add__eq)).
% 68.49/10.22 thf(f2289,plain,(
% 68.49/10.22 spl93_82),
% 68.49/10.22 inference(avatar_split_clause,[],[f1218,f2287])).
% 68.49/10.22 thf(f1218,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f797])).
% 68.49/10.22 thf(f797,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f325])).
% 68.49/10.22 thf(f325,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f324])).
% 68.49/10.22 thf(f324,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2))))),
% 68.49/10.22 inference(rectify,[],[f148])).
% 68.49/10.22 thf(f148,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X6 : X0,X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_147_add__diff__cancel__right)).
% 68.49/10.22 thf(f2285,plain,(
% 68.49/10.22 spl93_81),
% 68.49/10.22 inference(avatar_split_clause,[],[f1217,f2283])).
% 68.49/10.22 thf(f1217,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f796])).
% 68.49/10.22 thf(f796,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f323])).
% 68.49/10.22 thf(f323,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 68.49/10.22 inference(fool_elimination,[],[f322])).
% 68.49/10.22 thf(f322,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X3)),X2)))),
% 68.49/10.22 inference(rectify,[],[f166])).
% 68.49/10.22 thf(f166,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X6 : X0,X8 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X8)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)),X8)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_165_diff__right__commute)).
% 68.49/10.22 thf(f2281,plain,(
% 68.49/10.22 spl93_80),
% 68.49/10.22 inference(avatar_split_clause,[],[f1216,f2279])).
% 68.49/10.22 thf(f1216,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f795])).
% 68.49/10.22 thf(f795,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f321])).
% 68.49/10.22 thf(f321,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))))),
% 68.49/10.22 inference(fool_elimination,[],[f320])).
% 68.49/10.22 thf(f320,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3))))),
% 68.49/10.22 inference(rectify,[],[f175])).
% 68.49/10.22 thf(f175,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)),X8) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X8))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_diff__diff__add)).
% 68.49/10.22 thf(f2277,plain,(
% 68.49/10.22 spl93_79),
% 68.49/10.22 inference(avatar_split_clause,[],[f1215,f2275])).
% 68.49/10.22 thf(f1215,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel146912293up_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f794])).
% 68.49/10.22 thf(f794,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f319])).
% 68.49/10.22 thf(f319,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 68.49/10.22 inference(fool_elimination,[],[f318])).
% 68.49/10.22 thf(f318,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X3) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 68.49/10.22 inference(rectify,[],[f150])).
% 68.49/10.22 thf(f150,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X8 : X0,X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_add__diff__cancel__left)).
% 68.49/10.22 thf(f2273,plain,(
% 68.49/10.22 spl93_78),
% 68.49/10.22 inference(avatar_split_clause,[],[f1208,f2271])).
% 68.49/10.22 thf(f1208,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f787])).
% 68.49/10.22 thf(f787,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (ab_semigroup_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f305])).
% 68.49/10.22 thf(f305,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f304])).
% 68.49/10.22 thf(f304,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(rectify,[],[f165])).
% 68.49/10.22 thf(f165,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X8)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_ab__semigroup__add__class_Oadd__ac_I1_J)).
% 68.49/10.22 thf(f2269,plain,(
% 68.49/10.22 spl93_77),
% 68.49/10.22 inference(avatar_split_clause,[],[f1207,f2267])).
% 68.49/10.22 thf(f1207,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f786])).
% 68.49/10.22 thf(f786,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))) | (ab_semigroup_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f303])).
% 68.49/10.22 thf(f303,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 68.49/10.22 inference(fool_elimination,[],[f302])).
% 68.49/10.22 thf(f302,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3))))),
% 68.49/10.22 inference(rectify,[],[f157])).
% 68.49/10.22 thf(f157,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X7 : X0,X6 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X8))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_add_Oleft__commute)).
% 68.49/10.22 thf(f2265,plain,(
% 68.49/10.22 spl93_76),
% 68.49/10.22 inference(avatar_split_clause,[],[f1201,f2263])).
% 68.49/10.22 thf(f1201,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f779])).
% 68.49/10.22 thf(f779,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)) | (semigroup_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f291])).
% 68.49/10.22 thf(f291,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(fool_elimination,[],[f290])).
% 68.49/10.22 thf(f290,plain,(
% 68.49/10.22 ! [X0 : $tType] : (semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3)))),
% 68.49/10.22 inference(rectify,[],[f161])).
% 68.49/10.22 thf(f161,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (semigroup_add(X0) => ! [X6 : X0,X7 : X0,X8 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X8)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X8)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_add_Oassoc)).
% 68.49/10.22 thf(f2258,plain,(
% 68.49/10.22 spl93_75),
% 68.49/10.22 inference(avatar_split_clause,[],[f1432,f2256])).
% 68.49/10.22 thf(f1432,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : ((vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f769])).
% 68.49/10.22 thf(f769,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : (vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_rec_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))),
% 68.49/10.22 inference(rectify,[],[f101])).
% 68.49/10.22 thf(f101,axiom,(
% 68.49/10.22 ! [X0 : $tType,X3 : $tType,X2 : $tType,X51 : X0 > X2 > X3,X6 : X0,X7 : X2] : (vAPP(product_prod(X0,X2),X3,vAPP(sTfun(X0,sTfun(X2,X3)),sTfun(product_prod(X0,X2),X3),product_rec_prod(X0,X2,X3),X51),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X6),X7)) = vAPP(X2,X3,vAPP(X0,sTfun(X2,X3),X51,X6),X7))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_100_old_Oprod_Orec)).
% 68.49/10.22 thf(f2250,plain,(
% 68.49/10.22 spl93_73 | spl93_74),
% 68.49/10.22 inference(avatar_split_clause,[],[f1194,f2247,f2243])).
% 68.49/10.22 thf(f1194,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,group(a,ring_ext(a,b)),r) = $true) | ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK6),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))),
% 68.49/10.22 inference(cnf_transformation,[],[f1090])).
% 68.49/10.22 thf(f2241,plain,(
% 68.49/10.22 spl93_72),
% 68.49/10.22 inference(avatar_split_clause,[],[f1315,f2239])).
% 68.49/10.22 thf(f1315,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),sTfun(X1,sTfun(X1,X1)),mult(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f757])).
% 68.49/10.22 thf(f757,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),sTfun(X1,sTfun(X1,X1)),mult(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),sTfun(X1,sTfun(X1,X1)),mult(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))),
% 68.49/10.22 inference(rectify,[],[f221])).
% 68.49/10.22 thf(f221,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),sTfun(X0,sTfun(X0,X0)),mult(X0,X2),X54) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),sTfun(X0,sTfun(X0,X0)),mult(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X2),X54)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_220_units__of__mult)).
% 68.49/10.22 thf(f2196,plain,(
% 68.49/10.22 spl93_71 | ~spl93_22 | spl93_69),
% 68.49/10.22 inference(avatar_split_clause,[],[f2179,f2174,f1832,f2193])).
% 68.49/10.22 thf(f2193,plain,(
% 68.49/10.22 spl93_71 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $false)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_71])])).
% 68.49/10.22 thf(f2179,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $false) | (~spl93_22 | spl93_69)),
% 68.49/10.22 inference(trivial_inequality_removal,[],[f2178])).
% 68.49/10.22 thf(f2178,plain,(
% 68.49/10.22 ($true != $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $false) | (~spl93_22 | spl93_69)),
% 68.49/10.22 inference(superposition,[],[f2175,f1833])).
% 68.49/10.22 thf(f2175,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) != $true) | spl93_69),
% 68.49/10.22 inference(avatar_component_clause,[],[f2174])).
% 68.49/10.22 thf(f2183,plain,(
% 68.49/10.22 spl93_70),
% 68.49/10.22 inference(avatar_split_clause,[],[f1719,f2181])).
% 68.49/10.22 thf(f1719,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) )),
% 68.49/10.22 inference(forward_demodulation,[],[f1314,f1313])).
% 68.49/10.22 thf(f1314,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f756])).
% 68.49/10.22 thf(f756,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2)),X1))),
% 68.49/10.22 inference(rectify,[],[f138])).
% 68.49/10.22 thf(f138,axiom,(
% 68.49/10.22 ! [X48 : nat,X50 : nat,X47 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X48),X50)),X47) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X48),X47)),X50))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_137_diff__commute)).
% 68.49/10.22 thf(f2177,plain,(
% 68.49/10.22 spl93_67 | ~spl93_68 | spl93_69),
% 68.49/10.22 inference(avatar_split_clause,[],[f1716,f2174,f2170,f2166])).
% 68.49/10.22 thf(f2170,plain,(
% 68.49/10.22 spl93_68 <=> (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = sK5)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_68])])).
% 68.49/10.22 thf(f1716,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != sK5) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = sK5)),
% 68.49/10.22 inference(inner_rewriting,[],[f1192])).
% 68.49/10.22 thf(f1192,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != sK5) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(cnf_transformation,[],[f1088])).
% 68.49/10.22 thf(f1088,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true) | (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK5),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != sK5) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK5),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f775,f1087])).
% 68.49/10.22 thf(f1087,plain,(
% 68.49/10.22 ? [X0 : a] : (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) => (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),sK5),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != sK5) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),sK5),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f775,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true) | ? [X0 : a] : (! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(flattening,[],[f774])).
% 68.49/10.22 thf(f774,plain,(
% 68.49/10.22 ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true) | ? [X0 : a] : ((! [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) != vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) | ($true != vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))) & (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))) | (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(ennf_transformation,[],[f283])).
% 68.49/10.22 thf(f283,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) => (! [X0 : a] : (($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) & ($true = vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)))))) => (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r) = $true))),
% 68.49/10.22 inference(fool_elimination,[],[f282])).
% 68.49/10.22 thf(f282,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) => (! [X0 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X0),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X0) => ? [X1 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X0),X1)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X1),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))) => vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r))),
% 68.49/10.22 inference(rectify,[],[f97])).
% 68.49/10.22 thf(f97,axiom,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)) => (! [X33 : a] : (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X33),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) => ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) != X33) => ? [X49 : a] : ((vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r) = vAPP(a,a,vAPP(a,sTfun(a,a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,sTfun(a,a)),mult(a,ring_ext(a,b)),r),X33),X49)) & vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),X49),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))))) => vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,field(a,b),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_cring__fieldI2)).
% 68.49/10.22 thf(f2164,plain,(
% 68.49/10.22 spl93_66),
% 68.49/10.22 inference(avatar_split_clause,[],[f1483,f2161])).
% 68.49/10.22 thf(f1483,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f723])).
% 68.49/10.22 thf(f723,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f722])).
% 68.49/10.22 thf(f722,plain,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))),
% 68.49/10.22 inference(rectify,[],[f83])).
% 68.49/10.22 thf(f83,axiom,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_semiring__simprules_I4_J)).
% 68.49/10.22 thf(f2159,plain,(
% 68.49/10.22 spl93_65),
% 68.49/10.22 inference(avatar_split_clause,[],[f1313,f2157])).
% 68.49/10.22 thf(f2155,plain,(
% 68.49/10.22 spl93_64),
% 68.49/10.22 inference(avatar_split_clause,[],[f1312,f2153])).
% 68.49/10.22 thf(f1312,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f754])).
% 68.49/10.22 thf(f754,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 68.49/10.22 inference(rectify,[],[f145])).
% 68.49/10.22 thf(f145,axiom,(
% 68.49/10.22 ! [X53 : nat,X47 : nat,X52 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X53),X52) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X53),X47)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X52),X47)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_144_diff__cancel2)).
% 68.49/10.22 thf(f2151,plain,(
% 68.49/10.22 spl93_63),
% 68.49/10.22 inference(avatar_split_clause,[],[f1311,f2149])).
% 68.49/10.22 thf(f1311,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f753])).
% 68.49/10.22 thf(f753,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 68.49/10.22 inference(rectify,[],[f146])).
% 68.49/10.22 thf(f146,axiom,(
% 68.49/10.22 ! [X47 : nat,X53 : nat,X52 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X53),X52) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X47),X53)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X47),X52)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_145_Nat_Odiff__cancel)).
% 68.49/10.22 thf(f2144,plain,(
% 68.49/10.22 spl93_62),
% 68.49/10.22 inference(avatar_split_clause,[],[f1482,f2141])).
% 68.49/10.22 thf(f1482,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f721])).
% 68.49/10.22 thf(f721,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f720])).
% 68.49/10.22 thf(f720,plain,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(rectify,[],[f183])).
% 68.49/10.22 thf(f183,axiom,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,one(a,ring_ext(a,b)),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),units(a,ring_ext(a,b)),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_182_Units__one__closed)).
% 68.49/10.22 thf(f2139,plain,(
% 68.49/10.22 spl93_61),
% 68.49/10.22 inference(avatar_split_clause,[],[f1481,f2136])).
% 68.49/10.22 thf(f1481,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f719])).
% 68.49/10.22 thf(f719,plain,(
% 68.49/10.22 (vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f718])).
% 68.49/10.22 thf(f718,plain,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))),
% 68.49/10.22 inference(rectify,[],[f40])).
% 68.49/10.22 thf(f40,axiom,(
% 68.49/10.22 vAPP(set(a),$o,vAPP(a,sTfun(set(a),$o),member(a),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),set(a),partial_carrier(a,monoid_ext(a,ring_ext(a,b))),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_zero__closed)).
% 68.49/10.22 thf(f2134,plain,(
% 68.49/10.22 spl93_60),
% 68.49/10.22 inference(avatar_split_clause,[],[f1179,f2131])).
% 68.49/10.22 thf(f1179,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 inference(cnf_transformation,[],[f218])).
% 68.49/10.22 thf(f218,axiom,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r) = vAPP(a,a,vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),sTfun(a,a),a_inv(a,b),r),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),a,zero(a,b),r)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_local_Ominus__zero)).
% 68.49/10.22 thf(f2114,plain,(
% 68.49/10.22 spl93_59),
% 68.49/10.22 inference(avatar_split_clause,[],[f1701,f2112])).
% 68.49/10.22 thf(f1701,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | (X1 != X2)) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1700])).
% 68.49/10.22 thf(f1700,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1696])).
% 68.49/10.22 thf(f1696,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_char_0(X0) != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 68.49/10.22 inference(binary_proxy_clausification,[],[f1200])).
% 68.49/10.22 thf(f1200,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | (semiring_char_0(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f778])).
% 68.49/10.22 thf(f778,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : nat,X2 : nat] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | (semiring_char_0(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f289])).
% 68.49/10.22 thf(f289,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((semiring_char_0(X0) = $true) => ! [X1 : nat,X2 : nat] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)))),
% 68.49/10.22 inference(fool_elimination,[],[f288])).
% 68.49/10.22 thf(f288,plain,(
% 68.49/10.22 ! [X0 : $tType] : (semiring_char_0(X0) => ! [X1 : nat,X2 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) = vAPP(nat,X0,semiring_1_of_nat(X0),X2)) = (X1 = X2)))),
% 68.49/10.22 inference(rectify,[],[f250])).
% 68.49/10.22 thf(f250,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (semiring_char_0(X0) => ! [X53 : nat,X52 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X53) = vAPP(nat,X0,semiring_1_of_nat(X0),X52)) = (X52 = X53)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_249_of__nat__eq__iff)).
% 68.49/10.22 thf(f2110,plain,(
% 68.49/10.22 spl93_58),
% 68.49/10.22 inference(avatar_split_clause,[],[f1356,f2108])).
% 68.49/10.22 thf(f1356,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f918])).
% 68.49/10.22 thf(f918,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f499])).
% 68.49/10.22 thf(f499,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)))),
% 68.49/10.22 inference(fool_elimination,[],[f498])).
% 68.49/10.22 thf(f498,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0)))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),$o,field(X1,X0),X2) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,zero(X1,X0),X2) != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,ring_ext(X1,X0))),X1,one(X1,ring_ext(X1,X0)),X2)))),
% 68.49/10.22 inference(rectify,[],[f108])).
% 68.49/10.22 thf(f108,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X46 : partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2)))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),$o,field(X0,X2),X46) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,zero(X0,X2),X46) != vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,ring_ext(X0,X2))),X0,one(X0,ring_ext(X0,X2)),X46)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_one__not__zero)).
% 68.49/10.22 thf(f2106,plain,(
% 68.49/10.22 spl93_57),
% 68.49/10.22 inference(avatar_split_clause,[],[f1234,f2104])).
% 68.49/10.22 thf(f1234,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f813])).
% 68.49/10.22 thf(f813,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f357])).
% 68.49/10.22 thf(f357,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))))),
% 68.49/10.22 inference(fool_elimination,[],[f356])).
% 68.49/10.22 thf(f356,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),vAPP(X0,X0,uminus_uminus(X0),X1))))),
% 68.49/10.22 inference(rectify,[],[f246])).
% 68.49/10.22 thf(f246,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X7)),vAPP(X0,X0,uminus_uminus(X0),X6))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_245_add_Oinverse__distrib__swap)).
% 68.49/10.22 thf(f2102,plain,(
% 68.49/10.22 spl93_56),
% 68.49/10.22 inference(avatar_split_clause,[],[f1222,f2100])).
% 68.49/10.22 thf(f1222,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f801])).
% 68.49/10.22 thf(f801,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f333])).
% 68.49/10.22 thf(f333,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f332])).
% 68.49/10.22 thf(f332,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,uminus_uminus(X0),X2))))),
% 68.49/10.22 inference(rectify,[],[f238])).
% 68.49/10.22 thf(f238,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X6)),vAPP(X0,X0,uminus_uminus(X0),X7))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_237_minus__add__distrib)).
% 68.49/10.22 thf(f2098,plain,(
% 68.49/10.22 spl93_55),
% 68.49/10.22 inference(avatar_split_clause,[],[f1199,f2096])).
% 68.49/10.22 thf(f1199,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_1(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f777])).
% 68.49/10.22 thf(f777,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : nat,X2 : nat] : (vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_1(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f287])).
% 68.49/10.22 thf(f287,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((semiring_1(X0) = $true) => ! [X1 : nat,X2 : nat] : (vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f286])).
% 68.49/10.22 thf(f286,plain,(
% 68.49/10.22 ! [X0 : $tType] : (semiring_1(X0) => ! [X1 : nat,X2 : nat] : (vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))))),
% 68.49/10.22 inference(rectify,[],[f251])).
% 68.49/10.22 thf(f251,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (semiring_1(X0) => ! [X53 : nat,X52 : nat] : (vAPP(nat,X0,semiring_1_of_nat(X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X53),X52)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X53)),vAPP(nat,X0,semiring_1_of_nat(X0),X52))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_250_of__nat__add)).
% 68.49/10.22 thf(f2084,plain,(
% 68.49/10.22 spl93_54),
% 68.49/10.22 inference(avatar_split_clause,[],[f1352,f2082])).
% 68.49/10.22 thf(f1352,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0)))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1141])).
% 68.49/10.22 thf(f1141,plain,(
% 68.49/10.22 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0))) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0))))) | ($true != vAPP(nat,$o,X0,X1)))),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f915,f1140])).
% 68.49/10.22 thf(f1140,plain,(
% 68.49/10.22 ! [X0 : nat > $o] : (? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)))) => (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0))) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,vAPP(sTfun(nat,$o),nat,sK30,X0))))))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f915,plain,(
% 68.49/10.22 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 68.49/10.22 inference(flattening,[],[f914])).
% 68.49/10.22 thf(f914,plain,(
% 68.49/10.22 ! [X0 : nat > $o,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3))))) | ($true != vAPP(nat,$o,X0,X1)))),
% 68.49/10.22 inference(ennf_transformation,[],[f493])).
% 68.49/10.22 thf(f493,plain,(
% 68.49/10.22 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,X0,X1)) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3))) => ($true = vAPP(nat,$o,X0,X3))) => ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2)))))),
% 68.49/10.22 inference(fool_elimination,[],[f492])).
% 68.49/10.22 thf(f492,plain,(
% 68.49/10.22 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (vAPP(nat,$o,X0,X1) => (! [X3 : nat] : (vAPP(nat,$o,X0,vAPP(nat,nat,suc,X3)) => vAPP(nat,$o,X0,X3)) => vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))))),
% 68.49/10.22 inference(rectify,[],[f142])).
% 68.49/10.22 thf(f142,axiom,(
% 68.49/10.22 ! [X26 : nat > $o,X47 : nat,X48 : nat] : (vAPP(nat,$o,X26,X47) => (! [X59 : nat] : (vAPP(nat,$o,X26,vAPP(nat,nat,suc,X59)) => vAPP(nat,$o,X26,X59)) => vAPP(nat,$o,X26,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X47),X48))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_zero__induct__lemma)).
% 68.49/10.22 thf(f2076,plain,(
% 68.49/10.22 spl93_53),
% 68.49/10.22 inference(avatar_split_clause,[],[f1355,f2074])).
% 68.49/10.22 thf(f1355,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),units(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f917])).
% 68.49/10.22 thf(f917,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),units(X1,X0),X2)) | ($true != vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)))),
% 68.49/10.22 inference(ennf_transformation,[],[f497])).
% 68.49/10.22 thf(f497,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (($true = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2)) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),units(X1,X0),X2)))),
% 68.49/10.22 inference(fool_elimination,[],[f496])).
% 68.49/10.22 thf(f496,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),$o,group(X1,X0),X2) => (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),partial_carrier(X1,monoid_ext(X1,X0)),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),set(X1),units(X1,X0),X2)))),
% 68.49/10.22 inference(rectify,[],[f189])).
% 68.49/10.22 thf(f189,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),$o,group(X0,X2),X54) => (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),partial_carrier(X0,monoid_ext(X0,X2)),X54) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),set(X0),units(X0,X2),X54)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_group_OUnits__eq)).
% 68.49/10.22 thf(f2068,plain,(
% 68.49/10.22 spl93_52),
% 68.49/10.22 inference(avatar_split_clause,[],[f1221,f2066])).
% 68.49/10.22 thf(f1221,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f800])).
% 68.49/10.22 thf(f800,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f331])).
% 68.49/10.22 thf(f331,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)))),
% 68.49/10.22 inference(fool_elimination,[],[f330])).
% 68.49/10.22 thf(f330,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X2)),X1)))),
% 68.49/10.22 inference(rectify,[],[f247])).
% 68.49/10.22 thf(f247,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X7 : X0,X6 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X7)),X6) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,uminus_uminus(X0),X6)),X7)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_246_minus__diff__commute)).
% 68.49/10.22 thf(f2064,plain,(
% 68.49/10.22 spl93_51),
% 68.49/10.22 inference(avatar_split_clause,[],[f1699,f2062])).
% 68.49/10.22 thf(f1699,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) != vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | (X1 = X2)) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1698])).
% 68.49/10.22 thf(f1698,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : ((vAPP(nat,X0,semiring_1_of_nat(X0),X1) != vAPP(nat,X0,semiring_1_of_nat(X0),X2)) | (semiring_char_0(X0) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1697])).
% 68.49/10.22 thf(f1697,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : nat,X1 : nat] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(nat,X0,semiring_1_of_nat(X0),X1)),vAPP(nat,X0,semiring_1_of_nat(X0),X2))) | (semiring_char_0(X0) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2))) )),
% 68.49/10.22 inference(binary_proxy_clausification,[],[f1200])).
% 68.49/10.22 thf(f2050,plain,(
% 68.49/10.22 spl93_50),
% 68.49/10.22 inference(avatar_split_clause,[],[f1353,f2048])).
% 68.49/10.22 thf(f1353,plain,(
% 68.49/10.22 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X1),X2))) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK30,X0))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1141])).
% 68.49/10.22 thf(f2046,plain,(
% 68.49/10.22 spl93_49),
% 68.49/10.22 inference(avatar_split_clause,[],[f1278,f2044])).
% 68.49/10.22 thf(f1278,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X1 : set(X0)] : ((vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f417])).
% 68.49/10.22 thf(f417,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),X1)) = X1)),
% 68.49/10.22 inference(fool_elimination,[],[f416])).
% 68.49/10.22 thf(f416,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X2 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))) = X1)),
% 68.49/10.22 inference(rectify,[],[f47])).
% 68.49/10.22 thf(f47,axiom,(
% 68.49/10.22 ! [X0 : $tType,X27 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X28 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X28),X27)))) = X27)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)).
% 68.49/10.22 thf(f2033,plain,(
% 68.49/10.22 spl93_48),
% 68.49/10.22 inference(avatar_split_clause,[],[f1385,f2031])).
% 68.49/10.22 thf(f1385,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK33(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK34(X0,X1),X2)) = X2)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1145])).
% 68.49/10.22 thf(f1145,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK33(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK34(X0,X1),X2)) = X2)),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34])],[f764,f1144])).
% 68.49/10.22 thf(f1144,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2) => (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK33(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK34(X0,X1),X2)) = X2))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f764,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : ? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2)),
% 68.49/10.22 inference(rectify,[],[f69])).
% 68.49/10.22 thf(f69,axiom,(
% 68.49/10.22 ! [X0 : $tType,X2 : $tType,X44 : product_prod(X0,X2)] : ? [X23 : X0,X45 : X2] : (vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X23),X45) = X44)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_surj__pair)).
% 68.49/10.22 thf(f2029,plain,(
% 68.49/10.22 spl93_47),
% 68.49/10.22 inference(avatar_split_clause,[],[f1384,f2027])).
% 68.49/10.22 thf(f1384,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : ((vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK31(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK32(X0,X1),X2)) = X2)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f1143])).
% 68.49/10.22 thf(f1143,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK31(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK32(X0,X1),X2)) = X2)),
% 68.49/10.22 inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32])],[f966,f1142])).
% 68.49/10.22 thf(f1142,plain,(
% 68.49/10.22 ! [X1 : $tType,X0 : $tType,X2 : product_prod(X0,X1)] : (? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2) => (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),vAPP(product_prod(X0,X1),X0,sK31(X0,X1),X2)),vAPP(product_prod(X0,X1),X1,sK32(X0,X1),X2)) = X2))),
% 68.49/10.22 introduced(choice_axiom,[])).
% 68.49/10.22 thf(f966,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : ? [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) = X2)),
% 68.49/10.22 inference(ennf_transformation,[],[f763])).
% 68.49/10.22 thf(f763,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X0,X1)] : ~! [X3 : X0,X4 : X1] : (vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4) != X2)),
% 68.49/10.22 inference(rectify,[],[f56])).
% 68.49/10.22 thf(f56,axiom,(
% 68.49/10.22 ! [X0 : $tType,X2 : $tType,X14 : product_prod(X0,X2)] : ~! [X33 : X0,X34 : X2] : (vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X33),X34) != X14)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_old_Oprod_Oexhaust)).
% 68.49/10.22 thf(f2025,plain,(
% 68.49/10.22 spl93_46),
% 68.49/10.22 inference(avatar_split_clause,[],[f1310,f2023])).
% 68.49/10.22 thf(f1310,plain,(
% 68.49/10.22 ( ! [X1 : $tType,X0 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : ((vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),X1,one(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f752])).
% 68.49/10.22 thf(f752,plain,(
% 68.49/10.22 ! [X0 : $tType,X1 : $tType,X2 : partia1265057091ct_ext(X1,monoid_ext(X1,X0))] : (vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),X1,one(X1,X0),X2) = vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),X1,one(X1,product_unit),vAPP(partia1265057091ct_ext(X1,monoid_ext(X1,X0)),partia1265057091ct_ext(X1,monoid_ext(X1,product_unit)),units_of(X1,X0),X2)))),
% 68.49/10.22 inference(rectify,[],[f225])).
% 68.49/10.22 thf(f225,axiom,(
% 68.49/10.22 ! [X2 : $tType,X0 : $tType,X54 : partia1265057091ct_ext(X0,monoid_ext(X0,X2))] : (vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),X0,one(X0,X2),X54) = vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),X0,one(X0,product_unit),vAPP(partia1265057091ct_ext(X0,monoid_ext(X0,X2)),partia1265057091ct_ext(X0,monoid_ext(X0,product_unit)),units_of(X0,X2),X54)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_224_units__of__one)).
% 68.49/10.22 thf(f1999,plain,(
% 68.49/10.22 spl93_45),
% 68.49/10.22 inference(avatar_split_clause,[],[f1233,f1997])).
% 68.49/10.22 thf(f1233,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f812])).
% 68.49/10.22 thf(f812,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f355])).
% 68.49/10.22 thf(f355,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2))),
% 68.49/10.22 inference(fool_elimination,[],[f354])).
% 68.49/10.22 thf(f354,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = X2))),
% 68.49/10.22 inference(rectify,[],[f237])).
% 68.49/10.22 thf(f237,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = X7))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_236_minus__add__cancel)).
% 68.49/10.22 thf(f1995,plain,(
% 68.49/10.22 spl93_44),
% 68.49/10.22 inference(avatar_split_clause,[],[f1232,f1993])).
% 68.49/10.22 thf(f1232,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f811])).
% 68.49/10.22 thf(f811,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f353])).
% 68.49/10.22 thf(f353,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2))),
% 68.49/10.22 inference(fool_elimination,[],[f352])).
% 68.49/10.22 thf(f352,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2)) = X2))),
% 68.49/10.22 inference(rectify,[],[f236])).
% 68.49/10.22 thf(f236,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X6)),X7)) = X7))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_235_add__minus__cancel)).
% 68.49/10.22 thf(f1991,plain,(
% 68.49/10.22 spl93_43),
% 68.49/10.22 inference(avatar_split_clause,[],[f1231,f1989])).
% 68.49/10.22 thf(f1231,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2))) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f810])).
% 68.49/10.22 thf(f810,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2))) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f351])).
% 68.49/10.22 thf(f351,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f350])).
% 68.49/10.22 thf(f350,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1) = vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2))))),
% 68.49/10.22 inference(rectify,[],[f239])).
% 68.49/10.22 thf(f239,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,uminus_uminus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X6)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_238_minus__diff__eq)).
% 68.49/10.22 thf(f1987,plain,(
% 68.49/10.22 spl93_42),
% 68.49/10.22 inference(avatar_split_clause,[],[f1230,f1985])).
% 68.49/10.22 thf(f1230,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f809])).
% 68.49/10.22 thf(f809,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f349])).
% 68.49/10.22 thf(f349,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))))),
% 68.49/10.22 inference(fool_elimination,[],[f348])).
% 68.49/10.22 thf(f348,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),vAPP(X0,X0,uminus_uminus(X0),X2))))),
% 68.49/10.22 inference(rectify,[],[f240])).
% 68.49/10.22 thf(f240,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),vAPP(X0,X0,uminus_uminus(X0),X7))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_239_diff__minus__eq__add)).
% 68.49/10.22 thf(f1983,plain,(
% 68.49/10.22 spl93_41),
% 68.49/10.22 inference(avatar_split_clause,[],[f1220,f1981])).
% 68.49/10.22 thf(f1220,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) | (ab_group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f799])).
% 68.49/10.22 thf(f799,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)) | (ab_group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f329])).
% 68.49/10.22 thf(f329,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)))),
% 68.49/10.22 inference(fool_elimination,[],[f328])).
% 68.49/10.22 thf(f328,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X1)),X2) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X2),X1)))),
% 68.49/10.22 inference(rectify,[],[f241])).
% 68.49/10.22 thf(f241,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,uminus_uminus(X0),X6)),X7) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X7),X6)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_240_uminus__add__conv__diff)).
% 68.49/10.22 thf(f1970,plain,(
% 68.49/10.22 spl93_40),
% 68.49/10.22 inference(avatar_split_clause,[],[f1271,f1968])).
% 68.49/10.22 thf(f1271,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f746])).
% 68.49/10.22 thf(f746,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,suc,X1)))),
% 68.49/10.22 inference(rectify,[],[f133])).
% 68.49/10.22 thf(f133,axiom,(
% 68.49/10.22 ! [X53 : nat,X52 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X53),vAPP(nat,nat,suc,X52)) = vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X53),X52)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_132_add__Suc__right)).
% 68.49/10.22 thf(f1966,plain,(
% 68.49/10.22 spl93_39),
% 68.49/10.22 inference(avatar_split_clause,[],[f1270,f1964])).
% 68.49/10.22 thf(f1270,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f745])).
% 68.49/10.22 thf(f745,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X0)),X1))),
% 68.49/10.22 inference(rectify,[],[f139])).
% 68.49/10.22 thf(f139,axiom,(
% 68.49/10.22 ! [X53 : nat,X52 : nat] : (vAPP(nat,nat,suc,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X53),X52)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,suc,X53)),X52))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_138_add__Suc)).
% 68.49/10.22 thf(f1962,plain,(
% 68.49/10.22 spl93_38),
% 68.49/10.22 inference(avatar_split_clause,[],[f1269,f1960])).
% 68.49/10.22 thf(f1960,plain,(
% 68.49/10.22 spl93_38 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_38])])).
% 68.49/10.22 thf(f1269,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f744])).
% 68.49/10.22 thf(f744,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)))),
% 68.49/10.22 inference(rectify,[],[f132])).
% 68.49/10.22 thf(f132,axiom,(
% 68.49/10.22 ! [X53 : nat,X52 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),X53),X52) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,suc,X53)),vAPP(nat,nat,suc,X52)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_131_diff__Suc__Suc)).
% 68.49/10.22 thf(f1958,plain,(
% 68.49/10.22 spl93_37),
% 68.49/10.22 inference(avatar_split_clause,[],[f1480,f1955])).
% 68.49/10.22 thf(f1480,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f717])).
% 68.49/10.22 thf(f717,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f716])).
% 68.49/10.22 thf(f716,plain,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(rectify,[],[f195])).
% 68.49/10.22 thf(f195,axiom,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_194_units__group)).
% 68.49/10.22 thf(f1953,plain,(
% 68.49/10.22 spl93_36),
% 68.49/10.22 inference(avatar_split_clause,[],[f1479,f1950])).
% 68.49/10.22 thf(f1479,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,comm_group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f715])).
% 68.49/10.22 thf(f715,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,comm_group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r)) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f714])).
% 68.49/10.22 thf(f714,plain,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,comm_group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),
% 68.49/10.22 inference(rectify,[],[f249])).
% 68.49/10.22 thf(f249,axiom,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,product_unit)),$o,comm_group(a,product_unit),vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),partia1265057091ct_ext(a,monoid_ext(a,product_unit)),units_of(a,ring_ext(a,b)),r))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_248_units__comm__group)).
% 68.49/10.22 thf(f1948,plain,(
% 68.49/10.22 spl93_35),
% 68.49/10.22 inference(avatar_split_clause,[],[f1647,f1946])).
% 68.49/10.22 thf(f1946,plain,(
% 68.49/10.22 spl93_35 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1)) | (X0 != X1))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_35])])).
% 68.49/10.22 thf(f1647,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1)) | (X0 != X1)) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1646])).
% 68.49/10.22 thf(f1646,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1642])).
% 68.49/10.22 thf(f1642,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) )),
% 68.49/10.22 inference(binary_proxy_clausification,[],[f1275])).
% 68.49/10.22 thf(f1275,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) )),
% 68.49/10.22 inference(cnf_transformation,[],[f411])).
% 68.49/10.22 thf(f411,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))),
% 68.49/10.22 inference(fool_elimination,[],[f410])).
% 68.49/10.22 thf(f410,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) = vAPP(nat,nat,suc,X1)) = (X0 = X1))),
% 68.49/10.22 inference(rectify,[],[f135])).
% 68.49/10.22 thf(f135,axiom,(
% 68.49/10.22 ! [X57 : nat,X58 : nat] : ((vAPP(nat,nat,suc,X57) = vAPP(nat,nat,suc,X58)) = (X57 = X58))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_134_old_Onat_Oinject)).
% 68.49/10.22 thf(f1918,plain,(
% 68.49/10.22 spl93_34),
% 68.49/10.22 inference(avatar_split_clause,[],[f1506,f1916])).
% 68.49/10.22 thf(f1506,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel1352612707id_add(X0) != $true)) )),
% 68.49/10.22 inference(equality_resolution,[],[f1202])).
% 68.49/10.22 thf(f1202,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != X3) | (cancel1352612707id_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f780])).
% 68.49/10.22 thf(f780,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) != X3)) | (cancel1352612707id_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f293])).
% 68.49/10.22 thf(f293,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel1352612707id_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = X3) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1)))),
% 68.49/10.22 inference(fool_elimination,[],[f292])).
% 68.49/10.22 thf(f292,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2) = X3) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X3),X2) = X1)))),
% 68.49/10.22 inference(rectify,[],[f176])).
% 68.49/10.22 thf(f176,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel1352612707id_add(X0) => ! [X8 : X0,X7 : X0,X6 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X8),X7) = X6) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7) = X8)))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_175_add__implies__diff)).
% 68.49/10.22 thf(f1914,plain,(
% 68.49/10.22 spl93_33),
% 68.49/10.22 inference(avatar_split_clause,[],[f1229,f1912])).
% 68.49/10.22 thf(f1229,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f808])).
% 68.49/10.22 thf(f808,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f347])).
% 68.49/10.22 thf(f347,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1))),
% 68.49/10.22 inference(fool_elimination,[],[f346])).
% 68.49/10.22 thf(f346,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X1),X2)),X2) = X1))),
% 68.49/10.22 inference(rectify,[],[f154])).
% 68.49/10.22 thf(f154,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),X6),X7)),X7) = X6))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_diff__add__cancel)).
% 68.49/10.22 thf(f1910,plain,(
% 68.49/10.22 spl93_32),
% 68.49/10.22 inference(avatar_split_clause,[],[f1228,f1908])).
% 68.49/10.22 thf(f1228,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f807])).
% 68.49/10.22 thf(f807,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (group_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f345])).
% 68.49/10.22 thf(f345,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 68.49/10.22 inference(fool_elimination,[],[f344])).
% 68.49/10.22 thf(f344,plain,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 68.49/10.22 inference(rectify,[],[f153])).
% 68.49/10.22 thf(f153,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X7) = X6))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_152_add__diff__cancel)).
% 68.49/10.22 thf(f1906,plain,(
% 68.49/10.22 spl93_31),
% 68.49/10.22 inference(avatar_split_clause,[],[f1214,f1904])).
% 68.49/10.22 thf(f1214,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f793])).
% 68.49/10.22 thf(f793,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f317])).
% 68.49/10.22 thf(f317,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2))),
% 68.49/10.22 inference(fool_elimination,[],[f316])).
% 68.49/10.22 thf(f316,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X1) = X2))),
% 68.49/10.22 inference(rectify,[],[f149])).
% 68.49/10.22 thf(f149,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X6) = X7))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_148_add__diff__cancel__left_H)).
% 68.49/10.22 thf(f1902,plain,(
% 68.49/10.22 spl93_30),
% 68.49/10.22 inference(avatar_split_clause,[],[f1213,f1900])).
% 68.49/10.22 thf(f1213,plain,(
% 68.49/10.22 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f792])).
% 68.49/10.22 thf(f792,plain,(
% 68.49/10.22 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1) | (cancel146912293up_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f315])).
% 68.49/10.22 thf(f315,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((cancel146912293up_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 68.49/10.22 inference(fool_elimination,[],[f314])).
% 68.49/10.22 thf(f314,plain,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X2) = X1))),
% 68.49/10.22 inference(rectify,[],[f147])).
% 68.49/10.22 thf(f147,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (cancel146912293up_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),minus_minus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X7) = X6))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_146_add__diff__cancel__right_H)).
% 68.49/10.22 thf(f1898,plain,(
% 68.49/10.22 spl93_29),
% 68.49/10.22 inference(avatar_split_clause,[],[f1645,f1896])).
% 68.49/10.22 thf(f1896,plain,(
% 68.49/10.22 spl93_29 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1)) | (X0 = X1))),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_29])])).
% 68.49/10.22 thf(f1645,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1)) | (X0 = X1)) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1644])).
% 68.49/10.22 thf(f1644,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,suc,X0) != vAPP(nat,nat,suc,X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) )),
% 68.49/10.22 inference(equality_proxy_clausification,[],[f1643])).
% 68.49/10.22 thf(f1643,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),vAPP(nat,nat,suc,X0)),vAPP(nat,nat,suc,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) )),
% 68.49/10.22 inference(binary_proxy_clausification,[],[f1275])).
% 68.49/10.22 thf(f1888,plain,(
% 68.49/10.22 spl93_28),
% 68.49/10.22 inference(avatar_split_clause,[],[f1206,f1886])).
% 68.49/10.22 thf(f1206,plain,(
% 68.49/10.22 ( ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) != $true)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f785])).
% 68.49/10.22 thf(f785,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))) | (ab_semigroup_add(X0) != $true))),
% 68.49/10.22 inference(ennf_transformation,[],[f301])).
% 68.49/10.22 thf(f301,plain,(
% 68.49/10.22 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) => (plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0))))),
% 68.49/10.22 inference(fool_elimination,[],[f300])).
% 68.49/10.22 thf(f300,plain,(
% 68.49/10.22 ! [X0 : $tType] : (ab_semigroup_add(X0) => (plus_plus(X0) = (^[X1 : X0, X2 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X1)))))),
% 68.49/10.22 inference(rectify,[],[f158])).
% 68.49/10.22 thf(f158,axiom,(
% 68.49/10.22 ! [X0 : $tType] : (ab_semigroup_add(X0) => (plus_plus(X0) = (^[X60 : X0, X61 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X61),X60)))))),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_157_add_Ocommute)).
% 68.49/10.22 thf(f1884,plain,(
% 68.49/10.22 spl93_27),
% 68.49/10.22 inference(avatar_split_clause,[],[f1268,f1882])).
% 68.49/10.22 thf(f1268,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f743])).
% 68.49/10.22 thf(f743,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0) = X1)),
% 68.49/10.22 inference(rectify,[],[f144])).
% 68.49/10.22 thf(f144,axiom,(
% 68.49/10.22 ! [X52 : nat,X53 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X52),X53)),X52) = X53)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_diff__add__inverse)).
% 68.49/10.22 thf(f1880,plain,(
% 68.49/10.22 spl93_26),
% 68.49/10.22 inference(avatar_split_clause,[],[f1267,f1878])).
% 68.49/10.22 thf(f1267,plain,(
% 68.49/10.22 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f742])).
% 68.49/10.22 thf(f742,plain,(
% 68.49/10.22 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1) = X0)),
% 68.49/10.22 inference(rectify,[],[f143])).
% 68.49/10.22 thf(f143,axiom,(
% 68.49/10.22 ! [X53 : nat,X52 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),minus_minus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X53),X52)),X52) = X53)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_diff__add__inverse2)).
% 68.49/10.22 thf(f1876,plain,(
% 68.49/10.22 spl93_25),
% 68.49/10.22 inference(avatar_split_clause,[],[f1478,f1873])).
% 68.49/10.22 thf(f1478,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f713])).
% 68.49/10.22 thf(f713,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f712])).
% 68.49/10.22 thf(f712,plain,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r)),
% 68.49/10.22 inference(rectify,[],[f117])).
% 68.49/10.22 thf(f117,axiom,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,abelian_group(a,b),r)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_116_is__abelian__group)).
% 68.49/10.22 thf(f1871,plain,(
% 68.49/10.22 spl93_24),
% 68.49/10.22 inference(avatar_split_clause,[],[f1477,f1868])).
% 68.49/10.22 thf(f1477,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f711])).
% 68.49/10.22 thf(f711,plain,(
% 68.49/10.22 (vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f710])).
% 68.49/10.22 thf(f710,plain,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r)),
% 68.49/10.22 inference(rectify,[],[f23])).
% 68.49/10.22 thf(f23,axiom,(
% 68.49/10.22 vAPP(partia1265057091ct_ext(a,monoid_ext(a,ring_ext(a,b))),$o,semiring(a,b),r)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_local_Osemiring__axioms)).
% 68.49/10.22 thf(f1866,plain,(
% 68.49/10.22 spl93_23),
% 68.49/10.22 inference(avatar_split_clause,[],[f1196,f1864])).
% 68.49/10.22 thf(f1864,plain,(
% 68.49/10.22 spl93_23 <=> ! [X0 : nat] : (vAPP(nat,nat,suc,X0) != X0)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_23])])).
% 68.49/10.22 thf(f1196,plain,(
% 68.49/10.22 ( ! [X0 : nat] : ((vAPP(nat,nat,suc,X0) != X0)) )),
% 68.49/10.22 inference(cnf_transformation,[],[f739])).
% 68.49/10.22 thf(f739,plain,(
% 68.49/10.22 ! [X0 : nat] : (vAPP(nat,nat,suc,X0) != X0)),
% 68.49/10.22 inference(rectify,[],[f137])).
% 68.49/10.22 thf(f137,axiom,(
% 68.49/10.22 ! [X52 : nat] : (vAPP(nat,nat,suc,X52) != X52)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_136_n__not__Suc__n)).
% 68.49/10.22 thf(f1834,plain,(
% 68.49/10.22 spl93_22),
% 68.49/10.22 inference(avatar_split_clause,[],[f279,f1832])).
% 68.49/10.22 thf(f279,plain,(
% 68.49/10.22 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 68.49/10.22 introduced(fool_axiom,[])).
% 68.49/10.22 thf(f1830,plain,(
% 68.49/10.22 spl93_21),
% 68.49/10.22 inference(avatar_split_clause,[],[f1476,f1827])).
% 68.49/10.22 thf(f1476,plain,(
% 68.49/10.22 (group_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f709])).
% 68.49/10.22 thf(f709,plain,(
% 68.49/10.22 (group_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f708])).
% 68.49/10.22 thf(f708,plain,(
% 68.49/10.22 group_add(int)),
% 68.49/10.22 inference(rectify,[],[f266])).
% 68.49/10.22 thf(f266,axiom,(
% 68.49/10.22 group_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ogroup__add)).
% 68.49/10.22 thf(f1825,plain,(
% 68.49/10.22 spl93_20),
% 68.49/10.22 inference(avatar_split_clause,[],[f1475,f1822])).
% 68.49/10.22 thf(f1475,plain,(
% 68.49/10.22 (ab_group_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f707])).
% 68.49/10.22 thf(f707,plain,(
% 68.49/10.22 (ab_group_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f706])).
% 68.49/10.22 thf(f706,plain,(
% 68.49/10.22 ab_group_add(int)),
% 68.49/10.22 inference(rectify,[],[f264])).
% 68.49/10.22 thf(f264,axiom,(
% 68.49/10.22 ab_group_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__group__add)).
% 68.49/10.22 thf(f1820,plain,(
% 68.49/10.22 spl93_19),
% 68.49/10.22 inference(avatar_split_clause,[],[f1474,f1817])).
% 68.49/10.22 thf(f1817,plain,(
% 68.49/10.22 spl93_19 <=> (cancel146912293up_add(nat) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_19])])).
% 68.49/10.22 thf(f1474,plain,(
% 68.49/10.22 (cancel146912293up_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f705])).
% 68.49/10.22 thf(f705,plain,(
% 68.49/10.22 (cancel146912293up_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f704])).
% 68.49/10.22 thf(f704,plain,(
% 68.49/10.22 cancel146912293up_add(nat)),
% 68.49/10.22 inference(rectify,[],[f268])).
% 68.49/10.22 thf(f268,axiom,(
% 68.49/10.22 cancel146912293up_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__ab__semigroup__add_2)).
% 68.49/10.22 thf(f1815,plain,(
% 68.49/10.22 spl93_18),
% 68.49/10.22 inference(avatar_split_clause,[],[f1473,f1812])).
% 68.49/10.22 thf(f1473,plain,(
% 68.49/10.22 (cancel146912293up_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f703])).
% 68.49/10.22 thf(f703,plain,(
% 68.49/10.22 (cancel146912293up_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f702])).
% 68.49/10.22 thf(f702,plain,(
% 68.49/10.22 cancel146912293up_add(int)),
% 68.49/10.22 inference(rectify,[],[f257])).
% 68.49/10.22 thf(f257,axiom,(
% 68.49/10.22 cancel146912293up_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__ab__semigroup__add)).
% 68.49/10.22 thf(f1810,plain,(
% 68.49/10.22 spl93_17),
% 68.49/10.22 inference(avatar_split_clause,[],[f1472,f1807])).
% 68.49/10.22 thf(f1472,plain,(
% 68.49/10.22 (cancel_semigroup_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f701])).
% 68.49/10.22 thf(f701,plain,(
% 68.49/10.22 (cancel_semigroup_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f700])).
% 68.49/10.22 thf(f700,plain,(
% 68.49/10.22 cancel_semigroup_add(nat)),
% 68.49/10.22 inference(rectify,[],[f270])).
% 68.49/10.22 thf(f270,axiom,(
% 68.49/10.22 cancel_semigroup_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add_4)).
% 68.49/10.22 thf(f1805,plain,(
% 68.49/10.22 spl93_16),
% 68.49/10.22 inference(avatar_split_clause,[],[f1471,f1802])).
% 68.49/10.22 thf(f1471,plain,(
% 68.49/10.22 (cancel_semigroup_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f699])).
% 68.49/10.22 thf(f699,plain,(
% 68.49/10.22 (cancel_semigroup_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f698])).
% 68.49/10.22 thf(f698,plain,(
% 68.49/10.22 cancel_semigroup_add(int)),
% 68.49/10.22 inference(rectify,[],[f259])).
% 68.49/10.22 thf(f259,axiom,(
% 68.49/10.22 cancel_semigroup_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__semigroup__add)).
% 68.49/10.22 thf(f1800,plain,(
% 68.49/10.22 spl93_15),
% 68.49/10.22 inference(avatar_split_clause,[],[f1470,f1797])).
% 68.49/10.22 thf(f1470,plain,(
% 68.49/10.22 (ab_semigroup_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f697])).
% 68.49/10.22 thf(f697,plain,(
% 68.49/10.22 (ab_semigroup_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f696])).
% 68.49/10.22 thf(f696,plain,(
% 68.49/10.22 ab_semigroup_add(nat)),
% 68.49/10.22 inference(rectify,[],[f271])).
% 68.49/10.22 thf(f271,axiom,(
% 68.49/10.22 ab_semigroup_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add_5)).
% 68.49/10.22 thf(f1795,plain,(
% 68.49/10.22 spl93_14),
% 68.49/10.22 inference(avatar_split_clause,[],[f1469,f1792])).
% 68.49/10.22 thf(f1469,plain,(
% 68.49/10.22 (ab_semigroup_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f695])).
% 68.49/10.22 thf(f695,plain,(
% 68.49/10.22 (ab_semigroup_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f694])).
% 68.49/10.22 thf(f694,plain,(
% 68.49/10.22 ab_semigroup_add(int)),
% 68.49/10.22 inference(rectify,[],[f260])).
% 68.49/10.22 thf(f260,axiom,(
% 68.49/10.22 ab_semigroup_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oab__semigroup__add)).
% 68.49/10.22 thf(f1790,plain,(
% 68.49/10.22 spl93_13),
% 68.49/10.22 inference(avatar_split_clause,[],[f1468,f1787])).
% 68.49/10.22 thf(f1787,plain,(
% 68.49/10.22 spl93_13 <=> (comm_monoid_add(nat) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_13])])).
% 68.49/10.22 thf(f1468,plain,(
% 68.49/10.22 (comm_monoid_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f693])).
% 68.49/10.22 thf(f693,plain,(
% 68.49/10.22 (comm_monoid_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f692])).
% 68.49/10.22 thf(f692,plain,(
% 68.49/10.22 comm_monoid_add(nat)),
% 68.49/10.22 inference(rectify,[],[f272])).
% 68.49/10.22 thf(f272,axiom,(
% 68.49/10.22 comm_monoid_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add_6)).
% 68.49/10.22 thf(f1785,plain,(
% 68.49/10.22 spl93_12),
% 68.49/10.22 inference(avatar_split_clause,[],[f1467,f1782])).
% 68.49/10.22 thf(f1782,plain,(
% 68.49/10.22 spl93_12 <=> (comm_monoid_add(int) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_12])])).
% 68.49/10.22 thf(f1467,plain,(
% 68.49/10.22 (comm_monoid_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f691])).
% 68.49/10.22 thf(f691,plain,(
% 68.49/10.22 (comm_monoid_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f690])).
% 68.49/10.22 thf(f690,plain,(
% 68.49/10.22 comm_monoid_add(int)),
% 68.49/10.22 inference(rectify,[],[f261])).
% 68.49/10.22 thf(f261,axiom,(
% 68.49/10.22 comm_monoid_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocomm__monoid__add)).
% 68.49/10.22 thf(f1780,plain,(
% 68.49/10.22 spl93_11),
% 68.49/10.22 inference(avatar_split_clause,[],[f1466,f1777])).
% 68.49/10.22 thf(f1466,plain,(
% 68.49/10.22 (semigroup_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f689])).
% 68.49/10.22 thf(f689,plain,(
% 68.49/10.22 (semigroup_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f688])).
% 68.49/10.22 thf(f688,plain,(
% 68.49/10.22 semigroup_add(nat)),
% 68.49/10.22 inference(rectify,[],[f273])).
% 68.49/10.22 thf(f273,axiom,(
% 68.49/10.22 semigroup_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add_7)).
% 68.49/10.22 thf(f1775,plain,(
% 68.49/10.22 spl93_10),
% 68.49/10.22 inference(avatar_split_clause,[],[f1465,f1772])).
% 68.49/10.22 thf(f1772,plain,(
% 68.49/10.22 spl93_10 <=> (cancel1352612707id_add(nat) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_10])])).
% 68.49/10.22 thf(f1465,plain,(
% 68.49/10.22 (cancel1352612707id_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f687])).
% 68.49/10.22 thf(f687,plain,(
% 68.49/10.22 (cancel1352612707id_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f686])).
% 68.49/10.22 thf(f686,plain,(
% 68.49/10.22 cancel1352612707id_add(nat)),
% 68.49/10.22 inference(rectify,[],[f269])).
% 68.49/10.22 thf(f269,axiom,(
% 68.49/10.22 cancel1352612707id_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__comm__monoid__add_3)).
% 68.49/10.22 thf(f1770,plain,(
% 68.49/10.22 spl93_9),
% 68.49/10.22 inference(avatar_split_clause,[],[f1464,f1767])).
% 68.49/10.22 thf(f1464,plain,(
% 68.49/10.22 (semiring_char_0(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f685])).
% 68.49/10.22 thf(f685,plain,(
% 68.49/10.22 (semiring_char_0(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f684])).
% 68.49/10.22 thf(f684,plain,(
% 68.49/10.22 semiring_char_0(nat)),
% 68.49/10.22 inference(rectify,[],[f274])).
% 68.49/10.22 thf(f274,axiom,(
% 68.49/10.22 semiring_char_0(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osemiring__char__0_8)).
% 68.49/10.22 thf(f1765,plain,(
% 68.49/10.22 spl93_8),
% 68.49/10.22 inference(avatar_split_clause,[],[f1463,f1762])).
% 68.49/10.22 thf(f1463,plain,(
% 68.49/10.22 (semiring_1(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f683])).
% 68.49/10.22 thf(f683,plain,(
% 68.49/10.22 (semiring_1(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f682])).
% 68.49/10.22 thf(f682,plain,(
% 68.49/10.22 semiring_1(nat)),
% 68.49/10.22 inference(rectify,[],[f275])).
% 68.49/10.22 thf(f275,axiom,(
% 68.49/10.22 semiring_1(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Rings_Osemiring__1_9)).
% 68.49/10.22 thf(f1760,plain,(
% 68.49/10.22 spl93_7),
% 68.49/10.22 inference(avatar_split_clause,[],[f1462,f1757])).
% 68.49/10.22 thf(f1757,plain,(
% 68.49/10.22 spl93_7 <=> (ordere779506340up_add(nat) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_7])])).
% 68.49/10.22 thf(f1462,plain,(
% 68.49/10.22 (ordere779506340up_add(nat) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f681])).
% 68.49/10.22 thf(f681,plain,(
% 68.49/10.22 (ordere779506340up_add(nat) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f680])).
% 68.49/10.22 thf(f680,plain,(
% 68.49/10.22 ordere779506340up_add(nat)),
% 68.49/10.22 inference(rectify,[],[f267])).
% 68.49/10.22 thf(f267,axiom,(
% 68.49/10.22 ordere779506340up_add(nat)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add_1)).
% 68.49/10.22 thf(f1755,plain,(
% 68.49/10.22 spl93_6),
% 68.49/10.22 inference(avatar_split_clause,[],[f1461,f1752])).
% 68.49/10.22 thf(f1461,plain,(
% 68.49/10.22 (semiring_1(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f679])).
% 68.49/10.22 thf(f679,plain,(
% 68.49/10.22 (semiring_1(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f678])).
% 68.49/10.22 thf(f678,plain,(
% 68.49/10.22 semiring_1(int)),
% 68.49/10.22 inference(rectify,[],[f265])).
% 68.49/10.22 thf(f265,axiom,(
% 68.49/10.22 semiring_1(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Rings_Osemiring__1)).
% 68.49/10.22 thf(f1750,plain,(
% 68.49/10.22 spl93_5),
% 68.49/10.22 inference(avatar_split_clause,[],[f1460,f1747])).
% 68.49/10.22 thf(f1747,plain,(
% 68.49/10.22 spl93_5 <=> (ordere779506340up_add(int) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_5])])).
% 68.49/10.22 thf(f1460,plain,(
% 68.49/10.22 (ordere779506340up_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f677])).
% 68.49/10.22 thf(f677,plain,(
% 68.49/10.22 (ordere779506340up_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f676])).
% 68.49/10.22 thf(f676,plain,(
% 68.49/10.22 ordere779506340up_add(int)),
% 68.49/10.22 inference(rectify,[],[f256])).
% 68.49/10.22 thf(f256,axiom,(
% 68.49/10.22 ordere779506340up_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Oordered__ab__semigroup__add)).
% 68.49/10.22 thf(f1745,plain,(
% 68.49/10.22 spl93_4),
% 68.49/10.22 inference(avatar_split_clause,[],[f1459,f1742])).
% 68.49/10.22 thf(f1742,plain,(
% 68.49/10.22 spl93_4 <=> (cancel1352612707id_add(int) = $true)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_4])])).
% 68.49/10.22 thf(f1459,plain,(
% 68.49/10.22 (cancel1352612707id_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f675])).
% 68.49/10.22 thf(f675,plain,(
% 68.49/10.22 (cancel1352612707id_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f674])).
% 68.49/10.22 thf(f674,plain,(
% 68.49/10.22 cancel1352612707id_add(int)),
% 68.49/10.22 inference(rectify,[],[f258])).
% 68.49/10.22 thf(f258,axiom,(
% 68.49/10.22 cancel1352612707id_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Ocancel__comm__monoid__add)).
% 68.49/10.22 thf(f1740,plain,(
% 68.49/10.22 spl93_3),
% 68.49/10.22 inference(avatar_split_clause,[],[f1458,f1737])).
% 68.49/10.22 thf(f1458,plain,(
% 68.49/10.22 (semiring_char_0(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f673])).
% 68.49/10.22 thf(f673,plain,(
% 68.49/10.22 (semiring_char_0(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f672])).
% 68.49/10.22 thf(f672,plain,(
% 68.49/10.22 semiring_char_0(int)),
% 68.49/10.22 inference(rectify,[],[f263])).
% 68.49/10.22 thf(f263,axiom,(
% 68.49/10.22 semiring_char_0(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Nat_Osemiring__char__0)).
% 68.49/10.22 thf(f1735,plain,(
% 68.49/10.22 spl93_2),
% 68.49/10.22 inference(avatar_split_clause,[],[f1457,f1732])).
% 68.49/10.22 thf(f1457,plain,(
% 68.49/10.22 (semigroup_add(int) = $true)),
% 68.49/10.22 inference(cnf_transformation,[],[f671])).
% 68.49/10.22 thf(f671,plain,(
% 68.49/10.22 (semigroup_add(int) = $true)),
% 68.49/10.22 inference(fool_elimination,[],[f670])).
% 68.49/10.22 thf(f670,plain,(
% 68.49/10.22 semigroup_add(int)),
% 68.49/10.22 inference(rectify,[],[f262])).
% 68.49/10.22 thf(f262,axiom,(
% 68.49/10.22 semigroup_add(int)),
% 68.49/10.22 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Groups_Osemigroup__add)).
% 68.49/10.22 thf(f1730,plain,(
% 68.49/10.22 ~spl93_1),
% 68.49/10.22 inference(avatar_split_clause,[],[f278,f1727])).
% 68.49/10.22 thf(f1727,plain,(
% 68.49/10.22 spl93_1 <=> ($true = $false)),
% 68.49/10.22 introduced(avatar_definition,[new_symbols(naming,[spl93_1])])).
% 68.49/10.22 thf(f278,plain,(
% 68.49/10.22 ($true != $false)),
% 68.49/10.22 introduced(fool_axiom,[])).
% 68.49/10.22 % SZS output end Proof for theBenchmark
% 68.49/10.22 % (16506)------------------------------
% 68.49/10.22 % (16506)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 68.49/10.22 % (16506)Termination reason: Refutation
% 68.49/10.22
% 68.49/10.22 % (16506)Memory used [KB]: 44844
% 68.49/10.22 % (16506)Time elapsed: 9.768 s
% 68.49/10.22 % (16506)Instructions burned: 24125 (million)
% 68.49/10.22 % (16501)Success in time 9.863 s
%------------------------------------------------------------------------------