TSTP Solution File: ITP048^2 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP048^2 : 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 : n007.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 22:48:43 EDT 2024
% Result : Theorem 78.92s 11.74s
% Output : Refutation 79.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : ITP048^2 : TPTP v8.2.0. Released v7.5.0.
% 0.08/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.37 % Computer : n007.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat May 18 17:04:07 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.14/0.37 % (8914)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.42 % (8917)WARNING: value z3 for option sas not known
% 0.22/0.42 % (8920)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)
% 0.22/0.42 % (8919)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)
% 0.22/0.42 % (8918)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.22/0.42 % (8921)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)
% 0.22/0.42 % (8915)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.22/0.42 % (8916)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.22/0.42 % (8917)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)
% 0.22/0.46 % (8921)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.47 % Exception at run slice level
% 0.22/0.47 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.48 % Exception at run slice level
% 0.22/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.48 % Exception at run slice level
% 0.22/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.49 % (8922)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.22/0.49 % (8923)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)
% 0.22/0.50 % (8924)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)
% 0.22/0.54 % (8923)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.54 % (8922)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.22/0.55 % Exception at run slice level
% 0.22/0.55 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.57 % (8925)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)
% 77.96/11.55 % (8919)First to succeed.
% 78.92/11.73 % (8919)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8914"
% 78.92/11.74 % (8919)Refutation found. Thanks to Tanya!
% 78.92/11.74 % SZS status Theorem for theBenchmark
% 78.92/11.74 % SZS output start Proof for theBenchmark
% 78.92/11.74 thf(type_def_5, type, nat: $tType).
% 78.92/11.74 thf(type_def_6, type, product_prod: ($tType * $tType) > $tType).
% 78.92/11.74 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 78.92/11.74 thf(type_def_8, type, list: $tType > $tType).
% 78.92/11.74 thf(type_def_9, type, set: $tType > $tType).
% 78.92/11.74 thf(type_def_10, type, capacity: $tType).
% 78.92/11.74 thf(type_def_11, type, a: $tType).
% 78.92/11.74 thf(func_def_0, type, product_prod: ($tType * $tType) > $tType).
% 78.92/11.74 thf(func_def_1, type, list: $tType > $tType).
% 78.92/11.74 thf(func_def_2, type, capacity: $tType).
% 78.92/11.74 thf(func_def_3, type, set: $tType > $tType).
% 78.92/11.74 thf(func_def_4, type, nat: $tType).
% 78.92/11.74 thf(func_def_5, type, a: $tType).
% 78.92/11.74 thf(func_def_6, type, type: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_7, type, size: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_10, type, group_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_11, type, no_bot: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_12, type, no_top: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_13, type, linorder: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_14, type, preorder: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_15, type, wellorder: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_16, type, semigroup_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_17, type, dense_order: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_18, type, linordered_idom: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_19, type, comm_monoid_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_20, type, ab_semigroup_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_21, type, cancel_semigroup_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_22, type, ordere779506340up_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_23, type, canoni770627133id_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_24, type, ordere236663937imp_le: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_25, type, ordere223160158up_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_26, type, strict2144017051up_add: !>[X0: $tType]:($o)).
% 78.92/11.74 thf(func_def_27, type, connected: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > nat > $o)).
% 78.92/11.74 thf(func_def_28, type, dist: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > nat > nat > $o)).
% 78.92/11.74 thf(func_def_29, type, isPath: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > list(product_prod(nat,nat)) > nat > $o)).
% 78.92/11.74 thf(func_def_30, type, isShortestPath: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > list(product_prod(nat,nat)) > nat > $o)).
% 78.92/11.74 thf(func_def_31, type, isSimplePath: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > list(product_prod(nat,nat)) > nat > $o)).
% 78.92/11.74 thf(func_def_32, type, min_dist: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > nat > nat)).
% 78.92/11.74 thf(func_def_33, type, reachableNodes: !>[X0: $tType]:((product_prod(nat,nat) > X0) > nat > set(nat))).
% 78.92/11.74 thf(func_def_34, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 78.92/11.74 thf(func_def_35, type, size_size: !>[X0: $tType]:(X0 > nat)).
% 78.92/11.74 thf(func_def_36, type, ord_Least: !>[X0: $tType]:((X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_37, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_38, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_39, type, collect: !>[X0: $tType]:((X0 > $o) > set(X0))).
% 78.92/11.74 thf(func_def_40, type, member: !>[X0: $tType]:(X0 > set(X0) > $o)).
% 78.92/11.74 thf(func_def_41, type, c: product_prod(nat,nat) > capacity).
% 78.92/11.74 thf(func_def_42, type, c2: product_prod(nat,nat) > a).
% 78.92/11.74 thf(func_def_43, type, p: list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_44, type, p1: list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_45, type, p1a: list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_46, type, p2: list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_47, type, p2_a: list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_48, type, p3: list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_49, type, s: nat).
% 78.92/11.74 thf(func_def_50, type, t: nat).
% 78.92/11.74 thf(func_def_51, type, u: nat).
% 78.92/11.74 thf(func_def_52, type, ua: nat).
% 78.92/11.74 thf(func_def_53, type, v: nat).
% 78.92/11.74 thf(func_def_54, type, va: nat).
% 78.92/11.74 thf(func_def_58, type, vAND: $o > $o > $o).
% 78.92/11.74 thf(func_def_59, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_60, type, vNOT: $o > $o).
% 78.92/11.74 thf(func_def_61, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 78.92/11.74 thf(func_def_62, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 78.92/11.74 thf(func_def_63, type, vOR: $o > $o > $o).
% 78.92/11.74 thf(func_def_64, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 78.92/11.74 thf(func_def_65, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 78.92/11.74 thf(func_def_66, type, vIMP: $o > $o > $o).
% 78.92/11.74 thf(func_def_67, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 78.92/11.74 thf(func_def_68, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_69, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_70, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_71, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 78.92/11.74 thf(func_def_72, type, sK4: !>[X0: $tType]:(X0 > X0)).
% 78.92/11.74 thf(func_def_73, type, sK5: !>[X0: $tType]:(X0 > X0 > X0)).
% 78.92/11.74 thf(func_def_74, type, sK6: !>[X0: $tType]:(X0 > X0)).
% 78.92/11.74 thf(func_def_75, type, sK7: !>[X0: $tType]:(X0 > X0 > X0)).
% 78.92/11.74 thf(func_def_76, type, sK8: !>[X0: $tType]:((X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_77, type, sK9: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_78, type, sK10: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_79, type, sK11: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_80, type, sK12: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_81, type, sK13: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_82, type, sK14: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_83, type, sK15: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_84, type, sK16: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_85, type, sK17: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_86, type, sK18: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_87, type, sK19: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_88, type, sK20: !>[X0: $tType]:(nat > nat > (product_prod(nat,nat) > X0) > list(product_prod(nat,nat)))).
% 78.92/11.74 thf(func_def_89, type, sK21: !>[X0: $tType]:((nat > $o) > nat > nat > (product_prod(nat,nat) > X0) > nat)).
% 78.92/11.74 thf(func_def_90, type, sK22: !>[X0: $tType]:(nat > nat > (product_prod(nat,nat) > X0) > nat)).
% 78.92/11.74 thf(func_def_91, type, sK23: !>[X0: $tType]:(nat > nat > nat > (product_prod(nat,nat) > X0) > nat)).
% 78.92/11.74 thf(func_def_92, type, sK24: !>[X0: $tType]:(nat > nat > (product_prod(nat,nat) > X0) > list(product_prod(nat,nat)))).
% 78.92/11.74 thf(func_def_93, type, sK25: !>[X0: $tType]:(nat > nat > (product_prod(nat,nat) > X0) > nat)).
% 78.92/11.74 thf(func_def_94, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_95, type, sK27: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_96, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_97, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_98, type, sK30: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_99, type, sK31: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_100, type, sK32: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_101, type, sK33: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_102, type, sK34: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_103, type, sK35: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_104, type, sK36: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_105, type, sK37: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 78.92/11.74 thf(func_def_106, type, sK38: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_107, type, sK39: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_108, type, sK40: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_109, type, sK41: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_110, type, sK42: (nat > $o) > nat).
% 78.92/11.74 thf(func_def_111, type, sK43: (nat > $o) > nat).
% 78.92/11.74 thf(func_def_112, type, sK44: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_113, type, sK45: !>[X0: $tType, X1: $tType]:((X1 > $o) > (X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_114, type, sK46: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_115, type, sK47: nat > nat > nat).
% 78.92/11.74 thf(func_def_116, type, sK48: nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_117, type, sK49: nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_118, type, sK50: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_119, type, sK51: (nat > nat) > nat).
% 78.92/11.74 thf(func_def_120, type, sK52: (nat > nat) > nat).
% 78.92/11.74 thf(func_def_121, type, sK53: (nat > nat) > nat).
% 78.92/11.74 thf(func_def_122, type, sK54: (nat > nat) > nat).
% 78.92/11.74 thf(func_def_123, type, sK55: (nat > $o) > nat).
% 78.92/11.74 thf(func_def_124, type, sK56: nat > (nat > $o) > nat).
% 78.92/11.74 thf(func_def_125, type, sK57: (nat > $o) > nat > nat > nat).
% 78.92/11.74 thf(func_def_126, type, sK58: nat > nat > nat).
% 78.92/11.74 thf(func_def_127, type, sK59: (nat > $o) > nat > nat > nat).
% 78.92/11.74 thf(func_def_128, type, sK60: nat > nat > nat).
% 78.92/11.74 thf(func_def_129, type, sK61: nat > nat > nat > nat).
% 78.92/11.74 thf(func_def_130, type, sK62: nat > nat > nat > nat).
% 78.92/11.74 thf(func_def_131, type, sK63: nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_132, type, sK64: nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_133, type, sK65: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 78.92/11.74 thf(func_def_134, type, sK66: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_135, type, sK67: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_136, type, sK68: nat > nat > nat).
% 78.92/11.74 thf(func_def_137, type, sK69: nat > nat > nat).
% 78.92/11.74 thf(func_def_138, type, sK70: !>[X0: $tType]:(nat > (X0 > nat) > X0 > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_139, type, sK71: !>[X0: $tType]:((X0 > nat) > (X0 > $o) > X0)).
% 78.92/11.74 thf(func_def_141, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 78.92/11.74 thf(func_def_142, type, sK73: list(product_prod(nat,nat)) > nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_143, type, sK74: list(product_prod(nat,nat)) > nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_144, type, sK75: nat > nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_145, type, sK76: nat > nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_146, type, sK77: nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_147, type, sK78: nat > nat > nat).
% 78.92/11.74 thf(func_def_148, type, sK79: nat > nat > list(product_prod(nat,nat))).
% 78.92/11.74 thf(func_def_149, type, sK80: nat > nat > nat).
% 78.92/11.74 thf(f73516,plain,(
% 78.92/11.74 $false),
% 78.92/11.74 inference(avatar_sat_refutation,[],[f1892,f1897,f1902,f1907,f1912,f1917,f1922,f1927,f1932,f1937,f1942,f1947,f1952,f1957,f1962,f1967,f1972,f1977,f1982,f1987,f1992,f1997,f2002,f2006,f2010,f2014,f2018,f2022,f2026,f2058,f2062,f2066,f2070,f2074,f2078,f2082,f2086,f2090,f2094,f2098,f2102,f2106,f2110,f2151,f2203,f2207,f2212,f2216,f2244,f2248,f2255,f2262,f2266,f2270,f2274,f2278,f2302,f2306,f2311,f2331,f2335,f2345,f2349,f2353,f2357,f2362,f2366,f2370,f2437,f2441,f2446,f2451,f2465,f2469,f2473,f2498,f2502,f2512,f2516,f2520,f2524,f2614,f2618,f2622,f2626,f2630,f2634,f2638,f2692,f2700,f2704,f2712,f2716,f2741,f2745,f2749,f2753,f2757,f2761,f2765,f2769,f2773,f2777,f2781,f2786,f2863,f2867,f2871,f2888,f2892,f2896,f2900,f2904,f2908,f2912,f2916,f2978,f2982,f3008,f3023,f3027,f3031,f3060,f3065,f3070,f3075,f3080,f3085,f3090,f3095,f3136,f3188,f3192,f3196,f3200,f3218,f3235,f3239,f3243,f3247,f3252,f3257,f3270,f3357,f3361,f3365,f3369,f3477,f3584,f3588,f3610,f3614,f3618,f3622,f3627,f3631,f3655,f3673,f3677,f3682,f3686,f3755,f3759,f3763,f3767,f3771,f3775,f3780,f3784,f3788,f3875,f3879,f3923,f3927,f3987,f3991,f3995,f3999,f4004,f4032,f4036,f4058,f4065,f4069,f4073,f4077,f4081,f4085,f4158,f4162,f4166,f4247,f4251,f4259,f4263,f4268,f4272,f4276,f4348,f4352,f4356,f4363,f4409,f4415,f4419,f4423,f4616,f4620,f4624,f4675,f4679,f4683,f4687,f4896,f4900,f4904,f4972,f5031,f5035,f5045,f5049,f5059,f5063,f5069,f5073,f5580,f5588,f5592,f5596,f5600,f5616,f5620,f5640,f5644,f5648,f5652,f5668,f5672,f5676,f5680,f5684,f5906,f5910,f5914,f5918,f5922,f5926,f5930,f5934,f5990,f6068,f6082,f6086,f6094,f6120,f6124,f6255,f6259,f6354,f6358,f6368,f6372,f6398,f6408,f6412,f6420,f6424,f6432,f6442,f6448,f6452,f6456,f6460,f6488,f6496,f6500,f6508,f6521,f6551,f6555,f6559,f6563,f6571,f6575,f6581,f6591,f6597,f6604,f6660,f6672,f6676,f6697,f6729,f6737,f6750,f6808,f6820,f6824,f6840,f6850,f6858,f6862,f6878,f6888,f6954,f6958,f6962,f6966,f6970,f6974,f7018,f7022,f7026,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7086,f7090,f7094,f7098,f7102,f7106,f7110,f7386,f7594,f7598,f7602,f7610,f7630,f7634,f7898,f7906,f7911,f7971,f7973,f7975,f7988,f7990,f11437,f11809,f11817,f12202,f12204,f12206,f12208,f12210,f12212,f12214,f12216,f12219,f12221,f12223,f12227,f12229,f12231,f12233,f12235,f12237,f12239,f12241,f12243,f12245,f12247,f12249,f12251,f12253,f12255,f12257,f12259,f12261,f12263,f12265,f12267,f12269,f12271,f12273,f12275,f12277,f12279,f12281,f12283,f12285,f12287,f12289,f12291,f12293,f12295,f12297,f12299,f12301,f12303,f12305,f12307,f12309,f12311,f12313,f12315,f12317,f12319,f12321,f12323,f12325,f12327,f12329,f12331,f12333,f12335,f12337,f12339,f12341,f12343,f12345,f12347,f12349,f12351,f12353,f12355,f12357,f12359,f12361,f12363,f16177,f16181,f16185,f16189,f16193,f16620,f16624,f16628,f16743,f16747,f17988,f18000,f18004,f18008,f18170,f18652,f18657,f18661,f18665,f18670,f18674,f19111,f19115,f19119,f19123,f19127,f19223,f19367,f19371,f19571,f19667,f19671,f19675,f19679,f19683,f19687,f19691,f19700,f19709,f19713,f19832,f20563,f20567,f20681,f20685,f20689,f20693,f20697,f20701,f20705,f20709,f20713,f21191,f23835,f23839,f23843,f23847,f23851,f23855,f23859,f23863,f23867,f23871,f23875,f23879,f23883,f23887,f23891,f24710,f24714,f24718,f26085,f26093,f26097,f26101,f26105,f26109,f26113,f26117,f26347,f26351,f26355,f26359,f26363,f26367,f26389,f26393,f26397,f26401,f26405,f26409,f27818,f27822,f27826,f27878,f27882,f27886,f28195,f28199,f28203,f28207,f28211,f28215,f28219,f28223,f28227,f28231,f28235,f28239,f28243,f28247,f28251,f28255,f28259,f28263,f28267,f28271,f28275,f28279,f28283,f28287,f28291,f28295,f29321,f31303,f31434,f31438,f31702,f31706,f31710,f31720,f31724,f32484,f32488,f32492,f32496,f32940,f32944,f32948,f32960,f32971,f32976,f33125,f33130,f33264,f33268,f33272,f33276,f33280,f33288,f33870,f33874,f33878,f33900,f33904,f33909,f33914,f33919,f33924,f33929,f33934,f33938,f35476,f35675,f35679,f35683,f35688,f35693,f35698,f35702,f35903,f36253,f36257,f36261,f36265,f36532,f36799,f36803,f36807,f36811,f36815,f36819,f36823,f36827,f36837,f38639,f38643,f38647,f38651,f38655,f38659,f40764,f40768,f40772,f40776,f40796,f40800,f40804,f40808,f40812,f40816,f40820,f42189,f42193,f42197,f42201,f42205,f42209,f42213,f42217,f42221,f42225,f42393,f42397,f42401,f42405,f42409,f42413,f42457,f42518,f42522,f42526,f42530,f42534,f42538,f42542,f43291,f43295,f43299,f43303,f43426,f43432,f43436,f43441,f43509,f43515,f43519,f43523,f43527,f43531,f43535,f43560,f43565,f43570,f43575,f43580,f43585,f43590,f43594,f43598,f43608,f43612,f43616,f43620,f43624,f43628,f43632,f43637,f46553,f46558,f46564,f46570,f46575,f47024,f47028,f47032,f47036,f47040,f47044,f47048,f47070,f47074,f47079,f47084,f47089,f47094,f47099,f47104,f47109,f47113,f47135,f47139,f47143,f48016,f48688,f48692,f48696,f48700,f48705,f48709,f48713,f48718,f48722,f48726,f48730,f48734,f48738,f48742,f48746,f49834,f51186,f51190,f51194,f51198,f51202,f51206,f51210,f51214,f51218,f51820,f51842,f51866,f51870,f51874,f51878,f51882,f51886,f51890,f52343,f52347,f52351,f52361,f52365,f52369,f52373,f52377,f52381,f56265,f56269,f56586,f56590,f56594,f56616,f56620,f56624,f56628,f56632,f56636,f58333,f58337,f58341,f58345,f58357,f58407,f58732,f58736,f58740,f59475,f59497,f59501,f59505,f59509,f59514,f59693,f59697,f59701,f59705,f59722,f60389,f60393,f60397,f61327,f61331,f63985,f63989,f64184,f64379,f64383,f64387,f64391,f64395,f65088,f65092,f65096,f65100,f65104,f65108,f65112,f65116,f65120,f66384,f66388,f67899,f67921,f67925,f67929,f67933,f67937,f67941,f67945,f67949,f67953,f67957,f67962,f67966,f67970,f67974,f67978,f67982,f67986,f67990,f67994,f67998,f68004,f72513,f72594,f72598,f72602,f72606,f72610,f72928,f72932,f72936,f72940,f72944,f73331,f73335,f73339,f73343,f73347,f73499])).
% 78.92/11.74 thf(f73499,plain,(
% 78.92/11.74 ~spl72_141 | ~spl72_214 | ~spl72_340 | ~spl72_770),
% 78.92/11.74 inference(avatar_contradiction_clause,[],[f73498])).
% 78.92/11.74 thf(f73498,plain,(
% 78.92/11.74 $false | (~spl72_141 | ~spl72_214 | ~spl72_340 | ~spl72_770)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f73497])).
% 78.92/11.74 thf(f73497,plain,(
% 78.92/11.74 ($true = $false) | (~spl72_141 | ~spl72_214 | ~spl72_340 | ~spl72_770)),
% 78.92/11.74 inference(forward_demodulation,[],[f73496,f7905])).
% 78.92/11.74 thf(f7905,plain,(
% 78.92/11.74 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $false) | ~spl72_340),
% 78.92/11.74 inference(avatar_component_clause,[],[f7903])).
% 78.92/11.74 thf(f7903,plain,(
% 78.92/11.74 spl72_340 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $false)),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_340])])).
% 78.92/11.74 thf(f73496,plain,(
% 78.92/11.74 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $true) | (~spl72_141 | ~spl72_214 | ~spl72_770)),
% 78.92/11.74 inference(forward_demodulation,[],[f73495,f4895])).
% 78.92/11.74 thf(f4895,plain,(
% 78.92/11.74 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))) | ~spl72_214),
% 78.92/11.74 inference(avatar_component_clause,[],[f4893])).
% 78.92/11.74 thf(f4893,plain,(
% 78.92/11.74 spl72_214 <=> (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_214])])).
% 78.92/11.74 thf(f73495,plain,(
% 78.92/11.74 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | (~spl72_141 | ~spl72_770)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f73432])).
% 78.92/11.74 thf(f73432,plain,(
% 78.92/11.74 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | (~spl72_141 | ~spl72_770)),
% 78.92/11.74 inference(superposition,[],[f73338,f3251])).
% 78.92/11.74 thf(f3251,plain,(
% 78.92/11.74 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)) = $true) | ~spl72_141),
% 78.92/11.74 inference(avatar_component_clause,[],[f3249])).
% 78.92/11.74 thf(f3249,plain,(
% 78.92/11.74 spl72_141 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)) = $true)),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_141])])).
% 78.92/11.74 thf(f73338,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))) ) | ~spl72_770),
% 78.92/11.74 inference(avatar_component_clause,[],[f73337])).
% 78.92/11.74 thf(f73337,plain,(
% 78.92/11.74 spl72_770 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_770])])).
% 78.92/11.74 thf(f73347,plain,(
% 78.92/11.74 spl72_772 | ~spl72_28 | ~spl72_217),
% 78.92/11.74 inference(avatar_split_clause,[],[f4994,f4970,f2020,f73345])).
% 78.92/11.74 thf(f73345,plain,(
% 78.92/11.74 spl72_772 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2)))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_772])])).
% 78.92/11.74 thf(f2020,plain,(
% 78.92/11.74 spl72_28 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_28])])).
% 78.92/11.74 thf(f4970,plain,(
% 78.92/11.74 spl72_217 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2)))) | (ord(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_217])])).
% 78.92/11.74 thf(f4994,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))))) ) | (~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4993])).
% 78.92/11.74 thf(f4993,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (($true != $true) | ($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))))) ) | (~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(superposition,[],[f4971,f2021])).
% 78.92/11.74 thf(f2021,plain,(
% 78.92/11.74 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl72_28),
% 78.92/11.74 inference(avatar_component_clause,[],[f2020])).
% 78.92/11.74 thf(f4971,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2)))) | ($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true)) ) | ~spl72_217),
% 78.92/11.74 inference(avatar_component_clause,[],[f4970])).
% 78.92/11.74 thf(f73343,plain,(
% 78.92/11.74 spl72_771 | ~spl72_15 | ~spl72_142 | ~spl72_188),
% 78.92/11.74 inference(avatar_split_clause,[],[f4153,f4083,f3254,f1959,f73341])).
% 78.92/11.74 thf(f73341,plain,(
% 78.92/11.74 spl72_771 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_771])])).
% 78.92/11.74 thf(f1959,plain,(
% 78.92/11.74 spl72_15 <=> (ordere223160158up_add(nat) = $true)),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_15])])).
% 78.92/11.74 thf(f3254,plain,(
% 78.92/11.74 spl72_142 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)) = $true)),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_142])])).
% 78.92/11.74 thf(f4083,plain,(
% 78.92/11.74 spl72_188 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_188])])).
% 78.92/11.74 thf(f4153,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X1)))) ) | (~spl72_15 | ~spl72_142 | ~spl72_188)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4152])).
% 78.92/11.74 thf(f4152,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X1)))) ) | (~spl72_15 | ~spl72_142 | ~spl72_188)),
% 78.92/11.74 inference(forward_demodulation,[],[f4138,f1961])).
% 78.92/11.74 thf(f1961,plain,(
% 78.92/11.74 (ordere223160158up_add(nat) = $true) | ~spl72_15),
% 78.92/11.74 inference(avatar_component_clause,[],[f1959])).
% 78.92/11.74 thf(f4138,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X1))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_142 | ~spl72_188)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4135])).
% 78.92/11.74 thf(f4135,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X1))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_142 | ~spl72_188)),
% 78.92/11.74 inference(superposition,[],[f4084,f3256])).
% 78.92/11.74 thf(f3256,plain,(
% 78.92/11.74 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)) = $true) | ~spl72_142),
% 78.92/11.74 inference(avatar_component_clause,[],[f3254])).
% 78.92/11.74 thf(f4084,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (ordere223160158up_add(X0) != $true)) ) | ~spl72_188),
% 78.92/11.74 inference(avatar_component_clause,[],[f4083])).
% 78.92/11.74 thf(f73339,plain,(
% 78.92/11.74 spl72_770 | ~spl72_15 | ~spl72_142 | ~spl72_187),
% 78.92/11.74 inference(avatar_split_clause,[],[f4129,f4079,f3254,f1959,f73337])).
% 78.92/11.74 thf(f4079,plain,(
% 78.92/11.74 spl72_187 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_187])])).
% 78.92/11.74 thf(f4129,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_15 | ~spl72_142 | ~spl72_187)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4128])).
% 78.92/11.74 thf(f4128,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_15 | ~spl72_142 | ~spl72_187)),
% 78.92/11.74 inference(forward_demodulation,[],[f4116,f1961])).
% 78.92/11.74 thf(f4116,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_142 | ~spl72_187)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4113])).
% 78.92/11.74 thf(f4113,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_142 | ~spl72_187)),
% 78.92/11.74 inference(superposition,[],[f4080,f3256])).
% 78.92/11.74 thf(f4080,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) ) | ~spl72_187),
% 78.92/11.74 inference(avatar_component_clause,[],[f4079])).
% 78.92/11.74 thf(f73335,plain,(
% 78.92/11.74 spl72_769 | ~spl72_46 | ~spl72_332),
% 78.92/11.74 inference(avatar_split_clause,[],[f7613,f7596,f2205,f73333])).
% 78.92/11.74 thf(f73333,plain,(
% 78.92/11.74 spl72_769 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,X1)))) | ($false = ord(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_769])])).
% 78.92/11.74 thf(f2205,plain,(
% 78.92/11.74 spl72_46 <=> ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X0,X1))) | ($true != ord(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_46])])).
% 78.92/11.74 thf(f7596,plain,(
% 78.92/11.74 spl72_332 <=> ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,X0))) | (ord(X0) = $false))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_332])])).
% 78.92/11.74 thf(f7613,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,X1)))) | ($false = ord(X1))) ) | (~spl72_46 | ~spl72_332)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f7612])).
% 78.92/11.74 thf(f7612,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X2,sTfun(X0,X1)))) | ($false = ord(X1))) ) | (~spl72_46 | ~spl72_332)),
% 78.92/11.74 inference(superposition,[],[f2206,f7597])).
% 78.92/11.74 thf(f7597,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,X0))) | (ord(X0) = $false)) ) | ~spl72_332),
% 78.92/11.74 inference(avatar_component_clause,[],[f7596])).
% 78.92/11.74 thf(f2206,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType] : (($true != ord(X1)) | ($true = ord(sTfun(X0,X1)))) ) | ~spl72_46),
% 78.92/11.74 inference(avatar_component_clause,[],[f2205])).
% 78.92/11.74 thf(f73331,plain,(
% 78.92/11.74 spl72_768 | ~spl72_141 | ~spl72_180),
% 78.92/11.74 inference(avatar_split_clause,[],[f4040,f4030,f3249,f73329])).
% 78.92/11.74 thf(f73329,plain,(
% 78.92/11.74 spl72_768 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_768])])).
% 78.92/11.74 thf(f4030,plain,(
% 78.92/11.74 spl72_180 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_180])])).
% 78.92/11.74 thf(f4040,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_141 | ~spl72_180)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4037])).
% 78.92/11.74 thf(f4037,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_141 | ~spl72_180)),
% 78.92/11.74 inference(superposition,[],[f4031,f3251])).
% 78.92/11.74 thf(f4031,plain,(
% 78.92/11.74 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl72_180),
% 78.92/11.74 inference(avatar_component_clause,[],[f4030])).
% 78.92/11.74 thf(f72944,plain,(
% 78.92/11.74 spl72_767 | ~spl72_20 | ~spl72_28 | ~spl72_217),
% 78.92/11.74 inference(avatar_split_clause,[],[f5011,f4970,f2020,f1984,f72942])).
% 78.92/11.74 thf(f72942,plain,(
% 78.92/11.74 spl72_767 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2))),$true)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X2),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_767])])).
% 78.92/11.74 thf(f1984,plain,(
% 78.92/11.74 spl72_20 <=> (ord($o) = $true)),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_20])])).
% 78.92/11.74 thf(f5011,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2))),$true)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X2),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f5010])).
% 78.92/11.74 thf(f5010,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2))),$true)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X2),X1)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(forward_demodulation,[],[f4984,f1986])).
% 78.92/11.74 thf(f1986,plain,(
% 78.92/11.74 (ord($o) = $true) | ~spl72_20),
% 78.92/11.74 inference(avatar_component_clause,[],[f1984])).
% 78.92/11.74 thf(f4984,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2))),$true)) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X2),X1)) | (ord($o) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X1),X2)))) ) | (~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(superposition,[],[f4971,f2021])).
% 78.92/11.74 thf(f72940,plain,(
% 78.92/11.74 spl72_766 | ~spl72_20 | ~spl72_28 | ~spl72_217),
% 78.92/11.74 inference(avatar_split_clause,[],[f4999,f4970,f2020,f1984,f72938])).
% 78.92/11.74 thf(f72938,plain,(
% 78.92/11.74 spl72_766 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_766])])).
% 78.92/11.74 thf(f4999,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4998])).
% 78.92/11.74 thf(f4998,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(forward_demodulation,[],[f4975,f1986])).
% 78.92/11.74 thf(f4975,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) | ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | (ord($o) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK46($o,X0),X2),X1)))) ) | (~spl72_28 | ~spl72_217)),
% 78.92/11.74 inference(superposition,[],[f4971,f2021])).
% 78.92/11.74 thf(f72936,plain,(
% 78.92/11.74 spl72_765 | ~spl72_28 | ~spl72_216),
% 78.92/11.74 inference(avatar_split_clause,[],[f4966,f4902,f2020,f72934])).
% 78.92/11.74 thf(f72934,plain,(
% 78.92/11.74 spl72_765 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X0),X1),X2))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_765])])).
% 78.92/11.74 thf(f4902,plain,(
% 78.92/11.74 spl72_216 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_216])])).
% 78.92/11.74 thf(f4966,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X0),X1),X2)))) ) | (~spl72_28 | ~spl72_216)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4965])).
% 78.92/11.74 thf(f4965,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X0),X1),X2)))) ) | (~spl72_28 | ~spl72_216)),
% 78.92/11.74 inference(superposition,[],[f4903,f2021])).
% 78.92/11.74 thf(f4903,plain,(
% 78.92/11.74 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0))) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) ) | ~spl72_216),
% 78.92/11.74 inference(avatar_component_clause,[],[f4902])).
% 78.92/11.74 thf(f72932,plain,(
% 78.92/11.74 spl72_764 | ~spl72_28 | ~spl72_215),
% 78.92/11.74 inference(avatar_split_clause,[],[f4956,f4898,f2020,f72930])).
% 78.92/11.74 thf(f72930,plain,(
% 78.92/11.74 spl72_764 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X0),X1),X2))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_764])])).
% 78.92/11.74 thf(f4898,plain,(
% 78.92/11.74 spl72_215 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_215])])).
% 78.92/11.74 thf(f4956,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X0),X1),X2)))) ) | (~spl72_28 | ~spl72_215)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4955])).
% 78.92/11.74 thf(f4955,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1)) | ($false = vAPP(nat,$o,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X0),X1),X2)))) ) | (~spl72_28 | ~spl72_215)),
% 78.92/11.74 inference(superposition,[],[f4899,f2021])).
% 78.92/11.74 thf(f4899,plain,(
% 78.92/11.74 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0))) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) ) | ~spl72_215),
% 78.92/11.74 inference(avatar_component_clause,[],[f4898])).
% 78.92/11.74 thf(f72928,plain,(
% 78.92/11.74 spl72_763 | ~spl72_45 | ~spl72_331),
% 78.92/11.74 inference(avatar_split_clause,[],[f7605,f7592,f2201,f72926])).
% 78.92/11.74 thf(f72926,plain,(
% 78.92/11.74 spl72_763 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,X1)))) | ($false = preorder(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_763])])).
% 78.92/11.74 thf(f2201,plain,(
% 78.92/11.74 spl72_45 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_45])])).
% 78.92/11.74 thf(f7592,plain,(
% 78.92/11.74 spl72_331 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,X0))) | (preorder(X0) = $false))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_331])])).
% 78.92/11.74 thf(f7605,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,X1)))) | ($false = preorder(X1))) ) | (~spl72_45 | ~spl72_331)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f7604])).
% 78.92/11.74 thf(f7604,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X2,sTfun(X0,X1)))) | ($false = preorder(X1))) ) | (~spl72_45 | ~spl72_331)),
% 78.92/11.74 inference(superposition,[],[f2202,f7593])).
% 78.92/11.74 thf(f7593,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,X0))) | (preorder(X0) = $false)) ) | ~spl72_331),
% 78.92/11.74 inference(avatar_component_clause,[],[f7592])).
% 78.92/11.74 thf(f2202,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType] : (($true != preorder(X1)) | ($true = preorder(sTfun(X0,X1)))) ) | ~spl72_45),
% 78.92/11.74 inference(avatar_component_clause,[],[f2201])).
% 78.92/11.74 thf(f72610,plain,(
% 78.92/11.74 spl72_762 | ~spl72_216),
% 78.92/11.74 inference(avatar_split_clause,[],[f4968,f4902,f72608])).
% 78.92/11.74 thf(f72608,plain,(
% 78.92/11.74 spl72_762 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_762])])).
% 78.92/11.74 thf(f4968,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1))) ) | ~spl72_216),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4967])).
% 78.92/11.74 thf(f4967,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1))) ) | ~spl72_216),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4962])).
% 78.92/11.74 thf(f4962,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X2),X1))) ) | ~spl72_216),
% 78.92/11.74 inference(primitive_instantiation,[],[f4903])).
% 78.92/11.74 thf(f72606,plain,(
% 78.92/11.74 spl72_761 | ~spl72_215),
% 78.92/11.74 inference(avatar_split_clause,[],[f4958,f4898,f72604])).
% 78.92/11.74 thf(f72604,plain,(
% 78.92/11.74 spl72_761 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_761])])).
% 78.92/11.74 thf(f4958,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2) != X0) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1))) ) | ~spl72_215),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4957])).
% 78.92/11.74 thf(f4957,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1))) ) | ~spl72_215),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4952])).
% 78.92/11.74 thf(f4952,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X2),X1))) ) | ~spl72_215),
% 78.92/11.74 inference(primitive_instantiation,[],[f4899])).
% 78.92/11.74 thf(f72602,plain,(
% 78.92/11.74 spl72_760 | ~spl72_28 | ~spl72_213),
% 78.92/11.74 inference(avatar_split_clause,[],[f4856,f4685,f2020,f72600])).
% 78.92/11.74 thf(f72600,plain,(
% 78.92/11.74 spl72_760 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : X1 > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X3),X4)) | ($true != ord(X1)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK32(X1,X0),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK33(X1,X0),X2)))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_760])])).
% 78.92/11.74 thf(f4685,plain,(
% 78.92/11.74 spl72_213 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : X0 > X1,X3 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_213])])).
% 78.92/11.74 thf(f4856,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X3),X4)) | ($true != ord(X1)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK32(X1,X0),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK33(X1,X0),X2))))) ) | (~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4855])).
% 78.92/11.74 thf(f4855,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X3),X4)) | ($true != ord(X1)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK32(X1,X0),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK33(X1,X0),X2))))) ) | (~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(superposition,[],[f4686,f2021])).
% 78.92/11.74 thf(f4686,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_213),
% 78.92/11.74 inference(avatar_component_clause,[],[f4685])).
% 78.92/11.74 thf(f72598,plain,(
% 78.92/11.74 spl72_759 | ~spl72_28 | ~spl72_212),
% 78.92/11.74 inference(avatar_split_clause,[],[f4805,f4681,f2020,f72596])).
% 78.92/11.74 thf(f72596,plain,(
% 78.92/11.74 spl72_759 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : X1 > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X3),X4)) | ($true != ord(X1)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK30(X1,X0),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK31(X1,X0),X2)))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_759])])).
% 78.92/11.74 thf(f4681,plain,(
% 78.92/11.74 spl72_212 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : X0 > X1,X3 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_212])])).
% 78.92/11.74 thf(f4805,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X3),X4)) | ($true != ord(X1)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK30(X1,X0),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK31(X1,X0),X2))))) ) | (~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4804])).
% 78.92/11.74 thf(f4804,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X3),X4)) | ($true != ord(X1)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK30(X1,X0),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK31(X1,X0),X2))))) ) | (~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(superposition,[],[f4682,f2021])).
% 78.92/11.74 thf(f4682,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_212),
% 78.92/11.74 inference(avatar_component_clause,[],[f4681])).
% 78.92/11.74 thf(f72594,plain,(
% 78.92/11.74 spl72_758 | ~spl72_28 | ~spl72_211),
% 78.92/11.74 inference(avatar_split_clause,[],[f4754,f4677,f2020,f72592])).
% 78.92/11.74 thf(f72592,plain,(
% 78.92/11.74 spl72_758 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : X1 > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X3),X4)) | (ord(X0) != $true) | ($true != ord(X1)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X2)))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_758])])).
% 78.92/11.74 thf(f4677,plain,(
% 78.92/11.74 spl72_211 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_211])])).
% 78.92/11.74 thf(f4754,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X3),X4)) | (ord(X0) != $true) | ($true != ord(X1)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X2))))) ) | (~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4753])).
% 78.92/11.74 thf(f4753,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X3),X4)) | (ord(X0) != $true) | ($true != ord(X1)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X2))))) ) | (~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(superposition,[],[f4678,f2021])).
% 78.92/11.74 thf(f4678,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_211),
% 78.92/11.74 inference(avatar_component_clause,[],[f4677])).
% 78.92/11.74 thf(f72513,plain,(
% 78.92/11.74 spl72_757 | ~spl72_28 | ~spl72_210),
% 78.92/11.74 inference(avatar_split_clause,[],[f4703,f4673,f2020,f72511])).
% 78.92/11.74 thf(f72511,plain,(
% 78.92/11.74 spl72_757 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1,X2 : X1 > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X3),X4)) | (ord(X0) != $true) | ($true != ord(X1)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X2)))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_757])])).
% 78.92/11.74 thf(f4673,plain,(
% 78.92/11.74 spl72_210 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_210])])).
% 78.92/11.74 thf(f4703,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X3),X4)) | (ord(X0) != $true) | ($true != ord(X1)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X2))))) ) | (~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4702])).
% 78.92/11.74 thf(f4702,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X3),X4)) | (ord(X0) != $true) | ($true != ord(X1)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X2))),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X2))))) ) | (~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(superposition,[],[f4674,f2021])).
% 78.92/11.74 thf(f4674,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_210),
% 78.92/11.74 inference(avatar_component_clause,[],[f4673])).
% 78.92/11.74 thf(f68004,plain,(
% 78.92/11.74 spl72_756 | ~spl72_340 | ~spl72_455),
% 78.92/11.74 inference(avatar_split_clause,[],[f29654,f28245,f7903,f68001])).
% 78.92/11.74 thf(f68001,plain,(
% 78.92/11.74 spl72_756 <=> ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_756])])).
% 78.92/11.74 thf(f28245,plain,(
% 78.92/11.74 spl72_455 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_455])])).
% 78.92/11.74 thf(f29654,plain,(
% 78.92/11.74 ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | (~spl72_340 | ~spl72_455)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f29518])).
% 78.92/11.74 thf(f29518,plain,(
% 78.92/11.74 ($true = $false) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | (~spl72_340 | ~spl72_455)),
% 78.92/11.74 inference(superposition,[],[f28246,f7905])).
% 78.92/11.74 thf(f28246,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl72_455),
% 78.92/11.74 inference(avatar_component_clause,[],[f28245])).
% 78.92/11.74 thf(f67998,plain,(
% 78.92/11.74 spl72_755 | ~spl72_20 | ~spl72_28 | ~spl72_213),
% 78.92/11.74 inference(avatar_split_clause,[],[f4877,f4685,f2020,f1984,f67996])).
% 78.92/11.74 thf(f67996,plain,(
% 78.92/11.74 spl72_755 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_755])])).
% 78.92/11.74 thf(f4877,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4876])).
% 78.92/11.74 thf(f4876,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(forward_demodulation,[],[f4848,f1986])).
% 78.92/11.74 thf(f4848,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) ) | (~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(superposition,[],[f4686,f2021])).
% 78.92/11.74 thf(f67994,plain,(
% 78.92/11.74 spl72_754 | ~spl72_20 | ~spl72_28 | ~spl72_213),
% 78.92/11.74 inference(avatar_split_clause,[],[f4875,f4685,f2020,f1984,f67992])).
% 78.92/11.74 thf(f67992,plain,(
% 78.92/11.74 spl72_754 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK33($o,X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_754])])).
% 78.92/11.74 thf(f4875,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK33($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4874])).
% 78.92/11.74 thf(f4874,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK33($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(forward_demodulation,[],[f4845,f1986])).
% 78.92/11.74 thf(f4845,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK33($o,X0),X1))) ) | (~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(superposition,[],[f4686,f2021])).
% 78.92/11.74 thf(f67990,plain,(
% 78.92/11.74 spl72_753 | ~spl72_20 | ~spl72_28 | ~spl72_213),
% 78.92/11.74 inference(avatar_split_clause,[],[f4861,f4685,f2020,f1984,f67988])).
% 78.92/11.74 thf(f67988,plain,(
% 78.92/11.74 spl72_753 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_753])])).
% 78.92/11.74 thf(f4861,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4860])).
% 78.92/11.74 thf(f4860,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(forward_demodulation,[],[f4841,f1986])).
% 78.92/11.74 thf(f4841,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK33(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK32(X0,$o),X1)))) ) | (~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(superposition,[],[f4686,f2021])).
% 78.92/11.74 thf(f67986,plain,(
% 78.92/11.74 spl72_752 | ~spl72_20 | ~spl72_28 | ~spl72_213),
% 78.92/11.74 inference(avatar_split_clause,[],[f4859,f4685,f2020,f1984,f67984])).
% 78.92/11.74 thf(f67984,plain,(
% 78.92/11.74 spl72_752 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK33($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK32($o,X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_752])])).
% 78.92/11.74 thf(f4859,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK33($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4858])).
% 78.92/11.74 thf(f4858,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK33($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(forward_demodulation,[],[f4838,f1986])).
% 78.92/11.74 thf(f4838,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK33($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK32($o,X0),X1))) ) | (~spl72_28 | ~spl72_213)),
% 78.92/11.74 inference(superposition,[],[f4686,f2021])).
% 78.92/11.74 thf(f67982,plain,(
% 78.92/11.74 spl72_751 | ~spl72_20 | ~spl72_28 | ~spl72_212),
% 78.92/11.74 inference(avatar_split_clause,[],[f4825,f4681,f2020,f1984,f67980])).
% 78.92/11.74 thf(f67980,plain,(
% 78.92/11.74 spl72_751 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_751])])).
% 78.92/11.74 thf(f4825,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4824])).
% 78.92/11.74 thf(f4824,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(forward_demodulation,[],[f4800,f1986])).
% 78.92/11.74 thf(f4800,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) ) | (~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(superposition,[],[f4682,f2021])).
% 78.92/11.74 thf(f67978,plain,(
% 78.92/11.74 spl72_750 | ~spl72_20 | ~spl72_28 | ~spl72_212),
% 78.92/11.74 inference(avatar_split_clause,[],[f4823,f4681,f2020,f1984,f67976])).
% 78.92/11.74 thf(f67976,plain,(
% 78.92/11.74 spl72_750 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK31($o,X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_750])])).
% 78.92/11.74 thf(f4823,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK31($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4822])).
% 78.92/11.74 thf(f4822,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK31($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(forward_demodulation,[],[f4797,f1986])).
% 78.92/11.74 thf(f4797,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK31($o,X0),X1))) ) | (~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(superposition,[],[f4682,f2021])).
% 78.92/11.74 thf(f67974,plain,(
% 78.92/11.74 spl72_749 | ~spl72_20 | ~spl72_28 | ~spl72_212),
% 78.92/11.74 inference(avatar_split_clause,[],[f4809,f4681,f2020,f1984,f67972])).
% 78.92/11.74 thf(f67972,plain,(
% 78.92/11.74 spl72_749 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_749])])).
% 78.92/11.74 thf(f4809,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4808])).
% 78.92/11.74 thf(f4808,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(forward_demodulation,[],[f4793,f1986])).
% 78.92/11.74 thf(f4793,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK31(X0,$o),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK30(X0,$o),X1)))) ) | (~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(superposition,[],[f4682,f2021])).
% 78.92/11.74 thf(f67970,plain,(
% 78.92/11.74 spl72_748 | ~spl72_20 | ~spl72_28 | ~spl72_212),
% 78.92/11.74 inference(avatar_split_clause,[],[f4807,f4681,f2020,f1984,f67968])).
% 78.92/11.74 thf(f67968,plain,(
% 78.92/11.74 spl72_748 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK31($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK30($o,X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_748])])).
% 78.92/11.74 thf(f4807,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK31($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4806])).
% 78.92/11.74 thf(f4806,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK31($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(forward_demodulation,[],[f4790,f1986])).
% 78.92/11.74 thf(f4790,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK31($o,X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK30($o,X0),X1))) ) | (~spl72_28 | ~spl72_212)),
% 78.92/11.74 inference(superposition,[],[f4682,f2021])).
% 78.92/11.74 thf(f67966,plain,(
% 78.92/11.74 spl72_747 | ~spl72_20 | ~spl72_28 | ~spl72_211),
% 78.92/11.74 inference(avatar_split_clause,[],[f4775,f4677,f2020,f1984,f67964])).
% 78.92/11.74 thf(f67964,plain,(
% 78.92/11.74 spl72_747 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_747])])).
% 78.92/11.74 thf(f4775,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4774])).
% 78.92/11.74 thf(f4774,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(forward_demodulation,[],[f4746,f1986])).
% 78.92/11.74 thf(f4746,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) ) | (~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(superposition,[],[f4678,f2021])).
% 78.92/11.74 thf(f67962,plain,(
% 78.92/11.74 spl72_746 | ~spl72_340 | ~spl72_454),
% 78.92/11.74 inference(avatar_split_clause,[],[f29468,f28241,f7903,f67959])).
% 78.92/11.74 thf(f67959,plain,(
% 78.92/11.74 spl72_746 <=> ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_746])])).
% 78.92/11.74 thf(f28241,plain,(
% 78.92/11.74 spl72_454 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_454])])).
% 78.92/11.74 thf(f29468,plain,(
% 78.92/11.74 ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (~spl72_340 | ~spl72_454)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f29332])).
% 78.92/11.74 thf(f29332,plain,(
% 78.92/11.74 ($true = $false) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (~spl72_340 | ~spl72_454)),
% 78.92/11.74 inference(superposition,[],[f28242,f7905])).
% 78.92/11.74 thf(f28242,plain,(
% 78.92/11.74 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl72_454),
% 78.92/11.74 inference(avatar_component_clause,[],[f28241])).
% 78.92/11.74 thf(f67957,plain,(
% 78.92/11.74 spl72_745 | ~spl72_20 | ~spl72_28 | ~spl72_211),
% 78.92/11.74 inference(avatar_split_clause,[],[f4773,f4677,f2020,f1984,f67955])).
% 78.92/11.74 thf(f67955,plain,(
% 78.92/11.74 spl72_745 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_745])])).
% 78.92/11.74 thf(f4773,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4772])).
% 78.92/11.74 thf(f4772,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(forward_demodulation,[],[f4743,f1986])).
% 78.92/11.74 thf(f4743,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1))) ) | (~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(superposition,[],[f4678,f2021])).
% 78.92/11.74 thf(f67953,plain,(
% 78.92/11.74 spl72_744 | ~spl72_20 | ~spl72_28 | ~spl72_211),
% 78.92/11.74 inference(avatar_split_clause,[],[f4759,f4677,f2020,f1984,f67951])).
% 78.92/11.74 thf(f67951,plain,(
% 78.92/11.74 spl72_744 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_744])])).
% 78.92/11.74 thf(f4759,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4758])).
% 78.92/11.74 thf(f4758,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(forward_demodulation,[],[f4739,f1986])).
% 78.92/11.74 thf(f4739,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK29($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK28($o,X0),X1)))) ) | (~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(superposition,[],[f4678,f2021])).
% 78.92/11.74 thf(f67949,plain,(
% 78.92/11.74 spl72_743 | ~spl72_20 | ~spl72_28 | ~spl72_211),
% 78.92/11.74 inference(avatar_split_clause,[],[f4757,f4677,f2020,f1984,f67947])).
% 78.92/11.74 thf(f67947,plain,(
% 78.92/11.74 spl72_743 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_743])])).
% 78.92/11.74 thf(f4757,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4756])).
% 78.92/11.74 thf(f4756,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(forward_demodulation,[],[f4736,f1986])).
% 78.92/11.74 thf(f4736,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK29(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK28(X0,$o),X1))) ) | (~spl72_28 | ~spl72_211)),
% 78.92/11.74 inference(superposition,[],[f4678,f2021])).
% 78.92/11.74 thf(f67945,plain,(
% 78.92/11.74 spl72_742 | ~spl72_20 | ~spl72_28 | ~spl72_210),
% 78.92/11.74 inference(avatar_split_clause,[],[f4723,f4673,f2020,f1984,f67943])).
% 78.92/11.74 thf(f67943,plain,(
% 78.92/11.74 spl72_742 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_742])])).
% 78.92/11.74 thf(f4723,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4722])).
% 78.92/11.74 thf(f4722,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(forward_demodulation,[],[f4698,f1986])).
% 78.92/11.74 thf(f4698,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1))),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) ) | (~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(superposition,[],[f4674,f2021])).
% 78.92/11.74 thf(f67941,plain,(
% 78.92/11.74 spl72_741 | ~spl72_20 | ~spl72_28 | ~spl72_210),
% 78.92/11.74 inference(avatar_split_clause,[],[f4721,f4673,f2020,f1984,f67939])).
% 78.92/11.74 thf(f67939,plain,(
% 78.92/11.74 spl72_741 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_741])])).
% 78.92/11.74 thf(f4721,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4720])).
% 78.92/11.74 thf(f4720,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(forward_demodulation,[],[f4695,f1986])).
% 78.92/11.74 thf(f4695,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))),vAPP($o,X0,X1,$true))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1))) ) | (~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(superposition,[],[f4674,f2021])).
% 78.92/11.74 thf(f67937,plain,(
% 78.92/11.74 spl72_740 | ~spl72_20 | ~spl72_28 | ~spl72_210),
% 78.92/11.74 inference(avatar_split_clause,[],[f4707,f4673,f2020,f1984,f67935])).
% 78.92/11.74 thf(f67935,plain,(
% 78.92/11.74 spl72_740 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_740])])).
% 78.92/11.74 thf(f4707,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4706])).
% 78.92/11.74 thf(f4706,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1)))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(forward_demodulation,[],[f4691,f1986])).
% 78.92/11.74 thf(f4691,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK27($o,X0),X1)))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X2)),vAPP(X0,$o,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord($o) != $true) | (ord(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK26($o,X0),X1)))) ) | (~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(superposition,[],[f4674,f2021])).
% 78.92/11.74 thf(f67933,plain,(
% 78.92/11.74 spl72_739 | ~spl72_20 | ~spl72_28 | ~spl72_210),
% 78.92/11.74 inference(avatar_split_clause,[],[f4705,f4673,f2020,f1984,f67931])).
% 78.92/11.74 thf(f67931,plain,(
% 78.92/11.74 spl72_739 <=> ! [X0 : $tType,X3 : $o,X2 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_739])])).
% 78.92/11.74 thf(f4705,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4704])).
% 78.92/11.74 thf(f4704,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))) ) | (~spl72_20 | ~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(forward_demodulation,[],[f4688,f1986])).
% 78.92/11.74 thf(f4688,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : $o,X3 : $o,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,$true)),vAPP($o,X0,X1,vAPP(sTfun($o,X0),$o,sK27(X0,$o),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X1,X2)),vAPP($o,X0,X1,X3))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X3)) | (ord(X0) != $true) | (ord($o) != $true) | ($false = vAPP(sTfun($o,X0),$o,sK26(X0,$o),X1))) ) | (~spl72_28 | ~spl72_210)),
% 78.92/11.74 inference(superposition,[],[f4674,f2021])).
% 78.92/11.74 thf(f67929,plain,(
% 78.92/11.74 spl72_738 | ~spl72_206),
% 78.92/11.74 inference(avatar_split_clause,[],[f4586,f4421,f67927])).
% 78.92/11.74 thf(f67927,plain,(
% 78.92/11.74 spl72_738 <=> ! [X0 : $tType,X4 : nat,X3 : X0 > nat,X2 : X0,X1 : X0] : ((X1 != X2) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_738])])).
% 78.92/11.74 thf(f4421,plain,(
% 78.92/11.74 spl72_206 <=> ! [X0 : $tType,X4 : nat,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_206])])).
% 78.92/11.74 thf(f4586,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : nat] : ((X1 != X2) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1) | (vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1)) ) | ~spl72_206),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4585])).
% 78.92/11.74 thf(f4585,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : nat] : ((X1 != X2) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))))) ) | ~spl72_206),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4584])).
% 78.92/11.74 thf(f4584,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : nat] : ((X1 != X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))))) ) | ~spl72_206),
% 78.92/11.74 inference(equality_proxy_clausification,[],[f4545])).
% 78.92/11.74 thf(f4545,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : nat] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))))) ) | ~spl72_206),
% 78.92/11.74 inference(primitive_instantiation,[],[f4422])).
% 78.92/11.74 thf(f4422,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : nat] : (($true != vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1)))) ) | ~spl72_206),
% 78.92/11.74 inference(avatar_component_clause,[],[f4421])).
% 78.92/11.74 thf(f67925,plain,(
% 78.92/11.74 spl72_737 | ~spl72_138),
% 78.92/11.74 inference(avatar_split_clause,[],[f3262,f3237,f67923])).
% 78.92/11.74 thf(f67923,plain,(
% 78.92/11.74 spl72_737 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X0) = vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X1)) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_737])])).
% 78.92/11.74 thf(f3237,plain,(
% 78.92/11.74 spl72_138 <=> ! [X0 : nat] : (vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_138])])).
% 78.92/11.74 thf(f3262,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X0) = vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X1)) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X1))) ) | ~spl72_138),
% 78.92/11.74 inference(constrained_superposition,[],[f3238,f3238])).
% 78.92/11.74 thf(f3238,plain,(
% 78.92/11.74 ( ! [X0 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0)))) ) | ~spl72_138),
% 78.92/11.74 inference(avatar_component_clause,[],[f3237])).
% 78.92/11.74 thf(f67921,plain,(
% 78.92/11.74 spl72_736 | ~spl72_137 | ~spl72_138),
% 78.92/11.74 inference(avatar_split_clause,[],[f3261,f3237,f3233,f67919])).
% 78.92/11.74 thf(f67919,plain,(
% 78.92/11.74 spl72_736 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X1)) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_736])])).
% 78.92/11.74 thf(f3233,plain,(
% 78.92/11.74 spl72_137 <=> ! [X0 : nat] : (vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_137])])).
% 78.92/11.74 thf(f3261,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X1)) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X1))) ) | (~spl72_137 | ~spl72_138)),
% 78.92/11.74 inference(constrained_superposition,[],[f3238,f3234])).
% 78.92/11.74 thf(f3234,plain,(
% 78.92/11.74 ( ! [X0 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0)))) ) | ~spl72_137),
% 78.92/11.74 inference(avatar_component_clause,[],[f3233])).
% 78.92/11.74 thf(f67899,plain,(
% 78.92/11.74 spl72_735 | ~spl72_137),
% 78.92/11.74 inference(avatar_split_clause,[],[f3258,f3233,f67897])).
% 78.92/11.74 thf(f67897,plain,(
% 78.92/11.74 spl72_735 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X1)) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_735])])).
% 78.92/11.74 thf(f3258,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X1)) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X1))) ) | ~spl72_137),
% 78.92/11.74 inference(constrained_superposition,[],[f3234,f3234])).
% 78.92/11.74 thf(f66388,plain,(
% 78.92/11.74 spl72_734 | ~spl72_28 | ~spl72_209),
% 78.92/11.74 inference(avatar_split_clause,[],[f4641,f4622,f2020,f66386])).
% 78.92/11.74 thf(f66386,plain,(
% 78.92/11.74 spl72_734 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_734])])).
% 78.92/11.74 thf(f4622,plain,(
% 78.92/11.74 spl72_209 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_209])])).
% 78.92/11.74 thf(f4641,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)))) ) | (~spl72_28 | ~spl72_209)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4640])).
% 78.92/11.74 thf(f4640,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)))) ) | (~spl72_28 | ~spl72_209)),
% 78.92/11.74 inference(superposition,[],[f4623,f2021])).
% 78.92/11.74 thf(f4623,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true)) ) | ~spl72_209),
% 78.92/11.74 inference(avatar_component_clause,[],[f4622])).
% 78.92/11.74 thf(f66384,plain,(
% 78.92/11.74 spl72_733 | ~spl72_28 | ~spl72_208),
% 78.92/11.74 inference(avatar_split_clause,[],[f4628,f4618,f2020,f66382])).
% 78.92/11.74 thf(f66382,plain,(
% 78.92/11.74 spl72_733 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) = $false))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_733])])).
% 78.92/11.74 thf(f4618,plain,(
% 78.92/11.74 spl72_208 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_208])])).
% 78.92/11.74 thf(f4628,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) = $false)) ) | (~spl72_28 | ~spl72_208)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4627])).
% 78.92/11.74 thf(f4627,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) = $false)) ) | (~spl72_28 | ~spl72_208)),
% 78.92/11.74 inference(superposition,[],[f4619,f2021])).
% 78.92/11.74 thf(f4619,plain,(
% 78.92/11.74 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : ((linorder(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))) ) | ~spl72_208),
% 78.92/11.74 inference(avatar_component_clause,[],[f4618])).
% 78.92/11.74 thf(f65120,plain,(
% 78.92/11.74 ~spl72_337 | spl72_732 | ~spl72_68 | ~spl72_174),
% 78.92/11.74 inference(avatar_split_clause,[],[f13639,f3925,f2368,f65118,f7888])).
% 78.92/11.74 thf(f7888,plain,(
% 78.92/11.74 spl72_337 <=> ($true = wellorder($o))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_337])])).
% 78.92/11.74 thf(f65118,plain,(
% 78.92/11.74 spl72_732 <=> ! [X0 : nat,X3 : nat,X2 : nat > $o,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK45($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,X3)) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_732])])).
% 78.92/11.74 thf(f2368,plain,(
% 78.92/11.74 spl72_68 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_68])])).
% 78.92/11.74 thf(f3925,plain,(
% 78.92/11.74 spl72_174 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1,X6 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2)))) | (wellorder(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_174])])).
% 78.92/11.74 thf(f13639,plain,(
% 78.92/11.74 ( ! [X2 : nat > $o,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK45($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) | ($true = vAPP(nat,$o,X2,X3)) | ($true != wellorder($o))) ) | (~spl72_68 | ~spl72_174)),
% 78.92/11.74 inference(superposition,[],[f3926,f2369])).
% 78.92/11.74 thf(f2369,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) ) | ~spl72_68),
% 78.92/11.74 inference(avatar_component_clause,[],[f2368])).
% 78.92/11.74 thf(f3926,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2)))) | ($true = vAPP(X1,$o,X3,X6)) | ($true = vAPP(X1,$o,X3,X4)) | (wellorder(X0) != $true)) ) | ~spl72_174),
% 78.92/11.74 inference(avatar_component_clause,[],[f3925])).
% 78.92/11.74 thf(f65116,plain,(
% 78.92/11.74 ~spl72_337 | spl72_731 | ~spl72_67 | ~spl72_174),
% 78.92/11.74 inference(avatar_split_clause,[],[f13638,f3925,f2364,f65114,f7888])).
% 78.92/11.74 thf(f65114,plain,(
% 78.92/11.74 spl72_731 <=> ! [X0 : nat,X3 : nat,X2 : nat > $o,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK45($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,X3)) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_731])])).
% 78.92/11.74 thf(f2364,plain,(
% 78.92/11.74 spl72_67 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_67])])).
% 78.92/11.74 thf(f13638,plain,(
% 78.92/11.74 ( ! [X2 : nat > $o,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK45($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) | ($true = vAPP(nat,$o,X2,X3)) | ($true != wellorder($o))) ) | (~spl72_67 | ~spl72_174)),
% 78.92/11.74 inference(superposition,[],[f3926,f2365])).
% 78.92/11.74 thf(f2365,plain,(
% 78.92/11.74 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) ) | ~spl72_67),
% 78.92/11.74 inference(avatar_component_clause,[],[f2364])).
% 78.92/11.74 thf(f65112,plain,(
% 78.92/11.74 ~spl72_337 | spl72_730 | ~spl72_68 | ~spl72_173),
% 78.92/11.74 inference(avatar_split_clause,[],[f13600,f3921,f2368,f65110,f7888])).
% 78.92/11.74 thf(f65110,plain,(
% 78.92/11.74 spl72_730 <=> ! [X0 : nat,X3 : nat,X2 : nat > $o,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK44($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,X3)) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_730])])).
% 78.92/11.74 thf(f3921,plain,(
% 78.92/11.74 spl72_173 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1,X6 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2)))) | (wellorder(X0) != $true))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_173])])).
% 78.92/11.74 thf(f13600,plain,(
% 78.92/11.74 ( ! [X2 : nat > $o,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK44($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) | ($true = vAPP(nat,$o,X2,X3)) | ($true != wellorder($o))) ) | (~spl72_68 | ~spl72_173)),
% 78.92/11.74 inference(superposition,[],[f3922,f2369])).
% 78.92/11.74 thf(f3922,plain,(
% 78.92/11.74 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2)))) | ($true = vAPP(X1,$o,X3,X6)) | ($true = vAPP(X1,$o,X3,X4)) | (wellorder(X0) != $true)) ) | ~spl72_173),
% 78.92/11.74 inference(avatar_component_clause,[],[f3921])).
% 78.92/11.74 thf(f65108,plain,(
% 78.92/11.74 ~spl72_337 | spl72_729 | ~spl72_67 | ~spl72_173),
% 78.92/11.74 inference(avatar_split_clause,[],[f13599,f3921,f2364,f65106,f7888])).
% 78.92/11.74 thf(f65106,plain,(
% 78.92/11.74 spl72_729 <=> ! [X0 : nat,X3 : nat,X2 : nat > $o,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK44($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,X3)) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_729])])).
% 78.92/11.74 thf(f13599,plain,(
% 78.92/11.74 ( ! [X2 : nat > $o,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK44($o,nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) | ($true = vAPP(nat,$o,X2,X3)) | ($true != wellorder($o))) ) | (~spl72_67 | ~spl72_173)),
% 78.92/11.74 inference(superposition,[],[f3922,f2365])).
% 78.92/11.74 thf(f65104,plain,(
% 78.92/11.74 spl72_728 | ~spl72_16 | ~spl72_28 | ~spl72_209),
% 78.92/11.74 inference(avatar_split_clause,[],[f4669,f4622,f2020,f1964,f65102])).
% 78.92/11.74 thf(f65102,plain,(
% 78.92/11.74 spl72_728 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)))),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_728])])).
% 78.92/11.74 thf(f1964,plain,(
% 78.92/11.74 spl72_16 <=> (linorder($o) = $true)),
% 78.92/11.74 introduced(avatar_definition,[new_symbols(naming,[spl72_16])])).
% 78.92/11.74 thf(f4669,plain,(
% 78.92/11.74 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_209)),
% 78.92/11.74 inference(trivial_inequality_removal,[],[f4668])).
% 78.92/11.74 thf(f4668,plain,(
% 78.92/11.74 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_209)),
% 78.92/11.74 inference(forward_demodulation,[],[f4636,f1966])).
% 78.92/11.74 thf(f1966,plain,(
% 78.92/11.74 (linorder($o) = $true) | ~spl72_16),
% 78.92/11.74 inference(avatar_component_clause,[],[f1964])).
% 78.92/11.74 thf(f4636,plain,(
% 78.92/11.74 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | (linorder($o) != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) ) | (~spl72_28 | ~spl72_209)),
% 78.92/11.75 inference(superposition,[],[f4623,f2021])).
% 78.92/11.75 thf(f65100,plain,(
% 78.92/11.75 spl72_727 | ~spl72_16 | ~spl72_28 | ~spl72_209),
% 78.92/11.75 inference(avatar_split_clause,[],[f4667,f4622,f2020,f1964,f65098])).
% 78.92/11.75 thf(f65098,plain,(
% 78.92/11.75 spl72_727 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_727])])).
% 78.92/11.75 thf(f4667,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_209)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4666])).
% 78.92/11.75 thf(f4666,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_209)),
% 78.92/11.75 inference(forward_demodulation,[],[f4635,f1966])).
% 78.92/11.75 thf(f4635,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | (linorder($o) != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) ) | (~spl72_28 | ~spl72_209)),
% 78.92/11.75 inference(superposition,[],[f4623,f2021])).
% 78.92/11.75 thf(f65096,plain,(
% 78.92/11.75 spl72_726 | ~spl72_28 | ~spl72_206),
% 78.92/11.75 inference(avatar_split_clause,[],[f4564,f4421,f2020,f65094])).
% 78.92/11.75 thf(f65094,plain,(
% 78.92/11.75 spl72_726 <=> ! [X0 : $tType,X4 : nat,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_726])])).
% 78.92/11.75 thf(f4564,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : nat] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_206)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4563])).
% 78.92/11.75 thf(f4563,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : nat] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_206)),
% 78.92/11.75 inference(superposition,[],[f4422,f2021])).
% 78.92/11.75 thf(f65092,plain,(
% 78.92/11.75 spl72_725 | ~spl72_28 | ~spl72_205),
% 78.92/11.75 inference(avatar_split_clause,[],[f4486,f4417,f2020,f65090])).
% 78.92/11.75 thf(f65090,plain,(
% 78.92/11.75 spl72_725 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_725])])).
% 78.92/11.75 thf(f4417,plain,(
% 78.92/11.75 spl72_205 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_205])])).
% 78.92/11.75 thf(f4486,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1)))) ) | (~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4485])).
% 78.92/11.75 thf(f4485,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1)))) ) | (~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(superposition,[],[f4418,f2021])).
% 78.92/11.75 thf(f4418,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true)) ) | ~spl72_205),
% 78.92/11.75 inference(avatar_component_clause,[],[f4417])).
% 78.92/11.75 thf(f65088,plain,(
% 78.92/11.75 spl72_724 | ~spl72_28 | ~spl72_204),
% 78.92/11.75 inference(avatar_split_clause,[],[f4434,f4413,f2020,f65086])).
% 78.92/11.75 thf(f65086,plain,(
% 78.92/11.75 spl72_724 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_724])])).
% 78.92/11.75 thf(f4413,plain,(
% 78.92/11.75 spl72_204 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_204])])).
% 78.92/11.75 thf(f4434,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1)))) ) | (~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4433])).
% 78.92/11.75 thf(f4433,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1)))) ) | (~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(superposition,[],[f4414,f2021])).
% 78.92/11.75 thf(f4414,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true)) ) | ~spl72_204),
% 78.92/11.75 inference(avatar_component_clause,[],[f4413])).
% 78.92/11.75 thf(f64395,plain,(
% 78.92/11.75 spl72_723 | ~spl72_206),
% 78.92/11.75 inference(avatar_split_clause,[],[f4611,f4421,f64393])).
% 78.92/11.75 thf(f64393,plain,(
% 78.92/11.75 spl72_723 <=> ! [X0 : $tType,X3 : nat,X2 : X0,X1 : X0 > nat] : ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X3),X1),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_723])])).
% 78.92/11.75 thf(f4611,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : nat,X1 : X0 > nat] : ((vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X3),X1),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2)) ) | ~spl72_206),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f4539])).
% 78.92/11.75 thf(f4539,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : nat,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X3),X1),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)))) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2)) ) | ~spl72_206),
% 78.92/11.75 inference(leibniz_equality_elimination,[],[f4422])).
% 78.92/11.75 thf(f64391,plain,(
% 78.92/11.75 spl72_722 | ~spl72_16 | ~spl72_28 | ~spl72_205),
% 78.92/11.75 inference(avatar_split_clause,[],[f4536,f4417,f2020,f1964,f64389])).
% 78.92/11.75 thf(f64389,plain,(
% 78.92/11.75 spl72_722 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_722])])).
% 78.92/11.75 thf(f4536,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4535])).
% 78.92/11.75 thf(f4535,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(forward_demodulation,[],[f4481,f1966])).
% 78.92/11.75 thf(f4481,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | (linorder($o) != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) ) | (~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(superposition,[],[f4418,f2021])).
% 78.92/11.75 thf(f64387,plain,(
% 78.92/11.75 spl72_721 | ~spl72_16 | ~spl72_28 | ~spl72_205),
% 78.92/11.75 inference(avatar_split_clause,[],[f4534,f4417,f2020,f1964,f64385])).
% 78.92/11.75 thf(f64385,plain,(
% 78.92/11.75 spl72_721 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_721])])).
% 78.92/11.75 thf(f4534,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4533])).
% 78.92/11.75 thf(f4533,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(forward_demodulation,[],[f4480,f1966])).
% 78.92/11.75 thf(f4480,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | (linorder($o) != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0))) ) | (~spl72_28 | ~spl72_205)),
% 78.92/11.75 inference(superposition,[],[f4418,f2021])).
% 78.92/11.75 thf(f64383,plain,(
% 78.92/11.75 spl72_720 | ~spl72_16 | ~spl72_28 | ~spl72_204),
% 78.92/11.75 inference(avatar_split_clause,[],[f4473,f4413,f2020,f1964,f64381])).
% 78.92/11.75 thf(f64381,plain,(
% 78.92/11.75 spl72_720 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_720])])).
% 78.92/11.75 thf(f4473,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4472])).
% 78.92/11.75 thf(f4472,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(forward_demodulation,[],[f4429,f1966])).
% 78.92/11.75 thf(f4429,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | (linorder($o) != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) ) | (~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(superposition,[],[f4414,f2021])).
% 78.92/11.75 thf(f64379,plain,(
% 78.92/11.75 spl72_719 | ~spl72_16 | ~spl72_28 | ~spl72_204),
% 78.92/11.75 inference(avatar_split_clause,[],[f4471,f4413,f2020,f1964,f64377])).
% 78.92/11.75 thf(f64377,plain,(
% 78.92/11.75 spl72_719 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_719])])).
% 78.92/11.75 thf(f4471,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4470])).
% 78.92/11.75 thf(f4470,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0))) ) | (~spl72_16 | ~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(forward_demodulation,[],[f4428,f1966])).
% 78.92/11.75 thf(f4428,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,$true),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)) | (linorder($o) != $true) | ($false = vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0))) ) | (~spl72_28 | ~spl72_204)),
% 78.92/11.75 inference(superposition,[],[f4414,f2021])).
% 78.92/11.75 thf(f64184,plain,(
% 78.92/11.75 spl72_718 | ~spl72_48 | ~spl72_520),
% 78.92/11.75 inference(avatar_split_clause,[],[f39876,f36530,f2214,f64182])).
% 78.92/11.75 thf(f64182,plain,(
% 78.92/11.75 spl72_718 <=> ! [X3 : $tType,X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_718])])).
% 78.92/11.75 thf(f2214,plain,(
% 78.92/11.75 spl72_48 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | ($true != order(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_48])])).
% 78.92/11.75 thf(f36530,plain,(
% 78.92/11.75 spl72_520 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,set(X1)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_520])])).
% 78.92/11.75 thf(f39876,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = order(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))) ) | (~spl72_48 | ~spl72_520)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f39859])).
% 78.92/11.75 thf(f39859,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))) ) | (~spl72_48 | ~spl72_520)),
% 78.92/11.75 inference(superposition,[],[f2215,f36531])).
% 78.92/11.75 thf(f36531,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,set(X1)))))) ) | ~spl72_520),
% 78.92/11.75 inference(avatar_component_clause,[],[f36530])).
% 78.92/11.75 thf(f2215,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true != order(X1)) | ($true = order(sTfun(X0,X1)))) ) | ~spl72_48),
% 78.92/11.75 inference(avatar_component_clause,[],[f2214])).
% 78.92/11.75 thf(f63989,plain,(
% 78.92/11.75 spl72_717),
% 78.92/11.75 inference(avatar_split_clause,[],[f1817,f63987])).
% 78.92/11.75 thf(f63987,plain,(
% 78.92/11.75 spl72_717 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_717])])).
% 78.92/11.75 thf(f1817,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1),X2))) )),
% 78.92/11.75 inference(pi_clausification,[],[f1814])).
% 78.92/11.75 thf(f1814,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) | ($false = vAPP(sTfun(nat,$o),$o,vSIGMA(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1)))) )),
% 78.92/11.75 inference(binary_proxy_clausification,[],[f1537])).
% 78.92/11.75 thf(f1537,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) = vAPP(sTfun(nat,$o),$o,vSIGMA(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1)))) )),
% 78.92/11.75 inference(cnf_transformation,[],[f630])).
% 78.92/11.75 thf(f630,plain,(
% 78.92/11.75 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) = vAPP(sTfun(nat,$o),$o,vSIGMA(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1)))),
% 78.92/11.75 inference(fool_elimination,[],[f629])).
% 78.92/11.75 thf(f629,plain,(
% 78.92/11.75 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) = ? [X2 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X2),X1))),
% 78.92/11.75 inference(rectify,[],[f158])).
% 78.92/11.75 thf(f158,axiom,(
% 78.92/11.75 ! [X12 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X12),X19) = ? [X20 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X20),X19))),
% 78.92/11.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_157_g_H_Oconnected__by__dist)).
% 78.92/11.75 thf(f63985,plain,(
% 78.92/11.75 spl72_716),
% 78.92/11.75 inference(avatar_split_clause,[],[f1809,f63983])).
% 78.92/11.75 thf(f63983,plain,(
% 78.92/11.75 spl72_716 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_716])])).
% 78.92/11.75 thf(f1809,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1),X2))) )),
% 78.92/11.75 inference(pi_clausification,[],[f1806])).
% 78.92/11.75 thf(f1806,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) | ($false = vAPP(sTfun(nat,$o),$o,vSIGMA(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1)))) )),
% 78.92/11.75 inference(binary_proxy_clausification,[],[f1539])).
% 78.92/11.75 thf(f1539,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) = vAPP(sTfun(nat,$o),$o,vSIGMA(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1)))) )),
% 78.92/11.75 inference(cnf_transformation,[],[f634])).
% 78.92/11.75 thf(f634,plain,(
% 78.92/11.75 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) = vAPP(sTfun(nat,$o),$o,vSIGMA(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1)))),
% 78.92/11.75 inference(fool_elimination,[],[f633])).
% 78.92/11.75 thf(f633,plain,(
% 78.92/11.75 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) = ? [X2 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X2),X1))),
% 78.92/11.75 inference(rectify,[],[f18])).
% 78.92/11.75 thf(f18,axiom,(
% 78.92/11.75 ! [X12 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X12),X19) = ? [X20 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X20),X19))),
% 78.92/11.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_connected__by__dist)).
% 78.92/11.75 thf(f61331,plain,(
% 78.92/11.75 spl72_715 | ~spl72_16 | ~spl72_208),
% 78.92/11.75 inference(avatar_split_clause,[],[f4630,f4618,f1964,f61329])).
% 78.92/11.75 thf(f61329,plain,(
% 78.92/11.75 spl72_715 <=> ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_715])])).
% 78.92/11.75 thf(f4630,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2))) ) | (~spl72_16 | ~spl72_208)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4625])).
% 78.92/11.75 thf(f4625,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o > $o > $o,X1 : $o] : (($true != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,vAPP(sTfun($o,sTfun($o,$o)),$o,sK17($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK16($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK18($o),X0)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK19($o),X0))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),X0,X1),X2))) ) | (~spl72_16 | ~spl72_208)),
% 78.92/11.75 inference(superposition,[],[f4619,f1966])).
% 78.92/11.75 thf(f61327,plain,(
% 78.92/11.75 spl72_714 | ~spl72_17 | ~spl72_208),
% 78.92/11.75 inference(avatar_split_clause,[],[f4629,f4618,f1969,f61325])).
% 78.92/11.75 thf(f61325,plain,(
% 78.92/11.75 spl72_714 <=> ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_714])])).
% 78.92/11.75 thf(f1969,plain,(
% 78.92/11.75 spl72_17 <=> (linorder(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_17])])).
% 78.92/11.75 thf(f4629,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2))) ) | (~spl72_17 | ~spl72_208)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4626])).
% 78.92/11.75 thf(f4626,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),X0)),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),X0))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),X0,X1),X2))) ) | (~spl72_17 | ~spl72_208)),
% 78.92/11.75 inference(superposition,[],[f4619,f1971])).
% 78.92/11.75 thf(f1971,plain,(
% 78.92/11.75 (linorder(nat) = $true) | ~spl72_17),
% 78.92/11.75 inference(avatar_component_clause,[],[f1969])).
% 78.92/11.75 thf(f60397,plain,(
% 78.92/11.75 spl72_713 | ~spl72_147),
% 78.92/11.75 inference(avatar_split_clause,[],[f3553,f3367,f60395])).
% 78.92/11.75 thf(f60395,plain,(
% 78.92/11.75 spl72_713 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1) = vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_713])])).
% 78.92/11.75 thf(f3367,plain,(
% 78.92/11.75 spl72_147 <=> ! [X0 : $tType,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_147])])).
% 78.92/11.75 thf(f3553,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1) = vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))),X1))) ) | ~spl72_147),
% 78.92/11.75 inference(leibniz_equality_elimination,[],[f3368])).
% 78.92/11.75 thf(f3368,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true != vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) ) | ~spl72_147),
% 78.92/11.75 inference(avatar_component_clause,[],[f3367])).
% 78.92/11.75 thf(f60393,plain,(
% 78.92/11.75 spl72_712 | ~spl72_46 | ~spl72_515),
% 78.92/11.75 inference(avatar_split_clause,[],[f38633,f35901,f2205,f60391])).
% 78.92/11.75 thf(f60391,plain,(
% 78.92/11.75 spl72_712 <=> ! [X3 : $tType,X1 : $tType,X0 : $tType,X2 : $tType] : ($true = ord(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_712])])).
% 78.92/11.75 thf(f35901,plain,(
% 78.92/11.75 spl72_515 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = ord(sTfun(X2,sTfun(X0,set(X1)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_515])])).
% 78.92/11.75 thf(f38633,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = ord(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))) ) | (~spl72_46 | ~spl72_515)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f38632])).
% 78.92/11.75 thf(f38632,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))) ) | (~spl72_46 | ~spl72_515)),
% 78.92/11.75 inference(superposition,[],[f2206,f35902])).
% 78.92/11.75 thf(f35902,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,set(X1)))))) ) | ~spl72_515),
% 78.92/11.75 inference(avatar_component_clause,[],[f35901])).
% 78.92/11.75 thf(f60389,plain,(
% 78.92/11.75 spl72_711 | ~spl72_145),
% 78.92/11.75 inference(avatar_split_clause,[],[f3445,f3359,f60387])).
% 78.92/11.75 thf(f60387,plain,(
% 78.92/11.75 spl72_711 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1) = vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_711])])).
% 78.92/11.75 thf(f3359,plain,(
% 78.92/11.75 spl72_145 <=> ! [X0 : $tType,X4 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X4)) | (wellorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_145])])).
% 78.92/11.75 thf(f3445,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1) = vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))),X1))) ) | ~spl72_145),
% 78.92/11.75 inference(leibniz_equality_elimination,[],[f3360])).
% 78.92/11.75 thf(f3360,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X1,X4)) | (wellorder(X0) != $true)) ) | ~spl72_145),
% 78.92/11.75 inference(avatar_component_clause,[],[f3359])).
% 78.92/11.75 thf(f59722,plain,(
% 78.92/11.75 spl72_339 | spl72_707 | spl72_708 | spl72_339 | spl72_709 | ~spl72_710 | ~spl72_16 | ~spl72_257),
% 78.92/11.75 inference(avatar_split_clause,[],[f6300,f6253,f1964,f59719,f59715,f7896,f59711,f59707,f7896])).
% 78.92/11.75 thf(f59707,plain,(
% 78.92/11.75 spl72_707 <=> ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_707])])).
% 78.92/11.75 thf(f59711,plain,(
% 78.92/11.75 spl72_708 <=> ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_708])])).
% 78.92/11.75 thf(f7896,plain,(
% 78.92/11.75 spl72_339 <=> ! [X0 : $o] : ($true = X0)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_339])])).
% 78.92/11.75 thf(f59715,plain,(
% 78.92/11.75 spl72_709 <=> ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_709])])).
% 78.92/11.75 thf(f59719,plain,(
% 78.92/11.75 spl72_710 <=> ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_710])])).
% 78.92/11.75 thf(f6253,plain,(
% 78.92/11.75 spl72_257 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_257])])).
% 78.92/11.75 thf(f6300,plain,(
% 78.92/11.75 ( ! [X0 : $o,X1 : $o] : (($true != vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR)) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR)) | ($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR))) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR)) | ($true = X0)) ) | (~spl72_16 | ~spl72_257)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6299])).
% 78.92/11.75 thf(f6299,plain,(
% 78.92/11.75 ( ! [X0 : $o,X1 : $o] : (($true != $true) | ($true != vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR)) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR)) | ($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR))) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR)) | ($true = X0)) ) | (~spl72_16 | ~spl72_257)),
% 78.92/11.75 inference(forward_demodulation,[],[f6287,f1966])).
% 78.92/11.75 thf(f6287,plain,(
% 78.92/11.75 ( ! [X0 : $o,X1 : $o] : (($true != vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR)) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR)) | ($true = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR))) | (linorder($o) != $true) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR)) | ($true = X0)) ) | ~spl72_257),
% 78.92/11.75 inference(binary_proxy_clausification,[],[f6286])).
% 78.92/11.75 thf(f6286,plain,(
% 78.92/11.75 ( ! [X0 : $o,X1 : $o] : (($true != vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR)) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR))) | (linorder($o) != $true) | ($true = vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR))) ) | ~spl72_257),
% 78.92/11.75 inference(binary_proxy_clausification,[],[f6285])).
% 78.92/11.75 thf(f6285,plain,(
% 78.92/11.75 ( ! [X0 : $o,X1 : $o] : (($true != vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR))) | (linorder($o) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(boolean_simplification,[],[f6267])).
% 78.92/11.75 thf(f6267,plain,(
% 78.92/11.75 ( ! [X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK13($o),vOR))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(sTfun($o,sTfun($o,$o)),$o,sK12($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK11($o),vOR))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(sTfun($o,sTfun($o,$o)),$o,sK14($o),vOR)),vAPP(sTfun($o,sTfun($o,$o)),$o,sK15($o),vOR))) | (linorder($o) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(primitive_instantiation,[],[f6254])).
% 78.92/11.75 thf(f6254,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(avatar_component_clause,[],[f6253])).
% 78.92/11.75 thf(f59705,plain,(
% 78.92/11.75 spl72_706 | ~spl72_116 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4911,f4893,f2914,f59703])).
% 78.92/11.75 thf(f59703,plain,(
% 78.92/11.75 spl72_706 <=> ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_706])])).
% 78.92/11.75 thf(f2914,plain,(
% 78.92/11.75 spl72_116 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_116])])).
% 78.92/11.75 thf(f4911,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0))) ) | (~spl72_116 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2915,f4895])).
% 78.92/11.75 thf(f2915,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) ) | ~spl72_116),
% 78.92/11.75 inference(avatar_component_clause,[],[f2914])).
% 78.92/11.75 thf(f59701,plain,(
% 78.92/11.75 spl72_705 | ~spl72_115 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4910,f4893,f2910,f59699])).
% 78.92/11.75 thf(f59699,plain,(
% 78.92/11.75 spl72_705 <=> ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_705])])).
% 78.92/11.75 thf(f2910,plain,(
% 78.92/11.75 spl72_115 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_115])])).
% 78.92/11.75 thf(f4910,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0))) ) | (~spl72_115 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2911,f4895])).
% 78.92/11.75 thf(f2911,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))) ) | ~spl72_115),
% 78.92/11.75 inference(avatar_component_clause,[],[f2910])).
% 78.92/11.75 thf(f59697,plain,(
% 78.92/11.75 spl72_704 | ~spl72_114 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4909,f4893,f2906,f59695])).
% 78.92/11.75 thf(f59695,plain,(
% 78.92/11.75 spl72_704 <=> ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_704])])).
% 78.92/11.75 thf(f2906,plain,(
% 78.92/11.75 spl72_114 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_114])])).
% 78.92/11.75 thf(f4909,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0))) ) | (~spl72_114 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2907,f4895])).
% 78.92/11.75 thf(f2907,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))) ) | ~spl72_114),
% 78.92/11.75 inference(avatar_component_clause,[],[f2906])).
% 78.92/11.75 thf(f59693,plain,(
% 78.92/11.75 spl72_703 | ~spl72_28 | ~spl72_198),
% 78.92/11.75 inference(avatar_split_clause,[],[f4325,f4274,f2020,f59691])).
% 78.92/11.75 thf(f59691,plain,(
% 78.92/11.75 spl72_703 <=> ! [X3 : $tType,X0 : $tType,X4 : X0 > X3,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X3),X0,sK32(X0,X3),X4)),vAPP(sTfun(X0,X3),X0,sK33(X0,X3),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less_eq(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | (ord(X0) != $true) | ($true != ord(X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_703])])).
% 78.92/11.75 thf(f4274,plain,(
% 78.92/11.75 spl72_198 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : X0 > X1,X3 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_198])])).
% 78.92/11.75 thf(f4325,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X3),X0,sK32(X0,X3),X4)),vAPP(sTfun(X0,X3),X0,sK33(X0,X3),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less_eq(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | (ord(X0) != $true) | ($true != ord(X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4324])).
% 78.92/11.75 thf(f4324,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X3),X0,sK32(X0,X3),X4)),vAPP(sTfun(X0,X3),X0,sK33(X0,X3),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less_eq(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | (ord(X0) != $true) | ($true != ord(X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_198)),
% 78.92/11.75 inference(superposition,[],[f4275,f2021])).
% 78.92/11.75 thf(f4275,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_198),
% 78.92/11.75 inference(avatar_component_clause,[],[f4274])).
% 78.92/11.75 thf(f59514,plain,(
% 78.92/11.75 spl72_702 | ~spl72_28 | spl72_696),
% 78.92/11.75 inference(avatar_split_clause,[],[f59477,f59468,f2020,f59511])).
% 78.92/11.75 thf(f59511,plain,(
% 78.92/11.75 spl72_702 <=> ($false = dense_order(nat))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_702])])).
% 78.92/11.75 thf(f59468,plain,(
% 78.92/11.75 spl72_696 <=> ($true = dense_order(nat))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_696])])).
% 78.92/11.75 thf(f59477,plain,(
% 78.92/11.75 ($false = dense_order(nat)) | (~spl72_28 | spl72_696)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f59476])).
% 78.92/11.75 thf(f59476,plain,(
% 78.92/11.75 ($true != $true) | ($false = dense_order(nat)) | (~spl72_28 | spl72_696)),
% 78.92/11.75 inference(superposition,[],[f59470,f2021])).
% 78.92/11.75 thf(f59470,plain,(
% 78.92/11.75 ($true != dense_order(nat)) | spl72_696),
% 78.92/11.75 inference(avatar_component_clause,[],[f59468])).
% 78.92/11.75 thf(f59509,plain,(
% 78.92/11.75 spl72_701 | ~spl72_28 | ~spl72_197),
% 78.92/11.75 inference(avatar_split_clause,[],[f4313,f4270,f2020,f59507])).
% 78.92/11.75 thf(f59507,plain,(
% 78.92/11.75 spl72_701 <=> ! [X3 : $tType,X0 : $tType,X4 : X0 > X3,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X3),X0,sK30(X0,X3),X4)),vAPP(sTfun(X0,X3),X0,sK31(X0,X3),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | (ord(X0) != $true) | ($true != ord(X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_701])])).
% 78.92/11.75 thf(f4270,plain,(
% 78.92/11.75 spl72_197 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X4 : X0 > X1,X3 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_197])])).
% 78.92/11.75 thf(f4313,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X3),X0,sK30(X0,X3),X4)),vAPP(sTfun(X0,X3),X0,sK31(X0,X3),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | (ord(X0) != $true) | ($true != ord(X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_197)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4312])).
% 78.92/11.75 thf(f4312,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X3),X0,sK30(X0,X3),X4)),vAPP(sTfun(X0,X3),X0,sK31(X0,X3),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | (ord(X0) != $true) | ($true != ord(X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_197)),
% 78.92/11.75 inference(superposition,[],[f4271,f2021])).
% 78.92/11.75 thf(f4271,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_197),
% 78.92/11.75 inference(avatar_component_clause,[],[f4270])).
% 78.92/11.75 thf(f59505,plain,(
% 78.92/11.75 spl72_700 | ~spl72_28 | ~spl72_195),
% 78.92/11.75 inference(avatar_split_clause,[],[f4291,f4261,f2020,f59503])).
% 78.92/11.75 thf(f59503,plain,(
% 78.92/11.75 spl72_700 <=> ! [X3 : $tType,X0 : $tType,X4 : X0 > X3,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X3),X0,sK28(X3,X0),X4)),vAPP(sTfun(X0,X3),X0,sK29(X3,X0),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less_eq(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | ($true != ord(X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_700])])).
% 78.92/11.75 thf(f4261,plain,(
% 78.92/11.75 spl72_195 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_195])])).
% 78.92/11.75 thf(f4291,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X3),X0,sK28(X3,X0),X4)),vAPP(sTfun(X0,X3),X0,sK29(X3,X0),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less_eq(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | ($true != ord(X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4290])).
% 78.92/11.75 thf(f4290,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X3),X0,sK28(X3,X0),X4)),vAPP(sTfun(X0,X3),X0,sK29(X3,X0),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less_eq(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | ($true != ord(X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_195)),
% 78.92/11.75 inference(superposition,[],[f4262,f2021])).
% 78.92/11.75 thf(f4262,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_195),
% 78.92/11.75 inference(avatar_component_clause,[],[f4261])).
% 78.92/11.75 thf(f59501,plain,(
% 78.92/11.75 spl72_699 | ~spl72_28 | ~spl72_194),
% 78.92/11.75 inference(avatar_split_clause,[],[f4279,f4257,f2020,f59499])).
% 78.92/11.75 thf(f59499,plain,(
% 78.92/11.75 spl72_699 <=> ! [X3 : $tType,X0 : $tType,X4 : X0 > X3,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X3),X0,sK26(X3,X0),X4)),vAPP(sTfun(X0,X3),X0,sK27(X3,X0),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | ($true != ord(X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_699])])).
% 78.92/11.75 thf(f4257,plain,(
% 78.92/11.75 spl72_194 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_194])])).
% 78.92/11.75 thf(f4279,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X3),X0,sK26(X3,X0),X4)),vAPP(sTfun(X0,X3),X0,sK27(X3,X0),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | ($true != ord(X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_194)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4278])).
% 78.92/11.75 thf(f4278,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X3 : $tType,X2 : X0,X1 : X0,X4 : X0 > X3] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X3),X0,sK26(X3,X0),X4)),vAPP(sTfun(X0,X3),X0,sK27(X3,X0),X4))) | ($true = vAPP(X3,$o,vAPP(X3,sTfun(X3,$o),ord_less(X3),vAPP(X0,X3,X4,X1)),vAPP(X0,X3,X4,X2))) | ($true != ord(X3)) | (ord(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_194)),
% 78.92/11.75 inference(superposition,[],[f4258,f2021])).
% 78.92/11.75 thf(f4258,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | (ord(X0) != $true) | ($true != ord(X1))) ) | ~spl72_194),
% 78.92/11.75 inference(avatar_component_clause,[],[f4257])).
% 78.92/11.75 thf(f59497,plain,(
% 78.92/11.75 spl72_698 | ~spl72_74 | ~spl72_159),
% 78.92/11.75 inference(avatar_split_clause,[],[f3725,f3675,f2467,f59495])).
% 78.92/11.75 thf(f59495,plain,(
% 78.92/11.75 spl72_698 <=> ! [X0 : nat,X3 : nat,X2 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_698])])).
% 78.92/11.75 thf(f2467,plain,(
% 78.92/11.75 spl72_74 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_74])])).
% 78.92/11.75 thf(f3675,plain,(
% 78.92/11.75 spl72_159 <=> ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X5 : X0,X1 : X0 > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_159])])).
% 78.92/11.75 thf(f3725,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_159)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3700])).
% 78.92/11.75 thf(f3700,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_159)),
% 78.92/11.75 inference(superposition,[],[f3676,f2468])).
% 78.92/11.75 thf(f2468,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | ~spl72_74),
% 78.92/11.75 inference(avatar_component_clause,[],[f2467])).
% 78.92/11.75 thf(f3676,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X5 : X0] : (($true != vAPP(X0,$o,X1,X5)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X2))) ) | ~spl72_159),
% 78.92/11.75 inference(avatar_component_clause,[],[f3675])).
% 78.92/11.75 thf(f59475,plain,(
% 78.92/11.75 ~spl72_696 | spl72_697 | ~spl72_121 | ~spl72_141),
% 78.92/11.75 inference(avatar_split_clause,[],[f3300,f3249,f3025,f59472,f59468])).
% 78.92/11.75 thf(f59472,plain,(
% 78.92/11.75 spl72_697 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK5(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_697])])).
% 78.92/11.75 thf(f3025,plain,(
% 78.92/11.75 spl72_121 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_121])])).
% 78.92/11.75 thf(f3300,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK5(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != dense_order(nat)) | (~spl72_121 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3287])).
% 78.92/11.75 thf(f3287,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK5(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != dense_order(nat)) | (~spl72_121 | ~spl72_141)),
% 78.92/11.75 inference(superposition,[],[f3026,f3251])).
% 78.92/11.75 thf(f3026,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) | (dense_order(X0) != $true)) ) | ~spl72_121),
% 78.92/11.75 inference(avatar_component_clause,[],[f3025])).
% 78.92/11.75 thf(f58740,plain,(
% 78.92/11.75 spl72_695 | ~spl72_28 | ~spl72_193),
% 78.92/11.75 inference(avatar_split_clause,[],[f4255,f4249,f2020,f58738])).
% 78.92/11.75 thf(f58738,plain,(
% 78.92/11.75 spl72_695 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_695])])).
% 78.92/11.75 thf(f4249,plain,(
% 78.92/11.75 spl72_193 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_193])])).
% 78.92/11.75 thf(f4255,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) ) | (~spl72_28 | ~spl72_193)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4254])).
% 78.92/11.75 thf(f4254,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) ) | (~spl72_28 | ~spl72_193)),
% 78.92/11.75 inference(superposition,[],[f4250,f2021])).
% 78.92/11.75 thf(f4250,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1))) ) | ~spl72_193),
% 78.92/11.75 inference(avatar_component_clause,[],[f4249])).
% 78.92/11.75 thf(f58736,plain,(
% 78.92/11.75 spl72_694 | ~spl72_45 | ~spl72_507),
% 78.92/11.75 inference(avatar_split_clause,[],[f36831,f35474,f2201,f58734])).
% 78.92/11.75 thf(f58734,plain,(
% 78.92/11.75 spl72_694 <=> ! [X3 : $tType,X1 : $tType,X0 : $tType,X2 : $tType] : ($true = preorder(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_694])])).
% 78.92/11.75 thf(f35474,plain,(
% 78.92/11.75 spl72_507 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = preorder(sTfun(X2,sTfun(X0,set(X1)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_507])])).
% 78.92/11.75 thf(f36831,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true = preorder(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))) ) | (~spl72_45 | ~spl72_507)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f36830])).
% 78.92/11.75 thf(f36830,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X3 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X3,sTfun(X0,sTfun(X1,set(X2))))))) ) | (~spl72_45 | ~spl72_507)),
% 78.92/11.75 inference(superposition,[],[f2202,f35475])).
% 78.92/11.75 thf(f35475,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,set(X1)))))) ) | ~spl72_507),
% 78.92/11.75 inference(avatar_component_clause,[],[f35474])).
% 78.92/11.75 thf(f58732,plain,(
% 78.92/11.75 spl72_693 | ~spl72_28 | ~spl72_192),
% 78.92/11.75 inference(avatar_split_clause,[],[f4253,f4245,f2020,f58730])).
% 78.92/11.75 thf(f58730,plain,(
% 78.92/11.75 spl72_693 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_693])])).
% 78.92/11.75 thf(f4245,plain,(
% 78.92/11.75 spl72_192 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_192])])).
% 78.92/11.75 thf(f4253,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) ) | (~spl72_28 | ~spl72_192)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4252])).
% 78.92/11.75 thf(f4252,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) ) | (~spl72_28 | ~spl72_192)),
% 78.92/11.75 inference(superposition,[],[f4246,f2021])).
% 78.92/11.75 thf(f4246,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1))) ) | ~spl72_192),
% 78.92/11.75 inference(avatar_component_clause,[],[f4245])).
% 78.92/11.75 thf(f58407,plain,(
% 78.92/11.75 ~spl72_691 | spl72_692 | spl72_689 | ~spl72_17 | ~spl72_50 | ~spl72_209),
% 78.92/11.75 inference(avatar_split_clause,[],[f4671,f4622,f2246,f1969,f58351,f58404,f58400])).
% 78.92/11.75 thf(f58400,plain,(
% 78.92/11.75 spl72_691 <=> (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_691])])).
% 78.92/11.75 thf(f58404,plain,(
% 78.92/11.75 spl72_692 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_692])])).
% 78.92/11.75 thf(f58351,plain,(
% 78.92/11.75 spl72_689 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_689])])).
% 78.92/11.75 thf(f2246,plain,(
% 78.92/11.75 spl72_50 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_50])])).
% 78.92/11.75 thf(f4671,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) ) | (~spl72_17 | ~spl72_50 | ~spl72_209)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4670])).
% 78.92/11.75 thf(f4670,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) ) | (~spl72_17 | ~spl72_50 | ~spl72_209)),
% 78.92/11.75 inference(forward_demodulation,[],[f4642,f1971])).
% 78.92/11.75 thf(f4642,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) | (linorder(nat) != $true) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) ) | (~spl72_50 | ~spl72_209)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4637])).
% 78.92/11.75 thf(f4637,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) | (linorder(nat) != $true) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) ) | (~spl72_50 | ~spl72_209)),
% 78.92/11.75 inference(constrained_superposition,[],[f4623,f2247])).
% 78.92/11.75 thf(f2247,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))) ) | ~spl72_50),
% 78.92/11.75 inference(avatar_component_clause,[],[f2246])).
% 78.92/11.75 thf(f58357,plain,(
% 78.92/11.75 ~spl72_688 | spl72_689 | spl72_690 | ~spl72_17 | ~spl72_50 | ~spl72_204),
% 78.92/11.75 inference(avatar_split_clause,[],[f4475,f4413,f2246,f1969,f58354,f58351,f58347])).
% 78.92/11.75 thf(f58347,plain,(
% 78.92/11.75 spl72_688 <=> (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat)) = vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_688])])).
% 78.92/11.75 thf(f58354,plain,(
% 78.92/11.75 spl72_690 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_690])])).
% 78.92/11.75 thf(f4475,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) ) | (~spl72_17 | ~spl72_50 | ~spl72_204)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4474])).
% 78.92/11.75 thf(f4474,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) ) | (~spl72_17 | ~spl72_50 | ~spl72_204)),
% 78.92/11.75 inference(forward_demodulation,[],[f4435,f1971])).
% 78.92/11.75 thf(f4435,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (linorder(nat) != $true) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) ) | (~spl72_50 | ~spl72_204)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4430])).
% 78.92/11.75 thf(f4430,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK17(nat),ord_less_eq(nat))),vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK16(nat),ord_less_eq(nat)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (linorder(nat) != $true) | (vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK18(nat),ord_less_eq(nat)) != vAPP(sTfun(nat,sTfun(nat,$o)),nat,sK19(nat),ord_less_eq(nat)))) ) | (~spl72_50 | ~spl72_204)),
% 78.92/11.75 inference(constrained_superposition,[],[f4414,f2247])).
% 78.92/11.75 thf(f58345,plain,(
% 78.92/11.75 spl72_687 | ~spl72_67 | ~spl72_159),
% 78.92/11.75 inference(avatar_split_clause,[],[f3727,f3675,f2364,f58343])).
% 78.92/11.75 thf(f58343,plain,(
% 78.92/11.75 spl72_687 <=> ! [X0 : nat,X3 : nat,X2 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_687])])).
% 78.92/11.75 thf(f3727,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3))) ) | (~spl72_67 | ~spl72_159)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3698])).
% 78.92/11.75 thf(f3698,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3))) ) | (~spl72_67 | ~spl72_159)),
% 78.92/11.75 inference(superposition,[],[f3676,f2365])).
% 78.92/11.75 thf(f58341,plain,(
% 78.92/11.75 spl72_686 | ~spl72_68 | ~spl72_159),
% 78.92/11.75 inference(avatar_split_clause,[],[f3726,f3675,f2368,f58339])).
% 78.92/11.75 thf(f58339,plain,(
% 78.92/11.75 spl72_686 <=> ! [X0 : nat,X3 : nat,X2 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_686])])).
% 78.92/11.75 thf(f3726,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3))) ) | (~spl72_68 | ~spl72_159)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3699])).
% 78.92/11.75 thf(f3699,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X2),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X3))) ) | (~spl72_68 | ~spl72_159)),
% 78.92/11.75 inference(superposition,[],[f3676,f2369])).
% 78.92/11.75 thf(f58337,plain,(
% 78.92/11.75 spl72_685 | ~spl72_107 | ~spl72_138),
% 78.92/11.75 inference(avatar_split_clause,[],[f3263,f3237,f2865,f58335])).
% 78.92/11.75 thf(f58335,plain,(
% 78.92/11.75 spl72_685 <=> ! [X0 : set(nat),X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X1) = X0) | (vAPP(set(nat),sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set(nat),$o)),sTfun(set(nat),sTfun(nat,$o)),cCOMB,member(nat)),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_685])])).
% 78.92/11.75 thf(f2865,plain,(
% 78.92/11.75 spl72_107 <=> ! [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,$o)),cCOMB,member(X0)),X1)) = X1)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_107])])).
% 78.92/11.75 thf(f3263,plain,(
% 78.92/11.75 ( ! [X0 : set(nat),X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X1) = X0) | (vAPP(set(nat),sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set(nat),$o)),sTfun(set(nat),sTfun(nat,$o)),cCOMB,member(nat)),X0) != vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X1))) ) | (~spl72_107 | ~spl72_138)),
% 78.92/11.75 inference(constrained_superposition,[],[f3238,f2866])).
% 78.92/11.75 thf(f2866,plain,(
% 78.92/11.75 ( ! [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,$o)),cCOMB,member(X0)),X1)) = X1)) ) | ~spl72_107),
% 78.92/11.75 inference(avatar_component_clause,[],[f2865])).
% 78.92/11.75 thf(f58333,plain,(
% 78.92/11.75 spl72_684 | ~spl72_107 | ~spl72_137),
% 78.92/11.75 inference(avatar_split_clause,[],[f3259,f3233,f2865,f58331])).
% 78.92/11.75 thf(f58331,plain,(
% 78.92/11.75 spl72_684 <=> ! [X0 : set(nat),X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X1) = X0) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X1) != vAPP(set(nat),sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set(nat),$o)),sTfun(set(nat),sTfun(nat,$o)),cCOMB,member(nat)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_684])])).
% 78.92/11.75 thf(f3259,plain,(
% 78.92/11.75 ( ! [X0 : set(nat),X1 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X1) = X0) | (vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X1) != vAPP(set(nat),sTfun(nat,$o),vAPP(sTfun(nat,sTfun(set(nat),$o)),sTfun(set(nat),sTfun(nat,$o)),cCOMB,member(nat)),X0))) ) | (~spl72_107 | ~spl72_137)),
% 78.92/11.75 inference(constrained_superposition,[],[f3234,f2866])).
% 78.92/11.75 thf(f56636,plain,(
% 78.92/11.75 spl72_683 | ~spl72_23 | ~spl72_50 | ~spl72_225),
% 78.92/11.75 inference(avatar_split_clause,[],[f5570,f5071,f2246,f1999,f56634])).
% 78.92/11.75 thf(f56634,plain,(
% 78.92/11.75 spl72_683 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK40(nat,X0),X1)),vAPP(sTfun(X0,nat),X0,sK41(nat,X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | (order(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_683])])).
% 78.92/11.75 thf(f1999,plain,(
% 78.92/11.75 spl72_23 <=> (order(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_23])])).
% 78.92/11.75 thf(f5071,plain,(
% 78.92/11.75 spl72_225 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_225])])).
% 78.92/11.75 thf(f5570,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK40(nat,X0),X1)),vAPP(sTfun(X0,nat),X0,sK41(nat,X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | (order(X0) != $true)) ) | (~spl72_23 | ~spl72_50 | ~spl72_225)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5569])).
% 78.92/11.75 thf(f5569,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK40(nat,X0),X1)),vAPP(sTfun(X0,nat),X0,sK41(nat,X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | (order(X0) != $true)) ) | (~spl72_23 | ~spl72_50 | ~spl72_225)),
% 78.92/11.75 inference(forward_demodulation,[],[f5482,f2001])).
% 78.92/11.75 thf(f2001,plain,(
% 78.92/11.75 (order(nat) = $true) | ~spl72_23),
% 78.92/11.75 inference(avatar_component_clause,[],[f1999])).
% 78.92/11.75 thf(f5482,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK40(nat,X0),X1)),vAPP(sTfun(X0,nat),X0,sK41(nat,X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | (order(nat) != $true) | (order(X0) != $true)) ) | (~spl72_50 | ~spl72_225)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5464])).
% 78.92/11.75 thf(f5464,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK40(nat,X0),X1)),vAPP(sTfun(X0,nat),X0,sK41(nat,X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | (order(nat) != $true) | (order(X0) != $true)) ) | (~spl72_50 | ~spl72_225)),
% 78.92/11.75 inference(superposition,[],[f5072,f2247])).
% 78.92/11.75 thf(f5072,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | (order(X0) != $true) | ($true != order(X1))) ) | ~spl72_225),
% 78.92/11.75 inference(avatar_component_clause,[],[f5071])).
% 78.92/11.75 thf(f56632,plain,(
% 78.92/11.75 spl72_682 | ~spl72_23 | ~spl72_50 | ~spl72_223),
% 78.92/11.75 inference(avatar_split_clause,[],[f5316,f5061,f2246,f1999,f56630])).
% 78.92/11.75 thf(f56630,plain,(
% 78.92/11.75 spl72_682 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK36(X0,nat),X1)),vAPP(sTfun(X0,nat),X0,sK37(X0,nat),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X3)),vAPP(X0,nat,X1,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | (order(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_682])])).
% 78.92/11.75 thf(f5061,plain,(
% 78.92/11.75 spl72_223 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X4 : X0 > X1,X5 : X1,X2 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_223])])).
% 78.92/11.75 thf(f5316,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK36(X0,nat),X1)),vAPP(sTfun(X0,nat),X0,sK37(X0,nat),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X3)),vAPP(X0,nat,X1,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | (order(X0) != $true)) ) | (~spl72_23 | ~spl72_50 | ~spl72_223)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5315])).
% 78.92/11.75 thf(f5315,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK36(X0,nat),X1)),vAPP(sTfun(X0,nat),X0,sK37(X0,nat),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X3)),vAPP(X0,nat,X1,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | (order(X0) != $true)) ) | (~spl72_23 | ~spl72_50 | ~spl72_223)),
% 78.92/11.75 inference(forward_demodulation,[],[f5229,f2001])).
% 78.92/11.75 thf(f5229,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK36(X0,nat),X1)),vAPP(sTfun(X0,nat),X0,sK37(X0,nat),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X3)),vAPP(X0,nat,X1,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | (order(X0) != $true) | (order(nat) != $true)) ) | (~spl72_50 | ~spl72_223)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5212])).
% 78.92/11.75 thf(f5212,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,nat),X0,sK36(X0,nat),X1)),vAPP(sTfun(X0,nat),X0,sK37(X0,nat),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X3)),vAPP(X0,nat,X1,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | (order(X0) != $true) | (order(nat) != $true)) ) | (~spl72_50 | ~spl72_223)),
% 78.92/11.75 inference(superposition,[],[f5062,f2247])).
% 78.92/11.75 thf(f5062,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1))) ) | ~spl72_223),
% 78.92/11.75 inference(avatar_component_clause,[],[f5061])).
% 78.92/11.75 thf(f56628,plain,(
% 78.92/11.75 spl72_681 | ~spl72_21 | ~spl72_74 | ~spl72_198),
% 78.92/11.75 inference(avatar_split_clause,[],[f4340,f4274,f2467,f1989,f56626])).
% 78.92/11.75 thf(f56626,plain,(
% 78.92/11.75 spl72_681 <=> ! [X2 : $tType,X0 : nat,X3 : nat > X2,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_681])])).
% 78.92/11.75 thf(f1989,plain,(
% 78.92/11.75 spl72_21 <=> (ord(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_21])])).
% 78.92/11.75 thf(f4340,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_21 | ~spl72_74 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4339])).
% 78.92/11.75 thf(f4339,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_21 | ~spl72_74 | ~spl72_198)),
% 78.92/11.75 inference(forward_demodulation,[],[f4329,f1991])).
% 78.92/11.75 thf(f1991,plain,(
% 78.92/11.75 (ord(nat) = $true) | ~spl72_21),
% 78.92/11.75 inference(avatar_component_clause,[],[f1989])).
% 78.92/11.75 thf(f4329,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | (ord(nat) != $true) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4320])).
% 78.92/11.75 thf(f4320,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | (ord(nat) != $true) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_198)),
% 78.92/11.75 inference(superposition,[],[f4275,f2468])).
% 78.92/11.75 thf(f56624,plain,(
% 78.92/11.75 spl72_680 | ~spl72_21 | ~spl72_74 | ~spl72_195),
% 78.92/11.75 inference(avatar_split_clause,[],[f4306,f4261,f2467,f1989,f56622])).
% 78.92/11.75 thf(f56622,plain,(
% 78.92/11.75 spl72_680 <=> ! [X2 : $tType,X0 : nat,X3 : nat > X2,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_680])])).
% 78.92/11.75 thf(f4306,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_21 | ~spl72_74 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4305])).
% 78.92/11.75 thf(f4305,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_21 | ~spl72_74 | ~spl72_195)),
% 78.92/11.75 inference(forward_demodulation,[],[f4295,f1991])).
% 78.92/11.75 thf(f4295,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | (ord(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4286])).
% 78.92/11.75 thf(f4286,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,X1))) | ($true != ord(X2)) | (ord(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_195)),
% 78.92/11.75 inference(superposition,[],[f4262,f2468])).
% 78.92/11.75 thf(f56620,plain,(
% 78.92/11.75 spl72_679 | ~spl72_28 | ~spl72_190),
% 78.92/11.75 inference(avatar_split_clause,[],[f4168,f4160,f2020,f56618])).
% 78.92/11.75 thf(f56618,plain,(
% 78.92/11.75 spl72_679 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_679])])).
% 78.92/11.75 thf(f4160,plain,(
% 78.92/11.75 spl72_190 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_190])])).
% 78.92/11.75 thf(f4168,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0))))) ) | (~spl72_28 | ~spl72_190)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4167])).
% 78.92/11.75 thf(f4167,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0))))) ) | (~spl72_28 | ~spl72_190)),
% 78.92/11.75 inference(superposition,[],[f4161,f2021])).
% 78.92/11.75 thf(f4161,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)))) ) | ~spl72_190),
% 78.92/11.75 inference(avatar_component_clause,[],[f4160])).
% 78.92/11.75 thf(f56616,plain,(
% 78.92/11.75 spl72_678 | ~spl72_15 | ~spl72_141 | ~spl72_169),
% 78.92/11.75 inference(avatar_split_clause,[],[f3866,f3782,f3249,f1959,f56614])).
% 78.92/11.75 thf(f56614,plain,(
% 78.92/11.75 spl72_678 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_678])])).
% 78.92/11.75 thf(f3782,plain,(
% 78.92/11.75 spl72_169 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_169])])).
% 78.92/11.75 thf(f3866,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))))) ) | (~spl72_15 | ~spl72_141 | ~spl72_169)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3865])).
% 78.92/11.75 thf(f3865,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))))) ) | (~spl72_15 | ~spl72_141 | ~spl72_169)),
% 78.92/11.75 inference(forward_demodulation,[],[f3864,f1961])).
% 78.92/11.75 thf(f3864,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_141 | ~spl72_169)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3861])).
% 78.92/11.75 thf(f3861,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_141 | ~spl72_169)),
% 78.92/11.75 inference(superposition,[],[f3783,f3251])).
% 78.92/11.75 thf(f3783,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true)) ) | ~spl72_169),
% 78.92/11.75 inference(avatar_component_clause,[],[f3782])).
% 78.92/11.75 thf(f56594,plain,(
% 78.92/11.75 spl72_677 | ~spl72_12 | ~spl72_142 | ~spl72_162),
% 78.92/11.75 inference(avatar_split_clause,[],[f3810,f3753,f3254,f1944,f56592])).
% 78.92/11.75 thf(f56592,plain,(
% 78.92/11.75 spl72_677 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_677])])).
% 78.92/11.75 thf(f1944,plain,(
% 78.92/11.75 spl72_12 <=> (ordere779506340up_add(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_12])])).
% 78.92/11.75 thf(f3753,plain,(
% 78.92/11.75 spl72_162 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_162])])).
% 78.92/11.75 thf(f3810,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))) ) | (~spl72_12 | ~spl72_142 | ~spl72_162)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3809])).
% 78.92/11.75 thf(f3809,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))) ) | (~spl72_12 | ~spl72_142 | ~spl72_162)),
% 78.92/11.75 inference(forward_demodulation,[],[f3797,f1946])).
% 78.92/11.75 thf(f1946,plain,(
% 78.92/11.75 (ordere779506340up_add(nat) = $true) | ~spl72_12),
% 78.92/11.75 inference(avatar_component_clause,[],[f1944])).
% 78.92/11.75 thf(f3797,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | (ordere779506340up_add(nat) != $true)) ) | (~spl72_142 | ~spl72_162)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3794])).
% 78.92/11.75 thf(f3794,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))) | (ordere779506340up_add(nat) != $true)) ) | (~spl72_142 | ~spl72_162)),
% 78.92/11.75 inference(superposition,[],[f3754,f3256])).
% 78.92/11.75 thf(f3754,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true)) ) | ~spl72_162),
% 78.92/11.75 inference(avatar_component_clause,[],[f3753])).
% 78.92/11.75 thf(f56590,plain,(
% 78.92/11.75 spl72_676 | ~spl72_142 | ~spl72_150),
% 78.92/11.75 inference(avatar_split_clause,[],[f3601,f3586,f3254,f56588])).
% 78.92/11.75 thf(f56588,plain,(
% 78.92/11.75 spl72_676 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_676])])).
% 78.92/11.75 thf(f3586,plain,(
% 78.92/11.75 spl72_150 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_150])])).
% 78.92/11.75 thf(f3601,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))) ) | (~spl72_142 | ~spl72_150)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3598])).
% 78.92/11.75 thf(f3598,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))) ) | (~spl72_142 | ~spl72_150)),
% 78.92/11.75 inference(superposition,[],[f3587,f3256])).
% 78.92/11.75 thf(f3587,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | ~spl72_150),
% 78.92/11.75 inference(avatar_component_clause,[],[f3586])).
% 78.92/11.75 thf(f56586,plain,(
% 78.92/11.75 spl72_675 | ~spl72_141 | ~spl72_149),
% 78.92/11.75 inference(avatar_split_clause,[],[f3592,f3582,f3249,f56584])).
% 78.92/11.75 thf(f56584,plain,(
% 78.92/11.75 spl72_675 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_675])])).
% 78.92/11.75 thf(f3582,plain,(
% 78.92/11.75 spl72_149 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_149])])).
% 78.92/11.75 thf(f3592,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))) ) | (~spl72_141 | ~spl72_149)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3589])).
% 78.92/11.75 thf(f3589,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))) ) | (~spl72_141 | ~spl72_149)),
% 78.92/11.75 inference(superposition,[],[f3583,f3251])).
% 78.92/11.75 thf(f3583,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | ~spl72_149),
% 78.92/11.75 inference(avatar_component_clause,[],[f3582])).
% 78.92/11.75 thf(f56269,plain,(
% 78.92/11.75 spl72_674 | ~spl72_21 | ~spl72_50 | ~spl72_217),
% 78.92/11.75 inference(avatar_split_clause,[],[f5023,f4970,f2246,f1989,f56267])).
% 78.92/11.75 thf(f56267,plain,(
% 78.92/11.75 spl72_674 <=> ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > nat] : (($true = vAPP(sTfun(X0,nat),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),$o),ord_less_eq(sTfun(X0,nat)),X1),X2)) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)) != vAPP(X0,nat,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_674])])).
% 78.92/11.75 thf(f5023,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > nat] : (($true = vAPP(sTfun(X0,nat),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),$o),ord_less_eq(sTfun(X0,nat)),X1),X2)) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)) != vAPP(X0,nat,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)))) ) | (~spl72_21 | ~spl72_50 | ~spl72_217)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5022])).
% 78.92/11.75 thf(f5022,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(sTfun(X0,nat),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),$o),ord_less_eq(sTfun(X0,nat)),X1),X2)) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)) != vAPP(X0,nat,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)))) ) | (~spl72_21 | ~spl72_50 | ~spl72_217)),
% 78.92/11.75 inference(forward_demodulation,[],[f4997,f1991])).
% 78.92/11.75 thf(f4997,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > nat] : (($true = vAPP(sTfun(X0,nat),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),$o),ord_less_eq(sTfun(X0,nat)),X1),X2)) | (ord(nat) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)) != vAPP(X0,nat,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)))) ) | (~spl72_50 | ~spl72_217)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4990])).
% 78.92/11.75 thf(f4990,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > nat,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(sTfun(X0,nat),$o,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),$o),ord_less_eq(sTfun(X0,nat)),X1),X2)) | (ord(nat) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)) != vAPP(X0,nat,X2,vAPP(sTfun(X0,nat),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,nat),X0),sK46(nat,X0),X2),X1)))) ) | (~spl72_50 | ~spl72_217)),
% 78.92/11.75 inference(constrained_superposition,[],[f4971,f2247])).
% 78.92/11.75 thf(f56265,plain,(
% 78.92/11.75 spl72_673 | ~spl72_28 | ~spl72_217),
% 78.92/11.75 inference(avatar_split_clause,[],[f4981,f4970,f2020,f56263])).
% 78.92/11.75 thf(f56263,plain,(
% 78.92/11.75 spl72_673 <=> ! [X0 : $tType,X2 : $o > X0,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X2,$true)),vAPP($o,X0,X1,$true))) | ($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),ord_less_eq(sTfun($o,X0)),X2),X1)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),sK46(X0,$o),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_673])])).
% 78.92/11.75 thf(f4981,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : $o > X0,X1 : $o > X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP($o,X0,X2,$true)),vAPP($o,X0,X1,$true))) | ($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),ord_less_eq(sTfun($o,X0)),X2),X1)) | (ord(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),sK46(X0,$o),X1),X2))) ) | (~spl72_28 | ~spl72_217)),
% 78.92/11.75 inference(superposition,[],[f4971,f2021])).
% 78.92/11.75 thf(f52381,plain,(
% 78.92/11.75 ~spl72_337 | spl72_672 | ~spl72_50 | ~spl72_174),
% 78.92/11.75 inference(avatar_split_clause,[],[f13637,f3925,f2246,f52379,f7888])).
% 78.92/11.75 thf(f52379,plain,(
% 78.92/11.75 spl72_672 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK45($o,nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,X1,X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_672])])).
% 78.92/11.75 thf(f13637,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK45($o,nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != wellorder($o))) ) | (~spl72_50 | ~spl72_174)),
% 78.92/11.75 inference(superposition,[],[f3926,f2247])).
% 78.92/11.75 thf(f52377,plain,(
% 78.92/11.75 ~spl72_337 | spl72_671 | ~spl72_50 | ~spl72_173),
% 78.92/11.75 inference(avatar_split_clause,[],[f13598,f3921,f2246,f52375,f7888])).
% 78.92/11.75 thf(f52375,plain,(
% 78.92/11.75 spl72_671 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK44($o,nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,X1,X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_671])])).
% 78.92/11.75 thf(f13598,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK44($o,nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($true != wellorder($o))) ) | (~spl72_50 | ~spl72_173)),
% 78.92/11.75 inference(superposition,[],[f3922,f2247])).
% 78.92/11.75 thf(f52373,plain,(
% 78.92/11.75 spl72_670 | ~spl72_28 | ~spl72_188),
% 78.92/11.75 inference(avatar_split_clause,[],[f4137,f4083,f2020,f52371])).
% 78.92/11.75 thf(f52371,plain,(
% 78.92/11.75 spl72_670 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_670])])).
% 78.92/11.75 thf(f4137,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4136])).
% 78.92/11.75 thf(f4136,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_188)),
% 78.92/11.75 inference(superposition,[],[f4084,f2021])).
% 78.92/11.75 thf(f52369,plain,(
% 78.92/11.75 spl72_669 | ~spl72_28 | ~spl72_187),
% 78.92/11.75 inference(avatar_split_clause,[],[f4115,f4079,f2020,f52367])).
% 78.92/11.75 thf(f52367,plain,(
% 78.92/11.75 spl72_669 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_669])])).
% 78.92/11.75 thf(f4115,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4114])).
% 78.92/11.75 thf(f4114,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_187)),
% 78.92/11.75 inference(superposition,[],[f4080,f2021])).
% 78.92/11.75 thf(f52365,plain,(
% 78.92/11.75 spl72_668 | ~spl72_28 | ~spl72_186),
% 78.92/11.75 inference(avatar_split_clause,[],[f4106,f4075,f2020,f52363])).
% 78.92/11.75 thf(f52363,plain,(
% 78.92/11.75 spl72_668 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_668])])).
% 78.92/11.75 thf(f4075,plain,(
% 78.92/11.75 spl72_186 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_186])])).
% 78.92/11.75 thf(f4106,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_186)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4105])).
% 78.92/11.75 thf(f4105,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_186)),
% 78.92/11.75 inference(superposition,[],[f4076,f2021])).
% 78.92/11.75 thf(f4076,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) ) | ~spl72_186),
% 78.92/11.75 inference(avatar_component_clause,[],[f4075])).
% 78.92/11.75 thf(f52361,plain,(
% 78.92/11.75 spl72_667 | ~spl72_28 | ~spl72_185),
% 78.92/11.75 inference(avatar_split_clause,[],[f4097,f4071,f2020,f52359])).
% 78.92/11.75 thf(f52359,plain,(
% 78.92/11.75 spl72_667 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_667])])).
% 78.92/11.75 thf(f4071,plain,(
% 78.92/11.75 spl72_185 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_185])])).
% 78.92/11.75 thf(f4097,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_185)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4096])).
% 78.92/11.75 thf(f4096,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_185)),
% 78.92/11.75 inference(superposition,[],[f4072,f2021])).
% 78.92/11.75 thf(f4072,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) ) | ~spl72_185),
% 78.92/11.75 inference(avatar_component_clause,[],[f4071])).
% 78.92/11.75 thf(f52351,plain,(
% 78.92/11.75 spl72_666 | ~spl72_28 | ~spl72_184),
% 78.92/11.75 inference(avatar_split_clause,[],[f4088,f4067,f2020,f52349])).
% 78.92/11.75 thf(f52349,plain,(
% 78.92/11.75 spl72_666 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (strict2144017051up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_666])])).
% 78.92/11.75 thf(f4067,plain,(
% 78.92/11.75 spl72_184 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (strict2144017051up_add(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_184])])).
% 78.92/11.75 thf(f4088,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (strict2144017051up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_184)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4087])).
% 78.92/11.75 thf(f4087,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | (strict2144017051up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_184)),
% 78.92/11.75 inference(superposition,[],[f4068,f2021])).
% 78.92/11.75 thf(f4068,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (strict2144017051up_add(X0) != $true)) ) | ~spl72_184),
% 78.92/11.75 inference(avatar_component_clause,[],[f4067])).
% 78.92/11.75 thf(f52347,plain,(
% 78.92/11.75 spl72_665),
% 78.92/11.75 inference(avatar_split_clause,[],[f1745,f52345])).
% 78.92/11.75 thf(f52345,plain,(
% 78.92/11.75 spl72_665 <=> ! [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),sK50(X0),X2),X1))) | ($false = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_665])])).
% 78.92/11.75 thf(f1745,plain,(
% 78.92/11.75 ( ! [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),sK50(X0),X2),X1))) | ($false = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1)))) )),
% 78.92/11.75 inference(binary_proxy_clausification,[],[f1606])).
% 78.92/11.75 thf(f1606,plain,(
% 78.92/11.75 ( ! [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,$o),X0),sK50(X0),X2),X1)) != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1)))) )),
% 78.92/11.75 inference(cnf_transformation,[],[f1307])).
% 78.92/11.75 thf(f1307,plain,(
% 78.92/11.75 ! [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,$o),X0),sK50(X0),X2),X1)) != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1))))),
% 78.92/11.75 inference(skolemisation,[status(esa),new_symbols(skolem,[sK50])],[f1156,f1306])).
% 78.92/11.75 thf(f1306,plain,(
% 78.92/11.75 ! [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,$o),X0),sK50(X0),X2),X1)) != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1))))),
% 78.92/11.75 introduced(choice_axiom,[])).
% 78.92/11.75 thf(f1156,plain,(
% 78.92/11.75 ! [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)))),
% 78.92/11.75 inference(ennf_transformation,[],[f920])).
% 78.92/11.75 thf(f920,plain,(
% 78.92/11.75 ! [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)))),
% 78.92/11.75 inference(rectify,[],[f48])).
% 78.92/11.75 thf(f48,axiom,(
% 78.92/11.75 ! [X0 : $tType,X29 : X0 > $o,X24 : X0 > $o] : (! [X31 : X0] : (vAPP(X0,$o,X29,X31) = vAPP(X0,$o,X24,X31)) => (vAPP(sTfun(X0,$o),set(X0),collect(X0),X29) = vAPP(sTfun(X0,$o),set(X0),collect(X0),X24)))),
% 78.92/11.75 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_Collect__cong)).
% 78.92/11.75 thf(f52343,plain,(
% 78.92/11.75 spl72_664),
% 78.92/11.75 inference(avatar_split_clause,[],[f1744,f52341])).
% 78.92/11.75 thf(f52341,plain,(
% 78.92/11.75 spl72_664 <=> ! [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),sK50(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_664])])).
% 78.92/11.75 thf(f1744,plain,(
% 78.92/11.75 ( ! [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),sK50(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK50(X0),X2),X1)))) )),
% 78.92/11.75 inference(binary_proxy_clausification,[],[f1606])).
% 78.92/11.75 thf(f51890,plain,(
% 78.92/11.75 spl72_663 | ~spl72_21 | ~spl72_50 | ~spl72_213),
% 78.92/11.75 inference(avatar_split_clause,[],[f4891,f4685,f2246,f1989,f51888])).
% 78.92/11.75 thf(f51888,plain,(
% 78.92/11.75 spl72_663 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK32(X0,nat),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK33(X0,nat),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_663])])).
% 78.92/11.75 thf(f4891,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK32(X0,nat),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK33(X0,nat),X1)))) ) | (~spl72_21 | ~spl72_50 | ~spl72_213)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4890])).
% 78.92/11.75 thf(f4890,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK32(X0,nat),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK33(X0,nat),X1)))) ) | (~spl72_21 | ~spl72_50 | ~spl72_213)),
% 78.92/11.75 inference(forward_demodulation,[],[f4857,f1991])).
% 78.92/11.75 thf(f4857,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (ord(nat) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK32(X0,nat),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK33(X0,nat),X1)))) ) | (~spl72_50 | ~spl72_213)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4852])).
% 78.92/11.75 thf(f4852,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (ord(nat) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK32(X0,nat),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK33(X0,nat),X1)))) ) | (~spl72_50 | ~spl72_213)),
% 78.92/11.75 inference(constrained_superposition,[],[f4686,f2247])).
% 78.92/11.75 thf(f51886,plain,(
% 78.92/11.75 spl72_662 | ~spl72_21 | ~spl72_50 | ~spl72_211),
% 78.92/11.75 inference(avatar_split_clause,[],[f4789,f4677,f2246,f1989,f51884])).
% 78.92/11.75 thf(f51884,plain,(
% 78.92/11.75 spl72_662 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK28(nat,X0),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK29(nat,X0),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_662])])).
% 78.92/11.75 thf(f4789,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK28(nat,X0),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK29(nat,X0),X1)))) ) | (~spl72_21 | ~spl72_50 | ~spl72_211)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4788])).
% 78.92/11.75 thf(f4788,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK28(nat,X0),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK29(nat,X0),X1)))) ) | (~spl72_21 | ~spl72_50 | ~spl72_211)),
% 78.92/11.75 inference(forward_demodulation,[],[f4755,f1991])).
% 78.92/11.75 thf(f4755,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(nat) != $true) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK28(nat,X0),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK29(nat,X0),X1)))) ) | (~spl72_50 | ~spl72_211)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4750])).
% 78.92/11.75 thf(f4750,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(nat) != $true) | (ord(X0) != $true) | (vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK28(nat,X0),X1)) != vAPP(X0,nat,X1,vAPP(sTfun(X0,nat),X0,sK29(nat,X0),X1)))) ) | (~spl72_50 | ~spl72_211)),
% 78.92/11.75 inference(constrained_superposition,[],[f4678,f2247])).
% 78.92/11.75 thf(f51882,plain,(
% 78.92/11.75 spl72_661 | ~spl72_206),
% 78.92/11.75 inference(avatar_split_clause,[],[f4583,f4421,f51880])).
% 78.92/11.75 thf(f51880,plain,(
% 78.92/11.75 spl72_661 <=> ! [X2 : nat,X0 : $o,X1 : $o > nat] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK71($o),X1),vNOT)) | ($false = vAPP(sTfun($o,$o),$o,vAPP($o,sTfun(sTfun($o,$o),$o),vAPP(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o)),vAPP(nat,sTfun(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o))),sK70($o),X2),X1),X0),vNOT)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_661])])).
% 78.92/11.75 thf(f4583,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : $o,X1 : $o > nat] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK71($o),X1),vNOT)) | ($false = vAPP(sTfun($o,$o),$o,vAPP($o,sTfun(sTfun($o,$o),$o),vAPP(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o)),vAPP(nat,sTfun(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o))),sK70($o),X2),X1),X0),vNOT))) ) | ~spl72_206),
% 78.92/11.75 inference(not_proxy_clausification,[],[f4582])).
% 78.92/11.75 thf(f4582,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : $o,X1 : $o > nat] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK71($o),X1),vNOT)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP($o,sTfun(sTfun($o,$o),$o),vAPP(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o)),vAPP(nat,sTfun(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o))),sK70($o),X2),X1),X0),vNOT)))) ) | ~spl72_206),
% 78.92/11.75 inference(not_proxy_clausification,[],[f4581])).
% 78.92/11.75 thf(f4581,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : $o,X1 : $o > nat] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK71($o),X1),vNOT))) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP($o,sTfun(sTfun($o,$o),$o),vAPP(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o)),vAPP(nat,sTfun(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o))),sK70($o),X2),X1),X0),vNOT)))) ) | ~spl72_206),
% 78.92/11.75 inference(not_proxy_clausification,[],[f4546])).
% 78.92/11.75 thf(f4546,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : $o,X1 : $o > nat] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK71($o),X1),vNOT))) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP($o,sTfun(sTfun($o,$o),$o),vAPP(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o)),vAPP(nat,sTfun(sTfun($o,nat),sTfun($o,sTfun(sTfun($o,$o),$o))),sK70($o),X2),X1),X0),vNOT)))) ) | ~spl72_206),
% 78.92/11.75 inference(primitive_instantiation,[],[f4422])).
% 78.92/11.75 thf(f51878,plain,(
% 78.92/11.75 spl72_660 | ~spl72_21 | ~spl72_68 | ~spl72_198),
% 78.92/11.75 inference(avatar_split_clause,[],[f4338,f4274,f2368,f1989,f51876])).
% 78.92/11.75 thf(f51876,plain,(
% 78.92/11.75 spl72_660 <=> ! [X2 : $tType,X0 : nat,X3 : nat > X2,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_660])])).
% 78.92/11.75 thf(f4338,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_68 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4337])).
% 78.92/11.75 thf(f4337,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_68 | ~spl72_198)),
% 78.92/11.75 inference(forward_demodulation,[],[f4330,f1991])).
% 78.92/11.75 thf(f4330,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | (ord(nat) != $true) | ($true != ord(X2))) ) | (~spl72_68 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4319])).
% 78.92/11.75 thf(f4319,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | (ord(nat) != $true) | ($true != ord(X2))) ) | (~spl72_68 | ~spl72_198)),
% 78.92/11.75 inference(superposition,[],[f4275,f2369])).
% 78.92/11.75 thf(f51874,plain,(
% 78.92/11.75 spl72_659 | ~spl72_21 | ~spl72_67 | ~spl72_198),
% 78.92/11.75 inference(avatar_split_clause,[],[f4336,f4274,f2364,f1989,f51872])).
% 78.92/11.75 thf(f51872,plain,(
% 78.92/11.75 spl72_659 <=> ! [X2 : $tType,X0 : nat,X3 : nat > X2,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_659])])).
% 78.92/11.75 thf(f4336,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_67 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4335])).
% 78.92/11.75 thf(f4335,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_67 | ~spl72_198)),
% 78.92/11.75 inference(forward_demodulation,[],[f4331,f1991])).
% 78.92/11.75 thf(f4331,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | (ord(nat) != $true) | ($true != ord(X2))) ) | (~spl72_67 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4318])).
% 78.92/11.75 thf(f4318,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK32(nat,X2),X3)),vAPP(sTfun(nat,X2),nat,sK33(nat,X2),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | (ord(nat) != $true) | ($true != ord(X2))) ) | (~spl72_67 | ~spl72_198)),
% 78.92/11.75 inference(superposition,[],[f4275,f2365])).
% 78.92/11.75 thf(f51870,plain,(
% 78.92/11.75 spl72_658 | ~spl72_21 | ~spl72_68 | ~spl72_195),
% 78.92/11.75 inference(avatar_split_clause,[],[f4304,f4261,f2368,f1989,f51868])).
% 78.92/11.75 thf(f51868,plain,(
% 78.92/11.75 spl72_658 <=> ! [X2 : $tType,X0 : nat,X3 : nat > X2,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_658])])).
% 78.92/11.75 thf(f4304,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_68 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4303])).
% 78.92/11.75 thf(f4303,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_68 | ~spl72_195)),
% 78.92/11.75 inference(forward_demodulation,[],[f4296,f1991])).
% 78.92/11.75 thf(f4296,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2)) | (ord(nat) != $true)) ) | (~spl72_68 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4285])).
% 78.92/11.75 thf(f4285,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != ord(X2)) | (ord(nat) != $true)) ) | (~spl72_68 | ~spl72_195)),
% 78.92/11.75 inference(superposition,[],[f4262,f2369])).
% 78.92/11.75 thf(f51866,plain,(
% 78.92/11.75 spl72_657 | ~spl72_21 | ~spl72_67 | ~spl72_195),
% 78.92/11.75 inference(avatar_split_clause,[],[f4302,f4261,f2364,f1989,f51864])).
% 78.92/11.75 thf(f51864,plain,(
% 78.92/11.75 spl72_657 <=> ! [X2 : $tType,X0 : nat,X3 : nat > X2,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_657])])).
% 78.92/11.75 thf(f4302,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_67 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4301])).
% 78.92/11.75 thf(f4301,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2))) ) | (~spl72_21 | ~spl72_67 | ~spl72_195)),
% 78.92/11.75 inference(forward_demodulation,[],[f4297,f1991])).
% 78.92/11.75 thf(f4297,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2)) | (ord(nat) != $true)) ) | (~spl72_67 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4284])).
% 78.92/11.75 thf(f4284,plain,(
% 78.92/11.75 ( ! [X2 : $tType,X3 : nat > X2,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X2),nat,sK28(X2,nat),X3)),vAPP(sTfun(nat,X2),nat,sK29(X2,nat),X3))) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),vAPP(nat,X2,X3,X0)),vAPP(nat,X2,X3,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != ord(X2)) | (ord(nat) != $true)) ) | (~spl72_67 | ~spl72_195)),
% 78.92/11.75 inference(superposition,[],[f4262,f2365])).
% 78.92/11.75 thf(f51842,plain,(
% 78.92/11.75 spl72_656 | ~spl72_28 | ~spl72_182),
% 78.92/11.75 inference(avatar_split_clause,[],[f4060,f4056,f2020,f51840])).
% 78.92/11.75 thf(f51840,plain,(
% 78.92/11.75 spl72_656 <=> ! [X0 : $tType,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | (linordered_idom(X0) != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_656])])).
% 78.92/11.75 thf(f4056,plain,(
% 78.92/11.75 spl72_182 <=> ! [X0 : $tType,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_182])])).
% 78.92/11.75 thf(f4060,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | (linordered_idom(X0) != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) ) | (~spl72_28 | ~spl72_182)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4059])).
% 78.92/11.75 thf(f4059,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | (linordered_idom(X0) != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) ) | (~spl72_28 | ~spl72_182)),
% 78.92/11.75 inference(superposition,[],[f4057,f2021])).
% 78.92/11.75 thf(f4057,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | (linordered_idom(X0) != $true)) ) | ~spl72_182),
% 78.92/11.75 inference(avatar_component_clause,[],[f4056])).
% 78.92/11.75 thf(f51820,plain,(
% 78.92/11.75 spl72_655 | ~spl72_48 | ~spl72_469),
% 78.92/11.75 inference(avatar_split_clause,[],[f34074,f31301,f2214,f51818])).
% 78.92/11.75 thf(f51818,plain,(
% 78.92/11.75 spl72_655 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,a)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_655])])).
% 78.92/11.75 thf(f31301,plain,(
% 78.92/11.75 spl72_469 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,sTfun(X0,a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_469])])).
% 78.92/11.75 thf(f34074,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,a)))))) ) | (~spl72_48 | ~spl72_469)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f34057])).
% 78.92/11.75 thf(f34057,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,a)))))) ) | (~spl72_48 | ~spl72_469)),
% 78.92/11.75 inference(superposition,[],[f2215,f31302])).
% 78.92/11.75 thf(f31302,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,a))))) ) | ~spl72_469),
% 78.92/11.75 inference(avatar_component_clause,[],[f31301])).
% 78.92/11.75 thf(f51218,plain,(
% 78.92/11.75 spl72_654 | ~spl72_258),
% 78.92/11.75 inference(avatar_split_clause,[],[f6321,f6257,f51216])).
% 78.92/11.75 thf(f51216,plain,(
% 78.92/11.75 spl72_654 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_654])])).
% 78.92/11.75 thf(f6257,plain,(
% 78.92/11.75 spl72_258 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_258])])).
% 78.92/11.75 thf(f6321,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_258),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f6320])).
% 78.92/11.75 thf(f6320,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_258),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f6319])).
% 78.92/11.75 thf(f6319,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_258),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6318])).
% 78.92/11.75 thf(f6318,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_258),
% 78.92/11.75 inference(boolean_simplification,[],[f6310])).
% 78.92/11.75 thf(f6310,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_258),
% 78.92/11.75 inference(primitive_instantiation,[],[f6258])).
% 78.92/11.75 thf(f6258,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) ) | ~spl72_258),
% 78.92/11.75 inference(avatar_component_clause,[],[f6257])).
% 78.92/11.75 thf(f51214,plain,(
% 78.92/11.75 spl72_653 | ~spl72_257),
% 78.92/11.75 inference(avatar_split_clause,[],[f6280,f6253,f51212])).
% 78.92/11.75 thf(f51212,plain,(
% 78.92/11.75 spl72_653 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_653])])).
% 78.92/11.75 thf(f6280,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f6279])).
% 78.92/11.75 thf(f6279,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f6278])).
% 78.92/11.75 thf(f6278,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6277])).
% 78.92/11.75 thf(f6277,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(boolean_simplification,[],[f6269])).
% 78.92/11.75 thf(f6269,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_257),
% 78.92/11.75 inference(primitive_instantiation,[],[f6254])).
% 78.92/11.75 thf(f51210,plain,(
% 78.92/11.75 spl72_652 | ~spl72_209),
% 78.92/11.75 inference(avatar_split_clause,[],[f4644,f4622,f51208])).
% 78.92/11.75 thf(f51208,plain,(
% 78.92/11.75 spl72_652 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0)))) | (linorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_652])])).
% 78.92/11.75 thf(f4644,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | (X1 = X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_209),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f4643])).
% 78.92/11.75 thf(f4643,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_209),
% 78.92/11.75 inference(equality_proxy_clausification,[],[f4634])).
% 78.92/11.75 thf(f4634,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0)))) | (linorder(X0) != $true)) ) | ~spl72_209),
% 78.92/11.75 inference(primitive_instantiation,[],[f4623])).
% 78.92/11.75 thf(f51206,plain,(
% 78.92/11.75 spl72_651 | ~spl72_48 | ~spl72_468),
% 78.92/11.75 inference(avatar_split_clause,[],[f33896,f29319,f2214,f51204])).
% 78.92/11.75 thf(f51204,plain,(
% 78.92/11.75 spl72_651 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_651])])).
% 78.92/11.75 thf(f29319,plain,(
% 78.92/11.75 spl72_468 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,sTfun(X0,capacity))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_468])])).
% 78.92/11.75 thf(f33896,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))) ) | (~spl72_48 | ~spl72_468)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f33879])).
% 78.92/11.75 thf(f33879,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))) ) | (~spl72_48 | ~spl72_468)),
% 78.92/11.75 inference(superposition,[],[f2215,f29320])).
% 78.92/11.75 thf(f29320,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,capacity))))) ) | ~spl72_468),
% 78.92/11.75 inference(avatar_component_clause,[],[f29319])).
% 78.92/11.75 thf(f51202,plain,(
% 78.92/11.75 spl72_650 | ~spl72_15 | ~spl72_74 | ~spl72_188),
% 78.92/11.75 inference(avatar_split_clause,[],[f4151,f4083,f2467,f1959,f51200])).
% 78.92/11.75 thf(f51200,plain,(
% 78.92/11.75 spl72_650 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_650])])).
% 78.92/11.75 thf(f4151,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_15 | ~spl72_74 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4150])).
% 78.92/11.75 thf(f4150,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_15 | ~spl72_74 | ~spl72_188)),
% 78.92/11.75 inference(forward_demodulation,[],[f4140,f1961])).
% 78.92/11.75 thf(f4140,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | (ordere223160158up_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4133])).
% 78.92/11.75 thf(f4133,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | (ordere223160158up_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_188)),
% 78.92/11.75 inference(superposition,[],[f4084,f2468])).
% 78.92/11.75 thf(f51198,plain,(
% 78.92/11.75 spl72_649 | ~spl72_15 | ~spl72_74 | ~spl72_187),
% 78.92/11.75 inference(avatar_split_clause,[],[f4127,f4079,f2467,f1959,f51196])).
% 78.92/11.75 thf(f51196,plain,(
% 78.92/11.75 spl72_649 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_649])])).
% 78.92/11.75 thf(f4127,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_15 | ~spl72_74 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4126])).
% 78.92/11.75 thf(f4126,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_15 | ~spl72_74 | ~spl72_187)),
% 78.92/11.75 inference(forward_demodulation,[],[f4118,f1961])).
% 78.92/11.75 thf(f4118,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4111])).
% 78.92/11.75 thf(f4111,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_187)),
% 78.92/11.75 inference(superposition,[],[f4080,f2468])).
% 78.92/11.75 thf(f51194,plain,(
% 78.92/11.75 spl72_648 | ~spl72_74 | ~spl72_181),
% 78.92/11.75 inference(avatar_split_clause,[],[f4051,f4034,f2467,f51192])).
% 78.92/11.75 thf(f51192,plain,(
% 78.92/11.75 spl72_648 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_648])])).
% 78.92/11.75 thf(f4034,plain,(
% 78.92/11.75 spl72_181 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_181])])).
% 78.92/11.75 thf(f4051,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_181)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4044])).
% 78.92/11.75 thf(f4044,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_181)),
% 78.92/11.75 inference(superposition,[],[f4035,f2468])).
% 78.92/11.75 thf(f4035,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | ~spl72_181),
% 78.92/11.75 inference(avatar_component_clause,[],[f4034])).
% 78.92/11.75 thf(f51190,plain,(
% 78.92/11.75 spl72_647 | ~spl72_28 | ~spl72_181),
% 78.92/11.75 inference(avatar_split_clause,[],[f4048,f4034,f2020,f51188])).
% 78.92/11.75 thf(f51188,plain,(
% 78.92/11.75 spl72_647 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_647])])).
% 78.92/11.75 thf(f4048,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_181)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4047])).
% 78.92/11.75 thf(f4047,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_181)),
% 78.92/11.75 inference(superposition,[],[f4035,f2021])).
% 78.92/11.75 thf(f51186,plain,(
% 78.92/11.75 spl72_646 | ~spl72_28 | ~spl72_180),
% 78.92/11.75 inference(avatar_split_clause,[],[f4039,f4030,f2020,f51184])).
% 78.92/11.75 thf(f51184,plain,(
% 78.92/11.75 spl72_646 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_646])])).
% 78.92/11.75 thf(f4039,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_180)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4038])).
% 78.92/11.75 thf(f4038,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_180)),
% 78.92/11.75 inference(superposition,[],[f4031,f2021])).
% 78.92/11.75 thf(f49834,plain,(
% 78.92/11.75 spl72_645 | ~spl72_46 | ~spl72_467),
% 78.92/11.75 inference(avatar_split_clause,[],[f33283,f28293,f2205,f49832])).
% 78.92/11.75 thf(f49832,plain,(
% 78.92/11.75 spl72_645 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,a)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_645])])).
% 78.92/11.75 thf(f28293,plain,(
% 78.92/11.75 spl72_467 <=> ! [X1 : $tType,X0 : $tType] : ($true = ord(sTfun(X1,sTfun(X0,a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_467])])).
% 78.92/11.75 thf(f33283,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,a)))))) ) | (~spl72_46 | ~spl72_467)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f33282])).
% 78.92/11.75 thf(f33282,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,a)))))) ) | (~spl72_46 | ~spl72_467)),
% 78.92/11.75 inference(superposition,[],[f2206,f28294])).
% 78.92/11.75 thf(f28294,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,a))))) ) | ~spl72_467),
% 78.92/11.75 inference(avatar_component_clause,[],[f28293])).
% 78.92/11.75 thf(f48746,plain,(
% 78.92/11.75 spl72_644 | ~spl72_28 | ~spl72_178),
% 78.92/11.75 inference(avatar_split_clause,[],[f4028,f3997,f2020,f48744])).
% 78.92/11.75 thf(f48744,plain,(
% 78.92/11.75 spl72_644 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_644])])).
% 78.92/11.75 thf(f3997,plain,(
% 78.92/11.75 spl72_178 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_178])])).
% 78.92/11.75 thf(f4028,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) ) | (~spl72_28 | ~spl72_178)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4027])).
% 78.92/11.75 thf(f4027,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) ) | (~spl72_28 | ~spl72_178)),
% 78.92/11.75 inference(superposition,[],[f3998,f2021])).
% 78.92/11.75 thf(f3998,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2))) ) | ~spl72_178),
% 78.92/11.75 inference(avatar_component_clause,[],[f3997])).
% 78.92/11.75 thf(f48742,plain,(
% 78.92/11.75 spl72_643 | ~spl72_28 | ~spl72_177),
% 78.92/11.75 inference(avatar_split_clause,[],[f4026,f3993,f2020,f48740])).
% 78.92/11.75 thf(f48740,plain,(
% 78.92/11.75 spl72_643 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_643])])).
% 78.92/11.75 thf(f3993,plain,(
% 78.92/11.75 spl72_177 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_177])])).
% 78.92/11.75 thf(f4026,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) ) | (~spl72_28 | ~spl72_177)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4025])).
% 78.92/11.75 thf(f4025,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) ) | (~spl72_28 | ~spl72_177)),
% 78.92/11.75 inference(superposition,[],[f3994,f2021])).
% 78.92/11.75 thf(f3994,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2))) ) | ~spl72_177),
% 78.92/11.75 inference(avatar_component_clause,[],[f3993])).
% 78.92/11.75 thf(f48738,plain,(
% 78.92/11.75 spl72_642 | ~spl72_46 | ~spl72_456),
% 78.92/11.75 inference(avatar_split_clause,[],[f32979,f28249,f2205,f48736])).
% 78.92/11.75 thf(f48736,plain,(
% 78.92/11.75 spl72_642 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_642])])).
% 78.92/11.75 thf(f28249,plain,(
% 78.92/11.75 spl72_456 <=> ! [X1 : $tType,X0 : $tType] : ($true = ord(sTfun(X1,sTfun(X0,capacity))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_456])])).
% 78.92/11.75 thf(f32979,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))) ) | (~spl72_46 | ~spl72_456)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f32978])).
% 78.92/11.75 thf(f32978,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))) ) | (~spl72_46 | ~spl72_456)),
% 78.92/11.75 inference(superposition,[],[f2206,f28250])).
% 78.92/11.75 thf(f28250,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,capacity))))) ) | ~spl72_456),
% 78.92/11.75 inference(avatar_component_clause,[],[f28249])).
% 78.92/11.75 thf(f48734,plain,(
% 78.92/11.75 spl72_641 | ~spl72_74 | ~spl72_176),
% 78.92/11.75 inference(avatar_split_clause,[],[f4024,f3989,f2467,f48732])).
% 78.92/11.75 thf(f48732,plain,(
% 78.92/11.75 spl72_641 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_641])])).
% 78.92/11.75 thf(f3989,plain,(
% 78.92/11.75 spl72_176 <=> ! [X4 : nat,X0 : nat > $o,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_176])])).
% 78.92/11.75 thf(f4024,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)))) ) | (~spl72_74 | ~spl72_176)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4019])).
% 78.92/11.75 thf(f4019,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)))) ) | (~spl72_74 | ~spl72_176)),
% 78.92/11.75 inference(superposition,[],[f3990,f2468])).
% 78.92/11.75 thf(f3990,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > $o,X1 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X4)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X1))) ) | ~spl72_176),
% 78.92/11.75 inference(avatar_component_clause,[],[f3989])).
% 78.92/11.75 thf(f48730,plain,(
% 78.92/11.75 spl72_640 | ~spl72_28 | ~spl72_176),
% 78.92/11.75 inference(avatar_split_clause,[],[f4022,f3989,f2020,f48728])).
% 78.92/11.75 thf(f48728,plain,(
% 78.92/11.75 spl72_640 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_640])])).
% 78.92/11.75 thf(f4022,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat > $o] : (($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)),X0))) ) | (~spl72_28 | ~spl72_176)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4021])).
% 78.92/11.75 thf(f4021,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X3)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)),X0))) ) | (~spl72_28 | ~spl72_176)),
% 78.92/11.75 inference(superposition,[],[f3990,f2021])).
% 78.92/11.75 thf(f48726,plain,(
% 78.92/11.75 spl72_639 | ~spl72_74 | ~spl72_175),
% 78.92/11.75 inference(avatar_split_clause,[],[f4015,f3985,f2467,f48724])).
% 78.92/11.75 thf(f48724,plain,(
% 78.92/11.75 spl72_639 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_639])])).
% 78.92/11.75 thf(f3985,plain,(
% 78.92/11.75 spl72_175 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X0)),vAPP(sTfun(nat,nat),nat,sK52,X0))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_175])])).
% 78.92/11.75 thf(f4015,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_175)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4008])).
% 78.92/11.75 thf(f4008,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_175)),
% 78.92/11.75 inference(superposition,[],[f3986,f2468])).
% 78.92/11.75 thf(f3986,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X0)),vAPP(sTfun(nat,nat),nat,sK52,X0)))) ) | ~spl72_175),
% 78.92/11.75 inference(avatar_component_clause,[],[f3985])).
% 78.92/11.75 thf(f48722,plain,(
% 78.92/11.75 spl72_638 | ~spl72_28 | ~spl72_175),
% 78.92/11.75 inference(avatar_split_clause,[],[f4012,f3985,f2020,f48720])).
% 78.92/11.75 thf(f48720,plain,(
% 78.92/11.75 spl72_638 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_638])])).
% 78.92/11.75 thf(f4012,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_175)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4011])).
% 78.92/11.75 thf(f4011,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_175)),
% 78.92/11.75 inference(superposition,[],[f3986,f2021])).
% 78.92/11.75 thf(f48718,plain,(
% 78.92/11.75 spl72_637 | ~spl72_14 | ~spl72_83 | ~spl72_142),
% 78.92/11.75 inference(avatar_split_clause,[],[f3353,f3254,f2616,f1954,f48715])).
% 78.92/11.75 thf(f48715,plain,(
% 78.92/11.75 spl72_637 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_637])])).
% 78.92/11.75 thf(f1954,plain,(
% 78.92/11.75 spl72_14 <=> (wellorder(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_14])])).
% 78.92/11.75 thf(f2616,plain,(
% 78.92/11.75 spl72_83 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_83])])).
% 78.92/11.75 thf(f3353,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | (~spl72_14 | ~spl72_83 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3352])).
% 78.92/11.75 thf(f3352,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | (~spl72_14 | ~spl72_83 | ~spl72_142)),
% 78.92/11.75 inference(forward_demodulation,[],[f3335,f1956])).
% 78.92/11.75 thf(f1956,plain,(
% 78.92/11.75 (wellorder(nat) = $true) | ~spl72_14),
% 78.92/11.75 inference(avatar_component_clause,[],[f1954])).
% 78.92/11.75 thf(f3335,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3330])).
% 78.92/11.75 thf(f3330,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_142)),
% 78.92/11.75 inference(superposition,[],[f2617,f3256])).
% 78.92/11.75 thf(f2617,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | (wellorder(X0) != $true)) ) | ~spl72_83),
% 78.92/11.75 inference(avatar_component_clause,[],[f2616])).
% 78.92/11.75 thf(f48713,plain,(
% 78.92/11.75 spl72_636 | ~spl72_23 | ~spl72_135 | ~spl72_142),
% 78.92/11.75 inference(avatar_split_clause,[],[f3349,f3254,f3198,f1999,f48711])).
% 78.92/11.75 thf(f48711,plain,(
% 78.92/11.75 spl72_636 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_636])])).
% 78.92/11.75 thf(f3198,plain,(
% 78.92/11.75 spl72_135 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_135])])).
% 78.92/11.75 thf(f3349,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0))) ) | (~spl72_23 | ~spl72_135 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3348])).
% 78.92/11.75 thf(f3348,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0))) ) | (~spl72_23 | ~spl72_135 | ~spl72_142)),
% 78.92/11.75 inference(forward_demodulation,[],[f3341,f2001])).
% 78.92/11.75 thf(f3341,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)) | (order(nat) != $true)) ) | (~spl72_135 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3324])).
% 78.92/11.75 thf(f3324,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)) | (order(nat) != $true)) ) | (~spl72_135 | ~spl72_142)),
% 78.92/11.75 inference(superposition,[],[f3199,f3256])).
% 78.92/11.75 thf(f3199,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) ) | ~spl72_135),
% 78.92/11.75 inference(avatar_component_clause,[],[f3198])).
% 78.92/11.75 thf(f48709,plain,(
% 78.92/11.75 spl72_635 | ~spl72_119 | ~spl72_142),
% 78.92/11.75 inference(avatar_split_clause,[],[f3342,f3254,f3006,f48707])).
% 78.92/11.75 thf(f48707,plain,(
% 78.92/11.75 spl72_635 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_635])])).
% 78.92/11.75 thf(f3006,plain,(
% 78.92/11.75 spl72_119 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_119])])).
% 78.92/11.75 thf(f3342,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))) ) | (~spl72_119 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3323])).
% 78.92/11.75 thf(f3323,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))) ) | (~spl72_119 | ~spl72_142)),
% 78.92/11.75 inference(superposition,[],[f3007,f3256])).
% 78.92/11.75 thf(f3007,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | ~spl72_119),
% 78.92/11.75 inference(avatar_component_clause,[],[f3006])).
% 78.92/11.75 thf(f48705,plain,(
% 78.92/11.75 spl72_634 | ~spl72_14 | ~spl72_83 | ~spl72_141),
% 78.92/11.75 inference(avatar_split_clause,[],[f3315,f3249,f2616,f1954,f48702])).
% 78.92/11.75 thf(f48702,plain,(
% 78.92/11.75 spl72_634 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_634])])).
% 78.92/11.75 thf(f3315,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (~spl72_14 | ~spl72_83 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3314])).
% 78.92/11.75 thf(f3314,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (~spl72_14 | ~spl72_83 | ~spl72_141)),
% 78.92/11.75 inference(forward_demodulation,[],[f3296,f1956])).
% 78.92/11.75 thf(f3296,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3291])).
% 78.92/11.75 thf(f3291,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_141)),
% 78.92/11.75 inference(superposition,[],[f2617,f3251])).
% 78.92/11.75 thf(f48700,plain,(
% 78.92/11.75 spl72_633 | ~spl72_23 | ~spl72_134 | ~spl72_141),
% 78.92/11.75 inference(avatar_split_clause,[],[f3313,f3249,f3194,f1999,f48698])).
% 78.92/11.75 thf(f48698,plain,(
% 78.92/11.75 spl72_633 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_633])])).
% 78.92/11.75 thf(f3194,plain,(
% 78.92/11.75 spl72_134 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_134])])).
% 78.92/11.75 thf(f3313,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0))) ) | (~spl72_23 | ~spl72_134 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3312])).
% 78.92/11.75 thf(f3312,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0))) ) | (~spl72_23 | ~spl72_134 | ~spl72_141)),
% 78.92/11.75 inference(forward_demodulation,[],[f3298,f2001])).
% 78.92/11.75 thf(f3298,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)) | (order(nat) != $true)) ) | (~spl72_134 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3289])).
% 78.92/11.75 thf(f3289,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)) | (order(nat) != $true)) ) | (~spl72_134 | ~spl72_141)),
% 78.92/11.75 inference(superposition,[],[f3195,f3251])).
% 78.92/11.75 thf(f3195,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) ) | ~spl72_134),
% 78.92/11.75 inference(avatar_component_clause,[],[f3194])).
% 78.92/11.75 thf(f48696,plain,(
% 78.92/11.75 spl72_632 | ~spl72_19 | ~spl72_132 | ~spl72_141),
% 78.92/11.75 inference(avatar_split_clause,[],[f3311,f3249,f3186,f1979,f48694])).
% 78.92/11.75 thf(f48694,plain,(
% 78.92/11.75 spl72_632 <=> ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_632])])).
% 78.92/11.75 thf(f1979,plain,(
% 78.92/11.75 spl72_19 <=> (preorder(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_19])])).
% 78.92/11.75 thf(f3186,plain,(
% 78.92/11.75 spl72_132 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_132])])).
% 78.92/11.75 thf(f3311,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))) ) | (~spl72_19 | ~spl72_132 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3310])).
% 78.92/11.75 thf(f3310,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))) ) | (~spl72_19 | ~spl72_132 | ~spl72_141)),
% 78.92/11.75 inference(forward_demodulation,[],[f3299,f1981])).
% 78.92/11.75 thf(f1981,plain,(
% 78.92/11.75 (preorder(nat) = $true) | ~spl72_19),
% 78.92/11.75 inference(avatar_component_clause,[],[f1979])).
% 78.92/11.75 thf(f3299,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (preorder(nat) != $true)) ) | (~spl72_132 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3288])).
% 78.92/11.75 thf(f3288,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (preorder(nat) != $true)) ) | (~spl72_132 | ~spl72_141)),
% 78.92/11.75 inference(superposition,[],[f3187,f3251])).
% 78.92/11.75 thf(f3187,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true)) ) | ~spl72_132),
% 78.92/11.75 inference(avatar_component_clause,[],[f3186])).
% 78.92/11.75 thf(f48692,plain,(
% 78.92/11.75 spl72_631 | ~spl72_45 | ~spl72_445),
% 78.92/11.75 inference(avatar_split_clause,[],[f32934,f28205,f2201,f48690])).
% 78.92/11.75 thf(f48690,plain,(
% 78.92/11.75 spl72_631 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,a)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_631])])).
% 78.92/11.75 thf(f28205,plain,(
% 78.92/11.75 spl72_445 <=> ! [X1 : $tType,X0 : $tType] : ($true = preorder(sTfun(X1,sTfun(X0,a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_445])])).
% 78.92/11.75 thf(f32934,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,a)))))) ) | (~spl72_45 | ~spl72_445)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f32933])).
% 78.92/11.75 thf(f32933,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,a)))))) ) | (~spl72_45 | ~spl72_445)),
% 78.92/11.75 inference(superposition,[],[f2202,f28206])).
% 78.92/11.75 thf(f28206,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,a))))) ) | ~spl72_445),
% 78.92/11.75 inference(avatar_component_clause,[],[f28205])).
% 78.92/11.75 thf(f48688,plain,(
% 78.92/11.75 spl72_630 | ~spl72_50 | ~spl72_118),
% 78.92/11.75 inference(avatar_split_clause,[],[f3000,f2980,f2246,f48686])).
% 78.92/11.75 thf(f48686,plain,(
% 78.92/11.75 spl72_630 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_630])])).
% 78.92/11.75 thf(f2980,plain,(
% 78.92/11.75 spl72_118 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_118])])).
% 78.92/11.75 thf(f3000,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_50 | ~spl72_118)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f2987])).
% 78.92/11.75 thf(f2987,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_50 | ~spl72_118)),
% 78.92/11.75 inference(superposition,[],[f2981,f2247])).
% 78.92/11.75 thf(f2981,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0)))) ) | ~spl72_118),
% 78.92/11.75 inference(avatar_component_clause,[],[f2980])).
% 78.92/11.75 thf(f48016,plain,(
% 78.92/11.75 spl72_629 | ~spl72_45 | ~spl72_438),
% 78.92/11.75 inference(avatar_split_clause,[],[f31714,f27824,f2201,f48014])).
% 78.92/11.75 thf(f48014,plain,(
% 78.92/11.75 spl72_629 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_629])])).
% 78.92/11.75 thf(f27824,plain,(
% 78.92/11.75 spl72_438 <=> ! [X1 : $tType,X0 : $tType] : ($true = preorder(sTfun(X1,sTfun(X0,capacity))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_438])])).
% 78.92/11.75 thf(f31714,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))) ) | (~spl72_45 | ~spl72_438)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f31713])).
% 78.92/11.75 thf(f31713,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,capacity)))))) ) | (~spl72_45 | ~spl72_438)),
% 78.92/11.75 inference(superposition,[],[f2202,f27825])).
% 78.92/11.75 thf(f27825,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,capacity))))) ) | ~spl72_438),
% 78.92/11.75 inference(avatar_component_clause,[],[f27824])).
% 78.92/11.75 thf(f47143,plain,(
% 78.92/11.75 ~spl72_337 | spl72_628 | ~spl72_28 | ~spl72_174),
% 78.92/11.75 inference(avatar_split_clause,[],[f13665,f3925,f2020,f47141,f7888])).
% 78.92/11.75 thf(f47141,plain,(
% 78.92/11.75 spl72_628 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X3)),$true)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK45($o,X0),X2),X1))) | ($true = vAPP(X0,$o,X2,X4)) | ($true = vAPP(X0,$o,X2,X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_628])])).
% 78.92/11.75 thf(f13665,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o,X4 : X0] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X3)),$true)) | ($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X2,X4)) | ($true != wellorder($o)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK45($o,X0),X2),X1)))) ) | (~spl72_28 | ~spl72_174)),
% 78.92/11.75 inference(superposition,[],[f3926,f2021])).
% 78.92/11.75 thf(f47139,plain,(
% 78.92/11.75 ~spl72_337 | spl72_627 | ~spl72_28 | ~spl72_174),
% 78.92/11.75 inference(avatar_split_clause,[],[f13652,f3925,f2020,f47137,f7888])).
% 78.92/11.75 thf(f47137,plain,(
% 78.92/11.75 spl72_627 <=> ! [X0 : $tType,X4 : X0,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK45($o,X0),X3),X1)))) | ($false = vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($true = vAPP(X0,$o,X3,X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_627])])).
% 78.92/11.75 thf(f13652,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK45($o,X0),X3),X1)))) | ($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($true != wellorder($o)) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_174)),
% 78.92/11.75 inference(superposition,[],[f3926,f2021])).
% 78.92/11.75 thf(f47135,plain,(
% 78.92/11.75 ~spl72_337 | spl72_626 | ~spl72_28 | ~spl72_173),
% 78.92/11.75 inference(avatar_split_clause,[],[f13626,f3921,f2020,f47133,f7888])).
% 78.92/11.75 thf(f47133,plain,(
% 78.92/11.75 spl72_626 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X3)),$true)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK44($o,X0),X2),X1))) | ($true = vAPP(X0,$o,X2,X4)) | ($true = vAPP(X0,$o,X2,X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_626])])).
% 78.92/11.75 thf(f13626,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o,X4 : X0] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP(X0,$o,X1,X3)),$true)) | ($true = vAPP(X0,$o,X2,X3)) | ($true = vAPP(X0,$o,X2,X4)) | ($true != wellorder($o)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK44($o,X0),X2),X1)))) ) | (~spl72_28 | ~spl72_173)),
% 78.92/11.75 inference(superposition,[],[f3922,f2021])).
% 78.92/11.75 thf(f47113,plain,(
% 78.92/11.75 ~spl72_337 | spl72_625 | ~spl72_28 | ~spl72_173),
% 78.92/11.75 inference(avatar_split_clause,[],[f13613,f3921,f2020,f47111,f7888])).
% 78.92/11.75 thf(f47111,plain,(
% 78.92/11.75 spl72_625 <=> ! [X0 : $tType,X4 : X0,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK44($o,X0),X3),X1)))) | ($false = vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($true = vAPP(X0,$o,X3,X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_625])])).
% 78.92/11.75 thf(f13613,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK44($o,X0),X3),X1)))) | ($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($true != wellorder($o)) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_173)),
% 78.92/11.75 inference(superposition,[],[f3922,f2021])).
% 78.92/11.75 thf(f47109,plain,(
% 78.92/11.75 spl72_624 | ~spl72_128 | ~spl72_253),
% 78.92/11.75 inference(avatar_split_clause,[],[f6110,f6084,f3082,f47106])).
% 78.92/11.75 thf(f47106,plain,(
% 78.92/11.75 spl72_624 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),ua),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,t),ua)),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_624])])).
% 78.92/11.75 thf(f3082,plain,(
% 78.92/11.75 spl72_128 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a),t) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_128])])).
% 78.92/11.75 thf(f6084,plain,(
% 78.92/11.75 spl72_253 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,X2),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_253])])).
% 78.92/11.75 thf(f6110,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),ua),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,t),ua)),t)) | (~spl72_128 | ~spl72_253)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6103])).
% 78.92/11.75 thf(f6103,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),ua),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,t),ua)),t)) | (~spl72_128 | ~spl72_253)),
% 78.92/11.75 inference(superposition,[],[f6085,f3084])).
% 78.92/11.75 thf(f3084,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a),t) = $true) | ~spl72_128),
% 78.92/11.75 inference(avatar_component_clause,[],[f3082])).
% 78.92/11.75 thf(f6085,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,X2),X0)),X2))) ) | ~spl72_253),
% 78.92/11.75 inference(avatar_component_clause,[],[f6084])).
% 78.92/11.75 thf(f47104,plain,(
% 78.92/11.75 spl72_623 | ~spl72_129 | ~spl72_253),
% 78.92/11.75 inference(avatar_split_clause,[],[f6109,f6084,f3087,f47101])).
% 78.92/11.75 thf(f47101,plain,(
% 78.92/11.75 spl72_623 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,v),s)),v))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_623])])).
% 78.92/11.75 thf(f3087,plain,(
% 78.92/11.75 spl72_129 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1),v) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_129])])).
% 78.92/11.75 thf(f6109,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,v),s)),v)) | (~spl72_129 | ~spl72_253)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6104])).
% 78.92/11.75 thf(f6104,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,v),s)),v)) | (~spl72_129 | ~spl72_253)),
% 78.92/11.75 inference(superposition,[],[f6085,f3089])).
% 78.92/11.75 thf(f3089,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1),v) = $true) | ~spl72_129),
% 78.92/11.75 inference(avatar_component_clause,[],[f3087])).
% 78.92/11.75 thf(f47099,plain,(
% 78.92/11.75 spl72_622 | ~spl72_130 | ~spl72_253),
% 78.92/11.75 inference(avatar_split_clause,[],[f6108,f6084,f3092,f47096])).
% 78.92/11.75 thf(f47096,plain,(
% 78.92/11.75 spl72_622 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,va),s)),va))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_622])])).
% 78.92/11.75 thf(f3092,plain,(
% 78.92/11.75 spl72_130 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a),va) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_130])])).
% 78.92/11.75 thf(f6108,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,va),s)),va)) | (~spl72_130 | ~spl72_253)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6105])).
% 78.92/11.75 thf(f6105,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,va),s)),va)) | (~spl72_130 | ~spl72_253)),
% 78.92/11.75 inference(superposition,[],[f6085,f3094])).
% 78.92/11.75 thf(f3094,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a),va) = $true) | ~spl72_130),
% 78.92/11.75 inference(avatar_component_clause,[],[f3092])).
% 78.92/11.75 thf(f47094,plain,(
% 78.92/11.75 spl72_621 | ~spl72_124 | ~spl72_252),
% 78.92/11.75 inference(avatar_split_clause,[],[f6102,f6080,f3062,f47091])).
% 78.92/11.75 thf(f47091,plain,(
% 78.92/11.75 spl72_621 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),u),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),u)),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_621])])).
% 78.92/11.75 thf(f3062,plain,(
% 78.92/11.75 spl72_124 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2),t) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_124])])).
% 78.92/11.75 thf(f6080,plain,(
% 78.92/11.75 spl72_252 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,X2),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_252])])).
% 78.92/11.75 thf(f6102,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),u),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),u)),t)) | (~spl72_124 | ~spl72_252)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6095])).
% 78.92/11.75 thf(f6095,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),u),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),u)),t)) | (~spl72_124 | ~spl72_252)),
% 78.92/11.75 inference(superposition,[],[f6081,f3064])).
% 78.92/11.75 thf(f3064,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2),t) = $true) | ~spl72_124),
% 78.92/11.75 inference(avatar_component_clause,[],[f3062])).
% 78.92/11.75 thf(f6081,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,X2),X0)),X2))) ) | ~spl72_252),
% 78.92/11.75 inference(avatar_component_clause,[],[f6080])).
% 78.92/11.75 thf(f47089,plain,(
% 78.92/11.75 spl72_620 | ~spl72_125 | ~spl72_252),
% 78.92/11.75 inference(avatar_split_clause,[],[f6101,f6080,f3067,f47086])).
% 78.92/11.75 thf(f47086,plain,(
% 78.92/11.75 spl72_620 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),ua),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),ua)),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_620])])).
% 78.92/11.75 thf(f3067,plain,(
% 78.92/11.75 spl72_125 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a),t) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_125])])).
% 78.92/11.75 thf(f6101,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),ua),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),ua)),t)) | (~spl72_125 | ~spl72_252)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6096])).
% 78.92/11.75 thf(f6096,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),ua),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),ua)),t)) | (~spl72_125 | ~spl72_252)),
% 78.92/11.75 inference(superposition,[],[f6081,f3069])).
% 78.92/11.75 thf(f3069,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a),t) = $true) | ~spl72_125),
% 78.92/11.75 inference(avatar_component_clause,[],[f3067])).
% 78.92/11.75 thf(f47084,plain,(
% 78.92/11.75 spl72_619 | ~spl72_126 | ~spl72_252),
% 78.92/11.75 inference(avatar_split_clause,[],[f6100,f6080,f3072,f47081])).
% 78.92/11.75 thf(f47081,plain,(
% 78.92/11.75 spl72_619 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),s)),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_619])])).
% 78.92/11.75 thf(f3072,plain,(
% 78.92/11.75 spl72_126 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3),t) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_126])])).
% 78.92/11.75 thf(f6100,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),s)),t)) | (~spl72_126 | ~spl72_252)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f6097])).
% 78.92/11.75 thf(f6097,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,t),s)),t)) | (~spl72_126 | ~spl72_252)),
% 78.92/11.75 inference(superposition,[],[f6081,f3074])).
% 78.92/11.75 thf(f3074,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3),t) = $true) | ~spl72_126),
% 78.92/11.75 inference(avatar_component_clause,[],[f3072])).
% 78.92/11.75 thf(f47079,plain,(
% 78.92/11.75 spl72_618 | ~spl72_72 | ~spl72_221),
% 78.92/11.75 inference(avatar_split_clause,[],[f5055,f5047,f2448,f47076])).
% 78.92/11.75 thf(f47076,plain,(
% 78.92/11.75 spl72_618 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,ua),s)),ua))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_618])])).
% 78.92/11.75 thf(f2448,plain,(
% 78.92/11.75 spl72_72 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s),ua) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_72])])).
% 78.92/11.75 thf(f5047,plain,(
% 78.92/11.75 spl72_221 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_221])])).
% 78.92/11.75 thf(f5055,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,ua),s)),ua)) | (~spl72_72 | ~spl72_221)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5052])).
% 78.92/11.75 thf(f5052,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,ua),s)),ua)) | (~spl72_72 | ~spl72_221)),
% 78.92/11.75 inference(superposition,[],[f5048,f2450])).
% 78.92/11.75 thf(f2450,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s),ua) = $true) | ~spl72_72),
% 78.92/11.75 inference(avatar_component_clause,[],[f2448])).
% 78.92/11.75 thf(f5048,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,X1),X0)),X1))) ) | ~spl72_221),
% 78.92/11.75 inference(avatar_component_clause,[],[f5047])).
% 78.92/11.75 thf(f47074,plain,(
% 78.92/11.75 spl72_617 | ~spl72_6 | ~spl72_15 | ~spl72_68 | ~spl72_151 | ~spl72_188),
% 78.92/11.75 inference(avatar_split_clause,[],[f4149,f4083,f3608,f2368,f1959,f1914,f47072])).
% 78.92/11.75 thf(f47072,plain,(
% 78.92/11.75 spl72_617 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_617])])).
% 78.92/11.75 thf(f1914,plain,(
% 78.92/11.75 spl72_6 <=> (semigroup_add(nat) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_6])])).
% 78.92/11.75 thf(f3608,plain,(
% 78.92/11.75 spl72_151 <=> ! [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) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_151])])).
% 78.92/11.75 thf(f4149,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_6 | ~spl72_15 | ~spl72_68 | ~spl72_151 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4148])).
% 78.92/11.75 thf(f4148,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_6 | ~spl72_15 | ~spl72_68 | ~spl72_151 | ~spl72_188)),
% 78.92/11.75 inference(forward_demodulation,[],[f4147,f1961])).
% 78.92/11.75 thf(f4147,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_6 | ~spl72_68 | ~spl72_151 | ~spl72_188)),
% 78.92/11.75 inference(forward_demodulation,[],[f4141,f3635])).
% 78.92/11.75 thf(f3635,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | (~spl72_6 | ~spl72_151)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3632])).
% 78.92/11.75 thf(f3632,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (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) = 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)))) ) | (~spl72_6 | ~spl72_151)),
% 78.92/11.75 inference(superposition,[],[f3609,f1916])).
% 78.92/11.75 thf(f1916,plain,(
% 78.92/11.75 (semigroup_add(nat) = $true) | ~spl72_6),
% 78.92/11.75 inference(avatar_component_clause,[],[f1914])).
% 78.92/11.75 thf(f3609,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((semigroup_add(X0) != $true) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X3)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),X3))) ) | ~spl72_151),
% 78.92/11.75 inference(avatar_component_clause,[],[f3608])).
% 78.92/11.75 thf(f4141,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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)),X3))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_68 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4132])).
% 78.92/11.75 thf(f4132,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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)),X3))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_68 | ~spl72_188)),
% 78.92/11.75 inference(superposition,[],[f4084,f2369])).
% 78.92/11.75 thf(f47070,plain,(
% 78.92/11.75 spl72_616 | ~spl72_6 | ~spl72_15 | ~spl72_67 | ~spl72_151 | ~spl72_188),
% 78.92/11.75 inference(avatar_split_clause,[],[f4146,f4083,f3608,f2364,f1959,f1914,f47068])).
% 78.92/11.75 thf(f47068,plain,(
% 78.92/11.75 spl72_616 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_616])])).
% 78.92/11.75 thf(f4146,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_6 | ~spl72_15 | ~spl72_67 | ~spl72_151 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4145])).
% 78.92/11.75 thf(f4145,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_6 | ~spl72_15 | ~spl72_67 | ~spl72_151 | ~spl72_188)),
% 78.92/11.75 inference(forward_demodulation,[],[f4144,f1961])).
% 78.92/11.75 thf(f4144,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_6 | ~spl72_67 | ~spl72_151 | ~spl72_188)),
% 78.92/11.75 inference(forward_demodulation,[],[f4142,f3635])).
% 78.92/11.75 thf(f4142,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X3))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_67 | ~spl72_188)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4131])).
% 78.92/11.75 thf(f4131,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X3))) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_67 | ~spl72_188)),
% 78.92/11.75 inference(superposition,[],[f4084,f2365])).
% 78.92/11.75 thf(f47048,plain,(
% 78.92/11.75 spl72_615 | ~spl72_15 | ~spl72_68 | ~spl72_187),
% 78.92/11.75 inference(avatar_split_clause,[],[f4125,f4079,f2368,f1959,f47046])).
% 78.92/11.75 thf(f47046,plain,(
% 78.92/11.75 spl72_615 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_615])])).
% 78.92/11.75 thf(f4125,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_15 | ~spl72_68 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4124])).
% 78.92/11.75 thf(f4124,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_15 | ~spl72_68 | ~spl72_187)),
% 78.92/11.75 inference(forward_demodulation,[],[f4119,f1961])).
% 78.92/11.75 thf(f4119,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_68 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4110])).
% 78.92/11.75 thf(f4110,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_68 | ~spl72_187)),
% 78.92/11.75 inference(superposition,[],[f4080,f2369])).
% 78.92/11.75 thf(f47044,plain,(
% 78.92/11.75 spl72_614 | ~spl72_15 | ~spl72_67 | ~spl72_187),
% 78.92/11.75 inference(avatar_split_clause,[],[f4123,f4079,f2364,f1959,f47042])).
% 78.92/11.75 thf(f47042,plain,(
% 78.92/11.75 spl72_614 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_614])])).
% 78.92/11.75 thf(f4123,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_15 | ~spl72_67 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4122])).
% 78.92/11.75 thf(f4122,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) ) | (~spl72_15 | ~spl72_67 | ~spl72_187)),
% 78.92/11.75 inference(forward_demodulation,[],[f4120,f1961])).
% 78.92/11.75 thf(f4120,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_67 | ~spl72_187)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4109])).
% 78.92/11.75 thf(f4109,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (ordere223160158up_add(nat) != $true)) ) | (~spl72_67 | ~spl72_187)),
% 78.92/11.75 inference(superposition,[],[f4080,f2365])).
% 78.92/11.75 thf(f47040,plain,(
% 78.92/11.75 spl72_613 | ~spl72_67 | ~spl72_181),
% 78.92/11.75 inference(avatar_split_clause,[],[f4053,f4034,f2364,f47038])).
% 78.92/11.75 thf(f47038,plain,(
% 78.92/11.75 spl72_613 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_613])])).
% 78.92/11.75 thf(f4053,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))) ) | (~spl72_67 | ~spl72_181)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4042])).
% 78.92/11.75 thf(f4042,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))) ) | (~spl72_67 | ~spl72_181)),
% 78.92/11.75 inference(superposition,[],[f4035,f2365])).
% 78.92/11.75 thf(f47036,plain,(
% 78.92/11.75 spl72_612 | ~spl72_68 | ~spl72_181),
% 78.92/11.75 inference(avatar_split_clause,[],[f4052,f4034,f2368,f47034])).
% 78.92/11.75 thf(f47034,plain,(
% 78.92/11.75 spl72_612 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_612])])).
% 78.92/11.75 thf(f4052,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))) ) | (~spl72_68 | ~spl72_181)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4043])).
% 78.92/11.75 thf(f4043,plain,(
% 78.92/11.75 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))) ) | (~spl72_68 | ~spl72_181)),
% 78.92/11.75 inference(superposition,[],[f4035,f2369])).
% 78.92/11.75 thf(f47032,plain,(
% 78.92/11.75 spl72_611 | ~spl72_28 | ~spl72_174),
% 78.92/11.75 inference(avatar_split_clause,[],[f3975,f3925,f2020,f47030])).
% 78.92/11.75 thf(f47030,plain,(
% 78.92/11.75 spl72_611 <=> ! [X0 : $tType,X4 : $o,X3 : $o,X2 : $o > X0,X1 : $o > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X2,X3)),vAPP($o,X0,X2,$true))) | ($true = vAPP($o,$o,X1,X3)) | ($true = vAPP($o,$o,X1,X4)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_611])])).
% 78.92/11.75 thf(f3975,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : $o > X0,X3 : $o,X1 : $o > $o,X4 : $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X2,X3)),vAPP($o,X0,X2,$true))) | ($true = vAPP($o,$o,X1,X3)) | ($true = vAPP($o,$o,X1,X4)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),X1),X2))) ) | (~spl72_28 | ~spl72_174)),
% 78.92/11.75 inference(superposition,[],[f3926,f2021])).
% 78.92/11.75 thf(f47028,plain,(
% 78.92/11.75 spl72_610 | ~spl72_28 | ~spl72_173),
% 78.92/11.75 inference(avatar_split_clause,[],[f3947,f3921,f2020,f47026])).
% 78.92/11.75 thf(f47026,plain,(
% 78.92/11.75 spl72_610 <=> ! [X0 : $tType,X4 : $o,X3 : $o,X2 : $o > X0,X1 : $o > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X2,X3)),vAPP($o,X0,X2,$true))) | ($true = vAPP($o,$o,X1,X3)) | ($true = vAPP($o,$o,X1,X4)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_610])])).
% 78.92/11.75 thf(f3947,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : $o > X0,X3 : $o,X1 : $o > $o,X4 : $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP($o,X0,X2,X3)),vAPP($o,X0,X2,$true))) | ($true = vAPP($o,$o,X1,X3)) | ($true = vAPP($o,$o,X1,X4)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),X1),X2))) ) | (~spl72_28 | ~spl72_173)),
% 78.92/11.75 inference(superposition,[],[f3922,f2021])).
% 78.92/11.75 thf(f47024,plain,(
% 78.92/11.75 spl72_609 | ~spl72_107),
% 78.92/11.75 inference(avatar_split_clause,[],[f2872,f2865,f47022])).
% 78.92/11.75 thf(f47022,plain,(
% 78.92/11.75 spl72_609 <=> ! [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)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_609])])).
% 78.92/11.75 thf(f2872,plain,(
% 78.92/11.75 ( ! [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,$o)),cCOMB,member(X0)),X2))) ) | ~spl72_107),
% 78.92/11.75 inference(constrained_superposition,[],[f2866,f2866])).
% 78.92/11.75 thf(f46575,plain,(
% 78.92/11.75 spl72_608 | ~spl72_68 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4908,f4893,f2368,f46572])).
% 78.92/11.75 thf(f46572,plain,(
% 78.92/11.75 spl72_608 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_608])])).
% 78.92/11.75 thf(f4908,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t))) | (~spl72_68 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2369,f4895])).
% 78.92/11.75 thf(f46570,plain,(
% 78.92/11.75 spl72_607 | ~spl72_67 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4907,f4893,f2364,f46567])).
% 78.92/11.75 thf(f46567,plain,(
% 78.92/11.75 spl72_607 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_607])])).
% 78.92/11.75 thf(f4907,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t))) | (~spl72_67 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2365,f4895])).
% 78.92/11.75 thf(f46564,plain,(
% 78.92/11.75 ~spl72_606 | ~spl72_65 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4906,f4893,f2355,f46561])).
% 78.92/11.75 thf(f46561,plain,(
% 78.92/11.75 spl72_606 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_606])])).
% 78.92/11.75 thf(f2355,plain,(
% 78.92/11.75 spl72_65 <=> ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_65])])).
% 78.92/11.75 thf(f4906,plain,(
% 78.92/11.75 ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (~spl72_65 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2356,f4895])).
% 78.92/11.75 thf(f2356,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) ) | ~spl72_65),
% 78.92/11.75 inference(avatar_component_clause,[],[f2355])).
% 78.92/11.75 thf(f46558,plain,(
% 78.92/11.75 ~spl72_605 | ~spl72_64 | ~spl72_214),
% 78.92/11.75 inference(avatar_split_clause,[],[f4905,f4893,f2351,f46555])).
% 78.92/11.75 thf(f46555,plain,(
% 78.92/11.75 spl72_605 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_605])])).
% 78.92/11.75 thf(f2351,plain,(
% 78.92/11.75 spl72_64 <=> ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_64])])).
% 78.92/11.75 thf(f4905,plain,(
% 78.92/11.75 ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t))) | (~spl72_64 | ~spl72_214)),
% 78.92/11.75 inference(superposition,[],[f2352,f4895])).
% 78.92/11.75 thf(f2352,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))) ) | ~spl72_64),
% 78.92/11.75 inference(avatar_component_clause,[],[f2351])).
% 78.92/11.75 thf(f46553,plain,(
% 78.92/11.75 spl72_604 | ~spl72_50 | ~spl72_159),
% 78.92/11.75 inference(avatar_split_clause,[],[f3728,f3675,f2246,f46551])).
% 78.92/11.75 thf(f46551,plain,(
% 78.92/11.75 spl72_604 <=> ! [X2 : nat,X0 : nat,X1 : nat > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X1,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_604])])).
% 78.92/11.75 thf(f3728,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X1,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))) ) | (~spl72_50 | ~spl72_159)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3697])).
% 78.92/11.75 thf(f3697,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X1,vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))),vAPP(nat,nat,X1,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))) ) | (~spl72_50 | ~spl72_159)),
% 78.92/11.75 inference(superposition,[],[f3676,f2247])).
% 78.92/11.75 thf(f43637,plain,(
% 78.92/11.75 spl72_603 | ~spl72_72 | ~spl72_219),
% 78.92/11.75 inference(avatar_split_clause,[],[f5041,f5033,f2448,f43634])).
% 78.92/11.75 thf(f43634,plain,(
% 78.92/11.75 spl72_603 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),ua))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_603])])).
% 78.92/11.75 thf(f5033,plain,(
% 78.92/11.75 spl72_219 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_219])])).
% 78.92/11.75 thf(f5041,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),ua)) | (~spl72_72 | ~spl72_219)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f5038])).
% 78.92/11.75 thf(f5038,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),ua)) | (~spl72_72 | ~spl72_219)),
% 78.92/11.75 inference(superposition,[],[f5034,f2450])).
% 78.92/11.75 thf(f5034,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)),X1))) ) | ~spl72_219),
% 78.92/11.75 inference(avatar_component_clause,[],[f5033])).
% 78.92/11.75 thf(f43632,plain,(
% 78.92/11.75 spl72_602 | ~spl72_115 | ~spl72_191),
% 78.92/11.75 inference(avatar_split_clause,[],[f4227,f4164,f2910,f43630])).
% 78.92/11.75 thf(f43630,plain,(
% 78.92/11.75 spl72_602 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_602])])).
% 78.92/11.75 thf(f4164,plain,(
% 78.92/11.75 spl72_191 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_191])])).
% 78.92/11.75 thf(f4227,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))) ) | (~spl72_115 | ~spl72_191)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4170])).
% 78.92/11.75 thf(f4170,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))) ) | (~spl72_115 | ~spl72_191)),
% 78.92/11.75 inference(superposition,[],[f2911,f4165])).
% 78.92/11.75 thf(f4165,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))) ) | ~spl72_191),
% 78.92/11.75 inference(avatar_component_clause,[],[f4164])).
% 78.92/11.75 thf(f43628,plain,(
% 78.92/11.75 spl72_601 | ~spl72_67 | ~spl72_175),
% 78.92/11.75 inference(avatar_split_clause,[],[f4017,f3985,f2364,f43626])).
% 78.92/11.75 thf(f43626,plain,(
% 78.92/11.75 spl72_601 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_601])])).
% 78.92/11.75 thf(f4017,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2)))) ) | (~spl72_67 | ~spl72_175)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4006])).
% 78.92/11.75 thf(f4006,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2)))) ) | (~spl72_67 | ~spl72_175)),
% 78.92/11.75 inference(superposition,[],[f3986,f2365])).
% 78.92/11.75 thf(f43624,plain,(
% 78.92/11.75 spl72_600 | ~spl72_68 | ~spl72_175),
% 78.92/11.75 inference(avatar_split_clause,[],[f4016,f3985,f2368,f43622])).
% 78.92/11.75 thf(f43622,plain,(
% 78.92/11.75 spl72_600 <=> ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_600])])).
% 78.92/11.75 thf(f4016,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2)))) ) | (~spl72_68 | ~spl72_175)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4007])).
% 78.92/11.75 thf(f4007,plain,(
% 78.92/11.75 ( ! [X2 : nat > nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X2,X0)),vAPP(nat,nat,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X2)),vAPP(sTfun(nat,nat),nat,sK52,X2)))) ) | (~spl72_68 | ~spl72_175)),
% 78.92/11.75 inference(superposition,[],[f3986,f2369])).
% 78.92/11.75 thf(f43620,plain,(
% 78.92/11.75 spl72_599 | ~spl72_14 | ~spl72_50 | ~spl72_146),
% 78.92/11.75 inference(avatar_split_clause,[],[f3534,f3363,f2246,f1954,f43618])).
% 78.92/11.75 thf(f43618,plain,(
% 78.92/11.75 spl72_599 <=> ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK10(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_599])])).
% 78.92/11.75 thf(f3363,plain,(
% 78.92/11.75 spl72_146 <=> ! [X0 : $tType,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_146])])).
% 78.92/11.75 thf(f3534,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK10(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_14 | ~spl72_50 | ~spl72_146)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3533])).
% 78.92/11.75 thf(f3533,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK10(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_14 | ~spl72_50 | ~spl72_146)),
% 78.92/11.75 inference(forward_demodulation,[],[f3517,f1956])).
% 78.92/11.75 thf(f3517,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK10(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_146)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3486])).
% 78.92/11.75 thf(f3486,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK10(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_146)),
% 78.92/11.75 inference(superposition,[],[f3364,f2247])).
% 78.92/11.75 thf(f3364,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true)) ) | ~spl72_146),
% 78.92/11.75 inference(avatar_component_clause,[],[f3363])).
% 78.92/11.75 thf(f43616,plain,(
% 78.92/11.75 spl72_598 | ~spl72_14 | ~spl72_50 | ~spl72_144),
% 78.92/11.75 inference(avatar_split_clause,[],[f3426,f3355,f2246,f1954,f43614])).
% 78.92/11.75 thf(f43614,plain,(
% 78.92/11.75 spl72_598 <=> ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK9(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_598])])).
% 78.92/11.75 thf(f3355,plain,(
% 78.92/11.75 spl72_144 <=> ! [X0 : $tType,X4 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X4)) | (wellorder(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_144])])).
% 78.92/11.75 thf(f3426,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK9(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_14 | ~spl72_50 | ~spl72_144)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3425])).
% 78.92/11.75 thf(f3425,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK9(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_14 | ~spl72_50 | ~spl72_144)),
% 78.92/11.75 inference(forward_demodulation,[],[f3409,f1956])).
% 78.92/11.75 thf(f3409,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK9(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_144)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3378])).
% 78.92/11.75 thf(f3378,plain,(
% 78.92/11.75 ( ! [X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,$o),sTfun(sTfun(nat,$o),nat),sK9(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_144)),
% 78.92/11.75 inference(superposition,[],[f3356,f2247])).
% 78.92/11.75 thf(f3356,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) | ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true)) ) | ~spl72_144),
% 78.92/11.75 inference(avatar_component_clause,[],[f3355])).
% 78.92/11.75 thf(f43612,plain,(
% 78.92/11.75 spl72_597 | ~spl72_112 | ~spl72_142),
% 78.92/11.75 inference(avatar_split_clause,[],[f3344,f3254,f2898,f43610])).
% 78.92/11.75 thf(f43610,plain,(
% 78.92/11.75 spl72_597 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_597])])).
% 78.92/11.75 thf(f2898,plain,(
% 78.92/11.75 spl72_112 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_112])])).
% 78.92/11.75 thf(f3344,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))) ) | (~spl72_112 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3321])).
% 78.92/11.75 thf(f3321,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),X0)))) ) | (~spl72_112 | ~spl72_142)),
% 78.92/11.75 inference(superposition,[],[f2899,f3256])).
% 78.92/11.75 thf(f2899,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | ~spl72_112),
% 78.92/11.75 inference(avatar_component_clause,[],[f2898])).
% 78.92/11.75 thf(f43608,plain,(
% 78.92/11.75 spl72_596 | ~spl72_113 | ~spl72_142),
% 78.92/11.75 inference(avatar_split_clause,[],[f3343,f3254,f2902,f43606])).
% 78.92/11.75 thf(f43606,plain,(
% 78.92/11.75 spl72_596 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_596])])).
% 78.92/11.75 thf(f2902,plain,(
% 78.92/11.75 spl72_113 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_113])])).
% 78.92/11.75 thf(f3343,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))) ) | (~spl72_113 | ~spl72_142)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3322])).
% 78.92/11.75 thf(f3322,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))))) ) | (~spl72_113 | ~spl72_142)),
% 78.92/11.75 inference(superposition,[],[f2903,f3256])).
% 78.92/11.75 thf(f2903,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) ) | ~spl72_113),
% 78.92/11.75 inference(avatar_component_clause,[],[f2902])).
% 78.92/11.75 thf(f43598,plain,(
% 78.92/11.75 spl72_595 | ~spl72_111 | ~spl72_141),
% 78.92/11.75 inference(avatar_split_clause,[],[f3307,f3249,f2894,f43596])).
% 78.92/11.75 thf(f43596,plain,(
% 78.92/11.75 spl72_595 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_595])])).
% 78.92/11.75 thf(f2894,plain,(
% 78.92/11.75 spl72_111 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_111])])).
% 78.92/11.75 thf(f3307,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))))) ) | (~spl72_111 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3280])).
% 78.92/11.75 thf(f3280,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))))) ) | (~spl72_111 | ~spl72_141)),
% 78.92/11.75 inference(superposition,[],[f2895,f3251])).
% 78.92/11.75 thf(f2895,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))) ) | ~spl72_111),
% 78.92/11.75 inference(avatar_component_clause,[],[f2894])).
% 78.92/11.75 thf(f43594,plain,(
% 78.92/11.75 spl72_594 | ~spl72_110 | ~spl72_141),
% 78.92/11.75 inference(avatar_split_clause,[],[f3306,f3249,f2890,f43592])).
% 78.92/11.75 thf(f43592,plain,(
% 78.92/11.75 spl72_594 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_594])])).
% 78.92/11.75 thf(f2890,plain,(
% 78.92/11.75 spl72_110 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_110])])).
% 78.92/11.75 thf(f3306,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))) ) | (~spl72_110 | ~spl72_141)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3281])).
% 78.92/11.75 thf(f3281,plain,(
% 78.92/11.75 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),X0)))) ) | (~spl72_110 | ~spl72_141)),
% 78.92/11.75 inference(superposition,[],[f2891,f3251])).
% 78.92/11.75 thf(f2891,plain,(
% 78.92/11.75 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | ~spl72_110),
% 78.92/11.75 inference(avatar_component_clause,[],[f2890])).
% 78.92/11.75 thf(f43590,plain,(
% 78.92/11.75 spl72_593 | ~spl72_14 | ~spl72_83 | ~spl72_130),
% 78.92/11.75 inference(avatar_split_clause,[],[f3182,f3092,f2616,f1954,f43587])).
% 78.92/11.75 thf(f43587,plain,(
% 78.92/11.75 spl72_593 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a))),va))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_593])])).
% 78.92/11.75 thf(f3182,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a))),va)) | (~spl72_14 | ~spl72_83 | ~spl72_130)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3181])).
% 78.92/11.75 thf(f3181,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a))),va)) | (~spl72_14 | ~spl72_83 | ~spl72_130)),
% 78.92/11.75 inference(forward_demodulation,[],[f3179,f1956])).
% 78.92/11.75 thf(f3179,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a))),va)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_130)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3174])).
% 78.92/11.75 thf(f3174,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a))),va)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_130)),
% 78.92/11.75 inference(superposition,[],[f2617,f3094])).
% 78.92/11.75 thf(f43585,plain,(
% 78.92/11.75 spl72_592 | ~spl72_14 | ~spl72_83 | ~spl72_129),
% 78.92/11.75 inference(avatar_split_clause,[],[f3170,f3087,f2616,f1954,f43582])).
% 78.92/11.75 thf(f43582,plain,(
% 78.92/11.75 spl72_592 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1))),v))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_592])])).
% 78.92/11.75 thf(f3170,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1))),v)) | (~spl72_14 | ~spl72_83 | ~spl72_129)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3169])).
% 78.92/11.75 thf(f3169,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1))),v)) | (~spl72_14 | ~spl72_83 | ~spl72_129)),
% 78.92/11.75 inference(forward_demodulation,[],[f3167,f1956])).
% 78.92/11.75 thf(f3167,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1))),v)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_129)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3162])).
% 78.92/11.75 thf(f3162,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1))),v)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_129)),
% 78.92/11.75 inference(superposition,[],[f2617,f3089])).
% 78.92/11.75 thf(f43580,plain,(
% 78.92/11.75 spl72_591 | ~spl72_14 | ~spl72_83 | ~spl72_128),
% 78.92/11.75 inference(avatar_split_clause,[],[f3158,f3082,f2616,f1954,f43577])).
% 78.92/11.75 thf(f43577,plain,(
% 78.92/11.75 spl72_591 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a))),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_591])])).
% 78.92/11.75 thf(f3158,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_128)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3157])).
% 78.92/11.75 thf(f3157,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_128)),
% 78.92/11.75 inference(forward_demodulation,[],[f3155,f1956])).
% 78.92/11.75 thf(f3155,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_128)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3150])).
% 78.92/11.75 thf(f3150,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_128)),
% 78.92/11.75 inference(superposition,[],[f2617,f3084])).
% 78.92/11.75 thf(f43575,plain,(
% 78.92/11.75 spl72_590 | ~spl72_14 | ~spl72_83 | ~spl72_127),
% 78.92/11.75 inference(avatar_split_clause,[],[f3146,f3077,f2616,f1954,f43572])).
% 78.92/11.75 thf(f43572,plain,(
% 78.92/11.75 spl72_590 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p))),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_590])])).
% 78.92/11.75 thf(f3077,plain,(
% 78.92/11.75 spl72_127 <=> (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p),t) = $true)),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_127])])).
% 78.92/11.75 thf(f3146,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_127)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3145])).
% 78.92/11.75 thf(f3145,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_127)),
% 78.92/11.75 inference(forward_demodulation,[],[f3143,f1956])).
% 78.92/11.75 thf(f3143,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_127)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3138])).
% 78.92/11.75 thf(f3138,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_127)),
% 78.92/11.75 inference(superposition,[],[f2617,f3079])).
% 78.92/11.75 thf(f3079,plain,(
% 78.92/11.75 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p),t) = $true) | ~spl72_127),
% 78.92/11.75 inference(avatar_component_clause,[],[f3077])).
% 78.92/11.75 thf(f43570,plain,(
% 78.92/11.75 spl72_589 | ~spl72_14 | ~spl72_83 | ~spl72_126),
% 78.92/11.75 inference(avatar_split_clause,[],[f3129,f3072,f2616,f1954,f43567])).
% 78.92/11.75 thf(f43567,plain,(
% 78.92/11.75 spl72_589 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3))),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_589])])).
% 78.92/11.75 thf(f3129,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_126)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3128])).
% 78.92/11.75 thf(f3128,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_126)),
% 78.92/11.75 inference(forward_demodulation,[],[f3126,f1956])).
% 78.92/11.75 thf(f3126,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_126)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3121])).
% 78.92/11.75 thf(f3121,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_126)),
% 78.92/11.75 inference(superposition,[],[f2617,f3074])).
% 78.92/11.75 thf(f43565,plain,(
% 78.92/11.75 spl72_588 | ~spl72_14 | ~spl72_83 | ~spl72_125),
% 78.92/11.75 inference(avatar_split_clause,[],[f3117,f3067,f2616,f1954,f43562])).
% 78.92/11.75 thf(f43562,plain,(
% 78.92/11.75 spl72_588 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a))),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_588])])).
% 78.92/11.75 thf(f3117,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_125)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3116])).
% 78.92/11.75 thf(f3116,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_125)),
% 78.92/11.75 inference(forward_demodulation,[],[f3114,f1956])).
% 78.92/11.75 thf(f3114,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_125)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3109])).
% 78.92/11.75 thf(f3109,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_125)),
% 78.92/11.75 inference(superposition,[],[f2617,f3069])).
% 78.92/11.75 thf(f43560,plain,(
% 78.92/11.75 spl72_587 | ~spl72_14 | ~spl72_83 | ~spl72_124),
% 78.92/11.75 inference(avatar_split_clause,[],[f3105,f3062,f2616,f1954,f43557])).
% 78.92/11.75 thf(f43557,plain,(
% 78.92/11.75 spl72_587 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2))),t))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_587])])).
% 78.92/11.75 thf(f3105,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_124)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3104])).
% 78.92/11.75 thf(f3104,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2))),t)) | (~spl72_14 | ~spl72_83 | ~spl72_124)),
% 78.92/11.75 inference(forward_demodulation,[],[f3102,f1956])).
% 78.92/11.75 thf(f3102,plain,(
% 78.92/11.75 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_124)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3097])).
% 78.92/11.75 thf(f3097,plain,(
% 78.92/11.75 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2))),t)) | (wellorder(nat) != $true) | (~spl72_83 | ~spl72_124)),
% 78.92/11.75 inference(superposition,[],[f2617,f3064])).
% 78.92/11.75 thf(f43535,plain,(
% 78.92/11.75 ~spl72_575 | spl72_586 | ~spl72_28 | ~spl72_167),
% 78.92/11.75 inference(avatar_split_clause,[],[f3848,f3773,f2020,f43533,f43420])).
% 78.92/11.75 thf(f43420,plain,(
% 78.92/11.75 spl72_575 <=> ($true = ordere236663937imp_le($o))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_575])])).
% 78.92/11.75 thf(f43533,plain,(
% 78.92/11.75 spl72_586 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1)),$true)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_586])])).
% 78.92/11.75 thf(f3773,plain,(
% 78.92/11.75 spl72_167 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_167])])).
% 78.92/11.75 thf(f3848,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X0)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_167)),
% 78.92/11.75 inference(superposition,[],[f3774,f2021])).
% 78.92/11.75 thf(f3774,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true)) ) | ~spl72_167),
% 78.92/11.75 inference(avatar_component_clause,[],[f3773])).
% 78.92/11.75 thf(f43531,plain,(
% 78.92/11.75 ~spl72_575 | spl72_585 | ~spl72_28 | ~spl72_167),
% 78.92/11.75 inference(avatar_split_clause,[],[f3847,f3773,f2020,f43529,f43420])).
% 78.92/11.75 thf(f43529,plain,(
% 78.92/11.75 spl72_585 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_585])])).
% 78.92/11.75 thf(f3847,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X2)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_167)),
% 78.92/11.75 inference(superposition,[],[f3774,f2021])).
% 78.92/11.75 thf(f43527,plain,(
% 78.92/11.75 ~spl72_575 | spl72_584 | ~spl72_28 | ~spl72_166),
% 78.92/11.75 inference(avatar_split_clause,[],[f3834,f3769,f2020,f43525,f43420])).
% 78.92/11.75 thf(f43525,plain,(
% 78.92/11.75 spl72_584 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2)),$true)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_584])])).
% 78.92/11.75 thf(f3769,plain,(
% 78.92/11.75 spl72_166 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_166])])).
% 78.92/11.75 thf(f3834,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X2),X1)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_166)),
% 78.92/11.75 inference(superposition,[],[f3770,f2021])).
% 78.92/11.75 thf(f3770,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true)) ) | ~spl72_166),
% 78.92/11.75 inference(avatar_component_clause,[],[f3769])).
% 78.92/11.75 thf(f43523,plain,(
% 78.92/11.75 ~spl72_575 | spl72_583 | ~spl72_28 | ~spl72_166),
% 78.92/11.75 inference(avatar_split_clause,[],[f3833,f3769,f2020,f43521,f43420])).
% 78.92/11.75 thf(f43521,plain,(
% 78.92/11.75 spl72_583 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_583])])).
% 78.92/11.75 thf(f3833,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X1),X2)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_166)),
% 78.92/11.75 inference(superposition,[],[f3770,f2021])).
% 78.92/11.75 thf(f43519,plain,(
% 78.92/11.75 ~spl72_575 | spl72_582 | ~spl72_28 | ~spl72_165),
% 78.92/11.75 inference(avatar_split_clause,[],[f3830,f3765,f2020,f43517,f43420])).
% 78.92/11.75 thf(f43517,plain,(
% 78.92/11.75 spl72_582 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2)),$true)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_582])])).
% 78.92/11.75 thf(f3765,plain,(
% 78.92/11.75 spl72_165 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_165])])).
% 78.92/11.75 thf(f3830,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X1)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_165)),
% 78.92/11.75 inference(superposition,[],[f3766,f2021])).
% 78.92/11.75 thf(f3766,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true)) ) | ~spl72_165),
% 78.92/11.75 inference(avatar_component_clause,[],[f3765])).
% 78.92/11.75 thf(f43515,plain,(
% 78.92/11.75 ~spl72_575 | spl72_581 | ~spl72_28 | ~spl72_165),
% 78.92/11.75 inference(avatar_split_clause,[],[f3829,f3765,f2020,f43513,f43420])).
% 78.92/11.75 thf(f43513,plain,(
% 78.92/11.75 spl72_581 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X1),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_581])])).
% 78.92/11.75 thf(f3829,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X2))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X1),X2)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_165)),
% 78.92/11.75 inference(superposition,[],[f3766,f2021])).
% 78.92/11.75 thf(f43509,plain,(
% 78.92/11.75 ~spl72_575 | spl72_580 | ~spl72_28 | ~spl72_164),
% 78.92/11.75 inference(avatar_split_clause,[],[f3826,f3761,f2020,f43507,f43420])).
% 78.92/11.75 thf(f43507,plain,(
% 78.92/11.75 spl72_580 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1)),$true)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X0)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_580])])).
% 78.92/11.75 thf(f3761,plain,(
% 78.92/11.75 spl72_164 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_164])])).
% 78.92/11.75 thf(f3826,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1)),$true)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X2),X0)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_164)),
% 78.92/11.75 inference(superposition,[],[f3762,f2021])).
% 78.92/11.75 thf(f3762,plain,(
% 78.92/11.75 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true)) ) | ~spl72_164),
% 78.92/11.75 inference(avatar_component_clause,[],[f3761])).
% 78.92/11.75 thf(f43441,plain,(
% 78.92/11.75 spl72_579 | ~spl72_28 | spl72_575),
% 78.92/11.75 inference(avatar_split_clause,[],[f43428,f43420,f2020,f43438])).
% 78.92/11.75 thf(f43438,plain,(
% 78.92/11.75 spl72_579 <=> ($false = ordere236663937imp_le($o))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_579])])).
% 78.92/11.75 thf(f43428,plain,(
% 78.92/11.75 ($false = ordere236663937imp_le($o)) | (~spl72_28 | spl72_575)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f43427])).
% 78.92/11.75 thf(f43427,plain,(
% 78.92/11.75 ($true != $true) | ($false = ordere236663937imp_le($o)) | (~spl72_28 | spl72_575)),
% 78.92/11.75 inference(superposition,[],[f43422,f2021])).
% 78.92/11.75 thf(f43422,plain,(
% 78.92/11.75 ($true != ordere236663937imp_le($o)) | spl72_575),
% 78.92/11.75 inference(avatar_component_clause,[],[f43420])).
% 78.92/11.75 thf(f43436,plain,(
% 78.92/11.75 spl72_578 | ~spl72_28 | ~spl72_174),
% 78.92/11.75 inference(avatar_split_clause,[],[f3983,f3925,f2020,f43434])).
% 78.92/11.75 thf(f43434,plain,(
% 78.92/11.75 spl72_578 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X4),X2)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_578])])).
% 78.92/11.75 thf(f3983,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X4),X2))))) ) | (~spl72_28 | ~spl72_174)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3982])).
% 78.92/11.75 thf(f3982,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true != $true) | ($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X4),X2))))) ) | (~spl72_28 | ~spl72_174)),
% 78.92/11.75 inference(superposition,[],[f3926,f2021])).
% 78.92/11.75 thf(f43432,plain,(
% 78.92/11.75 spl72_577 | ~spl72_28 | ~spl72_173),
% 78.92/11.75 inference(avatar_split_clause,[],[f3955,f3921,f2020,f43430])).
% 78.92/11.75 thf(f43430,plain,(
% 78.92/11.75 spl72_577 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X4),X2)))))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_577])])).
% 78.92/11.75 thf(f3955,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X4),X2))))) ) | (~spl72_28 | ~spl72_173)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f3954])).
% 78.92/11.75 thf(f3954,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1,X4 : X1 > $o,X5 : X1] : (($true != $true) | ($true = vAPP(X1,$o,X4,X3)) | ($true = vAPP(X1,$o,X4,X5)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X3)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X4),X2))))) ) | (~spl72_28 | ~spl72_173)),
% 78.92/11.75 inference(superposition,[],[f3922,f2021])).
% 78.92/11.75 thf(f43426,plain,(
% 78.92/11.75 ~spl72_575 | spl72_576 | ~spl72_28 | ~spl72_164),
% 78.92/11.75 inference(avatar_split_clause,[],[f3825,f3761,f2020,f43424,f43420])).
% 78.92/11.75 thf(f43424,plain,(
% 78.92/11.75 spl72_576 <=> ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1))) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),X2)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_576])])).
% 78.92/11.75 thf(f3825,plain,(
% 78.92/11.75 ( ! [X2 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),$true),vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X2),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X0),X2)) | ($true != ordere236663937imp_le($o)) | ($false = vAPP($o,$o,vAPP($o,sTfun($o,$o),plus_plus($o),X0),X1))) ) | (~spl72_28 | ~spl72_164)),
% 78.92/11.75 inference(superposition,[],[f3762,f2021])).
% 78.92/11.75 thf(f43303,plain,(
% 78.92/11.75 spl72_574 | ~spl72_21 | ~spl72_50 | ~spl72_198),
% 78.92/11.75 inference(avatar_split_clause,[],[f4334,f4274,f2246,f1989,f43301])).
% 78.92/11.75 thf(f43301,plain,(
% 78.92/11.75 spl72_574 <=> ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK32(nat,X1),X2)),vAPP(sTfun(nat,X1),nat,sK33(nat,X1),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_574])])).
% 78.92/11.75 thf(f4334,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK32(nat,X1),X2)),vAPP(sTfun(nat,X1),nat,sK33(nat,X1),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1))) ) | (~spl72_21 | ~spl72_50 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4333])).
% 78.92/11.75 thf(f4333,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK32(nat,X1),X2)),vAPP(sTfun(nat,X1),nat,sK33(nat,X1),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1))) ) | (~spl72_21 | ~spl72_50 | ~spl72_198)),
% 78.92/11.75 inference(forward_demodulation,[],[f4332,f1991])).
% 78.92/11.75 thf(f4332,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK32(nat,X1),X2)),vAPP(sTfun(nat,X1),nat,sK33(nat,X1),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | (ord(nat) != $true) | ($true != ord(X1))) ) | (~spl72_50 | ~spl72_198)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4317])).
% 78.92/11.75 thf(f4317,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK32(nat,X1),X2)),vAPP(sTfun(nat,X1),nat,sK33(nat,X1),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | (ord(nat) != $true) | ($true != ord(X1))) ) | (~spl72_50 | ~spl72_198)),
% 78.92/11.75 inference(superposition,[],[f4275,f2247])).
% 78.92/11.75 thf(f43299,plain,(
% 78.92/11.75 spl72_573 | ~spl72_21 | ~spl72_50 | ~spl72_195),
% 78.92/11.75 inference(avatar_split_clause,[],[f4300,f4261,f2246,f1989,f43297])).
% 78.92/11.75 thf(f43297,plain,(
% 78.92/11.75 spl72_573 <=> ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK28(X1,nat),X2)),vAPP(sTfun(nat,X1),nat,sK29(X1,nat),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1)))),
% 78.92/11.75 introduced(avatar_definition,[new_symbols(naming,[spl72_573])])).
% 78.92/11.75 thf(f4300,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK28(X1,nat),X2)),vAPP(sTfun(nat,X1),nat,sK29(X1,nat),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1))) ) | (~spl72_21 | ~spl72_50 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4299])).
% 78.92/11.75 thf(f4299,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK28(X1,nat),X2)),vAPP(sTfun(nat,X1),nat,sK29(X1,nat),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1))) ) | (~spl72_21 | ~spl72_50 | ~spl72_195)),
% 78.92/11.75 inference(forward_demodulation,[],[f4298,f1991])).
% 78.92/11.75 thf(f4298,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK28(X1,nat),X2)),vAPP(sTfun(nat,X1),nat,sK29(X1,nat),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1)) | (ord(nat) != $true)) ) | (~spl72_50 | ~spl72_195)),
% 78.92/11.75 inference(trivial_inequality_removal,[],[f4283])).
% 78.92/11.75 thf(f4283,plain,(
% 78.92/11.75 ( ! [X1 : $tType,X2 : nat > X1,X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,X1),nat,sK28(X1,nat),X2)),vAPP(sTfun(nat,X1),nat,sK29(X1,nat),X2))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(nat,X1,X2,X0)),vAPP(nat,X1,X2,X0))) | ($true != ord(X1)) | (ord(nat) != $true)) ) | (~spl72_50 | ~spl72_195)),
% 78.92/11.76 inference(superposition,[],[f4262,f2247])).
% 78.92/11.76 thf(f43295,plain,(
% 78.92/11.76 spl72_572 | ~spl72_28 | ~spl72_158),
% 78.92/11.76 inference(avatar_split_clause,[],[f3687,f3671,f2020,f43293])).
% 78.92/11.76 thf(f43293,plain,(
% 78.92/11.76 spl72_572 <=> ! [X0 : $o > nat,X3 : $o,X2 : $o,X1 : $o > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP($o,nat,X0,X2)),vAPP($o,nat,X0,$true))) | ($true = vAPP($o,$o,X1,X2)) | ($true = vAPP($o,$o,X1,X3)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_572])])).
% 78.92/11.76 thf(f3671,plain,(
% 78.92/11.76 spl72_158 <=> ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X5 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_158])])).
% 78.92/11.76 thf(f3687,plain,(
% 78.92/11.76 ( ! [X2 : $o,X3 : $o,X0 : $o > nat,X1 : $o > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP($o,nat,X0,X2)),vAPP($o,nat,X0,$true))) | ($true = vAPP($o,$o,X1,X2)) | ($true = vAPP($o,$o,X1,X3)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),X1))) ) | (~spl72_28 | ~spl72_158)),
% 78.92/11.76 inference(superposition,[],[f3672,f2021])).
% 78.92/11.76 thf(f3672,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o,X5 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))) | ($true = vAPP(X0,$o,X1,X5)) | ($true = vAPP(X0,$o,X1,X3))) ) | ~spl72_158),
% 78.92/11.76 inference(avatar_component_clause,[],[f3671])).
% 78.92/11.76 thf(f43291,plain,(
% 78.92/11.76 spl72_571 | ~spl72_48 | ~spl72_403),
% 78.92/11.76 inference(avatar_split_clause,[],[f26967,f23853,f2214,f43289])).
% 78.92/11.76 thf(f43289,plain,(
% 78.92/11.76 spl72_571 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_571])])).
% 78.92/11.76 thf(f23853,plain,(
% 78.92/11.76 spl72_403 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,sTfun(X0,$o))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_403])])).
% 78.92/11.76 thf(f26967,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl72_48 | ~spl72_403)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f26950])).
% 78.92/11.76 thf(f26950,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl72_48 | ~spl72_403)),
% 78.92/11.76 inference(superposition,[],[f2215,f23854])).
% 78.92/11.76 thf(f23854,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,$o))))) ) | ~spl72_403),
% 78.92/11.76 inference(avatar_component_clause,[],[f23853])).
% 78.92/11.76 thf(f42542,plain,(
% 78.92/11.76 spl72_570 | ~spl72_116 | ~spl72_191),
% 78.92/11.76 inference(avatar_split_clause,[],[f4228,f4164,f2914,f42540])).
% 78.92/11.76 thf(f42540,plain,(
% 78.92/11.76 spl72_570 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_570])])).
% 78.92/11.76 thf(f4228,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))) ) | (~spl72_116 | ~spl72_191)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f4169])).
% 78.92/11.76 thf(f4169,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))) ) | (~spl72_116 | ~spl72_191)),
% 78.92/11.76 inference(superposition,[],[f2915,f4165])).
% 78.92/11.76 thf(f42538,plain,(
% 78.92/11.76 spl72_569 | ~spl72_28 | ~spl72_172),
% 78.92/11.76 inference(avatar_split_clause,[],[f3900,f3877,f2020,f42536])).
% 78.92/11.76 thf(f42536,plain,(
% 78.92/11.76 spl72_569 <=> ! [X0 : nat > $o,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X3)) | ($false = vAPP(nat,$o,X0,X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_569])])).
% 78.92/11.76 thf(f3877,plain,(
% 78.92/11.76 spl72_172 <=> ! [X4 : nat,X0 : nat > $o,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_172])])).
% 78.92/11.76 thf(f3900,plain,(
% 78.92/11.76 ( ! [X2 : nat,X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X3)) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl72_28 | ~spl72_172)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3899])).
% 78.92/11.76 thf(f3899,plain,(
% 78.92/11.76 ( ! [X2 : nat,X3 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X3)) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl72_28 | ~spl72_172)),
% 78.92/11.76 inference(superposition,[],[f3878,f2021])).
% 78.92/11.76 thf(f3878,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat > $o,X1 : nat,X4 : nat] : (($true != vAPP(nat,$o,X0,X4)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X1))) ) | ~spl72_172),
% 78.92/11.76 inference(avatar_component_clause,[],[f3877])).
% 78.92/11.76 thf(f42534,plain,(
% 78.92/11.76 spl72_568 | ~spl72_28 | ~spl72_157),
% 78.92/11.76 inference(avatar_split_clause,[],[f3665,f3653,f2020,f42532])).
% 78.92/11.76 thf(f42532,plain,(
% 78.92/11.76 spl72_568 <=> ! [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),sK65($o,X0),X2),X1))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK65($o,X0),X2),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_568])])).
% 78.92/11.76 thf(f3653,plain,(
% 78.92/11.76 spl72_157 <=> ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X2 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_157])])).
% 78.92/11.76 thf(f3665,plain,(
% 78.92/11.76 ( ! [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),sK65($o,X0),X2),X1))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK65($o,X0),X2),X1)))) ) | (~spl72_28 | ~spl72_157)),
% 78.92/11.76 inference(superposition,[],[f3654,f2021])).
% 78.92/11.76 thf(f3654,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2))) | (X2 = X3)) ) | ~spl72_157),
% 78.92/11.76 inference(avatar_component_clause,[],[f3653])).
% 78.92/11.76 thf(f42530,plain,(
% 78.92/11.76 spl72_567 | ~spl72_28 | ~spl72_157),
% 78.92/11.76 inference(avatar_split_clause,[],[f3658,f3653,f2020,f42528])).
% 78.92/11.76 thf(f42528,plain,(
% 78.92/11.76 spl72_567 <=> ! [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),sK65($o,X0),X1),X2))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK65($o,X0),X1),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_567])])).
% 78.92/11.76 thf(f3658,plain,(
% 78.92/11.76 ( ! [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),sK65($o,X0),X1),X2))) | (X1 = X2) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK65($o,X0),X1),X2)))) ) | (~spl72_28 | ~spl72_157)),
% 78.92/11.76 inference(superposition,[],[f3654,f2021])).
% 78.92/11.76 thf(f42526,plain,(
% 78.92/11.76 spl72_566 | ~spl72_48 | ~spl72_397),
% 78.92/11.76 inference(avatar_split_clause,[],[f26385,f21189,f2214,f42524])).
% 78.92/11.76 thf(f42524,plain,(
% 78.92/11.76 spl72_566 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_566])])).
% 78.92/11.76 thf(f21189,plain,(
% 78.92/11.76 spl72_397 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,sTfun(X0,nat))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_397])])).
% 78.92/11.76 thf(f26385,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl72_48 | ~spl72_397)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f26368])).
% 78.92/11.76 thf(f26368,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl72_48 | ~spl72_397)),
% 78.92/11.76 inference(superposition,[],[f2215,f21190])).
% 78.92/11.76 thf(f21190,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,nat))))) ) | ~spl72_397),
% 78.92/11.76 inference(avatar_component_clause,[],[f21189])).
% 78.92/11.76 thf(f42522,plain,(
% 78.92/11.76 spl72_565 | ~spl72_104),
% 78.92/11.76 inference(avatar_split_clause,[],[f2831,f2779,f42520])).
% 78.92/11.76 thf(f42520,plain,(
% 78.92/11.76 spl72_565 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X0] : (($true != wellorder(X1)) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK45(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_565])])).
% 78.92/11.76 thf(f2779,plain,(
% 78.92/11.76 spl72_104 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > $o,X2 : X1 > X0] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2))) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_104])])).
% 78.92/11.76 thf(f2831,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1] : (($true != wellorder(X1)) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK45(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2)) ) | ~spl72_104),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2780])).
% 78.92/11.76 thf(f2780,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2))) | ($true = vAPP(X1,$o,X3,X4)) | (wellorder(X0) != $true)) ) | ~spl72_104),
% 78.92/11.76 inference(avatar_component_clause,[],[f2779])).
% 78.92/11.76 thf(f42518,plain,(
% 78.92/11.76 spl72_564 | ~spl72_103),
% 78.92/11.76 inference(avatar_split_clause,[],[f2803,f2775,f42516])).
% 78.92/11.76 thf(f42516,plain,(
% 78.92/11.76 spl72_564 <=> ! [X1 : $tType,X0 : $tType,X3 : X0 > X1,X2 : X0] : (($true != wellorder(X1)) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK44(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_564])])).
% 78.92/11.76 thf(f2775,plain,(
% 78.92/11.76 spl72_103 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X1 > $o,X2 : X1 > X0] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2))) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_103])])).
% 78.92/11.76 thf(f2803,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1] : (($true != wellorder(X1)) | (vAPP(sTfun(X0,X1),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X1),X0),sK44(X1,X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))),X3) = X2)) ) | ~spl72_103),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2776])).
% 78.92/11.76 thf(f2776,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2))) | ($true = vAPP(X1,$o,X3,X4)) | (wellorder(X0) != $true)) ) | ~spl72_103),
% 78.92/11.76 inference(avatar_component_clause,[],[f2775])).
% 78.92/11.76 thf(f42457,plain,(
% 78.92/11.76 spl72_563 | ~spl72_46 | ~spl72_389),
% 78.92/11.76 inference(avatar_split_clause,[],[f26278,f20683,f2205,f42455])).
% 78.92/11.76 thf(f42455,plain,(
% 78.92/11.76 spl72_563 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_563])])).
% 78.92/11.76 thf(f20683,plain,(
% 78.92/11.76 spl72_389 <=> ! [X1 : $tType,X0 : $tType] : ($true = ord(sTfun(X1,sTfun(X0,$o))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_389])])).
% 78.92/11.76 thf(f26278,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl72_46 | ~spl72_389)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f26277])).
% 78.92/11.76 thf(f26277,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl72_46 | ~spl72_389)),
% 78.92/11.76 inference(superposition,[],[f2206,f20684])).
% 78.92/11.76 thf(f20684,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,$o))))) ) | ~spl72_389),
% 78.92/11.76 inference(avatar_component_clause,[],[f20683])).
% 78.92/11.76 thf(f42413,plain,(
% 78.92/11.76 spl72_562 | ~spl72_172),
% 78.92/11.76 inference(avatar_split_clause,[],[f3919,f3877,f42411])).
% 78.92/11.76 thf(f42411,plain,(
% 78.92/11.76 spl72_562 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)))) | (X1 != X2) | (vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_562])])).
% 78.92/11.76 thf(f3919,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)))) | (X1 != X2) | (vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1)) ) | ~spl72_172),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f3880])).
% 78.92/11.76 thf(f3880,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),X2)) | (vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1)) ) | ~spl72_172),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f3878])).
% 78.92/11.76 thf(f42409,plain,(
% 78.92/11.76 spl72_561 | ~spl72_28 | ~spl72_170),
% 78.92/11.76 inference(avatar_split_clause,[],[f3869,f3786,f2020,f42407])).
% 78.92/11.76 thf(f42407,plain,(
% 78.92/11.76 spl72_561 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_561])])).
% 78.92/11.76 thf(f3786,plain,(
% 78.92/11.76 spl72_170 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_170])])).
% 78.92/11.76 thf(f3869,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_170)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3868])).
% 78.92/11.76 thf(f3868,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_170)),
% 78.92/11.76 inference(superposition,[],[f3787,f2021])).
% 78.92/11.76 thf(f3787,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true)) ) | ~spl72_170),
% 78.92/11.76 inference(avatar_component_clause,[],[f3786])).
% 78.92/11.76 thf(f42405,plain,(
% 78.92/11.76 spl72_560 | ~spl72_28 | ~spl72_169),
% 78.92/11.76 inference(avatar_split_clause,[],[f3863,f3782,f2020,f42403])).
% 78.92/11.76 thf(f42403,plain,(
% 78.92/11.76 spl72_560 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_560])])).
% 78.92/11.76 thf(f3863,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_169)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3862])).
% 78.92/11.76 thf(f3862,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere223160158up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_169)),
% 78.92/11.76 inference(superposition,[],[f3783,f2021])).
% 78.92/11.76 thf(f42401,plain,(
% 78.92/11.76 spl72_559 | ~spl72_28 | ~spl72_163),
% 78.92/11.76 inference(avatar_split_clause,[],[f3818,f3757,f2020,f42399])).
% 78.92/11.76 thf(f42399,plain,(
% 78.92/11.76 spl72_559 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_559])])).
% 78.92/11.76 thf(f3757,plain,(
% 78.92/11.76 spl72_163 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_163])])).
% 78.92/11.76 thf(f3818,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_163)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3817])).
% 78.92/11.76 thf(f3817,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_163)),
% 78.92/11.76 inference(superposition,[],[f3758,f2021])).
% 78.92/11.76 thf(f3758,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true)) ) | ~spl72_163),
% 78.92/11.76 inference(avatar_component_clause,[],[f3757])).
% 78.92/11.76 thf(f42397,plain,(
% 78.92/11.76 spl72_558 | ~spl72_28 | ~spl72_162),
% 78.92/11.76 inference(avatar_split_clause,[],[f3796,f3753,f2020,f42395])).
% 78.92/11.76 thf(f42395,plain,(
% 78.92/11.76 spl72_558 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_558])])).
% 78.92/11.76 thf(f3796,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_162)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3795])).
% 78.92/11.76 thf(f3795,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere779506340up_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_162)),
% 78.92/11.76 inference(superposition,[],[f3754,f2021])).
% 78.92/11.76 thf(f42393,plain,(
% 78.92/11.76 spl72_557 | ~spl72_46 | ~spl72_385),
% 78.92/11.76 inference(avatar_split_clause,[],[f26088,f19830,f2205,f42391])).
% 78.92/11.76 thf(f42391,plain,(
% 78.92/11.76 spl72_557 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_557])])).
% 78.92/11.76 thf(f19830,plain,(
% 78.92/11.76 spl72_385 <=> ! [X1 : $tType,X0 : $tType] : ($true = ord(sTfun(X1,sTfun(X0,nat))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_385])])).
% 78.92/11.76 thf(f26088,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl72_46 | ~spl72_385)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f26087])).
% 78.92/11.76 thf(f26087,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl72_46 | ~spl72_385)),
% 78.92/11.76 inference(superposition,[],[f2206,f19831])).
% 78.92/11.76 thf(f19831,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,nat))))) ) | ~spl72_385),
% 78.92/11.76 inference(avatar_component_clause,[],[f19830])).
% 78.92/11.76 thf(f42225,plain,(
% 78.92/11.76 spl72_344 | spl72_556 | ~spl72_159),
% 78.92/11.76 inference(avatar_split_clause,[],[f3749,f3675,f42223,f11811])).
% 78.92/11.76 thf(f11811,plain,(
% 78.92/11.76 spl72_344 <=> ! [X0 : $o] : ($false = X0)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_344])])).
% 78.92/11.76 thf(f42223,plain,(
% 78.92/11.76 spl72_556 <=> ! [X2 : $o > nat,X0 : $o,X1 : $o] : (($false = X1) | ($false = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X2,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X2),vAPP($o,sTfun($o,$o),vAND,X0)))),vAPP($o,nat,X2,X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_556])])).
% 78.92/11.76 thf(f3749,plain,(
% 78.92/11.76 ( ! [X2 : $o > nat,X3 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X2,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X2),vAPP($o,sTfun($o,$o),vAND,X0)))),vAPP($o,nat,X2,X1))) | ($false = X3) | ($false = X0)) ) | ~spl72_159),
% 78.92/11.76 inference(duplicate_literal_removal,[],[f3748])).
% 78.92/11.76 thf(f3748,plain,(
% 78.92/11.76 ( ! [X2 : $o > nat,X3 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X2,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X2),vAPP($o,sTfun($o,$o),vAND,X0)))),vAPP($o,nat,X2,X1))) | ($false = X3) | ($false = X0) | ($false = X0)) ) | ~spl72_159),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f3747])).
% 78.92/11.76 thf(f3747,plain,(
% 78.92/11.76 ( ! [X2 : $o > nat,X3 : $o,X0 : $o,X1 : $o] : (($false = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X2,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X2),vAPP($o,sTfun($o,$o),vAND,X0)))),vAPP($o,nat,X2,X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X0),X3)) | ($false = X0)) ) | ~spl72_159),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f3692])).
% 78.92/11.76 thf(f3692,plain,(
% 78.92/11.76 ( ! [X2 : $o > nat,X3 : $o,X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X2,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X2),vAPP($o,sTfun($o,$o),vAND,X0)))),vAPP($o,nat,X2,X1))) | ($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X0),X3))) ) | ~spl72_159),
% 78.92/11.76 inference(primitive_instantiation,[],[f3676])).
% 78.92/11.76 thf(f42221,plain,(
% 78.92/11.76 spl72_555),
% 78.92/11.76 inference(avatar_split_clause,[],[f1863,f42219])).
% 78.92/11.76 thf(f42219,plain,(
% 78.92/11.76 spl72_555 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_555])])).
% 78.92/11.76 thf(f1863,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1382])).
% 78.92/11.76 thf(f1382,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f957])).
% 78.92/11.76 thf(f957,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f370])).
% 78.92/11.76 thf(f370,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))))),
% 78.92/11.76 inference(fool_elimination,[],[f369])).
% 78.92/11.76 thf(f369,plain,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))))),
% 78.92/11.76 inference(rectify,[],[f6])).
% 78.92/11.76 thf(f6,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X6 : X0,X5 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5))))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__less__cancel__right)).
% 78.92/11.76 thf(f42217,plain,(
% 78.92/11.76 spl72_554),
% 78.92/11.76 inference(avatar_split_clause,[],[f1862,f42215])).
% 78.92/11.76 thf(f42215,plain,(
% 78.92/11.76 spl72_554 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_554])])).
% 78.92/11.76 thf(f1862,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1382])).
% 78.92/11.76 thf(f42213,plain,(
% 78.92/11.76 spl72_553),
% 78.92/11.76 inference(avatar_split_clause,[],[f1861,f42211])).
% 78.92/11.76 thf(f42211,plain,(
% 78.92/11.76 spl72_553 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_553])])).
% 78.92/11.76 thf(f1861,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1383])).
% 78.92/11.76 thf(f1383,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f958])).
% 78.92/11.76 thf(f958,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f372])).
% 78.92/11.76 thf(f372,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))))),
% 78.92/11.76 inference(fool_elimination,[],[f371])).
% 78.92/11.76 thf(f371,plain,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))))),
% 78.92/11.76 inference(rectify,[],[f32])).
% 78.92/11.76 thf(f32,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X5 : X0,X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X7))))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_add__le__cancel__left)).
% 78.92/11.76 thf(f42209,plain,(
% 78.92/11.76 spl72_552),
% 78.92/11.76 inference(avatar_split_clause,[],[f1860,f42207])).
% 78.92/11.76 thf(f42207,plain,(
% 78.92/11.76 spl72_552 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_552])])).
% 78.92/11.76 thf(f1860,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1383])).
% 78.92/11.76 thf(f42205,plain,(
% 78.92/11.76 spl72_551),
% 78.92/11.76 inference(avatar_split_clause,[],[f1859,f42203])).
% 78.92/11.76 thf(f42203,plain,(
% 78.92/11.76 spl72_551 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_551])])).
% 78.92/11.76 thf(f1859,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1384])).
% 78.92/11.76 thf(f1384,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f959])).
% 78.92/11.76 thf(f959,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f374])).
% 78.92/11.76 thf(f374,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)))),
% 78.92/11.76 inference(fool_elimination,[],[f373])).
% 78.92/11.76 thf(f373,plain,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)))),
% 78.92/11.76 inference(rectify,[],[f5])).
% 78.92/11.76 thf(f5,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X5 : X0,X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X7)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7)))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_add__less__cancel__left)).
% 78.92/11.76 thf(f42201,plain,(
% 78.92/11.76 spl72_550),
% 78.92/11.76 inference(avatar_split_clause,[],[f1858,f42199])).
% 78.92/11.76 thf(f42199,plain,(
% 78.92/11.76 spl72_550 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_550])])).
% 78.92/11.76 thf(f1858,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1384])).
% 78.92/11.76 thf(f42197,plain,(
% 78.92/11.76 spl72_549),
% 78.92/11.76 inference(avatar_split_clause,[],[f1857,f42195])).
% 78.92/11.76 thf(f42195,plain,(
% 78.92/11.76 spl72_549 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_549])])).
% 78.92/11.76 thf(f1857,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1385])).
% 78.92/11.76 thf(f1385,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f960])).
% 78.92/11.76 thf(f960,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | (ordere236663937imp_le(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f376])).
% 78.92/11.76 thf(f376,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 78.92/11.76 inference(fool_elimination,[],[f375])).
% 78.92/11.76 thf(f375,plain,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 78.92/11.76 inference(rectify,[],[f31])).
% 78.92/11.76 thf(f31,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X6 : X0,X5 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_add__le__cancel__right)).
% 78.92/11.76 thf(f42193,plain,(
% 78.92/11.76 spl72_548),
% 78.92/11.76 inference(avatar_split_clause,[],[f1856,f42191])).
% 78.92/11.76 thf(f42191,plain,(
% 78.92/11.76 spl72_548 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_548])])).
% 78.92/11.76 thf(f1856,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1385])).
% 78.92/11.76 thf(f42189,plain,(
% 78.92/11.76 spl72_547 | ~spl72_45 | ~spl72_377),
% 78.92/11.76 inference(avatar_split_clause,[],[f24608,f19673,f2201,f42187])).
% 78.92/11.76 thf(f42187,plain,(
% 78.92/11.76 spl72_547 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_547])])).
% 78.92/11.76 thf(f19673,plain,(
% 78.92/11.76 spl72_377 <=> ! [X1 : $tType,X0 : $tType] : ($true = preorder(sTfun(X1,sTfun(X0,$o))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_377])])).
% 78.92/11.76 thf(f24608,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl72_45 | ~spl72_377)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f24607])).
% 78.92/11.76 thf(f24607,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,$o)))))) ) | (~spl72_45 | ~spl72_377)),
% 78.92/11.76 inference(superposition,[],[f2202,f19674])).
% 78.92/11.76 thf(f19674,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,$o))))) ) | ~spl72_377),
% 78.92/11.76 inference(avatar_component_clause,[],[f19673])).
% 78.92/11.76 thf(f40820,plain,(
% 78.92/11.76 spl72_546 | ~spl72_256),
% 78.92/11.76 inference(avatar_split_clause,[],[f6199,f6122,f40818])).
% 78.92/11.76 thf(f40818,plain,(
% 78.92/11.76 spl72_546 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_546])])).
% 78.92/11.76 thf(f6122,plain,(
% 78.92/11.76 spl72_256 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_256])])).
% 78.92/11.76 thf(f6199,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f6198])).
% 78.92/11.76 thf(f6198,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f6197])).
% 78.92/11.76 thf(f6197,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f6196])).
% 78.92/11.76 thf(f6196,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f6195])).
% 78.92/11.76 thf(f6195,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(boolean_simplification,[],[f6186])).
% 78.92/11.76 thf(f6186,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(primitive_instantiation,[],[f6123])).
% 78.92/11.76 thf(f6123,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true)) ) | ~spl72_256),
% 78.92/11.76 inference(avatar_component_clause,[],[f6122])).
% 78.92/11.76 thf(f40816,plain,(
% 78.92/11.76 spl72_545 | ~spl72_255),
% 78.92/11.76 inference(avatar_split_clause,[],[f6141,f6118,f40814])).
% 78.92/11.76 thf(f40814,plain,(
% 78.92/11.76 spl72_545 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_545])])).
% 78.92/11.76 thf(f6118,plain,(
% 78.92/11.76 spl72_255 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_255])])).
% 78.92/11.76 thf(f6141,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f6140])).
% 78.92/11.76 thf(f6140,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f6139])).
% 78.92/11.76 thf(f6139,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f6138])).
% 78.92/11.76 thf(f6138,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f6137])).
% 78.92/11.76 thf(f6137,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(boolean_simplification,[],[f6128])).
% 78.92/11.76 thf(f6128,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(primitive_instantiation,[],[f6119])).
% 78.92/11.76 thf(f6119,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (linorder(X0) != $true)) ) | ~spl72_255),
% 78.92/11.76 inference(avatar_component_clause,[],[f6118])).
% 78.92/11.76 thf(f40812,plain,(
% 78.92/11.76 spl72_544 | ~spl72_205),
% 78.92/11.76 inference(avatar_split_clause,[],[f4490,f4417,f40810])).
% 78.92/11.76 thf(f40810,plain,(
% 78.92/11.76 spl72_544 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_544])])).
% 78.92/11.76 thf(f4490,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true)) ) | ~spl72_205),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f4489])).
% 78.92/11.76 thf(f4489,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_205),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f4488])).
% 78.92/11.76 thf(f4488,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_205),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f4479])).
% 78.92/11.76 thf(f4479,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_205),
% 78.92/11.76 inference(primitive_instantiation,[],[f4418])).
% 78.92/11.76 thf(f40808,plain,(
% 78.92/11.76 spl72_543 | ~spl72_204),
% 78.92/11.76 inference(avatar_split_clause,[],[f4438,f4413,f40806])).
% 78.92/11.76 thf(f40806,plain,(
% 78.92/11.76 spl72_543 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_543])])).
% 78.92/11.76 thf(f4438,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | (X1 = X2) | (linorder(X0) != $true)) ) | ~spl72_204),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f4437])).
% 78.92/11.76 thf(f4437,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | (vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0)) = vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_204),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f4436])).
% 78.92/11.76 thf(f4436,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0)) != vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_204),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f4427])).
% 78.92/11.76 thf(f4427,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),vEQ(X0))),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),vEQ(X0)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true)) ) | ~spl72_204),
% 78.92/11.76 inference(primitive_instantiation,[],[f4414])).
% 78.92/11.76 thf(f40804,plain,(
% 78.92/11.76 spl72_542 | ~spl72_45 | ~spl72_371),
% 78.92/11.76 inference(avatar_split_clause,[],[f23938,f19221,f2201,f40802])).
% 78.92/11.76 thf(f40802,plain,(
% 78.92/11.76 spl72_542 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType] : ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_542])])).
% 78.92/11.76 thf(f19221,plain,(
% 78.92/11.76 spl72_371 <=> ! [X1 : $tType,X0 : $tType] : ($true = preorder(sTfun(X1,sTfun(X0,nat))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_371])])).
% 78.92/11.76 thf(f23938,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl72_45 | ~spl72_371)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f23937])).
% 78.92/11.76 thf(f23937,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X2,sTfun(X0,sTfun(X1,nat)))))) ) | (~spl72_45 | ~spl72_371)),
% 78.92/11.76 inference(superposition,[],[f2202,f19222])).
% 78.92/11.76 thf(f19222,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,nat))))) ) | ~spl72_371),
% 78.92/11.76 inference(avatar_component_clause,[],[f19221])).
% 78.92/11.76 thf(f40800,plain,(
% 78.92/11.76 spl72_541 | ~spl72_28 | ~spl72_159),
% 78.92/11.76 inference(avatar_split_clause,[],[f3713,f3675,f2020,f40798])).
% 78.92/11.76 thf(f40798,plain,(
% 78.92/11.76 spl72_541 <=> ! [X0 : $tType,X4 : X0,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X2))) | ($true != vAPP(X0,$o,X1,X4)) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_541])])).
% 78.92/11.76 thf(f3713,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X2))) | ($true != vAPP(X0,$o,X1,X4)) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_159)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3712])).
% 78.92/11.76 thf(f3712,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : X0] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X2))) | ($true != vAPP(X0,$o,X1,X4)) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_159)),
% 78.92/11.76 inference(superposition,[],[f3676,f2021])).
% 78.92/11.76 thf(f40796,plain,(
% 78.92/11.76 spl72_540 | ~spl72_28 | ~spl72_158),
% 78.92/11.76 inference(avatar_split_clause,[],[f3689,f3671,f2020,f40794])).
% 78.92/11.76 thf(f40794,plain,(
% 78.92/11.76 spl72_540 <=> ! [X0 : $tType,X4 : X0,X3 : X0 > $o,X2 : X0,X1 : X0 > nat] : (($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X1),X3)))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_540])])).
% 78.92/11.76 thf(f3689,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > nat,X4 : X0] : (($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X1),X3))))) ) | (~spl72_28 | ~spl72_158)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3688])).
% 78.92/11.76 thf(f3688,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > nat,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X3,X2)) | ($true = vAPP(X0,$o,X3,X4)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X1,X2)),vAPP(X0,nat,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X1),X3))))) ) | (~spl72_28 | ~spl72_158)),
% 78.92/11.76 inference(superposition,[],[f3672,f2021])).
% 78.92/11.76 thf(f40776,plain,(
% 78.92/11.76 ~spl72_337 | spl72_539 | ~spl72_28 | ~spl72_147),
% 78.92/11.76 inference(avatar_split_clause,[],[f13296,f3367,f2020,f40774,f7888])).
% 78.92/11.76 thf(f40774,plain,(
% 78.92/11.76 spl72_539 <=> ! [X2 : $o,X0 : $o > $o,X1 : $o > $o] : (($true != vAPP($o,$o,X0,$true)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),X0),X1)) | ($true != vAPP($o,$o,X1,X2)) | ($true = vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,ord_Least($o),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_539])])).
% 78.92/11.76 thf(f13296,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o > $o,X1 : $o > $o] : (($true != vAPP($o,$o,X0,$true)) | ($true = vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,ord_Least($o),X1))) | ($true != vAPP($o,$o,X1,X2)) | ($true != wellorder($o)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),X0),X1))) ) | (~spl72_28 | ~spl72_147)),
% 78.92/11.76 inference(superposition,[],[f3368,f2021])).
% 78.92/11.76 thf(f40772,plain,(
% 78.92/11.76 ~spl72_337 | spl72_538 | ~spl72_28 | ~spl72_145),
% 78.92/11.76 inference(avatar_split_clause,[],[f13213,f3359,f2020,f40770,f7888])).
% 78.92/11.76 thf(f40770,plain,(
% 78.92/11.76 spl72_538 <=> ! [X2 : $o,X0 : $o > $o,X1 : $o > $o] : (($true != vAPP($o,$o,X0,$true)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),X0),X1)) | ($true != vAPP($o,$o,X1,X2)) | ($true = vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,ord_Least($o),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_538])])).
% 78.92/11.76 thf(f13213,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o > $o,X1 : $o > $o] : (($true != vAPP($o,$o,X0,$true)) | ($true = vAPP($o,$o,X0,vAPP(sTfun($o,$o),$o,ord_Least($o),X1))) | ($true != vAPP($o,$o,X1,X2)) | ($true != wellorder($o)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),X0),X1))) ) | (~spl72_28 | ~spl72_145)),
% 78.92/11.76 inference(superposition,[],[f3360,f2021])).
% 78.92/11.76 thf(f40768,plain,(
% 78.92/11.76 spl72_537 | ~spl72_146),
% 78.92/11.76 inference(avatar_split_clause,[],[f3478,f3363,f40766])).
% 78.92/11.76 thf(f40766,plain,(
% 78.92/11.76 spl72_537 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)))) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_537])])).
% 78.92/11.76 thf(f3478,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)))) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2)) ) | ~spl72_146),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f3364])).
% 78.92/11.76 thf(f40764,plain,(
% 78.92/11.76 spl72_536 | ~spl72_144),
% 78.92/11.76 inference(avatar_split_clause,[],[f3370,f3355,f40762])).
% 78.92/11.76 thf(f40762,plain,(
% 78.92/11.76 spl72_536 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)))) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_536])])).
% 78.92/11.76 thf(f3370,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)))) | (wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2)) ) | ~spl72_144),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f3356])).
% 78.92/11.76 thf(f38659,plain,(
% 78.92/11.76 spl72_535 | ~spl72_28 | ~spl72_156),
% 78.92/11.76 inference(avatar_split_clause,[],[f3650,f3629,f2020,f38657])).
% 78.92/11.76 thf(f38657,plain,(
% 78.92/11.76 spl72_535 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_535])])).
% 78.92/11.76 thf(f3629,plain,(
% 78.92/11.76 spl72_156 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_156])])).
% 78.92/11.76 thf(f3650,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_156)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3649])).
% 78.92/11.76 thf(f3649,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_156)),
% 78.92/11.76 inference(superposition,[],[f3630,f2021])).
% 78.92/11.76 thf(f3630,plain,(
% 78.92/11.76 ( ! [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))) ) | ~spl72_156),
% 78.92/11.76 inference(avatar_component_clause,[],[f3629])).
% 78.92/11.76 thf(f38655,plain,(
% 78.92/11.76 spl72_534 | ~spl72_28 | ~spl72_154),
% 78.92/11.76 inference(avatar_split_clause,[],[f3646,f3620,f2020,f38653])).
% 78.92/11.76 thf(f38653,plain,(
% 78.92/11.76 spl72_534 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_534])])).
% 78.92/11.76 thf(f3620,plain,(
% 78.92/11.76 spl72_154 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_154])])).
% 78.92/11.76 thf(f3646,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_154)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3645])).
% 78.92/11.76 thf(f3645,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_154)),
% 78.92/11.76 inference(superposition,[],[f3621,f2021])).
% 78.92/11.76 thf(f3621,plain,(
% 78.92/11.76 ( ! [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)))) ) | ~spl72_154),
% 78.92/11.76 inference(avatar_component_clause,[],[f3620])).
% 78.92/11.76 thf(f38651,plain,(
% 78.92/11.76 spl72_533 | ~spl72_28 | ~spl72_153),
% 78.92/11.76 inference(avatar_split_clause,[],[f3642,f3616,f2020,f38649])).
% 78.92/11.76 thf(f38649,plain,(
% 78.92/11.76 spl72_533 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_533])])).
% 78.92/11.76 thf(f3616,plain,(
% 78.92/11.76 spl72_153 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_153])])).
% 78.92/11.76 thf(f3642,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_153)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3641])).
% 78.92/11.76 thf(f3641,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_153)),
% 78.92/11.76 inference(superposition,[],[f3617,f2021])).
% 78.92/11.76 thf(f3617,plain,(
% 78.92/11.76 ( ! [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))) ) | ~spl72_153),
% 78.92/11.76 inference(avatar_component_clause,[],[f3616])).
% 78.92/11.76 thf(f38647,plain,(
% 78.92/11.76 spl72_532 | ~spl72_28 | ~spl72_152),
% 78.92/11.76 inference(avatar_split_clause,[],[f3638,f3612,f2020,f38645])).
% 78.92/11.76 thf(f38645,plain,(
% 78.92/11.76 spl72_532 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_532])])).
% 78.92/11.76 thf(f3612,plain,(
% 78.92/11.76 spl72_152 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_152])])).
% 78.92/11.76 thf(f3638,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_152)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3637])).
% 78.92/11.76 thf(f3637,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_152)),
% 78.92/11.76 inference(superposition,[],[f3613,f2021])).
% 78.92/11.76 thf(f3613,plain,(
% 78.92/11.76 ( ! [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)))) ) | ~spl72_152),
% 78.92/11.76 inference(avatar_component_clause,[],[f3612])).
% 78.92/11.76 thf(f38643,plain,(
% 78.92/11.76 spl72_531 | ~spl72_28 | ~spl72_151),
% 78.92/11.76 inference(avatar_split_clause,[],[f3634,f3608,f2020,f38641])).
% 78.92/11.76 thf(f38641,plain,(
% 78.92/11.76 spl72_531 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_531])])).
% 78.92/11.76 thf(f3634,plain,(
% 78.92/11.76 ( ! [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)) ) | (~spl72_28 | ~spl72_151)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3633])).
% 78.92/11.76 thf(f3633,plain,(
% 78.92/11.76 ( ! [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) = $false)) ) | (~spl72_28 | ~spl72_151)),
% 78.92/11.76 inference(superposition,[],[f3609,f2021])).
% 78.92/11.76 thf(f38639,plain,(
% 78.92/11.76 spl72_530 | ~spl72_140),
% 78.92/11.76 inference(avatar_split_clause,[],[f3273,f3245,f38637])).
% 78.92/11.76 thf(f38637,plain,(
% 78.92/11.76 spl72_530 <=> ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))),X1)) | (vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_530])])).
% 78.92/11.76 thf(f3245,plain,(
% 78.92/11.76 spl72_140 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_140])])).
% 78.92/11.76 thf(f3273,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X1),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))),X1)) | (vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) = X0)) ) | ~spl72_140),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f3246])).
% 78.92/11.76 thf(f3246,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X1))) ) | ~spl72_140),
% 78.92/11.76 inference(avatar_component_clause,[],[f3245])).
% 78.92/11.76 thf(f36837,plain,(
% 78.92/11.76 spl72_529 | ~spl72_12 | ~spl72_74 | ~spl72_162),
% 78.92/11.76 inference(avatar_split_clause,[],[f3808,f3753,f2467,f1944,f36835])).
% 78.92/11.76 thf(f36835,plain,(
% 78.92/11.76 spl72_529 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_529])])).
% 78.92/11.76 thf(f3808,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_12 | ~spl72_74 | ~spl72_162)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3807])).
% 78.92/11.76 thf(f3807,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_12 | ~spl72_74 | ~spl72_162)),
% 78.92/11.76 inference(forward_demodulation,[],[f3799,f1946])).
% 78.92/11.76 thf(f3799,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | (ordere779506340up_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_162)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3792])).
% 78.92/11.76 thf(f3792,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | (ordere779506340up_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_162)),
% 78.92/11.76 inference(superposition,[],[f3754,f2468])).
% 78.92/11.76 thf(f36827,plain,(
% 78.92/11.76 spl72_528 | ~spl72_74 | ~spl72_150),
% 78.92/11.76 inference(avatar_split_clause,[],[f3603,f3586,f2467,f36825])).
% 78.92/11.76 thf(f36825,plain,(
% 78.92/11.76 spl72_528 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_528])])).
% 78.92/11.76 thf(f3603,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_150)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3596])).
% 78.92/11.76 thf(f3596,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_150)),
% 78.92/11.76 inference(superposition,[],[f3587,f2468])).
% 78.92/11.76 thf(f36823,plain,(
% 78.92/11.76 spl72_527 | ~spl72_28 | ~spl72_150),
% 78.92/11.76 inference(avatar_split_clause,[],[f3600,f3586,f2020,f36821])).
% 78.92/11.76 thf(f36821,plain,(
% 78.92/11.76 spl72_527 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_527])])).
% 78.92/11.76 thf(f3600,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_150)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3599])).
% 78.92/11.76 thf(f3599,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_150)),
% 78.92/11.76 inference(superposition,[],[f3587,f2021])).
% 78.92/11.76 thf(f36819,plain,(
% 78.92/11.76 spl72_526 | ~spl72_28 | ~spl72_149),
% 78.92/11.76 inference(avatar_split_clause,[],[f3591,f3582,f2020,f36817])).
% 78.92/11.76 thf(f36817,plain,(
% 78.92/11.76 spl72_526 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_526])])).
% 78.92/11.76 thf(f3591,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_149)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3590])).
% 78.92/11.76 thf(f3590,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_149)),
% 78.92/11.76 inference(superposition,[],[f3583,f2021])).
% 78.92/11.76 thf(f36815,plain,(
% 78.92/11.76 spl72_525 | ~spl72_80),
% 78.92/11.76 inference(avatar_split_clause,[],[f2545,f2518,f36813])).
% 78.92/11.76 thf(f36813,plain,(
% 78.92/11.76 spl72_525 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > nat] : (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))) = X2)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_525])])).
% 78.92/11.76 thf(f2518,plain,(
% 78.92/11.76 spl72_80 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_80])])).
% 78.92/11.76 thf(f2545,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > nat] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X1),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2))) = X2)) ) | ~spl72_80),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2519])).
% 78.92/11.76 thf(f2519,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1))) | ($true = vAPP(X0,$o,X1,X3))) ) | ~spl72_80),
% 78.92/11.76 inference(avatar_component_clause,[],[f2518])).
% 78.92/11.76 thf(f36811,plain,(
% 78.92/11.76 spl72_524),
% 78.92/11.76 inference(avatar_split_clause,[],[f1799,f36809])).
% 78.92/11.76 thf(f36809,plain,(
% 78.92/11.76 spl72_524 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(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))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_524])])).
% 78.92/11.76 thf(f1799,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(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))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1596])).
% 78.92/11.76 thf(f1596,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) )),
% 78.92/11.76 inference(cnf_transformation,[],[f918])).
% 78.92/11.76 thf(f918,plain,(
% 78.92/11.76 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))),
% 78.92/11.76 inference(rectify,[],[f4])).
% 78.92/11.76 thf(f4,axiom,(
% 78.92/11.76 ! [X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X4)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_nat__add__left__cancel__less)).
% 78.92/11.76 thf(f36807,plain,(
% 78.92/11.76 spl72_523),
% 78.92/11.76 inference(avatar_split_clause,[],[f1798,f36805])).
% 78.92/11.76 thf(f36805,plain,(
% 78.92/11.76 spl72_523 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(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))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_523])])).
% 78.92/11.76 thf(f1798,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(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))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1596])).
% 78.92/11.76 thf(f36803,plain,(
% 78.92/11.76 spl72_522),
% 78.92/11.76 inference(avatar_split_clause,[],[f1797,f36801])).
% 78.92/11.76 thf(f36801,plain,(
% 78.92/11.76 spl72_522 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_522])])).
% 78.92/11.76 thf(f1797,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1597])).
% 78.92/11.76 thf(f1597,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))) )),
% 78.92/11.76 inference(cnf_transformation,[],[f919])).
% 78.92/11.76 thf(f919,plain,(
% 78.92/11.76 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)))),
% 78.92/11.76 inference(rectify,[],[f33])).
% 78.92/11.76 thf(f33,axiom,(
% 78.92/11.76 ! [X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X3)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X4)) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_nat__add__left__cancel__le)).
% 78.92/11.76 thf(f36799,plain,(
% 78.92/11.76 spl72_521),
% 78.92/11.76 inference(avatar_split_clause,[],[f1796,f36797])).
% 78.92/11.76 thf(f36797,plain,(
% 78.92/11.76 spl72_521 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_521])])).
% 78.92/11.76 thf(f1796,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(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)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1597])).
% 78.92/11.76 thf(f36532,plain,(
% 78.92/11.76 spl72_520 | ~spl72_48 | ~spl72_313),
% 78.92/11.76 inference(avatar_split_clause,[],[f7041,f7024,f2214,f36530])).
% 78.92/11.76 thf(f7024,plain,(
% 78.92/11.76 spl72_313 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,set(X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_313])])).
% 78.92/11.76 thf(f7041,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = order(sTfun(X2,sTfun(X0,set(X1)))))) ) | (~spl72_48 | ~spl72_313)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f7040])).
% 78.92/11.76 thf(f7040,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = order(sTfun(X2,sTfun(X0,set(X1)))))) ) | (~spl72_48 | ~spl72_313)),
% 78.92/11.76 inference(superposition,[],[f2215,f7025])).
% 78.92/11.76 thf(f7025,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,set(X0))))) ) | ~spl72_313),
% 78.92/11.76 inference(avatar_component_clause,[],[f7024])).
% 78.92/11.76 thf(f36265,plain,(
% 78.92/11.76 spl72_519 | ~spl72_28 | ~spl72_147),
% 78.92/11.76 inference(avatar_split_clause,[],[f3565,f3367,f2020,f36263])).
% 78.92/11.76 thf(f36263,plain,(
% 78.92/11.76 spl72_519 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X1),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_519])])).
% 78.92/11.76 thf(f3565,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X1),X2)))) ) | (~spl72_28 | ~spl72_147)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3564])).
% 78.92/11.76 thf(f3564,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X1),X2)))) ) | (~spl72_28 | ~spl72_147)),
% 78.92/11.76 inference(superposition,[],[f3368,f2021])).
% 78.92/11.76 thf(f36261,plain,(
% 78.92/11.76 spl72_518 | ~spl72_28 | ~spl72_146),
% 78.92/11.76 inference(avatar_split_clause,[],[f3502,f3363,f2020,f36259])).
% 78.92/11.76 thf(f36259,plain,(
% 78.92/11.76 spl72_518 <=> ! [X0 : $tType,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_518])])).
% 78.92/11.76 thf(f3502,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_146)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3501])).
% 78.92/11.76 thf(f3501,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_146)),
% 78.92/11.76 inference(superposition,[],[f3364,f2021])).
% 78.92/11.76 thf(f36257,plain,(
% 78.92/11.76 spl72_517 | ~spl72_28 | ~spl72_145),
% 78.92/11.76 inference(avatar_split_clause,[],[f3457,f3359,f2020,f36255])).
% 78.92/11.76 thf(f36255,plain,(
% 78.92/11.76 spl72_517 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X1),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_517])])).
% 78.92/11.76 thf(f3457,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X1),X2)))) ) | (~spl72_28 | ~spl72_145)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3456])).
% 78.92/11.76 thf(f3456,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X1),X2)))) ) | (~spl72_28 | ~spl72_145)),
% 78.92/11.76 inference(superposition,[],[f3360,f2021])).
% 78.92/11.76 thf(f36253,plain,(
% 78.92/11.76 spl72_516 | ~spl72_28 | ~spl72_144),
% 78.92/11.76 inference(avatar_split_clause,[],[f3394,f3355,f2020,f36251])).
% 78.92/11.76 thf(f36251,plain,(
% 78.92/11.76 spl72_516 <=> ! [X0 : $tType,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_516])])).
% 78.92/11.76 thf(f3394,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_144)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3393])).
% 78.92/11.76 thf(f3393,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X3),X1))) | ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_144)),
% 78.92/11.76 inference(superposition,[],[f3356,f2021])).
% 78.92/11.76 thf(f35903,plain,(
% 78.92/11.76 spl72_515 | ~spl72_46 | ~spl72_312),
% 78.92/11.76 inference(avatar_split_clause,[],[f7033,f7020,f2205,f35901])).
% 78.92/11.76 thf(f7020,plain,(
% 78.92/11.76 spl72_312 <=> ! [X1 : $tType,X0 : $tType] : ($true = ord(sTfun(X1,set(X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_312])])).
% 78.92/11.76 thf(f7033,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = ord(sTfun(X2,sTfun(X0,set(X1)))))) ) | (~spl72_46 | ~spl72_312)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f7032])).
% 78.92/11.76 thf(f7032,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = ord(sTfun(X2,sTfun(X0,set(X1)))))) ) | (~spl72_46 | ~spl72_312)),
% 78.92/11.76 inference(superposition,[],[f2206,f7021])).
% 78.92/11.76 thf(f7021,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,set(X0))))) ) | ~spl72_312),
% 78.92/11.76 inference(avatar_component_clause,[],[f7020])).
% 78.92/11.76 thf(f35702,plain,(
% 78.92/11.76 spl72_514 | ~spl72_147),
% 78.92/11.76 inference(avatar_split_clause,[],[f3569,f3367,f35700])).
% 78.92/11.76 thf(f35700,plain,(
% 78.92/11.76 spl72_514 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2) = X1) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_514])])).
% 78.92/11.76 thf(f3569,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2) = X1) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true)) ) | ~spl72_147),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f3568])).
% 78.92/11.76 thf(f3568,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true)) ) | ~spl72_147),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f3559])).
% 78.92/11.76 thf(f3559,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true)) ) | ~spl72_147),
% 78.92/11.76 inference(primitive_instantiation,[],[f3368])).
% 78.92/11.76 thf(f35698,plain,(
% 78.92/11.76 spl72_513 | ~spl72_145),
% 78.92/11.76 inference(avatar_split_clause,[],[f3461,f3359,f35696])).
% 78.92/11.76 thf(f35696,plain,(
% 78.92/11.76 spl72_513 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2) = X1) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_513])])).
% 78.92/11.76 thf(f3461,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2) = X1) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true)) ) | ~spl72_145),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f3460])).
% 78.92/11.76 thf(f3460,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true)) ) | ~spl72_145),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f3451])).
% 78.92/11.76 thf(f3451,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X2))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true)) ) | ~spl72_145),
% 78.92/11.76 inference(primitive_instantiation,[],[f3360])).
% 78.92/11.76 thf(f35693,plain,(
% 78.92/11.76 ~spl72_512 | ~spl72_19 | ~spl72_86 | ~spl72_141),
% 78.92/11.76 inference(avatar_split_clause,[],[f3309,f3249,f2628,f1979,f35690])).
% 78.92/11.76 thf(f35690,plain,(
% 78.92/11.76 spl72_512 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_512])])).
% 78.92/11.76 thf(f2628,plain,(
% 78.92/11.76 spl72_86 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_86])])).
% 78.92/11.76 thf(f3309,plain,(
% 78.92/11.76 ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (~spl72_19 | ~spl72_86 | ~spl72_141)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3308])).
% 78.92/11.76 thf(f3308,plain,(
% 78.92/11.76 ($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (~spl72_19 | ~spl72_86 | ~spl72_141)),
% 78.92/11.76 inference(forward_demodulation,[],[f3304,f1981])).
% 78.92/11.76 thf(f3304,plain,(
% 78.92/11.76 ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (preorder(nat) != $true) | (~spl72_86 | ~spl72_141)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3283])).
% 78.92/11.76 thf(f3283,plain,(
% 78.92/11.76 ($true != $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua))) | (preorder(nat) != $true) | (~spl72_86 | ~spl72_141)),
% 78.92/11.76 inference(superposition,[],[f2629,f3251])).
% 78.92/11.76 thf(f2629,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true)) ) | ~spl72_86),
% 78.92/11.76 inference(avatar_component_clause,[],[f2628])).
% 78.92/11.76 thf(f35688,plain,(
% 78.92/11.76 spl72_511 | ~spl72_75 | ~spl72_141),
% 78.92/11.76 inference(avatar_split_clause,[],[f3305,f3249,f2471,f35685])).
% 78.92/11.76 thf(f35685,plain,(
% 78.92/11.76 spl72_511 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_511])])).
% 78.92/11.76 thf(f2471,plain,(
% 78.92/11.76 spl72_75 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_75])])).
% 78.92/11.76 thf(f3305,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (~spl72_75 | ~spl72_141)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3282])).
% 78.92/11.76 thf(f3282,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))) | (~spl72_75 | ~spl72_141)),
% 78.92/11.76 inference(superposition,[],[f2472,f3251])).
% 78.92/11.76 thf(f2472,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | ~spl72_75),
% 78.92/11.76 inference(avatar_component_clause,[],[f2471])).
% 78.92/11.76 thf(f35683,plain,(
% 78.92/11.76 spl72_510 | ~spl72_74 | ~spl72_140),
% 78.92/11.76 inference(avatar_split_clause,[],[f3279,f3245,f2467,f35681])).
% 78.92/11.76 thf(f35681,plain,(
% 78.92/11.76 spl72_510 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_510])])).
% 78.92/11.76 thf(f3279,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)))) ) | (~spl72_74 | ~spl72_140)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3274])).
% 78.92/11.76 thf(f3274,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)))) ) | (~spl72_74 | ~spl72_140)),
% 78.92/11.76 inference(superposition,[],[f3246,f2468])).
% 78.92/11.76 thf(f35679,plain,(
% 78.92/11.76 spl72_509 | ~spl72_28 | ~spl72_140),
% 78.92/11.76 inference(avatar_split_clause,[],[f3277,f3245,f2020,f35677])).
% 78.92/11.76 thf(f35677,plain,(
% 78.92/11.76 spl72_509 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_509])])).
% 78.92/11.76 thf(f3277,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)),X0))) ) | (~spl72_28 | ~spl72_140)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3276])).
% 78.92/11.76 thf(f3276,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,vAPP(sTfun(nat,$o),nat,sK55,X1))) | ($true != vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),X1)),X0))) ) | (~spl72_28 | ~spl72_140)),
% 78.92/11.76 inference(superposition,[],[f3246,f2021])).
% 78.92/11.76 thf(f35675,plain,(
% 78.92/11.76 spl72_508 | ~spl72_28 | ~spl72_139),
% 78.92/11.76 inference(avatar_split_clause,[],[f3272,f3241,f2020,f35673])).
% 78.92/11.76 thf(f35673,plain,(
% 78.92/11.76 spl72_508 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X4 : X0,X3 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X2,X4)),vAPP(X0,X1,X3,X4))) | ($true != ord(X1)) | ($false = vAPP(sTfun(X0,X1),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,X1),$o),ord_less_eq(sTfun(X0,X1)),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_508])])).
% 78.92/11.76 thf(f3241,plain,(
% 78.92/11.76 spl72_139 <=> ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X4 : X1,X3 : X1 > X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_139])])).
% 78.92/11.76 thf(f3272,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X3 : X0 > X1,X4 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X2,X4)),vAPP(X0,X1,X3,X4))) | ($true != ord(X1)) | ($false = vAPP(sTfun(X0,X1),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,X1),$o),ord_less_eq(sTfun(X0,X1)),X2),X3))) ) | (~spl72_28 | ~spl72_139)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3271])).
% 78.92/11.76 thf(f3271,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1,X3 : X0 > X1,X4 : X0] : (($true != $true) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X2,X4)),vAPP(X0,X1,X3,X4))) | ($true != ord(X1)) | ($false = vAPP(sTfun(X0,X1),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,X1),$o),ord_less_eq(sTfun(X0,X1)),X2),X3))) ) | (~spl72_28 | ~spl72_139)),
% 78.92/11.76 inference(superposition,[],[f3242,f2021])).
% 78.92/11.76 thf(f3242,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | (ord(X0) != $true)) ) | ~spl72_139),
% 78.92/11.76 inference(avatar_component_clause,[],[f3241])).
% 78.92/11.76 thf(f35476,plain,(
% 78.92/11.76 spl72_507 | ~spl72_45 | ~spl72_311),
% 78.92/11.76 inference(avatar_split_clause,[],[f7029,f7016,f2201,f35474])).
% 78.92/11.76 thf(f7016,plain,(
% 78.92/11.76 spl72_311 <=> ! [X1 : $tType,X0 : $tType] : ($true = preorder(sTfun(X1,set(X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_311])])).
% 78.92/11.76 thf(f7029,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true = preorder(sTfun(X2,sTfun(X0,set(X1)))))) ) | (~spl72_45 | ~spl72_311)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f7028])).
% 78.92/11.76 thf(f7028,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType,X2 : $tType] : (($true != $true) | ($true = preorder(sTfun(X2,sTfun(X0,set(X1)))))) ) | (~spl72_45 | ~spl72_311)),
% 78.92/11.76 inference(superposition,[],[f2202,f7017])).
% 78.92/11.76 thf(f7017,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,set(X0))))) ) | ~spl72_311),
% 78.92/11.76 inference(avatar_component_clause,[],[f7016])).
% 78.92/11.76 thf(f33938,plain,(
% 78.92/11.76 spl72_506 | ~spl72_6 | ~spl72_68 | ~spl72_150 | ~spl72_151),
% 78.92/11.76 inference(avatar_split_clause,[],[f8106,f3608,f3586,f2368,f1914,f33936])).
% 78.92/11.76 thf(f33936,plain,(
% 78.92/11.76 spl72_506 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_506])])).
% 78.92/11.76 thf(f8106,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),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))))) ) | (~spl72_6 | ~spl72_68 | ~spl72_150 | ~spl72_151)),
% 78.92/11.76 inference(forward_demodulation,[],[f3604,f3635])).
% 78.92/11.76 thf(f3604,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))) ) | (~spl72_68 | ~spl72_150)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3595])).
% 78.92/11.76 thf(f3595,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),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)))) ) | (~spl72_68 | ~spl72_150)),
% 78.92/11.76 inference(superposition,[],[f3587,f2369])).
% 78.92/11.76 thf(f33934,plain,(
% 78.92/11.76 spl72_505 | ~spl72_128 | ~spl72_232),
% 78.92/11.76 inference(avatar_split_clause,[],[f5636,f5618,f3082,f33931])).
% 78.92/11.76 thf(f33931,plain,(
% 78.92/11.76 spl72_505 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),ua),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),t))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_505])])).
% 78.92/11.76 thf(f5618,plain,(
% 78.92/11.76 spl72_232 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_232])])).
% 78.92/11.76 thf(f5636,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),ua),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),t)) | (~spl72_128 | ~spl72_232)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5629])).
% 78.92/11.76 thf(f5629,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),ua),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),t)) | (~spl72_128 | ~spl72_232)),
% 78.92/11.76 inference(superposition,[],[f5619,f3084])).
% 78.92/11.76 thf(f5619,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2))) ) | ~spl72_232),
% 78.92/11.76 inference(avatar_component_clause,[],[f5618])).
% 78.92/11.76 thf(f33929,plain,(
% 78.92/11.76 spl72_504 | ~spl72_129 | ~spl72_232),
% 78.92/11.76 inference(avatar_split_clause,[],[f5635,f5618,f3087,f33926])).
% 78.92/11.76 thf(f33926,plain,(
% 78.92/11.76 spl72_504 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1)),v))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_504])])).
% 78.92/11.76 thf(f5635,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1)),v)) | (~spl72_129 | ~spl72_232)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5630])).
% 78.92/11.76 thf(f5630,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1)),v)) | (~spl72_129 | ~spl72_232)),
% 78.92/11.76 inference(superposition,[],[f5619,f3089])).
% 78.92/11.76 thf(f33924,plain,(
% 78.92/11.76 spl72_503 | ~spl72_130 | ~spl72_232),
% 78.92/11.76 inference(avatar_split_clause,[],[f5634,f5618,f3092,f33921])).
% 78.92/11.76 thf(f33921,plain,(
% 78.92/11.76 spl72_503 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),va))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_503])])).
% 78.92/11.76 thf(f5634,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),va)) | (~spl72_130 | ~spl72_232)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5631])).
% 78.92/11.76 thf(f5631,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),va)) | (~spl72_130 | ~spl72_232)),
% 78.92/11.76 inference(superposition,[],[f5619,f3094])).
% 78.92/11.76 thf(f33919,plain,(
% 78.92/11.76 spl72_502 | ~spl72_124 | ~spl72_231),
% 78.92/11.76 inference(avatar_split_clause,[],[f5628,f5614,f3062,f33916])).
% 78.92/11.76 thf(f33916,plain,(
% 78.92/11.76 spl72_502 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),u),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),t))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_502])])).
% 78.92/11.76 thf(f5614,plain,(
% 78.92/11.76 spl72_231 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_231])])).
% 78.92/11.76 thf(f5628,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),u),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),t)) | (~spl72_124 | ~spl72_231)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5621])).
% 78.92/11.76 thf(f5621,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),u),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2)),t)) | (~spl72_124 | ~spl72_231)),
% 78.92/11.76 inference(superposition,[],[f5615,f3064])).
% 78.92/11.76 thf(f5615,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2))) ) | ~spl72_231),
% 78.92/11.76 inference(avatar_component_clause,[],[f5614])).
% 78.92/11.76 thf(f33914,plain,(
% 78.92/11.76 spl72_501 | ~spl72_125 | ~spl72_231),
% 78.92/11.76 inference(avatar_split_clause,[],[f5627,f5614,f3067,f33911])).
% 78.92/11.76 thf(f33911,plain,(
% 78.92/11.76 spl72_501 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),ua),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),t))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_501])])).
% 78.92/11.76 thf(f5627,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),ua),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),t)) | (~spl72_125 | ~spl72_231)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5622])).
% 78.92/11.76 thf(f5622,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),ua),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)),t)) | (~spl72_125 | ~spl72_231)),
% 78.92/11.76 inference(superposition,[],[f5615,f3069])).
% 78.92/11.76 thf(f33909,plain,(
% 78.92/11.76 spl72_500 | ~spl72_126 | ~spl72_231),
% 78.92/11.76 inference(avatar_split_clause,[],[f5626,f5614,f3072,f33906])).
% 78.92/11.76 thf(f33906,plain,(
% 78.92/11.76 spl72_500 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p3)),t))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_500])])).
% 78.92/11.76 thf(f5626,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p3)),t)) | (~spl72_126 | ~spl72_231)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5623])).
% 78.92/11.76 thf(f5623,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),s),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p3)),t)) | (~spl72_126 | ~spl72_231)),
% 78.92/11.76 inference(superposition,[],[f5615,f3074])).
% 78.92/11.76 thf(f33904,plain,(
% 78.92/11.76 spl72_499 | ~spl72_12 | ~spl72_68 | ~spl72_162),
% 78.92/11.76 inference(avatar_split_clause,[],[f3806,f3753,f2368,f1944,f33902])).
% 78.92/11.76 thf(f33902,plain,(
% 78.92/11.76 spl72_499 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_499])])).
% 78.92/11.76 thf(f3806,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))) ) | (~spl72_12 | ~spl72_68 | ~spl72_162)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3805])).
% 78.92/11.76 thf(f3805,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))) ) | (~spl72_12 | ~spl72_68 | ~spl72_162)),
% 78.92/11.76 inference(forward_demodulation,[],[f3800,f1946])).
% 78.92/11.76 thf(f3800,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | (ordere779506340up_add(nat) != $true)) ) | (~spl72_68 | ~spl72_162)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3791])).
% 78.92/11.76 thf(f3791,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X0)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) | (ordere779506340up_add(nat) != $true)) ) | (~spl72_68 | ~spl72_162)),
% 78.92/11.76 inference(superposition,[],[f3754,f2369])).
% 78.92/11.76 thf(f33900,plain,(
% 78.92/11.76 spl72_498 | ~spl72_10 | ~spl72_152),
% 78.92/11.76 inference(avatar_split_clause,[],[f3639,f3612,f1934,f33898])).
% 78.92/11.76 thf(f33898,plain,(
% 78.92/11.76 spl72_498 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (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)) = 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)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_498])])).
% 78.92/11.76 thf(f1934,plain,(
% 78.92/11.76 spl72_10 <=> (ab_semigroup_add(nat) = $true)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_10])])).
% 78.92/11.76 thf(f3639,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) ) | (~spl72_10 | ~spl72_152)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3636])).
% 78.92/11.76 thf(f3636,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | (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)) = 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)))) ) | (~spl72_10 | ~spl72_152)),
% 78.92/11.76 inference(superposition,[],[f3613,f1936])).
% 78.92/11.76 thf(f1936,plain,(
% 78.92/11.76 (ab_semigroup_add(nat) = $true) | ~spl72_10),
% 78.92/11.76 inference(avatar_component_clause,[],[f1934])).
% 78.92/11.76 thf(f33878,plain,(
% 78.92/11.76 spl72_497 | ~spl72_6 | ~spl72_151),
% 78.92/11.76 inference(avatar_split_clause,[],[f3635,f3608,f1914,f33876])).
% 78.92/11.76 thf(f33876,plain,(
% 78.92/11.76 spl72_497 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (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) = 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)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_497])])).
% 78.92/11.76 thf(f33874,plain,(
% 78.92/11.76 spl72_496 | ~spl72_7 | ~spl72_68 | ~spl72_122),
% 78.92/11.76 inference(avatar_split_clause,[],[f3053,f3029,f2368,f1919,f33872])).
% 78.92/11.76 thf(f33872,plain,(
% 78.92/11.76 spl72_496 <=> ! [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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_496])])).
% 78.92/11.76 thf(f1919,plain,(
% 78.92/11.76 spl72_7 <=> (canoni770627133id_add(nat) = $true)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_7])])).
% 78.92/11.76 thf(f3029,plain,(
% 78.92/11.76 spl72_122 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK7(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (canoni770627133id_add(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_122])])).
% 78.92/11.76 thf(f3053,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))) ) | (~spl72_7 | ~spl72_68 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3052])).
% 78.92/11.76 thf(f3052,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))) ) | (~spl72_7 | ~spl72_68 | ~spl72_122)),
% 78.92/11.76 inference(forward_demodulation,[],[f3045,f1921])).
% 78.92/11.76 thf(f1921,plain,(
% 78.92/11.76 (canoni770627133id_add(nat) = $true) | ~spl72_7),
% 78.92/11.76 inference(avatar_component_clause,[],[f1919])).
% 78.92/11.76 thf(f3045,plain,(
% 78.92/11.76 ( ! [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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) | (canoni770627133id_add(nat) != $true)) ) | (~spl72_68 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3038])).
% 78.92/11.76 thf(f3038,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) | (canoni770627133id_add(nat) != $true)) ) | (~spl72_68 | ~spl72_122)),
% 78.92/11.76 inference(superposition,[],[f3030,f2369])).
% 78.92/11.76 thf(f3030,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK7(X0),X2),X1)) = X2) | (canoni770627133id_add(X0) != $true)) ) | ~spl72_122),
% 78.92/11.76 inference(avatar_component_clause,[],[f3029])).
% 78.92/11.76 thf(f33870,plain,(
% 78.92/11.76 spl72_495 | ~spl72_7 | ~spl72_67 | ~spl72_122),
% 78.92/11.76 inference(avatar_split_clause,[],[f3051,f3029,f2364,f1919,f33868])).
% 78.92/11.76 thf(f33868,plain,(
% 78.92/11.76 spl72_495 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_495])])).
% 78.92/11.76 thf(f3051,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))) ) | (~spl72_7 | ~spl72_67 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3050])).
% 78.92/11.76 thf(f3050,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))) ) | (~spl72_7 | ~spl72_67 | ~spl72_122)),
% 78.92/11.76 inference(forward_demodulation,[],[f3046,f1921])).
% 78.92/11.76 thf(f3046,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0))) | (canoni770627133id_add(nat) != $true)) ) | (~spl72_67 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3037])).
% 78.92/11.76 thf(f3037,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0))) | (canoni770627133id_add(nat) != $true)) ) | (~spl72_67 | ~spl72_122)),
% 78.92/11.76 inference(superposition,[],[f3030,f2365])).
% 78.92/11.76 thf(f33288,plain,(
% 78.92/11.76 spl72_494 | ~spl72_28 | ~spl72_135),
% 78.92/11.76 inference(avatar_split_clause,[],[f3227,f3198,f2020,f33286])).
% 78.92/11.76 thf(f33286,plain,(
% 78.92/11.76 spl72_494 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_494])])).
% 78.92/11.76 thf(f3227,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_135)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3226])).
% 78.92/11.76 thf(f3226,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_135)),
% 78.92/11.76 inference(superposition,[],[f3199,f2021])).
% 78.92/11.76 thf(f33280,plain,(
% 78.92/11.76 spl72_493 | ~spl72_28 | ~spl72_134),
% 78.92/11.76 inference(avatar_split_clause,[],[f3220,f3194,f2020,f33278])).
% 78.92/11.76 thf(f33278,plain,(
% 78.92/11.76 spl72_493 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_493])])).
% 78.92/11.76 thf(f3220,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_134)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3219])).
% 78.92/11.76 thf(f3219,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_134)),
% 78.92/11.76 inference(superposition,[],[f3195,f2021])).
% 78.92/11.76 thf(f33276,plain,(
% 78.92/11.76 spl72_492 | ~spl72_28 | ~spl72_133),
% 78.92/11.76 inference(avatar_split_clause,[],[f3209,f3190,f2020,f33274])).
% 78.92/11.76 thf(f33274,plain,(
% 78.92/11.76 spl72_492 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_492])])).
% 78.92/11.76 thf(f3190,plain,(
% 78.92/11.76 spl72_133 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (preorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_133])])).
% 78.92/11.76 thf(f3209,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_133)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3208])).
% 78.92/11.76 thf(f3208,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_133)),
% 78.92/11.76 inference(superposition,[],[f3191,f2021])).
% 78.92/11.76 thf(f3191,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (preorder(X0) != $true)) ) | ~spl72_133),
% 78.92/11.76 inference(avatar_component_clause,[],[f3190])).
% 78.92/11.76 thf(f33272,plain,(
% 78.92/11.76 spl72_491 | ~spl72_28 | ~spl72_132),
% 78.92/11.76 inference(avatar_split_clause,[],[f3202,f3186,f2020,f33270])).
% 78.92/11.76 thf(f33270,plain,(
% 78.92/11.76 spl72_491 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_491])])).
% 78.92/11.76 thf(f3202,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_132)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3201])).
% 78.92/11.76 thf(f3201,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_132)),
% 78.92/11.76 inference(superposition,[],[f3187,f2021])).
% 78.92/11.76 thf(f33268,plain,(
% 78.92/11.76 spl72_490 | ~spl72_67 | ~spl72_108),
% 78.92/11.76 inference(avatar_split_clause,[],[f2883,f2869,f2364,f33266])).
% 78.92/11.76 thf(f33266,plain,(
% 78.92/11.76 spl72_490 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_490])])).
% 78.92/11.76 thf(f2869,plain,(
% 78.92/11.76 spl72_108 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_108])])).
% 78.92/11.76 thf(f2883,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))) ) | (~spl72_67 | ~spl72_108)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2874])).
% 78.92/11.76 thf(f2874,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))) ) | (~spl72_67 | ~spl72_108)),
% 78.92/11.76 inference(superposition,[],[f2870,f2365])).
% 78.92/11.76 thf(f2870,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1)) ) | ~spl72_108),
% 78.92/11.76 inference(avatar_component_clause,[],[f2869])).
% 78.92/11.76 thf(f33264,plain,(
% 78.92/11.76 spl72_489 | ~spl72_68 | ~spl72_108),
% 78.92/11.76 inference(avatar_split_clause,[],[f2882,f2869,f2368,f33262])).
% 78.92/11.76 thf(f33262,plain,(
% 78.92/11.76 spl72_489 <=> ! [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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_489])])).
% 78.92/11.76 thf(f2882,plain,(
% 78.92/11.76 ( ! [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),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))) ) | (~spl72_68 | ~spl72_108)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2875])).
% 78.92/11.76 thf(f2875,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))) ) | (~spl72_68 | ~spl72_108)),
% 78.92/11.76 inference(superposition,[],[f2870,f2369])).
% 78.92/11.76 thf(f33130,plain,(
% 78.92/11.76 spl72_488 | ~spl72_127 | ~spl72_230),
% 78.92/11.76 inference(avatar_split_clause,[],[f5612,f5598,f3077,f33127])).
% 78.92/11.76 thf(f33127,plain,(
% 78.92/11.76 spl72_488 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p),t))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_488])])).
% 78.92/11.76 thf(f5598,plain,(
% 78.92/11.76 spl72_230 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_230])])).
% 78.92/11.76 thf(f5612,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p),t)) | (~spl72_127 | ~spl72_230)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5609])).
% 78.92/11.76 thf(f5609,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p),t)) | (~spl72_127 | ~spl72_230)),
% 78.92/11.76 inference(superposition,[],[f5599,f3079])).
% 78.92/11.76 thf(f5599,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2))) ) | ~spl72_230),
% 78.92/11.76 inference(avatar_component_clause,[],[f5598])).
% 78.92/11.76 thf(f33125,plain,(
% 78.92/11.76 spl72_487 | ~spl72_127 | ~spl72_229),
% 78.92/11.76 inference(avatar_split_clause,[],[f5608,f5594,f3077,f33122])).
% 78.92/11.76 thf(f33122,plain,(
% 78.92/11.76 spl72_487 <=> ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),p),t))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_487])])).
% 78.92/11.76 thf(f5594,plain,(
% 78.92/11.76 spl72_229 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_229])])).
% 78.92/11.76 thf(f5608,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),p),t)) | (~spl72_127 | ~spl72_229)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f5605])).
% 78.92/11.76 thf(f5605,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),s),p),t)) | (~spl72_127 | ~spl72_229)),
% 78.92/11.76 inference(superposition,[],[f5595,f3079])).
% 78.92/11.76 thf(f5595,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X1),X2))) ) | ~spl72_229),
% 78.92/11.76 inference(avatar_component_clause,[],[f5594])).
% 78.92/11.76 thf(f32976,plain,(
% 78.92/11.76 spl72_486 | ~spl72_360 | ~spl72_485),
% 78.92/11.76 inference(avatar_split_clause,[],[f32972,f32969,f18168,f32974])).
% 78.92/11.76 thf(f32974,plain,(
% 78.92/11.76 spl72_486 <=> ! [X0 : $o,X1 : $o > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,$false)),vAPP($o,nat,X1,X0))) | ($true = X0))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_486])])).
% 78.92/11.76 thf(f18168,plain,(
% 78.92/11.76 spl72_360 <=> ! [X1 : $o > nat] : ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_360])])).
% 78.92/11.76 thf(f32969,plain,(
% 78.92/11.76 spl72_485 <=> ! [X0 : $o,X1 : $o > nat] : (($true = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))),vAPP($o,nat,X1,X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_485])])).
% 78.92/11.76 thf(f32972,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,$false)),vAPP($o,nat,X1,X0))) | ($true = X0)) ) | (~spl72_360 | ~spl72_485)),
% 78.92/11.76 inference(forward_demodulation,[],[f32970,f18169])).
% 78.92/11.76 thf(f18169,plain,(
% 78.92/11.76 ( ! [X1 : $o > nat] : (($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))) ) | ~spl72_360),
% 78.92/11.76 inference(avatar_component_clause,[],[f18168])).
% 78.92/11.76 thf(f32970,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > nat] : (($true = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))),vAPP($o,nat,X1,X0)))) ) | ~spl72_485),
% 78.92/11.76 inference(avatar_component_clause,[],[f32969])).
% 78.92/11.76 thf(f32971,plain,(
% 78.92/11.76 spl72_339 | spl72_485 | ~spl72_159),
% 78.92/11.76 inference(avatar_split_clause,[],[f3730,f3675,f32969,f7896])).
% 78.92/11.76 thf(f3730,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o,X1 : $o > nat] : (($true = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))),vAPP($o,nat,X1,X0))) | ($true = X2)) ) | ~spl72_159),
% 78.92/11.76 inference(not_proxy_clausification,[],[f3729])).
% 78.92/11.76 thf(f3729,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o,X1 : $o > nat] : (($true = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))),vAPP($o,nat,X1,X0))) | ($true != vAPP($o,$o,vNOT,X2))) ) | ~spl72_159),
% 78.92/11.76 inference(not_proxy_clausification,[],[f3696])).
% 78.92/11.76 thf(f3696,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o,X1 : $o > nat] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP($o,nat,X1,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))),vAPP($o,nat,X1,X0))) | ($true != vAPP($o,$o,vNOT,X2))) ) | ~spl72_159),
% 78.92/11.76 inference(primitive_instantiation,[],[f3676])).
% 78.92/11.76 thf(f32960,plain,(
% 78.92/11.76 spl72_484 | ~spl72_63),
% 78.92/11.76 inference(avatar_split_clause,[],[f2400,f2347,f32958])).
% 78.92/11.76 thf(f32958,plain,(
% 78.92/11.76 spl72_484 <=> ! [X0 : $tType,X1 : X0] : ((wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,sK8(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))) = X1))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_484])])).
% 78.92/11.76 thf(f2347,plain,(
% 78.92/11.76 spl72_63 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_63])])).
% 78.92/11.76 thf(f2400,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X1 : X0] : ((wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,sK8(X0),vAPP(sTfun(X0,$o),sTfun(X0,$o),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))) = X1)) ) | ~spl72_63),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2348])).
% 78.92/11.76 thf(f2348,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) | ($true = vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) ) | ~spl72_63),
% 78.92/11.76 inference(avatar_component_clause,[],[f2347])).
% 78.92/11.76 thf(f32948,plain,(
% 78.92/11.76 spl72_483 | ~spl72_28 | ~spl72_122),
% 78.92/11.76 inference(avatar_split_clause,[],[f3042,f3029,f2020,f32946])).
% 78.92/11.76 thf(f32946,plain,(
% 78.92/11.76 spl72_483 <=> ! [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),sK7(X0),X2),X1)) = X2) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_483])])).
% 78.92/11.76 thf(f3042,plain,(
% 78.92/11.76 ( ! [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),sK7(X0),X2),X1)) = X2) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3041])).
% 78.92/11.76 thf(f3041,plain,(
% 78.92/11.76 ( ! [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),sK7(X0),X2),X1)) = X2) | (canoni770627133id_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_122)),
% 78.92/11.76 inference(superposition,[],[f3030,f2021])).
% 78.92/11.76 thf(f32944,plain,(
% 78.92/11.76 spl72_482 | ~spl72_28 | ~spl72_121),
% 78.92/11.76 inference(avatar_split_clause,[],[f3035,f3025,f2020,f32942])).
% 78.92/11.76 thf(f32942,plain,(
% 78.92/11.76 spl72_482 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) | (dense_order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_482])])).
% 78.92/11.76 thf(f3035,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) | (dense_order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_121)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3034])).
% 78.92/11.76 thf(f3034,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) | (dense_order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_121)),
% 78.92/11.76 inference(superposition,[],[f3026,f2021])).
% 78.92/11.76 thf(f32940,plain,(
% 78.92/11.76 spl72_481 | ~spl72_28 | ~spl72_120),
% 78.92/11.76 inference(avatar_split_clause,[],[f3033,f3021,f2020,f32938])).
% 78.92/11.76 thf(f32938,plain,(
% 78.92/11.76 spl72_481 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1))) | (dense_order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_481])])).
% 78.92/11.76 thf(f3021,plain,(
% 78.92/11.76 spl72_120 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_120])])).
% 78.92/11.76 thf(f3033,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1))) | (dense_order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_120)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3032])).
% 78.92/11.76 thf(f3032,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1))) | (dense_order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_120)),
% 78.92/11.76 inference(superposition,[],[f3022,f2021])).
% 78.92/11.76 thf(f3022,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1))) | (dense_order(X0) != $true)) ) | ~spl72_120),
% 78.92/11.76 inference(avatar_component_clause,[],[f3021])).
% 78.92/11.76 thf(f32496,plain,(
% 78.92/11.76 ~spl72_337 | spl72_480 | ~spl72_28 | ~spl72_109),
% 78.92/11.76 inference(avatar_split_clause,[],[f12888,f2886,f2020,f32494,f7888])).
% 78.92/11.76 thf(f32494,plain,(
% 78.92/11.76 spl72_480 <=> ! [X2 : $o,X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X1),$true)) | ($false = vAPP(sTfun($o,$o),$o,sK8($o),X0)) | ($true = vAPP($o,$o,X0,X2)) | ($true = vAPP($o,$o,X0,X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_480])])).
% 78.92/11.76 thf(f2886,plain,(
% 78.92/11.76 spl72_109 <=> ! [X0 : $tType,X4 : X0,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_109])])).
% 78.92/11.76 thf(f12888,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X1),$true)) | ($true = vAPP($o,$o,X0,X1)) | ($true = vAPP($o,$o,X0,X2)) | ($true != wellorder($o)) | ($false = vAPP(sTfun($o,$o),$o,sK8($o),X0))) ) | (~spl72_28 | ~spl72_109)),
% 78.92/11.76 inference(superposition,[],[f2887,f2021])).
% 78.92/11.76 thf(f2887,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) | ($true = vAPP(X0,$o,X1,X4)) | ($true = vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) ) | ~spl72_109),
% 78.92/11.76 inference(avatar_component_clause,[],[f2886])).
% 78.92/11.76 thf(f32492,plain,(
% 78.92/11.76 spl72_479 | ~spl72_74 | ~spl72_119),
% 78.92/11.76 inference(avatar_split_clause,[],[f3017,f3006,f2467,f32490])).
% 78.92/11.76 thf(f32490,plain,(
% 78.92/11.76 spl72_479 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_479])])).
% 78.92/11.76 thf(f3017,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_119)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3012])).
% 78.92/11.76 thf(f3012,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_119)),
% 78.92/11.76 inference(superposition,[],[f3007,f2468])).
% 78.92/11.76 thf(f32488,plain,(
% 78.92/11.76 spl72_478 | ~spl72_28 | ~spl72_119),
% 78.92/11.76 inference(avatar_split_clause,[],[f3015,f3006,f2020,f32486])).
% 78.92/11.76 thf(f32486,plain,(
% 78.92/11.76 spl72_478 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_478])])).
% 78.92/11.76 thf(f3015,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_119)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3014])).
% 78.92/11.76 thf(f3014,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_119)),
% 78.92/11.76 inference(superposition,[],[f3007,f2021])).
% 78.92/11.76 thf(f32484,plain,(
% 78.92/11.76 spl72_477 | ~spl72_14 | ~spl72_74 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f2674,f2616,f2467,f1954,f32482])).
% 78.92/11.76 thf(f32482,plain,(
% 78.92/11.76 spl72_477 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_477])])).
% 78.92/11.76 thf(f2674,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_14 | ~spl72_74 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2673])).
% 78.92/11.76 thf(f2673,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_14 | ~spl72_74 | ~spl72_83)),
% 78.92/11.76 inference(forward_demodulation,[],[f2656,f1956])).
% 78.92/11.76 thf(f2656,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X1)) | (wellorder(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2649])).
% 78.92/11.76 thf(f2649,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X1)) | (wellorder(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_83)),
% 78.92/11.76 inference(superposition,[],[f2617,f2468])).
% 78.92/11.76 thf(f31724,plain,(
% 78.92/11.76 ~spl72_337 | spl72_476 | ~spl72_147),
% 78.92/11.76 inference(avatar_split_clause,[],[f13302,f3367,f31722,f7888])).
% 78.92/11.76 thf(f31722,plain,(
% 78.92/11.76 spl72_476 <=> ! [X0 : $o > $o,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),vNOT),X0)) | ($true != vAPP($o,$o,X0,X1)) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_476])])).
% 78.92/11.76 thf(f13302,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),vNOT),X0)) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),X0)) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o))) ) | ~spl72_147),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13301])).
% 78.92/11.76 thf(f13301,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),vNOT),X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),X0))) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o))) ) | ~spl72_147),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13295])).
% 78.92/11.76 thf(f13295,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),vNOT),X0))) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),X0))) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o))) ) | ~spl72_147),
% 78.92/11.76 inference(primitive_instantiation,[],[f3368])).
% 78.92/11.76 thf(f31720,plain,(
% 78.92/11.76 ~spl72_337 | spl72_475 | spl72_339 | ~spl72_146),
% 78.92/11.76 inference(avatar_split_clause,[],[f13274,f3363,f7896,f31718,f7888])).
% 78.92/11.76 thf(f31718,plain,(
% 78.92/11.76 spl72_475 <=> ! [X1 : $o > $o] : (($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),X1),vNOT)) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_475])])).
% 78.92/11.76 thf(f13274,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),X1),vNOT)) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_146),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13273])).
% 78.92/11.76 thf(f13273,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),X1),vNOT))) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_146),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13240])).
% 78.92/11.76 thf(f13240,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK10($o),X1),vNOT))) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_146),
% 78.92/11.76 inference(primitive_instantiation,[],[f3364])).
% 78.92/11.76 thf(f31710,plain,(
% 78.92/11.76 ~spl72_337 | spl72_474 | ~spl72_145),
% 78.92/11.76 inference(avatar_split_clause,[],[f13219,f3359,f31708,f7888])).
% 78.92/11.76 thf(f31708,plain,(
% 78.92/11.76 spl72_474 <=> ! [X0 : $o > $o,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),vNOT),X0)) | ($true != vAPP($o,$o,X0,X1)) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_474])])).
% 78.92/11.76 thf(f13219,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),vNOT),X0)) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),X0)) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o))) ) | ~spl72_145),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13218])).
% 78.92/11.76 thf(f13218,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),vNOT),X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),X0))) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o))) ) | ~spl72_145),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13212])).
% 78.92/11.76 thf(f13212,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),vNOT),X0))) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),X0))) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o))) ) | ~spl72_145),
% 78.92/11.76 inference(primitive_instantiation,[],[f3360])).
% 78.92/11.76 thf(f31706,plain,(
% 78.92/11.76 ~spl72_337 | spl72_473 | spl72_339 | ~spl72_144),
% 78.92/11.76 inference(avatar_split_clause,[],[f13191,f3355,f7896,f31704,f7888])).
% 78.92/11.76 thf(f31704,plain,(
% 78.92/11.76 spl72_473 <=> ! [X1 : $o > $o] : (($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),X1),vNOT)) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_473])])).
% 78.92/11.76 thf(f13191,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),X1),vNOT)) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_144),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13190])).
% 78.92/11.76 thf(f13190,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),X1),vNOT))) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_144),
% 78.92/11.76 inference(not_proxy_clausification,[],[f13157])).
% 78.92/11.76 thf(f13157,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o > $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,$o),$o),sK9($o),X1),vNOT))) | ($true = vAPP($o,$o,X1,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_144),
% 78.92/11.76 inference(primitive_instantiation,[],[f3356])).
% 78.92/11.76 thf(f31702,plain,(
% 78.92/11.76 spl72_472 | ~spl72_28 | ~spl72_118),
% 78.92/11.76 inference(avatar_split_clause,[],[f2994,f2980,f2020,f31700])).
% 78.92/11.76 thf(f31700,plain,(
% 78.92/11.76 spl72_472 <=> ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($false = vAPP(nat,$o,X0,X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_472])])).
% 78.92/11.76 thf(f2994,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl72_28 | ~spl72_118)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2993])).
% 78.92/11.76 thf(f2993,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($false = vAPP(nat,$o,X0,X1))) ) | (~spl72_28 | ~spl72_118)),
% 78.92/11.76 inference(superposition,[],[f2981,f2021])).
% 78.92/11.76 thf(f31438,plain,(
% 78.92/11.76 spl72_471 | ~spl72_118),
% 78.92/11.76 inference(avatar_split_clause,[],[f3004,f2980,f31436])).
% 78.92/11.76 thf(f31436,plain,(
% 78.92/11.76 spl72_471 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1) | (vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_471])])).
% 78.92/11.76 thf(f3004,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1) | (vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1)) ) | ~spl72_118),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f2983])).
% 78.92/11.76 thf(f2983,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1),vAPP(sTfun(nat,$o),nat,sK55,vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)))) | (vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X0),vAPP(nat,sTfun(nat,$o),vEQ(nat),X1)) = X1)) ) | ~spl72_118),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2981])).
% 78.92/11.76 thf(f31434,plain,(
% 78.92/11.76 spl72_470 | ~spl72_14 | ~spl72_72 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f2676,f2616,f2448,f1954,f31431])).
% 78.92/11.76 thf(f31431,plain,(
% 78.92/11.76 spl72_470 <=> ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s))),ua))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_470])])).
% 78.92/11.76 thf(f2676,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s))),ua)) | (~spl72_14 | ~spl72_72 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2675])).
% 78.92/11.76 thf(f2675,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s))),ua)) | (~spl72_14 | ~spl72_72 | ~spl72_83)),
% 78.92/11.76 inference(forward_demodulation,[],[f2654,f1956])).
% 78.92/11.76 thf(f2654,plain,(
% 78.92/11.76 ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s))),ua)) | (wellorder(nat) != $true) | (~spl72_72 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2651])).
% 78.92/11.76 thf(f2651,plain,(
% 78.92/11.76 ($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s))),ua)) | (wellorder(nat) != $true) | (~spl72_72 | ~spl72_83)),
% 78.92/11.76 inference(superposition,[],[f2617,f2450])).
% 78.92/11.76 thf(f31303,plain,(
% 78.92/11.76 spl72_469 | ~spl72_48 | ~spl72_343),
% 78.92/11.76 inference(avatar_split_clause,[],[f18455,f11807,f2214,f31301])).
% 78.92/11.76 thf(f11807,plain,(
% 78.92/11.76 spl72_343 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,a)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_343])])).
% 78.92/11.76 thf(f18455,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,a))))) ) | (~spl72_48 | ~spl72_343)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f18442])).
% 78.92/11.76 thf(f18442,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,sTfun(X0,a))))) ) | (~spl72_48 | ~spl72_343)),
% 78.92/11.76 inference(superposition,[],[f2215,f11808])).
% 78.92/11.76 thf(f11808,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = order(sTfun(X0,a)))) ) | ~spl72_343),
% 78.92/11.76 inference(avatar_component_clause,[],[f11807])).
% 78.92/11.76 thf(f29321,plain,(
% 78.92/11.76 spl72_468 | ~spl72_48 | ~spl72_342),
% 78.92/11.76 inference(avatar_split_clause,[],[f17370,f11435,f2214,f29319])).
% 78.92/11.76 thf(f11435,plain,(
% 78.92/11.76 spl72_342 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,capacity)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_342])])).
% 78.92/11.76 thf(f17370,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,capacity))))) ) | (~spl72_48 | ~spl72_342)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f17357])).
% 78.92/11.76 thf(f17357,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,sTfun(X0,capacity))))) ) | (~spl72_48 | ~spl72_342)),
% 78.92/11.76 inference(superposition,[],[f2215,f11436])).
% 78.92/11.76 thf(f11436,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = order(sTfun(X0,capacity)))) ) | ~spl72_342),
% 78.92/11.76 inference(avatar_component_clause,[],[f11435])).
% 78.92/11.76 thf(f28295,plain,(
% 78.92/11.76 spl72_467 | ~spl72_46 | ~spl72_334),
% 78.92/11.76 inference(avatar_split_clause,[],[f16477,f7608,f2205,f28293])).
% 78.92/11.76 thf(f7608,plain,(
% 78.92/11.76 spl72_334 <=> ! [X0 : $tType] : ($true = ord(sTfun(X0,a)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_334])])).
% 78.92/11.76 thf(f16477,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,a))))) ) | (~spl72_46 | ~spl72_334)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f16476])).
% 78.92/11.76 thf(f16476,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,sTfun(X0,a))))) ) | (~spl72_46 | ~spl72_334)),
% 78.92/11.76 inference(superposition,[],[f2206,f7609])).
% 78.92/11.76 thf(f7609,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,a)))) ) | ~spl72_334),
% 78.92/11.76 inference(avatar_component_clause,[],[f7608])).
% 78.92/11.76 thf(f28291,plain,(
% 78.92/11.76 spl72_466 | ~spl72_13 | ~spl72_50 | ~spl72_167),
% 78.92/11.76 inference(avatar_split_clause,[],[f3860,f3773,f2246,f1949,f28289])).
% 78.92/11.76 thf(f28289,plain,(
% 78.92/11.76 spl72_466 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | (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)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_466])])).
% 78.92/11.76 thf(f1949,plain,(
% 78.92/11.76 spl72_13 <=> (ordere236663937imp_le(nat) = $true)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_13])])).
% 78.92/11.76 thf(f3860,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | (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))) ) | (~spl72_13 | ~spl72_50 | ~spl72_167)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3859])).
% 78.92/11.76 thf(f3859,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | (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))) ) | (~spl72_13 | ~spl72_50 | ~spl72_167)),
% 78.92/11.76 inference(forward_demodulation,[],[f3858,f1951])).
% 78.92/11.76 thf(f1951,plain,(
% 78.92/11.76 (ordere236663937imp_le(nat) = $true) | ~spl72_13),
% 78.92/11.76 inference(avatar_component_clause,[],[f1949])).
% 78.92/11.76 thf(f3858,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | (ordere236663937imp_le(nat) != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) ) | (~spl72_50 | ~spl72_167)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3849])).
% 78.92/11.76 thf(f3849,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | (ordere236663937imp_le(nat) != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) ) | (~spl72_50 | ~spl72_167)),
% 78.92/11.76 inference(constrained_superposition,[],[f3774,f2247])).
% 78.92/11.76 thf(f28287,plain,(
% 78.92/11.76 spl72_465 | ~spl72_13 | ~spl72_50 | ~spl72_166),
% 78.92/11.76 inference(avatar_split_clause,[],[f3846,f3769,f2246,f1949,f28285])).
% 78.92/11.76 thf(f28285,plain,(
% 78.92/11.76 spl72_465 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_465])])).
% 78.92/11.76 thf(f3846,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) ) | (~spl72_13 | ~spl72_50 | ~spl72_166)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3845])).
% 78.92/11.76 thf(f3845,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) ) | (~spl72_13 | ~spl72_50 | ~spl72_166)),
% 78.92/11.76 inference(forward_demodulation,[],[f3844,f1951])).
% 78.92/11.76 thf(f3844,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (ordere236663937imp_le(nat) != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) ) | (~spl72_50 | ~spl72_166)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3835])).
% 78.92/11.76 thf(f3835,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (ordere236663937imp_le(nat) != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) ) | (~spl72_50 | ~spl72_166)),
% 78.92/11.76 inference(constrained_superposition,[],[f3770,f2247])).
% 78.92/11.76 thf(f28283,plain,(
% 78.92/11.76 spl72_464 | ~spl72_7 | ~spl72_74 | ~spl72_122),
% 78.92/11.76 inference(avatar_split_clause,[],[f3055,f3029,f2467,f1919,f28281])).
% 78.92/11.76 thf(f28281,plain,(
% 78.92/11.76 spl72_464 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X1),X0)) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_464])])).
% 78.92/11.76 thf(f3055,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X1),X0)) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_7 | ~spl72_74 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3054])).
% 78.92/11.76 thf(f3054,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X1),X0)) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_7 | ~spl72_74 | ~spl72_122)),
% 78.92/11.76 inference(forward_demodulation,[],[f3044,f1921])).
% 78.92/11.76 thf(f3044,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X1),X0)) = X1) | (canoni770627133id_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_122)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f3039])).
% 78.92/11.76 thf(f3039,plain,(
% 78.92/11.76 ( ! [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),sK7(nat),X1),X0)) = X1) | (canoni770627133id_add(nat) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_122)),
% 78.92/11.76 inference(superposition,[],[f3030,f2468])).
% 78.92/11.76 thf(f28279,plain,(
% 78.92/11.76 spl72_463 | ~spl72_28 | ~spl72_116),
% 78.92/11.76 inference(avatar_split_clause,[],[f2968,f2914,f2020,f28277])).
% 78.92/11.76 thf(f28277,plain,(
% 78.92/11.76 spl72_463 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_463])])).
% 78.92/11.76 thf(f2968,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl72_28 | ~spl72_116)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2967])).
% 78.92/11.76 thf(f2967,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl72_28 | ~spl72_116)),
% 78.92/11.76 inference(superposition,[],[f2915,f2021])).
% 78.92/11.76 thf(f28275,plain,(
% 78.92/11.76 spl72_462 | ~spl72_28 | ~spl72_115),
% 78.92/11.76 inference(avatar_split_clause,[],[f2956,f2910,f2020,f28273])).
% 78.92/11.76 thf(f28273,plain,(
% 78.92/11.76 spl72_462 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_462])])).
% 78.92/11.76 thf(f2956,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl72_28 | ~spl72_115)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2955])).
% 78.92/11.76 thf(f2955,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl72_28 | ~spl72_115)),
% 78.92/11.76 inference(superposition,[],[f2911,f2021])).
% 78.92/11.76 thf(f28271,plain,(
% 78.92/11.76 spl72_461 | ~spl72_28 | ~spl72_114),
% 78.92/11.76 inference(avatar_split_clause,[],[f2949,f2906,f2020,f28269])).
% 78.92/11.76 thf(f28269,plain,(
% 78.92/11.76 spl72_461 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_461])])).
% 78.92/11.76 thf(f2949,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl72_28 | ~spl72_114)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2948])).
% 78.92/11.76 thf(f2948,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) ) | (~spl72_28 | ~spl72_114)),
% 78.92/11.76 inference(superposition,[],[f2907,f2021])).
% 78.92/11.76 thf(f28267,plain,(
% 78.92/11.76 spl72_460 | ~spl72_74 | ~spl72_113),
% 78.92/11.76 inference(avatar_split_clause,[],[f2944,f2902,f2467,f28265])).
% 78.92/11.76 thf(f28265,plain,(
% 78.92/11.76 spl72_460 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_460])])).
% 78.92/11.76 thf(f2944,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_113)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2939])).
% 78.92/11.76 thf(f2939,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_113)),
% 78.92/11.76 inference(superposition,[],[f2903,f2468])).
% 78.92/11.76 thf(f28263,plain,(
% 78.92/11.76 spl72_459 | ~spl72_28 | ~spl72_113),
% 78.92/11.76 inference(avatar_split_clause,[],[f2942,f2902,f2020,f28261])).
% 78.92/11.76 thf(f28261,plain,(
% 78.92/11.76 spl72_459 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_459])])).
% 78.92/11.76 thf(f2942,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_113)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2941])).
% 78.92/11.76 thf(f2941,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_113)),
% 78.92/11.76 inference(superposition,[],[f2903,f2021])).
% 78.92/11.76 thf(f28259,plain,(
% 78.92/11.76 spl72_458 | ~spl72_74 | ~spl72_112),
% 78.92/11.76 inference(avatar_split_clause,[],[f2932,f2898,f2467,f28257])).
% 78.92/11.76 thf(f28257,plain,(
% 78.92/11.76 spl72_458 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_458])])).
% 78.92/11.76 thf(f2932,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_112)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2927])).
% 78.92/11.76 thf(f2927,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_112)),
% 78.92/11.76 inference(superposition,[],[f2899,f2468])).
% 78.92/11.76 thf(f28255,plain,(
% 78.92/11.76 spl72_457 | ~spl72_28 | ~spl72_112),
% 78.92/11.76 inference(avatar_split_clause,[],[f2930,f2898,f2020,f28253])).
% 78.92/11.76 thf(f28253,plain,(
% 78.92/11.76 spl72_457 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_457])])).
% 78.92/11.76 thf(f2930,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_112)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2929])).
% 78.92/11.76 thf(f2929,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_112)),
% 78.92/11.76 inference(superposition,[],[f2899,f2021])).
% 78.92/11.76 thf(f28251,plain,(
% 78.92/11.76 spl72_456 | ~spl72_46 | ~spl72_330),
% 78.92/11.76 inference(avatar_split_clause,[],[f16111,f7384,f2205,f28249])).
% 78.92/11.76 thf(f7384,plain,(
% 78.92/11.76 spl72_330 <=> ! [X0 : $tType] : ($true = ord(sTfun(X0,capacity)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_330])])).
% 78.92/11.76 thf(f16111,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,capacity))))) ) | (~spl72_46 | ~spl72_330)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f16110])).
% 78.92/11.76 thf(f16110,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,sTfun(X0,capacity))))) ) | (~spl72_46 | ~spl72_330)),
% 78.92/11.76 inference(superposition,[],[f2206,f7385])).
% 78.92/11.76 thf(f7385,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,capacity)))) ) | ~spl72_330),
% 78.92/11.76 inference(avatar_component_clause,[],[f7384])).
% 78.92/11.76 thf(f28247,plain,(
% 78.92/11.76 spl72_455 | ~spl72_28 | ~spl72_111),
% 78.92/11.76 inference(avatar_split_clause,[],[f2923,f2894,f2020,f28245])).
% 78.92/11.76 thf(f2923,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_111)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2922])).
% 78.92/11.76 thf(f2922,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_111)),
% 78.92/11.76 inference(superposition,[],[f2895,f2021])).
% 78.92/11.76 thf(f28243,plain,(
% 78.92/11.76 spl72_454 | ~spl72_28 | ~spl72_110),
% 78.92/11.76 inference(avatar_split_clause,[],[f2921,f2890,f2020,f28241])).
% 78.92/11.76 thf(f2921,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_110)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2920])).
% 78.92/11.76 thf(f2920,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_110)),
% 78.92/11.76 inference(superposition,[],[f2891,f2021])).
% 78.92/11.76 thf(f28239,plain,(
% 78.92/11.76 spl72_453 | ~spl72_28 | ~spl72_109),
% 78.92/11.76 inference(avatar_split_clause,[],[f2919,f2886,f2020,f28237])).
% 78.92/11.76 thf(f28237,plain,(
% 78.92/11.76 spl72_453 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > $o,X1 : X0] : (($true = vAPP(X0,$o,X2,X1)) | ($true = vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,sK8(X0),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_453])])).
% 78.92/11.76 thf(f2919,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,X2,X1)) | ($true = vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,sK8(X0),X2)))) ) | (~spl72_28 | ~spl72_109)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2918])).
% 78.92/11.76 thf(f2918,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X2,X1)) | ($true = vAPP(X0,$o,X2,X3)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,sK8(X0),X2)))) ) | (~spl72_28 | ~spl72_109)),
% 78.92/11.76 inference(superposition,[],[f2887,f2021])).
% 78.92/11.76 thf(f28235,plain,(
% 78.92/11.76 spl72_452 | ~spl72_28 | ~spl72_104),
% 78.92/11.76 inference(avatar_split_clause,[],[f2839,f2779,f2020,f28233])).
% 78.92/11.76 thf(f28233,plain,(
% 78.92/11.76 spl72_452 <=> ! [X0 : $tType,X3 : $o,X2 : $o > X0,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_452])])).
% 78.92/11.76 thf(f2839,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $o > X0,X3 : $o,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),X1),X2))) ) | (~spl72_28 | ~spl72_104)),
% 78.92/11.76 inference(superposition,[],[f2780,f2021])).
% 78.92/11.76 thf(f28231,plain,(
% 78.92/11.76 spl72_451 | ~spl72_28 | ~spl72_103),
% 78.92/11.76 inference(avatar_split_clause,[],[f2811,f2775,f2020,f28229])).
% 78.92/11.76 thf(f28229,plain,(
% 78.92/11.76 spl72_451 <=> ! [X0 : $tType,X3 : $o,X2 : $o > X0,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_451])])).
% 78.92/11.76 thf(f2811,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $o > X0,X3 : $o,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X3)) | (wellorder(X0) != $true) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),X1),X2))) ) | (~spl72_28 | ~spl72_103)),
% 78.92/11.76 inference(superposition,[],[f2776,f2021])).
% 78.92/11.76 thf(f28227,plain,(
% 78.92/11.76 spl72_450 | ~spl72_14 | ~spl72_68 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f2672,f2616,f2368,f1954,f28225])).
% 78.92/11.76 thf(f28225,plain,(
% 78.92/11.76 spl72_450 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_450])])).
% 78.92/11.76 thf(f2672,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) ) | (~spl72_14 | ~spl72_68 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2671])).
% 78.92/11.76 thf(f2671,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) ) | (~spl72_14 | ~spl72_68 | ~spl72_83)),
% 78.92/11.76 inference(forward_demodulation,[],[f2657,f1956])).
% 78.92/11.76 thf(f2657,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) | (wellorder(nat) != $true)) ) | (~spl72_68 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2648])).
% 78.92/11.76 thf(f2648,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))) | (wellorder(nat) != $true)) ) | (~spl72_68 | ~spl72_83)),
% 78.92/11.76 inference(superposition,[],[f2617,f2369])).
% 78.92/11.76 thf(f28223,plain,(
% 78.92/11.76 spl72_449 | ~spl72_14 | ~spl72_67 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f2670,f2616,f2364,f1954,f28221])).
% 78.92/11.76 thf(f28221,plain,(
% 78.92/11.76 spl72_449 <=> ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_449])])).
% 78.92/11.76 thf(f2670,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) ) | (~spl72_14 | ~spl72_67 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2669])).
% 78.92/11.76 thf(f2669,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) ) | (~spl72_14 | ~spl72_67 | ~spl72_83)),
% 78.92/11.76 inference(forward_demodulation,[],[f2658,f1956])).
% 78.92/11.76 thf(f2658,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) | (wellorder(nat) != $true)) ) | (~spl72_67 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2647])).
% 78.92/11.76 thf(f2647,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))) | (wellorder(nat) != $true)) ) | (~spl72_67 | ~spl72_83)),
% 78.92/11.76 inference(superposition,[],[f2617,f2365])).
% 78.92/11.76 thf(f28219,plain,(
% 78.92/11.76 spl72_448 | ~spl72_67 | ~spl72_79),
% 78.92/11.76 inference(avatar_split_clause,[],[f2544,f2514,f2364,f28217])).
% 78.92/11.76 thf(f28217,plain,(
% 78.92/11.76 spl72_448 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_448])])).
% 78.92/11.76 thf(f2514,plain,(
% 78.92/11.76 spl72_79 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_79])])).
% 78.92/11.76 thf(f2544,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0))) ) | (~spl72_67 | ~spl72_79)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2537])).
% 78.92/11.76 thf(f2537,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)),X0))) ) | (~spl72_67 | ~spl72_79)),
% 78.92/11.76 inference(superposition,[],[f2515,f2365])).
% 78.92/11.76 thf(f2515,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | ~spl72_79),
% 78.92/11.76 inference(avatar_component_clause,[],[f2514])).
% 78.92/11.76 thf(f28215,plain,(
% 78.92/11.76 spl72_447 | ~spl72_68 | ~spl72_79),
% 78.92/11.76 inference(avatar_split_clause,[],[f2543,f2514,f2368,f28213])).
% 78.92/11.76 thf(f28213,plain,(
% 78.92/11.76 spl72_447 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_447])])).
% 78.92/11.76 thf(f2543,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) ) | (~spl72_68 | ~spl72_79)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2538])).
% 78.92/11.76 thf(f2538,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) ) | (~spl72_68 | ~spl72_79)),
% 78.92/11.76 inference(superposition,[],[f2515,f2369])).
% 78.92/11.76 thf(f28211,plain,(
% 78.92/11.76 spl72_446 | ~spl72_67 | ~spl72_78),
% 78.92/11.76 inference(avatar_split_clause,[],[f2535,f2510,f2364,f28209])).
% 78.92/11.76 thf(f28209,plain,(
% 78.92/11.76 spl72_446 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_446])])).
% 78.92/11.76 thf(f2510,plain,(
% 78.92/11.76 spl72_78 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_78])])).
% 78.92/11.76 thf(f2535,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) ) | (~spl72_67 | ~spl72_78)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2526])).
% 78.92/11.76 thf(f2526,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) ) | (~spl72_67 | ~spl72_78)),
% 78.92/11.76 inference(superposition,[],[f2511,f2365])).
% 78.92/11.76 thf(f2511,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | ~spl72_78),
% 78.92/11.76 inference(avatar_component_clause,[],[f2510])).
% 78.92/11.76 thf(f28207,plain,(
% 78.92/11.76 spl72_445 | ~spl72_45 | ~spl72_327),
% 78.92/11.76 inference(avatar_split_clause,[],[f15589,f7100,f2201,f28205])).
% 78.92/11.76 thf(f7100,plain,(
% 78.92/11.76 spl72_327 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,a)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_327])])).
% 78.92/11.76 thf(f15589,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,a))))) ) | (~spl72_45 | ~spl72_327)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f15588])).
% 78.92/11.76 thf(f15588,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,sTfun(X0,a))))) ) | (~spl72_45 | ~spl72_327)),
% 78.92/11.76 inference(superposition,[],[f2202,f7101])).
% 78.92/11.76 thf(f7101,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,a)))) ) | ~spl72_327),
% 78.92/11.76 inference(avatar_component_clause,[],[f7100])).
% 78.92/11.76 thf(f28203,plain,(
% 78.92/11.76 spl72_444 | ~spl72_68 | ~spl72_78),
% 78.92/11.76 inference(avatar_split_clause,[],[f2534,f2510,f2368,f28201])).
% 78.92/11.76 thf(f28201,plain,(
% 78.92/11.76 spl72_444 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_444])])).
% 78.92/11.76 thf(f2534,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) ) | (~spl72_68 | ~spl72_78)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2527])).
% 78.92/11.76 thf(f2527,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1) = X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) ) | (~spl72_68 | ~spl72_78)),
% 78.92/11.76 inference(superposition,[],[f2511,f2369])).
% 78.92/11.76 thf(f28199,plain,(
% 78.92/11.76 spl72_443 | ~spl72_58),
% 78.92/11.76 inference(avatar_split_clause,[],[f2320,f2304,f28197])).
% 78.92/11.76 thf(f28197,plain,(
% 78.92/11.76 spl72_443 <=> ! [X0 : nat] : (vAPP(sTfun(nat,$o),nat,sK43,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_443])])).
% 78.92/11.76 thf(f2304,plain,(
% 78.92/11.76 spl72_58 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_58])])).
% 78.92/11.76 thf(f2320,plain,(
% 78.92/11.76 ( ! [X0 : nat] : ((vAPP(sTfun(nat,$o),nat,sK43,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl72_58),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2305])).
% 78.92/11.76 thf(f2305,plain,(
% 78.92/11.76 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl72_58),
% 78.92/11.76 inference(avatar_component_clause,[],[f2304])).
% 78.92/11.76 thf(f28195,plain,(
% 78.92/11.76 spl72_442 | ~spl72_57),
% 78.92/11.76 inference(avatar_split_clause,[],[f2312,f2300,f28193])).
% 78.92/11.76 thf(f28193,plain,(
% 78.92/11.76 spl72_442 <=> ! [X0 : nat] : (vAPP(sTfun(nat,$o),nat,sK42,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_442])])).
% 78.92/11.76 thf(f2300,plain,(
% 78.92/11.76 spl72_57 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_57])])).
% 78.92/11.76 thf(f2312,plain,(
% 78.92/11.76 ( ! [X0 : nat] : ((vAPP(sTfun(nat,$o),nat,sK42,vAPP(sTfun(nat,$o),sTfun(nat,$o),vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT),vAPP(nat,sTfun(nat,$o),vEQ(nat),X0))) = X0)) ) | ~spl72_57),
% 78.92/11.76 inference(leibniz_equality_elimination,[],[f2301])).
% 78.92/11.76 thf(f2301,plain,(
% 78.92/11.76 ( ! [X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0))) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl72_57),
% 78.92/11.76 inference(avatar_component_clause,[],[f2300])).
% 78.92/11.76 thf(f27886,plain,(
% 78.92/11.76 spl72_441 | ~spl72_74 | ~spl72_108),
% 78.92/11.76 inference(avatar_split_clause,[],[f2881,f2869,f2467,f27884])).
% 78.92/11.76 thf(f27884,plain,(
% 78.92/11.76 spl72_441 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_441])])).
% 78.92/11.76 thf(f2881,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_108)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2876])).
% 78.92/11.76 thf(f2876,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_108)),
% 78.92/11.76 inference(superposition,[],[f2870,f2468])).
% 78.92/11.76 thf(f27882,plain,(
% 78.92/11.76 spl72_440 | ~spl72_28 | ~spl72_108),
% 78.92/11.76 inference(avatar_split_clause,[],[f2879,f2869,f2020,f27880])).
% 78.92/11.76 thf(f27880,plain,(
% 78.92/11.76 spl72_440 <=> ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_440])])).
% 78.92/11.76 thf(f2879,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_108)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2878])).
% 78.92/11.76 thf(f2878,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_108)),
% 78.92/11.76 inference(superposition,[],[f2870,f2021])).
% 78.92/11.76 thf(f27878,plain,(
% 78.92/11.76 spl72_439 | ~spl72_50 | ~spl72_81),
% 78.92/11.76 inference(avatar_split_clause,[],[f2594,f2522,f2246,f27876])).
% 78.92/11.76 thf(f27876,plain,(
% 78.92/11.76 spl72_439 <=> ! [X0 : nat,X1 : nat > nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_439])])).
% 78.92/11.76 thf(f2522,plain,(
% 78.92/11.76 spl72_81 <=> ! [X0 : $tType,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_81])])).
% 78.92/11.76 thf(f2594,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat > nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_50 | ~spl72_81)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2581])).
% 78.92/11.76 thf(f2581,plain,(
% 78.92/11.76 ( ! [X0 : nat,X1 : nat > nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,vAPP(sTfun(nat,nat),sTfun(sTfun(nat,$o),nat),sK67(nat),X1),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_50 | ~spl72_81)),
% 78.92/11.76 inference(superposition,[],[f2523,f2247])).
% 78.92/11.76 thf(f2523,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1)))) ) | ~spl72_81),
% 78.92/11.76 inference(avatar_component_clause,[],[f2522])).
% 78.92/11.76 thf(f27826,plain,(
% 78.92/11.76 spl72_438 | ~spl72_45 | ~spl72_316),
% 78.92/11.76 inference(avatar_split_clause,[],[f15245,f7056,f2201,f27824])).
% 78.92/11.76 thf(f7056,plain,(
% 78.92/11.76 spl72_316 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,capacity)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_316])])).
% 78.92/11.76 thf(f15245,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,capacity))))) ) | (~spl72_45 | ~spl72_316)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f15244])).
% 78.92/11.76 thf(f15244,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,sTfun(X0,capacity))))) ) | (~spl72_45 | ~spl72_316)),
% 78.92/11.76 inference(superposition,[],[f2202,f7057])).
% 78.92/11.76 thf(f7057,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,capacity)))) ) | ~spl72_316),
% 78.92/11.76 inference(avatar_component_clause,[],[f7056])).
% 78.92/11.76 thf(f27822,plain,(
% 78.92/11.76 ~spl72_337 | spl72_437 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f12762,f2616,f27820,f7888])).
% 78.92/11.76 thf(f27820,plain,(
% 78.92/11.76 spl72_437 <=> ! [X0 : $o,X1 : $o] : (($false = X1) | ($false = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vAPP($o,sTfun($o,$o),vAND,X0))),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_437])])).
% 78.92/11.76 thf(f12762,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o] : (($false = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vAPP($o,sTfun($o,$o),vAND,X0))),X1)) | ($true != wellorder($o)) | ($false = X0)) ) | ~spl72_83),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f12737])).
% 78.92/11.76 thf(f12737,plain,(
% 78.92/11.76 ( ! [X0 : $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),vAND,X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vAPP($o,sTfun($o,$o),vAND,X0))),X1)) | ($true != wellorder($o))) ) | ~spl72_83),
% 78.92/11.76 inference(primitive_instantiation,[],[f2617])).
% 78.92/11.76 thf(f27818,plain,(
% 78.92/11.76 spl72_436 | ~spl72_28 | ~spl72_157),
% 78.92/11.76 inference(avatar_split_clause,[],[f3662,f3653,f2020,f27816])).
% 78.92/11.76 thf(f27816,plain,(
% 78.92/11.76 spl72_436 <=> ! [X0 : $tType,X2 : $o > X0,X1 : $o > X0] : ((vAPP($o,X0,X1,$true) != vAPP($o,X0,X2,$true)) | (X1 = X2) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),sK65(X0,$o),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_436])])).
% 78.92/11.76 thf(f3662,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $o > X0,X1 : $o > X0] : ((vAPP($o,X0,X1,$true) != vAPP($o,X0,X2,$true)) | (X1 = X2) | ($false = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,X0),sTfun(sTfun($o,X0),$o),sK65(X0,$o),X1),X2))) ) | (~spl72_28 | ~spl72_157)),
% 78.92/11.76 inference(superposition,[],[f3654,f2021])).
% 78.92/11.76 thf(f26409,plain,(
% 78.92/11.76 spl72_435 | ~spl72_67 | ~spl72_113),
% 78.92/11.76 inference(avatar_split_clause,[],[f2946,f2902,f2364,f26407])).
% 78.92/11.76 thf(f26407,plain,(
% 78.92/11.76 spl72_435 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_435])])).
% 78.92/11.76 thf(f2946,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(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),X0))))) ) | (~spl72_67 | ~spl72_113)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2937])).
% 78.92/11.76 thf(f2937,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(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),X0))))) ) | (~spl72_67 | ~spl72_113)),
% 78.92/11.76 inference(superposition,[],[f2903,f2365])).
% 78.92/11.76 thf(f26405,plain,(
% 78.92/11.76 spl72_434 | ~spl72_68 | ~spl72_113),
% 78.92/11.76 inference(avatar_split_clause,[],[f2945,f2902,f2368,f26403])).
% 78.92/11.76 thf(f26403,plain,(
% 78.92/11.76 spl72_434 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_434])])).
% 78.92/11.76 thf(f2945,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(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),X0),X1))))) ) | (~spl72_68 | ~spl72_113)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2938])).
% 78.92/11.76 thf(f2938,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(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),X0),X1))))) ) | (~spl72_68 | ~spl72_113)),
% 78.92/11.76 inference(superposition,[],[f2903,f2369])).
% 78.92/11.76 thf(f26401,plain,(
% 78.92/11.76 spl72_433 | ~spl72_28 | ~spl72_104),
% 78.92/11.76 inference(avatar_split_clause,[],[f2843,f2779,f2020,f26399])).
% 78.92/11.76 thf(f26399,plain,(
% 78.92/11.76 spl72_433 <=> ! [X0 : $tType,X2 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),X1),X3))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_433])])).
% 78.92/11.76 thf(f2843,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),X1),X3)))) ) | (~spl72_28 | ~spl72_104)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2842])).
% 78.92/11.76 thf(f2842,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),X1),X3)))) ) | (~spl72_28 | ~spl72_104)),
% 78.92/11.76 inference(superposition,[],[f2780,f2021])).
% 78.92/11.76 thf(f26397,plain,(
% 78.92/11.76 spl72_432 | ~spl72_28 | ~spl72_103),
% 78.92/11.76 inference(avatar_split_clause,[],[f2815,f2775,f2020,f26395])).
% 78.92/11.76 thf(f26395,plain,(
% 78.92/11.76 spl72_432 <=> ! [X0 : $tType,X2 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),X1),X3))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_432])])).
% 78.92/11.76 thf(f2815,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),X1),X3)))) ) | (~spl72_28 | ~spl72_103)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2814])).
% 78.92/11.76 thf(f2814,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0 > $o,X4 : X0] : (($true != $true) | ($true = vAPP(X0,$o,X1,X4)) | ($true != wellorder(X2)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),X1),X3)))) ) | (~spl72_28 | ~spl72_103)),
% 78.92/11.76 inference(superposition,[],[f2776,f2021])).
% 78.92/11.76 thf(f26393,plain,(
% 78.92/11.76 spl72_431 | ~spl72_28 | ~spl72_102),
% 78.92/11.76 inference(avatar_split_clause,[],[f2802,f2771,f2020,f26391])).
% 78.92/11.76 thf(f26391,plain,(
% 78.92/11.76 spl72_431 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_431])])).
% 78.92/11.76 thf(f2771,plain,(
% 78.92/11.76 spl72_102 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_102])])).
% 78.92/11.76 thf(f2802,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_102)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2801])).
% 78.92/11.76 thf(f2801,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_102)),
% 78.92/11.76 inference(superposition,[],[f2772,f2021])).
% 78.92/11.76 thf(f2772,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0))) ) | ~spl72_102),
% 78.92/11.76 inference(avatar_component_clause,[],[f2771])).
% 78.92/11.76 thf(f26389,plain,(
% 78.92/11.76 spl72_430 | ~spl72_28 | ~spl72_101),
% 78.92/11.76 inference(avatar_split_clause,[],[f2800,f2767,f2020,f26387])).
% 78.92/11.76 thf(f26387,plain,(
% 78.92/11.76 spl72_430 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_430])])).
% 78.92/11.76 thf(f2767,plain,(
% 78.92/11.76 spl72_101 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_101])])).
% 78.92/11.76 thf(f2800,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_101)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2799])).
% 78.92/11.76 thf(f2799,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_101)),
% 78.92/11.76 inference(superposition,[],[f2768,f2021])).
% 78.92/11.76 thf(f2768,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) ) | ~spl72_101),
% 78.92/11.76 inference(avatar_component_clause,[],[f2767])).
% 78.92/11.76 thf(f26367,plain,(
% 78.92/11.76 spl72_429 | ~spl72_28 | ~spl72_100),
% 78.92/11.76 inference(avatar_split_clause,[],[f2798,f2763,f2020,f26365])).
% 78.92/11.76 thf(f26365,plain,(
% 78.92/11.76 spl72_429 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_429])])).
% 78.92/11.76 thf(f2763,plain,(
% 78.92/11.76 spl72_100 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_100])])).
% 78.92/11.76 thf(f2798,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_100)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2797])).
% 78.92/11.76 thf(f2797,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_100)),
% 78.92/11.76 inference(superposition,[],[f2764,f2021])).
% 78.92/11.76 thf(f2764,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0))) ) | ~spl72_100),
% 78.92/11.76 inference(avatar_component_clause,[],[f2763])).
% 78.92/11.76 thf(f26363,plain,(
% 78.92/11.76 spl72_428 | ~spl72_28 | ~spl72_99),
% 78.92/11.76 inference(avatar_split_clause,[],[f2796,f2759,f2020,f26361])).
% 78.92/11.76 thf(f26361,plain,(
% 78.92/11.76 spl72_428 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_428])])).
% 78.92/11.76 thf(f2759,plain,(
% 78.92/11.76 spl72_99 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_99])])).
% 78.92/11.76 thf(f2796,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_99)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2795])).
% 78.92/11.76 thf(f2795,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_99)),
% 78.92/11.76 inference(superposition,[],[f2760,f2021])).
% 78.92/11.76 thf(f2760,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) ) | ~spl72_99),
% 78.92/11.76 inference(avatar_component_clause,[],[f2759])).
% 78.92/11.76 thf(f26359,plain,(
% 78.92/11.76 spl72_427 | ~spl72_28 | ~spl72_98),
% 78.92/11.76 inference(avatar_split_clause,[],[f2794,f2755,f2020,f26357])).
% 78.92/11.76 thf(f26357,plain,(
% 78.92/11.76 spl72_427 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_427])])).
% 78.92/11.76 thf(f2755,plain,(
% 78.92/11.76 spl72_98 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_98])])).
% 78.92/11.76 thf(f2794,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_98)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2793])).
% 78.92/11.76 thf(f2793,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_98)),
% 78.92/11.76 inference(superposition,[],[f2756,f2021])).
% 78.92/11.76 thf(f2756,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0))) ) | ~spl72_98),
% 78.92/11.76 inference(avatar_component_clause,[],[f2755])).
% 78.92/11.76 thf(f26355,plain,(
% 78.92/11.76 spl72_426 | ~spl72_28 | ~spl72_97),
% 78.92/11.76 inference(avatar_split_clause,[],[f2792,f2751,f2020,f26353])).
% 78.92/11.76 thf(f26353,plain,(
% 78.92/11.76 spl72_426 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_426])])).
% 78.92/11.76 thf(f2751,plain,(
% 78.92/11.76 spl72_97 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_97])])).
% 78.92/11.76 thf(f2792,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_97)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2791])).
% 78.92/11.76 thf(f2791,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_97)),
% 78.92/11.76 inference(superposition,[],[f2752,f2021])).
% 78.92/11.76 thf(f2752,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) ) | ~spl72_97),
% 78.92/11.76 inference(avatar_component_clause,[],[f2751])).
% 78.92/11.76 thf(f26351,plain,(
% 78.92/11.76 spl72_425 | ~spl72_28 | ~spl72_96),
% 78.92/11.76 inference(avatar_split_clause,[],[f2790,f2747,f2020,f26349])).
% 78.92/11.76 thf(f26349,plain,(
% 78.92/11.76 spl72_425 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_425])])).
% 78.92/11.76 thf(f2747,plain,(
% 78.92/11.76 spl72_96 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_96])])).
% 78.92/11.76 thf(f2790,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_96)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2789])).
% 78.92/11.76 thf(f2789,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_96)),
% 78.92/11.76 inference(superposition,[],[f2748,f2021])).
% 78.92/11.76 thf(f2748,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0))) ) | ~spl72_96),
% 78.92/11.76 inference(avatar_component_clause,[],[f2747])).
% 78.92/11.76 thf(f26347,plain,(
% 78.92/11.76 spl72_424 | ~spl72_28 | ~spl72_95),
% 78.92/11.76 inference(avatar_split_clause,[],[f2788,f2743,f2020,f26345])).
% 78.92/11.76 thf(f26345,plain,(
% 78.92/11.76 spl72_424 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X1),X2),X3)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_424])])).
% 78.92/11.76 thf(f2743,plain,(
% 78.92/11.76 spl72_95 <=> ! [X2 : $tType,X0 : X2,X3 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_95])])).
% 78.92/11.76 thf(f2788,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_95)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2787])).
% 78.92/11.76 thf(f2787,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X1),X2),X3))) ) | (~spl72_28 | ~spl72_95)),
% 78.92/11.76 inference(superposition,[],[f2744,f2021])).
% 78.92/11.76 thf(f2744,plain,(
% 78.92/11.76 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)) | ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) ) | ~spl72_95),
% 78.92/11.76 inference(avatar_component_clause,[],[f2743])).
% 78.92/11.76 thf(f26117,plain,(
% 78.92/11.76 ~spl72_337 | spl72_423 | ~spl72_28 | ~spl72_84),
% 78.92/11.76 inference(avatar_split_clause,[],[f12763,f2620,f2020,f26115,f7888])).
% 78.92/11.76 thf(f26115,plain,(
% 78.92/11.76 spl72_423 <=> ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X1),$true)) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),X0)) | ($true != vAPP($o,$o,X0,X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_423])])).
% 78.92/11.76 thf(f2620,plain,(
% 78.92/11.76 spl72_84 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true != vAPP(X0,$o,X2,X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_84])])).
% 78.92/11.76 thf(f12763,plain,(
% 78.92/11.76 ( ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less($o),X1),$true)) | ($true != vAPP($o,$o,X0,X1)) | ($true != wellorder($o)) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),X0))) ) | (~spl72_28 | ~spl72_84)),
% 78.92/11.76 inference(superposition,[],[f2621,f2021])).
% 78.92/11.76 thf(f2621,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | ($true != vAPP(X0,$o,X2,X1)) | (wellorder(X0) != $true)) ) | ~spl72_84),
% 78.92/11.76 inference(avatar_component_clause,[],[f2620])).
% 78.92/11.76 thf(f26113,plain,(
% 78.92/11.76 spl72_422 | ~spl72_104),
% 78.92/11.76 inference(avatar_split_clause,[],[f2847,f2779,f26111])).
% 78.92/11.76 thf(f26111,plain,(
% 78.92/11.76 spl72_422 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_422])])).
% 78.92/11.76 thf(f2847,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2))) ) | ~spl72_104),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f2846])).
% 78.92/11.76 thf(f2846,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl72_104),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f2837])).
% 78.92/11.76 thf(f2837,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK45(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl72_104),
% 78.92/11.76 inference(primitive_instantiation,[],[f2780])).
% 78.92/11.76 thf(f26109,plain,(
% 78.92/11.76 spl72_421 | ~spl72_103),
% 78.92/11.76 inference(avatar_split_clause,[],[f2819,f2775,f26107])).
% 78.92/11.76 thf(f26107,plain,(
% 78.92/11.76 spl72_421 <=> ! [X2 : $tType,X0 : $tType,X4 : X0,X3 : X0 > X2,X1 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_421])])).
% 78.92/11.76 thf(f2819,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | (X1 = X4) | ($true != wellorder(X2))) ) | ~spl72_103),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f2818])).
% 78.92/11.76 thf(f2818,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : ((vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl72_103),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f2809])).
% 78.92/11.76 thf(f2809,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : $tType,X3 : X0 > X2,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,X2),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,X2),X0),sK44(X2,X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4)) | ($true != wellorder(X2))) ) | ~spl72_103),
% 78.92/11.76 inference(primitive_instantiation,[],[f2776])).
% 78.92/11.76 thf(f26105,plain,(
% 78.92/11.76 spl72_420 | ~spl72_28 | ~spl72_92),
% 78.92/11.76 inference(avatar_split_clause,[],[f2723,f2710,f2020,f26103])).
% 78.92/11.76 thf(f26103,plain,(
% 78.92/11.76 spl72_420 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_420])])).
% 78.92/11.76 thf(f2710,plain,(
% 78.92/11.76 spl72_92 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (X1 = X2) | (order(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_92])])).
% 78.92/11.76 thf(f2723,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_92)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2722])).
% 78.92/11.76 thf(f2722,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) ) | (~spl72_28 | ~spl72_92)),
% 78.92/11.76 inference(superposition,[],[f2711,f2021])).
% 78.92/11.76 thf(f2711,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (X1 = X2) | (order(X0) != $true)) ) | ~spl72_92),
% 78.92/11.76 inference(avatar_component_clause,[],[f2710])).
% 78.92/11.76 thf(f26101,plain,(
% 78.92/11.76 spl72_419 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f2661,f2616,f26099])).
% 78.92/11.76 thf(f26099,plain,(
% 78.92/11.76 spl72_419 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 != X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))),X2)) | (wellorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_419])])).
% 78.92/11.76 thf(f2661,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 != X2) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))),X2)) | (wellorder(X0) != $true)) ) | ~spl72_83),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f2644])).
% 78.92/11.76 thf(f2644,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1))),X2)) | (wellorder(X0) != $true)) ) | ~spl72_83),
% 78.92/11.76 inference(primitive_instantiation,[],[f2617])).
% 78.92/11.76 thf(f26097,plain,(
% 78.92/11.76 spl72_418),
% 78.92/11.76 inference(avatar_split_clause,[],[f1851,f26095])).
% 78.92/11.76 thf(f26095,plain,(
% 78.92/11.76 spl72_418 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (linorder(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_418])])).
% 78.92/11.76 thf(f1851,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (linorder(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1850])).
% 78.92/11.76 thf(f1850,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | (linorder(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1849])).
% 78.92/11.76 thf(f1849,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (linorder(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))) )),
% 78.92/11.76 inference(not_proxy_clausification,[],[f1848])).
% 78.92/11.76 thf(f1848,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($false = vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2))) | (linorder(X0) != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1410])).
% 78.92/11.76 thf(f1410,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))) | (linorder(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f991])).
% 78.92/11.76 thf(f991,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))) | (linorder(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f420])).
% 78.92/11.76 thf(f420,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (vAPP($o,$o,vNOT,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)),vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))))),
% 78.92/11.76 inference(fool_elimination,[],[f419])).
% 78.92/11.76 thf(f419,plain,(
% 78.92/11.76 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0,X2 : X0] : ((X1 != X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 inference(rectify,[],[f239])).
% 78.92/11.76 thf(f239,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (linorder(X0) => ! [X51 : X0,X52 : X0] : ((X51 != X52) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X52),X51) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X52)))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_238_neq__iff)).
% 78.92/11.76 thf(f26093,plain,(
% 78.92/11.76 spl72_417),
% 78.92/11.76 inference(avatar_split_clause,[],[f1830,f26091])).
% 78.92/11.76 thf(f26091,plain,(
% 78.92/11.76 spl72_417 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_417])])).
% 78.92/11.76 thf(f1830,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1827])).
% 78.92/11.76 thf(f1827,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1469])).
% 78.92/11.76 thf(f1469,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f1046])).
% 78.92/11.76 thf(f1046,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f504])).
% 78.92/11.76 thf(f504,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))))),
% 78.92/11.76 inference(fool_elimination,[],[f503])).
% 78.92/11.76 thf(f503,plain,(
% 78.92/11.76 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) = (X1 = X2))))),
% 78.92/11.76 inference(rectify,[],[f201])).
% 78.92/11.76 thf(f201,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (order(X0) => ! [X52 : X0,X51 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X51) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X52) = (X51 = X52))))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_200_antisym__conv)).
% 78.92/11.76 thf(f26085,plain,(
% 78.92/11.76 spl72_416),
% 78.92/11.76 inference(avatar_split_clause,[],[f1829,f26083])).
% 78.92/11.76 thf(f26083,plain,(
% 78.92/11.76 spl72_416 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 != X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_416])])).
% 78.92/11.76 thf(f1829,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 != X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1828])).
% 78.92/11.76 thf(f1828,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1469])).
% 78.92/11.76 thf(f24718,plain,(
% 78.92/11.76 spl72_415 | ~spl72_28 | ~spl72_91),
% 78.92/11.76 inference(avatar_split_clause,[],[f2708,f2702,f2020,f24716])).
% 78.92/11.76 thf(f24716,plain,(
% 78.92/11.76 spl72_415 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK43,X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_415])])).
% 78.92/11.76 thf(f2702,plain,(
% 78.92/11.76 spl72_91 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK43,X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_91])])).
% 78.92/11.76 thf(f2708,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK43,X1)))) ) | (~spl72_28 | ~spl72_91)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2707])).
% 78.92/11.76 thf(f2707,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK43,X1)))) ) | (~spl72_28 | ~spl72_91)),
% 78.92/11.76 inference(superposition,[],[f2703,f2021])).
% 78.92/11.76 thf(f2703,plain,(
% 78.92/11.76 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK43,X0))) | ($true = vAPP(nat,$o,X0,X3)) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl72_91),
% 78.92/11.76 inference(avatar_component_clause,[],[f2702])).
% 78.92/11.76 thf(f24714,plain,(
% 78.92/11.76 spl72_414 | ~spl72_28 | ~spl72_90),
% 78.92/11.76 inference(avatar_split_clause,[],[f2706,f2698,f2020,f24712])).
% 78.92/11.76 thf(f24712,plain,(
% 78.92/11.76 spl72_414 <=> ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK42,X1))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_414])])).
% 78.92/11.76 thf(f2698,plain,(
% 78.92/11.76 spl72_90 <=> ! [X0 : nat > $o,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK42,X0))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_90])])).
% 78.92/11.76 thf(f2706,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK42,X1)))) ) | (~spl72_28 | ~spl72_90)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2705])).
% 78.92/11.76 thf(f2705,plain,(
% 78.92/11.76 ( ! [X2 : nat,X0 : nat,X1 : nat > $o] : (($true != $true) | ($true = vAPP(nat,$o,X1,X0)) | ($true = vAPP(nat,$o,X1,X2)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(sTfun(nat,$o),nat,sK42,X1)))) ) | (~spl72_28 | ~spl72_90)),
% 78.92/11.76 inference(superposition,[],[f2699,f2021])).
% 78.92/11.76 thf(f2699,plain,(
% 78.92/11.76 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK42,X0))) | ($true = vAPP(nat,$o,X0,X3)) | ($true = vAPP(nat,$o,X0,X1))) ) | ~spl72_90),
% 78.92/11.76 inference(avatar_component_clause,[],[f2698])).
% 78.92/11.76 thf(f24710,plain,(
% 78.92/11.76 spl72_413 | ~spl72_28 | ~spl72_80),
% 78.92/11.76 inference(avatar_split_clause,[],[f2553,f2518,f2020,f24708])).
% 78.92/11.76 thf(f24708,plain,(
% 78.92/11.76 spl72_413 <=> ! [X2 : $o,X0 : $o > nat,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X2)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),X1)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_413])])).
% 78.92/11.76 thf(f2553,plain,(
% 78.92/11.76 ( ! [X2 : $o,X0 : $o > nat,X1 : $o > $o] : (($true != vAPP($o,$o,X1,$true)) | ($true = vAPP($o,$o,X1,X2)) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),X1))) ) | (~spl72_28 | ~spl72_80)),
% 78.92/11.76 inference(superposition,[],[f2519,f2021])).
% 78.92/11.76 thf(f23891,plain,(
% 78.92/11.76 spl72_412 | ~spl72_28 | ~spl72_88),
% 78.92/11.76 inference(avatar_split_clause,[],[f2696,f2636,f2020,f23889])).
% 78.92/11.76 thf(f23889,plain,(
% 78.92/11.76 spl72_412 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_412])])).
% 78.92/11.76 thf(f2636,plain,(
% 78.92/11.76 spl72_88 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_88])])).
% 78.92/11.76 thf(f2696,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_88)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2695])).
% 78.92/11.76 thf(f2695,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_88)),
% 78.92/11.76 inference(superposition,[],[f2637,f2021])).
% 78.92/11.76 thf(f2637,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) ) | ~spl72_88),
% 78.92/11.76 inference(avatar_component_clause,[],[f2636])).
% 78.92/11.76 thf(f23887,plain,(
% 78.92/11.76 spl72_411 | ~spl72_28 | ~spl72_87),
% 78.92/11.76 inference(avatar_split_clause,[],[f2694,f2632,f2020,f23885])).
% 78.92/11.76 thf(f23885,plain,(
% 78.92/11.76 spl72_411 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_411])])).
% 78.92/11.76 thf(f2632,plain,(
% 78.92/11.76 spl72_87 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_87])])).
% 78.92/11.76 thf(f2694,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_87)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2693])).
% 78.92/11.76 thf(f2693,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_87)),
% 78.92/11.76 inference(superposition,[],[f2633,f2021])).
% 78.92/11.76 thf(f2633,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) ) | ~spl72_87),
% 78.92/11.76 inference(avatar_component_clause,[],[f2632])).
% 78.92/11.76 thf(f23883,plain,(
% 78.92/11.76 spl72_410 | ~spl72_28 | ~spl72_86),
% 78.92/11.76 inference(avatar_split_clause,[],[f2687,f2628,f2020,f23881])).
% 78.92/11.76 thf(f23881,plain,(
% 78.92/11.76 spl72_410 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_410])])).
% 78.92/11.76 thf(f2687,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_86)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2686])).
% 78.92/11.76 thf(f2686,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) ) | (~spl72_28 | ~spl72_86)),
% 78.92/11.76 inference(superposition,[],[f2629,f2021])).
% 78.92/11.76 thf(f23879,plain,(
% 78.92/11.76 spl72_409 | ~spl72_28 | ~spl72_85),
% 78.92/11.76 inference(avatar_split_clause,[],[f2683,f2624,f2020,f23877])).
% 78.92/11.76 thf(f23877,plain,(
% 78.92/11.76 spl72_409 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | (linorder(X0) = $false))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_409])])).
% 78.92/11.76 thf(f2624,plain,(
% 78.92/11.76 spl72_85 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linorder(X0) != $true))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_85])])).
% 78.92/11.76 thf(f2683,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | (linorder(X0) = $false)) ) | (~spl72_28 | ~spl72_85)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2682])).
% 78.92/11.76 thf(f2682,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | (linorder(X0) = $false)) ) | (~spl72_28 | ~spl72_85)),
% 78.92/11.76 inference(superposition,[],[f2625,f2021])).
% 78.92/11.76 thf(f2625,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((linorder(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) ) | ~spl72_85),
% 78.92/11.76 inference(avatar_component_clause,[],[f2624])).
% 78.92/11.76 thf(f23875,plain,(
% 78.92/11.76 spl72_408 | ~spl72_28 | ~spl72_84),
% 78.92/11.76 inference(avatar_split_clause,[],[f2679,f2620,f2020,f23873])).
% 78.92/11.76 thf(f23873,plain,(
% 78.92/11.76 spl72_408 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true != vAPP(X0,$o,X2,X1)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_408])])).
% 78.92/11.76 thf(f2679,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true != vAPP(X0,$o,X2,X1)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2)))) ) | (~spl72_28 | ~spl72_84)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2678])).
% 78.92/11.76 thf(f2678,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true != $true) | ($true != vAPP(X0,$o,X2,X1)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2)))) ) | (~spl72_28 | ~spl72_84)),
% 78.92/11.76 inference(superposition,[],[f2621,f2021])).
% 78.92/11.76 thf(f23871,plain,(
% 78.92/11.76 spl72_407 | ~spl72_28 | ~spl72_83),
% 78.92/11.76 inference(avatar_split_clause,[],[f2653,f2616,f2020,f23869])).
% 78.92/11.76 thf(f23869,plain,(
% 78.92/11.76 spl72_407 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_407])])).
% 78.92/11.76 thf(f2653,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_83)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f2652])).
% 78.92/11.76 thf(f2652,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_83)),
% 78.92/11.76 inference(superposition,[],[f2617,f2021])).
% 78.92/11.76 thf(f23867,plain,(
% 78.92/11.76 spl72_406),
% 78.92/11.76 inference(avatar_split_clause,[],[f1887,f23865])).
% 78.92/11.76 thf(f23865,plain,(
% 78.92/11.76 spl72_406 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : 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),X1),X2)) | (group_add(X0) != $true) | (X2 != X3))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_406])])).
% 78.92/11.76 thf(f1887,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (group_add(X0) != $true) | (X2 != X3)) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1886])).
% 78.92/11.76 thf(f1886,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1882])).
% 78.92/11.76 thf(f1882,plain,(
% 78.92/11.76 ( ! [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),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (group_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1362])).
% 78.92/11.76 thf(f1362,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (group_add(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f931])).
% 78.92/11.76 thf(f931,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (group_add(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f330])).
% 78.92/11.76 thf(f330,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((group_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))),
% 78.92/11.76 inference(fool_elimination,[],[f329])).
% 78.92/11.76 thf(f329,plain,(
% 78.92/11.76 ! [X0 : $tType] : (group_add(X0) => ! [X1 : X0,X2 : X0,X3 : 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),X1),X2)) = (X2 = X3)))),
% 78.92/11.76 inference(rectify,[],[f81])).
% 78.92/11.76 thf(f81,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (group_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = (X5 = X7)))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_add_Oleft__cancel)).
% 78.92/11.76 thf(f23863,plain,(
% 78.92/11.76 spl72_405),
% 78.92/11.76 inference(avatar_split_clause,[],[f1885,f23861])).
% 78.92/11.76 thf(f23861,plain,(
% 78.92/11.76 spl72_405 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : 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),X1),X2)) | (group_add(X0) != $true) | (X2 = X3))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_405])])).
% 78.92/11.76 thf(f1885,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (group_add(X0) != $true) | (X2 = X3)) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1884])).
% 78.92/11.76 thf(f1884,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1883])).
% 78.92/11.76 thf(f1883,plain,(
% 78.92/11.76 ( ! [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),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (group_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1362])).
% 78.92/11.76 thf(f23859,plain,(
% 78.92/11.76 spl72_404),
% 78.92/11.76 inference(avatar_split_clause,[],[f1881,f23857])).
% 78.92/11.76 thf(f23857,plain,(
% 78.92/11.76 spl72_404 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_404])])).
% 78.92/11.76 thf(f1881,plain,(
% 78.92/11.76 ( ! [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)) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1880])).
% 78.92/11.76 thf(f1880,plain,(
% 78.92/11.76 ( ! [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))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1876])).
% 78.92/11.76 thf(f1876,plain,(
% 78.92/11.76 ( ! [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))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1363])).
% 78.92/11.76 thf(f1363,plain,(
% 78.92/11.76 ( ! [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)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f932])).
% 78.92/11.76 thf(f932,plain,(
% 78.92/11.76 ! [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))),
% 78.92/11.76 inference(ennf_transformation,[],[f332])).
% 78.92/11.76 thf(f332,plain,(
% 78.92/11.76 ! [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)))),
% 78.92/11.76 inference(fool_elimination,[],[f331])).
% 78.92/11.76 thf(f331,plain,(
% 78.92/11.76 ! [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)))),
% 78.92/11.76 inference(rectify,[],[f80])).
% 78.92/11.76 thf(f80,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (group_add(X0) => ! [X7 : X0,X6 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X6)) = (X5 = X7)))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_add_Oright__cancel)).
% 78.92/11.76 thf(f23855,plain,(
% 78.92/11.76 spl72_403 | ~spl72_48 | ~spl72_310),
% 78.92/11.76 inference(avatar_split_clause,[],[f7009,f6972,f2214,f23853])).
% 78.92/11.76 thf(f6972,plain,(
% 78.92/11.76 spl72_310 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,$o)))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_310])])).
% 78.92/11.76 thf(f7009,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,$o))))) ) | (~spl72_48 | ~spl72_310)),
% 78.92/11.76 inference(trivial_inequality_removal,[],[f7008])).
% 78.92/11.76 thf(f7008,plain,(
% 78.92/11.76 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,sTfun(X0,$o))))) ) | (~spl72_48 | ~spl72_310)),
% 78.92/11.76 inference(superposition,[],[f2215,f6973])).
% 78.92/11.76 thf(f6973,plain,(
% 78.92/11.76 ( ! [X0 : $tType] : (($true = order(sTfun(X0,$o)))) ) | ~spl72_310),
% 78.92/11.76 inference(avatar_component_clause,[],[f6972])).
% 78.92/11.76 thf(f23851,plain,(
% 78.92/11.76 spl72_402),
% 78.92/11.76 inference(avatar_split_clause,[],[f1879,f23849])).
% 78.92/11.76 thf(f23849,plain,(
% 78.92/11.76 spl72_402 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_402])])).
% 78.92/11.76 thf(f1879,plain,(
% 78.92/11.76 ( ! [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)) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1878])).
% 78.92/11.76 thf(f1878,plain,(
% 78.92/11.76 ( ! [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))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1877])).
% 78.92/11.76 thf(f1877,plain,(
% 78.92/11.76 ( ! [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))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1363])).
% 78.92/11.76 thf(f23847,plain,(
% 78.92/11.76 spl72_401),
% 78.92/11.76 inference(avatar_split_clause,[],[f1875,f23845])).
% 78.92/11.76 thf(f23845,plain,(
% 78.92/11.76 spl72_401 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : 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),X1),X2)) | (cancel_semigroup_add(X0) != $true) | (X2 != X3))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_401])])).
% 78.92/11.76 thf(f1875,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (cancel_semigroup_add(X0) != $true) | (X2 != X3)) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1874])).
% 78.92/11.76 thf(f1874,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (cancel_semigroup_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1870])).
% 78.92/11.76 thf(f1870,plain,(
% 78.92/11.76 ( ! [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),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (cancel_semigroup_add(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1371])).
% 78.92/11.76 thf(f1371,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (cancel_semigroup_add(X0) != $true)) )),
% 78.92/11.76 inference(cnf_transformation,[],[f941])).
% 78.92/11.76 thf(f941,plain,(
% 78.92/11.76 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)) | (cancel_semigroup_add(X0) != $true))),
% 78.92/11.76 inference(ennf_transformation,[],[f348])).
% 78.92/11.76 thf(f348,plain,(
% 78.92/11.76 ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)) = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3)))),
% 78.92/11.76 inference(fool_elimination,[],[f347])).
% 78.92/11.76 thf(f347,plain,(
% 78.92/11.76 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X1 : X0,X2 : X0,X3 : 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),X1),X2)) = (X2 = X3)))),
% 78.92/11.76 inference(rectify,[],[f12])).
% 78.92/11.76 thf(f12,axiom,(
% 78.92/11.76 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = (X5 = X7)))),
% 78.92/11.76 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_add__left__cancel)).
% 78.92/11.76 thf(f23843,plain,(
% 78.92/11.76 spl72_400),
% 78.92/11.76 inference(avatar_split_clause,[],[f1873,f23841])).
% 78.92/11.76 thf(f23841,plain,(
% 78.92/11.76 spl72_400 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : 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),X1),X2)) | (cancel_semigroup_add(X0) != $true) | (X2 = X3))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_400])])).
% 78.92/11.76 thf(f1873,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (cancel_semigroup_add(X0) != $true) | (X2 = X3)) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1872])).
% 78.92/11.76 thf(f1872,plain,(
% 78.92/11.76 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : 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),X1),X2)) | (cancel_semigroup_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(equality_proxy_clausification,[],[f1871])).
% 78.92/11.76 thf(f1871,plain,(
% 78.92/11.76 ( ! [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),X3)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2))) | (cancel_semigroup_add(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X2),X3))) )),
% 78.92/11.76 inference(binary_proxy_clausification,[],[f1371])).
% 78.92/11.76 thf(f23839,plain,(
% 78.92/11.76 spl72_399),
% 78.92/11.76 inference(avatar_split_clause,[],[f1869,f23837])).
% 78.92/11.76 thf(f23837,plain,(
% 78.92/11.76 spl72_399 <=> ! [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))),
% 78.92/11.76 introduced(avatar_definition,[new_symbols(naming,[spl72_399])])).
% 78.92/11.76 thf(f1869,plain,(
% 78.92/11.76 ( ! [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)) )),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f1868])).
% 78.92/11.77 thf(f1868,plain,(
% 78.92/11.77 ( ! [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))) )),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f1864])).
% 78.92/11.77 thf(f1864,plain,(
% 78.92/11.77 ( ! [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))) )),
% 78.92/11.77 inference(binary_proxy_clausification,[],[f1372])).
% 78.92/11.77 thf(f1372,plain,(
% 78.92/11.77 ( ! [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)) )),
% 78.92/11.77 inference(cnf_transformation,[],[f942])).
% 78.92/11.77 thf(f942,plain,(
% 78.92/11.77 ! [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))),
% 78.92/11.77 inference(ennf_transformation,[],[f350])).
% 78.92/11.77 thf(f350,plain,(
% 78.92/11.77 ! [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)))),
% 78.92/11.77 inference(fool_elimination,[],[f349])).
% 78.92/11.77 thf(f349,plain,(
% 78.92/11.77 ! [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)))),
% 78.92/11.77 inference(rectify,[],[f13])).
% 78.92/11.77 thf(f13,axiom,(
% 78.92/11.77 ! [X0 : $tType] : (cancel_semigroup_add(X0) => ! [X7 : X0,X6 : X0,X5 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X6)) = (X5 = X7)))),
% 78.92/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_add__right__cancel)).
% 78.92/11.77 thf(f23835,plain,(
% 78.92/11.77 spl72_398),
% 78.92/11.77 inference(avatar_split_clause,[],[f1867,f23833])).
% 78.92/11.77 thf(f23833,plain,(
% 78.92/11.77 spl72_398 <=> ! [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))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_398])])).
% 78.92/11.77 thf(f1867,plain,(
% 78.92/11.77 ( ! [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)) )),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f1866])).
% 78.92/11.77 thf(f1866,plain,(
% 78.92/11.77 ( ! [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))) )),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f1865])).
% 78.92/11.77 thf(f1865,plain,(
% 78.92/11.77 ( ! [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))) )),
% 78.92/11.77 inference(binary_proxy_clausification,[],[f1372])).
% 78.92/11.77 thf(f21191,plain,(
% 78.92/11.77 spl72_397 | ~spl72_48 | ~spl72_309),
% 78.92/11.77 inference(avatar_split_clause,[],[f6997,f6968,f2214,f21189])).
% 78.92/11.77 thf(f6968,plain,(
% 78.92/11.77 spl72_309 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,nat)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_309])])).
% 78.92/11.77 thf(f6997,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,sTfun(X0,nat))))) ) | (~spl72_48 | ~spl72_309)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f6996])).
% 78.92/11.77 thf(f6996,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,sTfun(X0,nat))))) ) | (~spl72_48 | ~spl72_309)),
% 78.92/11.77 inference(superposition,[],[f2215,f6969])).
% 78.92/11.77 thf(f6969,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,nat)))) ) | ~spl72_309),
% 78.92/11.77 inference(avatar_component_clause,[],[f6968])).
% 78.92/11.77 thf(f20713,plain,(
% 78.92/11.77 spl72_396 | ~spl72_28 | ~spl72_81),
% 78.92/11.77 inference(avatar_split_clause,[],[f2588,f2522,f2020,f20711])).
% 78.92/11.77 thf(f20711,plain,(
% 78.92/11.77 spl72_396 <=> ! [X0 : $tType,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_396])])).
% 78.92/11.77 thf(f2588,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_81)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2587])).
% 78.92/11.77 thf(f2587,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_81)),
% 78.92/11.77 inference(superposition,[],[f2523,f2021])).
% 78.92/11.77 thf(f20709,plain,(
% 78.92/11.77 spl72_395 | ~spl72_28 | ~spl72_80),
% 78.92/11.77 inference(avatar_split_clause,[],[f2557,f2518,f2020,f20707])).
% 78.92/11.77 thf(f20707,plain,(
% 78.92/11.77 spl72_395 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_395])])).
% 78.92/11.77 thf(f2557,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))) ) | (~spl72_28 | ~spl72_80)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2556])).
% 78.92/11.77 thf(f2556,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,X3)) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))) ) | (~spl72_28 | ~spl72_80)),
% 78.92/11.77 inference(superposition,[],[f2519,f2021])).
% 78.92/11.77 thf(f20705,plain,(
% 78.92/11.77 spl72_394 | ~spl72_28 | ~spl72_79),
% 78.92/11.77 inference(avatar_split_clause,[],[f2542,f2514,f2020,f20703])).
% 78.92/11.77 thf(f20703,plain,(
% 78.92/11.77 spl72_394 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_394])])).
% 78.92/11.77 thf(f2542,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_79)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2541])).
% 78.92/11.77 thf(f2541,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_79)),
% 78.92/11.77 inference(superposition,[],[f2515,f2021])).
% 78.92/11.77 thf(f20701,plain,(
% 78.92/11.77 spl72_393 | ~spl72_74 | ~spl72_78),
% 78.92/11.77 inference(avatar_split_clause,[],[f2533,f2510,f2467,f20699])).
% 78.92/11.77 thf(f20699,plain,(
% 78.92/11.77 spl72_393 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_393])])).
% 78.92/11.77 thf(f2533,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_78)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2528])).
% 78.92/11.77 thf(f2528,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) ) | (~spl72_74 | ~spl72_78)),
% 78.92/11.77 inference(superposition,[],[f2511,f2468])).
% 78.92/11.77 thf(f20697,plain,(
% 78.92/11.77 spl72_392 | ~spl72_28 | ~spl72_78),
% 78.92/11.77 inference(avatar_split_clause,[],[f2531,f2510,f2020,f20695])).
% 78.92/11.77 thf(f20695,plain,(
% 78.92/11.77 spl72_392 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_392])])).
% 78.92/11.77 thf(f2531,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_78)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2530])).
% 78.92/11.77 thf(f2530,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != $true) | (X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) ) | (~spl72_28 | ~spl72_78)),
% 78.92/11.77 inference(superposition,[],[f2511,f2021])).
% 78.92/11.77 thf(f20693,plain,(
% 78.92/11.77 spl72_391),
% 78.92/11.77 inference(avatar_split_clause,[],[f1822,f20691])).
% 78.92/11.77 thf(f20691,plain,(
% 78.92/11.77 spl72_391 <=> ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_391])])).
% 78.92/11.77 thf(f1822,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 78.92/11.77 inference(binary_proxy_clausification,[],[f1821])).
% 78.92/11.77 thf(f1821,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f1820])).
% 78.92/11.77 thf(f1820,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 78.92/11.77 inference(not_proxy_clausification,[],[f1819])).
% 78.92/11.77 thf(f1819,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 78.92/11.77 inference(binary_proxy_clausification,[],[f1536])).
% 78.92/11.77 thf(f1536,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))) )),
% 78.92/11.77 inference(cnf_transformation,[],[f628])).
% 78.92/11.77 thf(f628,plain,(
% 78.92/11.77 ! [X0 : nat,X1 : nat] : (vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1)) = vAPP($o,$o,vAPP($o,sTfun($o,$o),vOR,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)),vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0)))),
% 78.92/11.77 inference(fool_elimination,[],[f627])).
% 78.92/11.77 thf(f627,plain,(
% 78.92/11.77 ! [X0 : nat,X1 : nat] : ((X0 != X1) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X0) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))),
% 78.92/11.77 inference(rectify,[],[f95])).
% 78.92/11.77 thf(f95,axiom,(
% 78.92/11.77 ! [X3 : nat,X4 : nat] : ((X3 != X4) = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X3) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4))),
% 78.92/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_nat__neq__iff)).
% 78.92/11.77 thf(f20689,plain,(
% 78.92/11.77 spl72_390),
% 78.92/11.77 inference(avatar_split_clause,[],[f1801,f20687])).
% 78.92/11.77 thf(f20687,plain,(
% 78.92/11.77 spl72_390 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($false = vAPP(X0,$o,X2,X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_390])])).
% 78.92/11.77 thf(f1801,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($false = vAPP(X0,$o,X2,X1)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)))) )),
% 78.92/11.77 inference(binary_proxy_clausification,[],[f1595])).
% 78.92/11.77 thf(f1595,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((vAPP(X0,$o,X2,X1) = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)))) )),
% 78.92/11.77 inference(cnf_transformation,[],[f917])).
% 78.92/11.77 thf(f917,plain,(
% 78.92/11.77 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (vAPP(X0,$o,X2,X1) = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)))),
% 78.92/11.77 inference(rectify,[],[f46])).
% 78.92/11.77 thf(f46,axiom,(
% 78.92/11.77 ! [X0 : $tType,X6 : X0,X29 : X0 > $o] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X6),vAPP(sTfun(X0,$o),set(X0),collect(X0),X29)) = vAPP(X0,$o,X29,X6))),
% 78.92/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_mem__Collect__eq)).
% 78.92/11.77 thf(f20685,plain,(
% 78.92/11.77 spl72_389 | ~spl72_46 | ~spl72_308),
% 78.92/11.77 inference(avatar_split_clause,[],[f6989,f6964,f2205,f20683])).
% 78.92/11.77 thf(f6964,plain,(
% 78.92/11.77 spl72_308 <=> ! [X0 : $tType] : ($true = ord(sTfun(X0,$o)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_308])])).
% 78.92/11.77 thf(f6989,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,$o))))) ) | (~spl72_46 | ~spl72_308)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f6988])).
% 78.92/11.77 thf(f6988,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,sTfun(X0,$o))))) ) | (~spl72_46 | ~spl72_308)),
% 78.92/11.77 inference(superposition,[],[f2206,f6965])).
% 78.92/11.77 thf(f6965,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,$o)))) ) | ~spl72_308),
% 78.92/11.77 inference(avatar_component_clause,[],[f6964])).
% 78.92/11.77 thf(f20681,plain,(
% 78.92/11.77 spl72_388),
% 78.92/11.77 inference(avatar_split_clause,[],[f1800,f20679])).
% 78.92/11.77 thf(f20679,plain,(
% 78.92/11.77 spl72_388 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP(X0,$o,X2,X1)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_388])])).
% 78.92/11.77 thf(f1800,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true = vAPP(X0,$o,X2,X1)) | ($false = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)))) )),
% 78.92/11.77 inference(binary_proxy_clausification,[],[f1595])).
% 78.92/11.77 thf(f20567,plain,(
% 78.92/11.77 spl72_387 | ~spl72_80),
% 78.92/11.77 inference(avatar_split_clause,[],[f2561,f2518,f20565])).
% 78.92/11.77 thf(f20565,plain,(
% 78.92/11.77 spl72_387 <=> ! [X0 : $tType,X3 : X0,X2 : X0 > nat,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | (X1 = X3))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_387])])).
% 78.92/11.77 thf(f2561,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | (X1 = X3)) ) | ~spl72_80),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2560])).
% 78.92/11.77 thf(f2560,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) ) | ~spl72_80),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2551])).
% 78.92/11.77 thf(f2551,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X3))) ) | ~spl72_80),
% 78.92/11.77 inference(primitive_instantiation,[],[f2519])).
% 78.92/11.77 thf(f20563,plain,(
% 78.92/11.77 spl72_386 | ~spl72_28 | ~spl72_77),
% 78.92/11.77 inference(avatar_split_clause,[],[f2506,f2500,f2020,f20561])).
% 78.92/11.77 thf(f20561,plain,(
% 78.92/11.77 spl72_386 <=> ! [X0 : $tType,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)) | (linordered_idom(X0) = $false))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_386])])).
% 78.92/11.77 thf(f2500,plain,(
% 78.92/11.77 spl72_77 <=> ! [X0 : $tType,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)) | (linordered_idom(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_77])])).
% 78.92/11.77 thf(f2506,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_77)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2505])).
% 78.92/11.77 thf(f2505,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_77)),
% 78.92/11.77 inference(superposition,[],[f2501,f2021])).
% 78.92/11.77 thf(f2501,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : nat,X1 : product_prod(nat,nat) > X0] : ((linordered_idom(X0) != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2))) ) | ~spl72_77),
% 78.92/11.77 inference(avatar_component_clause,[],[f2500])).
% 78.92/11.77 thf(f19832,plain,(
% 78.92/11.77 spl72_385 | ~spl72_46 | ~spl72_307),
% 78.92/11.77 inference(avatar_split_clause,[],[f6985,f6960,f2205,f19830])).
% 78.92/11.77 thf(f6960,plain,(
% 78.92/11.77 spl72_307 <=> ! [X0 : $tType] : ($true = ord(sTfun(X0,nat)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_307])])).
% 78.92/11.77 thf(f6985,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,sTfun(X0,nat))))) ) | (~spl72_46 | ~spl72_307)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f6984])).
% 78.92/11.77 thf(f6984,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,sTfun(X0,nat))))) ) | (~spl72_46 | ~spl72_307)),
% 78.92/11.77 inference(superposition,[],[f2206,f6961])).
% 78.92/11.77 thf(f6961,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,nat)))) ) | ~spl72_307),
% 78.92/11.77 inference(avatar_component_clause,[],[f6960])).
% 78.92/11.77 thf(f19713,plain,(
% 78.92/11.77 ~spl72_337 | spl72_384 | ~spl72_28 | ~spl72_63),
% 78.92/11.77 inference(avatar_split_clause,[],[f12592,f2347,f2020,f19711,f7888])).
% 78.92/11.77 thf(f19711,plain,(
% 78.92/11.77 spl72_384 <=> ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,X0,$true)) | ($false = vAPP(sTfun($o,$o),$o,sK8($o),X0)) | ($true = vAPP($o,$o,X0,X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_384])])).
% 78.92/11.77 thf(f12592,plain,(
% 78.92/11.77 ( ! [X0 : $o > $o,X1 : $o] : (($true != vAPP($o,$o,X0,$true)) | ($true = vAPP($o,$o,X0,X1)) | ($true != wellorder($o)) | ($false = vAPP(sTfun($o,$o),$o,sK8($o),X0))) ) | (~spl72_28 | ~spl72_63)),
% 78.92/11.77 inference(superposition,[],[f2348,f2021])).
% 78.92/11.77 thf(f19709,plain,(
% 78.92/11.77 spl72_383 | ~spl72_81 | ~spl72_159),
% 78.92/11.77 inference(avatar_split_clause,[],[f3750,f3675,f2522,f19707])).
% 78.92/11.77 thf(f19707,plain,(
% 78.92/11.77 spl72_383 <=> ! [X0 : $tType,X4 : X0,X3 : X0 > nat,X2 : X0,X1 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X1)),vAPP(X0,nat,X3,X2))) | (X1 != X2) | (X1 != X4))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_383])])).
% 78.92/11.77 thf(f3750,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X1)),vAPP(X0,nat,X3,X2))) | (X1 != X2) | (X1 != X4)) ) | (~spl72_81 | ~spl72_159)),
% 78.92/11.77 inference(forward_demodulation,[],[f3732,f2573])).
% 78.92/11.77 thf(f2573,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > nat] : ((vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2)) ) | ~spl72_81),
% 78.92/11.77 inference(leibniz_equality_elimination,[],[f2523])).
% 78.92/11.77 thf(f3732,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : X0] : ((X1 != X2) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))),vAPP(X0,nat,X3,X2))) | (X1 != X4)) ) | ~spl72_159),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f3731])).
% 78.92/11.77 thf(f3731,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : X0] : ((X1 != X2) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))),vAPP(X0,nat,X3,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4))) ) | ~spl72_159),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f3695])).
% 78.92/11.77 thf(f3695,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))),vAPP(X0,nat,X3,X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X4))) ) | ~spl72_159),
% 78.92/11.77 inference(primitive_instantiation,[],[f3676])).
% 78.92/11.77 thf(f19700,plain,(
% 78.92/11.77 spl72_344 | spl72_382 | ~spl72_104),
% 78.92/11.77 inference(avatar_split_clause,[],[f2845,f2779,f19698,f11811])).
% 78.92/11.77 thf(f19698,plain,(
% 78.92/11.77 spl72_382 <=> ! [X0 : $tType,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),vNOT),X1)) | (wellorder(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_382])])).
% 78.92/11.77 thf(f2845,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),vNOT),X1)) | ($false = X2) | (wellorder(X0) != $true)) ) | ~spl72_104),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2844])).
% 78.92/11.77 thf(f2844,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),vNOT),X1)) | ($true = vAPP($o,$o,vNOT,X2)) | (wellorder(X0) != $true)) ) | ~spl72_104),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2838])).
% 78.92/11.77 thf(f2838,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK45(X0,$o),vNOT),X1))) | ($true = vAPP($o,$o,vNOT,X2)) | (wellorder(X0) != $true)) ) | ~spl72_104),
% 78.92/11.77 inference(primitive_instantiation,[],[f2780])).
% 78.92/11.77 thf(f19691,plain,(
% 78.92/11.77 spl72_344 | spl72_381 | ~spl72_103),
% 78.92/11.77 inference(avatar_split_clause,[],[f2817,f2775,f19689,f11811])).
% 78.92/11.77 thf(f19689,plain,(
% 78.92/11.77 spl72_381 <=> ! [X0 : $tType,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),vNOT),X1)) | (wellorder(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_381])])).
% 78.92/11.77 thf(f2817,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),vNOT),X1)) | ($false = X2) | (wellorder(X0) != $true)) ) | ~spl72_103),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2816])).
% 78.92/11.77 thf(f2816,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true = vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),vNOT),X1)) | ($true = vAPP($o,$o,vNOT,X2)) | (wellorder(X0) != $true)) ) | ~spl72_103),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2810])).
% 78.92/11.77 thf(f2810,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : $o,X1 : $o > X0] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,X0),$o,vAPP(sTfun($o,$o),sTfun(sTfun($o,X0),$o),sK44(X0,$o),vNOT),X1))) | ($true = vAPP($o,$o,vNOT,X2)) | (wellorder(X0) != $true)) ) | ~spl72_103),
% 78.92/11.77 inference(primitive_instantiation,[],[f2776])).
% 78.92/11.77 thf(f19687,plain,(
% 78.92/11.77 spl72_380 | ~spl72_16 | ~spl72_85),
% 78.92/11.77 inference(avatar_split_clause,[],[f2685,f2624,f1964,f19685])).
% 78.92/11.77 thf(f19685,plain,(
% 78.92/11.77 spl72_380 <=> ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X1),X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_380])])).
% 78.92/11.77 thf(f2685,plain,(
% 78.92/11.77 ( ! [X0 : $o,X1 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X1),X0))) ) | (~spl72_16 | ~spl72_85)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2680])).
% 78.92/11.77 thf(f2680,plain,(
% 78.92/11.77 ( ! [X0 : $o,X1 : $o] : (($true != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X1)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X1),X0))) ) | (~spl72_16 | ~spl72_85)),
% 78.92/11.77 inference(superposition,[],[f2625,f1966])).
% 78.92/11.77 thf(f19683,plain,(
% 78.92/11.77 spl72_379 | ~spl72_14 | ~spl72_50 | ~spl72_83),
% 78.92/11.77 inference(avatar_split_clause,[],[f2668,f2616,f2246,f1954,f19681])).
% 78.92/11.77 thf(f19681,plain,(
% 78.92/11.77 spl72_379 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X0))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_379])])).
% 78.92/11.77 thf(f2668,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X0))) ) | (~spl72_14 | ~spl72_50 | ~spl72_83)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2667])).
% 78.92/11.77 thf(f2667,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X0))) ) | (~spl72_14 | ~spl72_50 | ~spl72_83)),
% 78.92/11.77 inference(forward_demodulation,[],[f2659,f1956])).
% 78.92/11.77 thf(f2659,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X0)) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_83)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2646])).
% 78.92/11.77 thf(f2646,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))),X0)) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_83)),
% 78.92/11.77 inference(superposition,[],[f2617,f2247])).
% 78.92/11.77 thf(f19679,plain,(
% 78.92/11.77 spl72_378 | ~spl72_28 | ~spl72_75),
% 78.92/11.77 inference(avatar_split_clause,[],[f2493,f2471,f2020,f19677])).
% 78.92/11.77 thf(f19677,plain,(
% 78.92/11.77 spl72_378 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_378])])).
% 78.92/11.77 thf(f2493,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_75)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2492])).
% 78.92/11.77 thf(f2492,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) ) | (~spl72_28 | ~spl72_75)),
% 78.92/11.77 inference(superposition,[],[f2472,f2021])).
% 78.92/11.77 thf(f19675,plain,(
% 78.92/11.77 spl72_377 | ~spl72_45 | ~spl72_306),
% 78.92/11.77 inference(avatar_split_clause,[],[f6981,f6956,f2201,f19673])).
% 78.92/11.77 thf(f6956,plain,(
% 78.92/11.77 spl72_306 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,$o)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_306])])).
% 78.92/11.77 thf(f6981,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,$o))))) ) | (~spl72_45 | ~spl72_306)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f6980])).
% 78.92/11.77 thf(f6980,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,sTfun(X0,$o))))) ) | (~spl72_45 | ~spl72_306)),
% 78.92/11.77 inference(superposition,[],[f2202,f6957])).
% 78.92/11.77 thf(f6957,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,$o)))) ) | ~spl72_306),
% 78.92/11.77 inference(avatar_component_clause,[],[f6956])).
% 78.92/11.77 thf(f19671,plain,(
% 78.92/11.77 spl72_376 | ~spl72_28 | ~spl72_73),
% 78.92/11.77 inference(avatar_split_clause,[],[f2476,f2463,f2020,f19669])).
% 78.92/11.77 thf(f19669,plain,(
% 78.92/11.77 spl72_376 <=> ! [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))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_376])])).
% 78.92/11.77 thf(f2463,plain,(
% 78.92/11.77 spl72_73 <=> ! [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))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_73])])).
% 78.92/11.77 thf(f2476,plain,(
% 78.92/11.77 ( ! [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)) ) | (~spl72_28 | ~spl72_73)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2475])).
% 78.92/11.77 thf(f2475,plain,(
% 78.92/11.77 ( ! [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)) ) | (~spl72_28 | ~spl72_73)),
% 78.92/11.77 inference(superposition,[],[f2464,f2021])).
% 78.92/11.77 thf(f2464,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : ((ab_semigroup_add(X0) != $true) | (plus_plus(X0) = vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,X0)),cCOMB,plus_plus(X0)))) ) | ~spl72_73),
% 78.92/11.77 inference(avatar_component_clause,[],[f2463])).
% 78.92/11.77 thf(f19667,plain,(
% 78.92/11.77 spl72_375 | ~spl72_14 | ~spl72_50 | ~spl72_62),
% 78.92/11.77 inference(avatar_split_clause,[],[f2399,f2343,f2246,f1954,f19665])).
% 78.92/11.77 thf(f19665,plain,(
% 78.92/11.77 spl72_375 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_375])])).
% 78.92/11.77 thf(f2343,plain,(
% 78.92/11.77 spl72_62 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_62])])).
% 78.92/11.77 thf(f2399,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_14 | ~spl72_50 | ~spl72_62)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2398])).
% 78.92/11.77 thf(f2398,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0))))) ) | (~spl72_14 | ~spl72_50 | ~spl72_62)),
% 78.92/11.77 inference(forward_demodulation,[],[f2382,f1956])).
% 78.92/11.77 thf(f2382,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_62)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2379])).
% 78.92/11.77 thf(f2379,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0)))) | (wellorder(nat) != $true)) ) | (~spl72_50 | ~spl72_62)),
% 78.92/11.77 inference(superposition,[],[f2344,f2247])).
% 78.92/11.77 thf(f2344,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true)) ) | ~spl72_62),
% 78.92/11.77 inference(avatar_component_clause,[],[f2343])).
% 78.92/11.77 thf(f19571,plain,(
% 78.92/11.77 spl72_374 | ~spl72_81),
% 78.92/11.77 inference(avatar_split_clause,[],[f2573,f2522,f19569])).
% 78.92/11.77 thf(f19569,plain,(
% 78.92/11.77 spl72_374 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > nat] : (vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X1),vAPP(X0,sTfun(X0,$o),vEQ(X0),X2)) = X2)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_374])])).
% 78.92/11.77 thf(f19371,plain,(
% 78.92/11.77 spl72_373 | ~spl72_2 | ~spl72_77),
% 78.92/11.77 inference(avatar_split_clause,[],[f2508,f2500,f1894,f19369])).
% 78.92/11.77 thf(f19369,plain,(
% 78.92/11.77 spl72_373 <=> ! [X0 : product_prod(nat,nat) > a,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),X0),X1),X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_373])])).
% 78.92/11.77 thf(f1894,plain,(
% 78.92/11.77 spl72_2 <=> (linordered_idom(a) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_2])])).
% 78.92/11.77 thf(f2508,plain,(
% 78.92/11.77 ( ! [X0 : product_prod(nat,nat) > a,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),X0),X1),X1))) ) | (~spl72_2 | ~spl72_77)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2503])).
% 78.92/11.77 thf(f2503,plain,(
% 78.92/11.77 ( ! [X0 : product_prod(nat,nat) > a,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),X0),X1),X1))) ) | (~spl72_2 | ~spl72_77)),
% 78.92/11.77 inference(superposition,[],[f2501,f1896])).
% 78.92/11.77 thf(f1896,plain,(
% 78.92/11.77 (linordered_idom(a) = $true) | ~spl72_2),
% 78.92/11.77 inference(avatar_component_clause,[],[f1894])).
% 78.92/11.77 thf(f19367,plain,(
% 78.92/11.77 spl72_372 | ~spl72_3 | ~spl72_77),
% 78.92/11.77 inference(avatar_split_clause,[],[f2507,f2500,f1899,f19365])).
% 78.92/11.77 thf(f19365,plain,(
% 78.92/11.77 spl72_372 <=> ! [X0 : product_prod(nat,nat) > capacity,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),X0),X1),X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_372])])).
% 78.92/11.77 thf(f1899,plain,(
% 78.92/11.77 spl72_3 <=> (linordered_idom(capacity) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_3])])).
% 78.92/11.77 thf(f2507,plain,(
% 78.92/11.77 ( ! [X0 : product_prod(nat,nat) > capacity,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),X0),X1),X1))) ) | (~spl72_3 | ~spl72_77)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2504])).
% 78.92/11.77 thf(f2504,plain,(
% 78.92/11.77 ( ! [X0 : product_prod(nat,nat) > capacity,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),X0),X1),X1))) ) | (~spl72_3 | ~spl72_77)),
% 78.92/11.77 inference(superposition,[],[f2501,f1901])).
% 78.92/11.77 thf(f1901,plain,(
% 78.92/11.77 (linordered_idom(capacity) = $true) | ~spl72_3),
% 78.92/11.77 inference(avatar_component_clause,[],[f1899])).
% 78.92/11.77 thf(f19223,plain,(
% 78.92/11.77 spl72_371 | ~spl72_45 | ~spl72_305),
% 78.92/11.77 inference(avatar_split_clause,[],[f6977,f6952,f2201,f19221])).
% 78.92/11.77 thf(f6952,plain,(
% 78.92/11.77 spl72_305 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,nat)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_305])])).
% 78.92/11.77 thf(f6977,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,sTfun(X0,nat))))) ) | (~spl72_45 | ~spl72_305)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f6976])).
% 78.92/11.77 thf(f6976,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,sTfun(X0,nat))))) ) | (~spl72_45 | ~spl72_305)),
% 78.92/11.77 inference(superposition,[],[f2202,f6953])).
% 78.92/11.77 thf(f6953,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,nat)))) ) | ~spl72_305),
% 78.92/11.77 inference(avatar_component_clause,[],[f6952])).
% 78.92/11.77 thf(f19127,plain,(
% 78.92/11.77 spl72_370 | ~spl72_7 | ~spl72_50 | ~spl72_122),
% 78.92/11.77 inference(avatar_split_clause,[],[f3049,f3029,f2246,f1919,f19125])).
% 78.92/11.77 thf(f19125,plain,(
% 78.92/11.77 spl72_370 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X0),X0)) = X0)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_370])])).
% 78.92/11.77 thf(f3049,plain,(
% 78.92/11.77 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X0),X0)) = X0)) ) | (~spl72_7 | ~spl72_50 | ~spl72_122)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f3048])).
% 78.92/11.77 thf(f3048,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X0),X0)) = X0)) ) | (~spl72_7 | ~spl72_50 | ~spl72_122)),
% 78.92/11.77 inference(forward_demodulation,[],[f3047,f1921])).
% 78.92/11.77 thf(f3047,plain,(
% 78.92/11.77 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X0),X0)) = X0) | (canoni770627133id_add(nat) != $true)) ) | (~spl72_50 | ~spl72_122)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f3036])).
% 78.92/11.77 thf(f3036,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK7(nat),X0),X0)) = X0) | (canoni770627133id_add(nat) != $true)) ) | (~spl72_50 | ~spl72_122)),
% 78.92/11.77 inference(superposition,[],[f3030,f2247])).
% 78.92/11.77 thf(f19123,plain,(
% 78.92/11.77 spl72_369 | ~spl72_28 | ~spl72_65),
% 78.92/11.77 inference(avatar_split_clause,[],[f2429,f2355,f2020,f19121])).
% 78.92/11.77 thf(f19121,plain,(
% 78.92/11.77 spl72_369 <=> ! [X0 : nat,X1 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_369])])).
% 78.92/11.77 thf(f2429,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) ) | (~spl72_28 | ~spl72_65)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2428])).
% 78.92/11.77 thf(f2428,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) ) | (~spl72_28 | ~spl72_65)),
% 78.92/11.77 inference(superposition,[],[f2356,f2021])).
% 78.92/11.77 thf(f19119,plain,(
% 78.92/11.77 spl72_368 | ~spl72_28 | ~spl72_64),
% 78.92/11.77 inference(avatar_split_clause,[],[f2427,f2351,f2020,f19117])).
% 78.92/11.77 thf(f19117,plain,(
% 78.92/11.77 spl72_368 <=> ! [X0 : nat,X1 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_368])])).
% 78.92/11.77 thf(f2427,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))) ) | (~spl72_28 | ~spl72_64)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2426])).
% 78.92/11.77 thf(f2426,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))) ) | (~spl72_28 | ~spl72_64)),
% 78.92/11.77 inference(superposition,[],[f2352,f2021])).
% 78.92/11.77 thf(f19115,plain,(
% 78.92/11.77 spl72_367 | ~spl72_28 | ~spl72_63),
% 78.92/11.77 inference(avatar_split_clause,[],[f2410,f2347,f2020,f19113])).
% 78.92/11.77 thf(f19113,plain,(
% 78.92/11.77 spl72_367 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_367])])).
% 78.92/11.77 thf(f2410,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1)))) ) | (~spl72_28 | ~spl72_63)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2409])).
% 78.92/11.77 thf(f2409,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1)))) ) | (~spl72_28 | ~spl72_63)),
% 78.92/11.77 inference(superposition,[],[f2348,f2021])).
% 78.92/11.77 thf(f19111,plain,(
% 78.92/11.77 spl72_366 | ~spl72_28 | ~spl72_62),
% 78.92/11.77 inference(avatar_split_clause,[],[f2381,f2343,f2020,f19109])).
% 78.92/11.77 thf(f19109,plain,(
% 78.92/11.77 spl72_366 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_366])])).
% 78.92/11.77 thf(f2381,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_62)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2380])).
% 78.92/11.77 thf(f2380,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true != $true) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (wellorder(X0) != $true) | ($false = vAPP(X0,$o,X1,X2))) ) | (~spl72_28 | ~spl72_62)),
% 78.92/11.77 inference(superposition,[],[f2344,f2021])).
% 78.92/11.77 thf(f18674,plain,(
% 78.92/11.77 ~spl72_337 | spl72_338 | spl72_339 | ~spl72_62),
% 78.92/11.77 inference(avatar_split_clause,[],[f12570,f2343,f7896,f7892,f7888])).
% 78.92/11.77 thf(f7892,plain,(
% 78.92/11.77 spl72_338 <=> ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_338])])).
% 78.92/11.77 thf(f12570,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)) | ($true != wellorder($o))) ) | ~spl72_62),
% 78.92/11.77 inference(not_proxy_clausification,[],[f12569])).
% 78.92/11.77 thf(f12569,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_62),
% 78.92/11.77 inference(not_proxy_clausification,[],[f12564])).
% 78.92/11.77 thf(f12564,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_62),
% 78.92/11.77 inference(primitive_instantiation,[],[f2344])).
% 78.92/11.77 thf(f18670,plain,(
% 78.92/11.77 spl72_365 | ~spl72_338 | ~spl72_364),
% 78.92/11.77 inference(avatar_split_clause,[],[f18666,f18663,f7892,f18668])).
% 78.92/11.77 thf(f18668,plain,(
% 78.92/11.77 spl72_365 <=> ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$false),X0)) | ($true = X0))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_365])])).
% 78.92/11.77 thf(f18663,plain,(
% 78.92/11.77 spl72_364 <=> ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)),X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_364])])).
% 78.92/11.77 thf(f18666,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),$false),X0)) | ($true = X0)) ) | (~spl72_338 | ~spl72_364)),
% 78.92/11.77 inference(forward_demodulation,[],[f18664,f7894])).
% 78.92/11.77 thf(f7894,plain,(
% 78.92/11.77 ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)) | ~spl72_338),
% 78.92/11.77 inference(avatar_component_clause,[],[f7892])).
% 78.92/11.77 thf(f18664,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)),X0)) | ($true = X0)) ) | ~spl72_364),
% 78.92/11.77 inference(avatar_component_clause,[],[f18663])).
% 78.92/11.77 thf(f18665,plain,(
% 78.92/11.77 spl72_364 | ~spl72_83 | ~spl72_337),
% 78.92/11.77 inference(avatar_split_clause,[],[f8036,f7888,f2616,f18663])).
% 78.92/11.77 thf(f8036,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)),X0))) ) | (~spl72_83 | ~spl72_337)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f8035])).
% 78.92/11.77 thf(f8035,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)),X0))) ) | (~spl72_83 | ~spl72_337)),
% 78.92/11.77 inference(forward_demodulation,[],[f2660,f7889])).
% 78.92/11.77 thf(f7889,plain,(
% 78.92/11.77 ($true = wellorder($o)) | ~spl72_337),
% 78.92/11.77 inference(avatar_component_clause,[],[f7888])).
% 78.92/11.77 thf(f2660,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)),X0)) | ($true != wellorder($o))) ) | ~spl72_83),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2645])).
% 78.92/11.77 thf(f2645,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)),X0)) | ($true != wellorder($o))) ) | ~spl72_83),
% 78.92/11.77 inference(primitive_instantiation,[],[f2617])).
% 78.92/11.77 thf(f18661,plain,(
% 78.92/11.77 spl72_363 | ~spl72_50 | ~spl72_108),
% 78.92/11.77 inference(avatar_split_clause,[],[f2884,f2869,f2246,f18659])).
% 78.92/11.77 thf(f18659,plain,(
% 78.92/11.77 spl72_363 <=> ! [X0 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X0),X0)) = X0)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_363])])).
% 78.92/11.77 thf(f2884,plain,(
% 78.92/11.77 ( ! [X0 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X0),X0)) = X0)) ) | (~spl72_50 | ~spl72_108)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2873])).
% 78.92/11.77 thf(f2873,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X0),X0)) = X0)) ) | (~spl72_50 | ~spl72_108)),
% 78.92/11.77 inference(superposition,[],[f2870,f2247])).
% 78.92/11.77 thf(f18657,plain,(
% 78.92/11.77 spl72_362 | ~spl72_10 | ~spl72_73),
% 78.92/11.77 inference(avatar_split_clause,[],[f2477,f2463,f1934,f18654])).
% 78.92/11.77 thf(f18654,plain,(
% 78.92/11.77 spl72_362 <=> (plus_plus(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus(nat)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_362])])).
% 78.92/11.77 thf(f2477,plain,(
% 78.92/11.77 (plus_plus(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus(nat))) | (~spl72_10 | ~spl72_73)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2474])).
% 78.92/11.77 thf(f2474,plain,(
% 78.92/11.77 ($true != $true) | (plus_plus(nat) = vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,nat)),cCOMB,plus_plus(nat))) | (~spl72_10 | ~spl72_73)),
% 78.92/11.77 inference(superposition,[],[f2464,f1936])).
% 78.92/11.77 thf(f18652,plain,(
% 78.92/11.77 spl72_361 | ~spl72_63),
% 78.92/11.77 inference(avatar_split_clause,[],[f2414,f2347,f18650])).
% 78.92/11.77 thf(f18650,plain,(
% 78.92/11.77 spl72_361 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,sK8(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | (X1 = X2) | (wellorder(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_361])])).
% 78.92/11.77 thf(f2414,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,sK8(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | (X1 = X2) | (wellorder(X0) != $true)) ) | ~spl72_63),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2413])).
% 78.92/11.77 thf(f2413,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(sTfun(X0,$o),X0,sK8(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) != X1) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (wellorder(X0) != $true)) ) | ~spl72_63),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2406])).
% 78.92/11.77 thf(f2406,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),vAPP(sTfun(X0,$o),X0,sK8(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vEQ(X0),X1),X2)) | (wellorder(X0) != $true)) ) | ~spl72_63),
% 78.92/11.77 inference(primitive_instantiation,[],[f2348])).
% 78.92/11.77 thf(f18170,plain,(
% 78.92/11.77 spl72_360 | spl72_339 | ~spl72_81),
% 78.92/11.77 inference(avatar_split_clause,[],[f2596,f2522,f7896,f18168])).
% 78.92/11.77 thf(f2596,plain,(
% 78.92/11.77 ( ! [X0 : $o,X1 : $o > nat] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT))) ) | ~spl72_81),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2595])).
% 78.92/11.77 thf(f2595,plain,(
% 78.92/11.77 ( ! [X0 : $o,X1 : $o > nat] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT)))) ) | ~spl72_81),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2580])).
% 78.92/11.77 thf(f2580,plain,(
% 78.92/11.77 ( ! [X0 : $o,X1 : $o > nat] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK67($o),X1),vNOT)))) ) | ~spl72_81),
% 78.92/11.77 inference(primitive_instantiation,[],[f2523])).
% 78.92/11.77 thf(f18008,plain,(
% 78.92/11.77 spl72_344 | spl72_359 | ~spl72_80),
% 78.92/11.77 inference(avatar_split_clause,[],[f2559,f2518,f18006,f11811])).
% 78.92/11.77 thf(f18006,plain,(
% 78.92/11.77 spl72_359 <=> ! [X0 : $o > nat] : ($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),vNOT))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_359])])).
% 78.92/11.77 thf(f2559,plain,(
% 78.92/11.77 ( ! [X0 : $o > nat,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),vNOT)) | ($false = X1)) ) | ~spl72_80),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2558])).
% 78.92/11.77 thf(f2558,plain,(
% 78.92/11.77 ( ! [X0 : $o > nat,X1 : $o] : (($true = vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),vNOT)) | ($true = vAPP($o,$o,vNOT,X1))) ) | ~spl72_80),
% 78.92/11.77 inference(not_proxy_clausification,[],[f2552])).
% 78.92/11.77 thf(f2552,plain,(
% 78.92/11.77 ( ! [X0 : $o > nat,X1 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,vAPP(sTfun($o,nat),sTfun(sTfun($o,$o),$o),sK66($o),X0),vNOT))) | ($true = vAPP($o,$o,vNOT,X1))) ) | ~spl72_80),
% 78.92/11.77 inference(primitive_instantiation,[],[f2519])).
% 78.92/11.77 thf(f18004,plain,(
% 78.92/11.77 spl72_358 | ~spl72_28 | ~spl72_61),
% 78.92/11.77 inference(avatar_split_clause,[],[f2340,f2333,f2020,f18002])).
% 78.92/11.77 thf(f18002,plain,(
% 78.92/11.77 spl72_358 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))) | (no_top(X0) = $false))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_358])])).
% 78.92/11.77 thf(f2333,plain,(
% 78.92/11.77 spl72_61 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))) | (no_top(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_61])])).
% 78.92/11.77 thf(f2340,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))) | (no_top(X0) = $false)) ) | (~spl72_28 | ~spl72_61)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2339])).
% 78.92/11.77 thf(f2339,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))) | (no_top(X0) = $false)) ) | (~spl72_28 | ~spl72_61)),
% 78.92/11.77 inference(superposition,[],[f2334,f2021])).
% 78.92/11.77 thf(f2334,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((no_top(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1)))) ) | ~spl72_61),
% 78.92/11.77 inference(avatar_component_clause,[],[f2333])).
% 78.92/11.77 thf(f18000,plain,(
% 78.92/11.77 spl72_357 | ~spl72_28 | ~spl72_60),
% 78.92/11.77 inference(avatar_split_clause,[],[f2337,f2329,f2020,f17998])).
% 78.92/11.77 thf(f17998,plain,(
% 78.92/11.77 spl72_357 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)) | (no_bot(X0) = $false))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_357])])).
% 78.92/11.77 thf(f2329,plain,(
% 78.92/11.77 spl72_60 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)) | (no_bot(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_60])])).
% 78.92/11.77 thf(f2337,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)) | (no_bot(X0) = $false)) ) | (~spl72_28 | ~spl72_60)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2336])).
% 78.92/11.77 thf(f2336,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)) | (no_bot(X0) = $false)) ) | (~spl72_28 | ~spl72_60)),
% 78.92/11.77 inference(superposition,[],[f2330,f2021])).
% 78.92/11.77 thf(f2330,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((no_bot(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1))) ) | ~spl72_60),
% 78.92/11.77 inference(avatar_component_clause,[],[f2329])).
% 78.92/11.77 thf(f17988,plain,(
% 78.92/11.77 spl72_356 | ~spl72_62),
% 78.92/11.77 inference(avatar_split_clause,[],[f2371,f2343,f17986])).
% 78.92/11.77 thf(f17986,plain,(
% 78.92/11.77 spl72_356 <=> ! [X0 : $tType,X1 : X0] : ((wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_356])])).
% 78.92/11.77 thf(f2371,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((wellorder(X0) != $true) | (vAPP(sTfun(X0,$o),X0,ord_Least(X0),vAPP(X0,sTfun(X0,$o),vEQ(X0),X1)) = X1)) ) | ~spl72_62),
% 78.92/11.77 inference(leibniz_equality_elimination,[],[f2344])).
% 78.92/11.77 thf(f16747,plain,(
% 78.92/11.77 spl72_355 | ~spl72_28 | ~spl72_58),
% 78.92/11.77 inference(avatar_split_clause,[],[f2325,f2304,f2020,f16745])).
% 78.92/11.77 thf(f16745,plain,(
% 78.92/11.77 spl72_355 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_355])])).
% 78.92/11.77 thf(f2325,plain,(
% 78.92/11.77 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)))) ) | (~spl72_28 | ~spl72_58)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2324])).
% 78.92/11.77 thf(f2324,plain,(
% 78.92/11.77 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)))) ) | (~spl72_28 | ~spl72_58)),
% 78.92/11.77 inference(superposition,[],[f2305,f2021])).
% 78.92/11.77 thf(f16743,plain,(
% 78.92/11.77 spl72_354 | ~spl72_28 | ~spl72_57),
% 78.92/11.77 inference(avatar_split_clause,[],[f2317,f2300,f2020,f16741])).
% 78.92/11.77 thf(f16741,plain,(
% 78.92/11.77 spl72_354 <=> ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0))))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_354])])).
% 78.92/11.77 thf(f2317,plain,(
% 78.92/11.77 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)))) ) | (~spl72_28 | ~spl72_57)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2316])).
% 78.92/11.77 thf(f2316,plain,(
% 78.92/11.77 ( ! [X0 : nat > $o,X1 : nat] : (($true != $true) | ($true = vAPP(nat,$o,X0,X1)) | ($false = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)))) ) | (~spl72_28 | ~spl72_57)),
% 78.92/11.77 inference(superposition,[],[f2301,f2021])).
% 78.92/11.77 thf(f16628,plain,(
% 78.92/11.77 spl72_353 | ~spl72_4 | ~spl72_61),
% 78.92/11.77 inference(avatar_split_clause,[],[f2341,f2333,f1904,f16626])).
% 78.92/11.77 thf(f16626,plain,(
% 78.92/11.77 spl72_353 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,sK6(nat),X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_353])])).
% 78.92/11.77 thf(f1904,plain,(
% 78.92/11.77 spl72_4 <=> (no_top(nat) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_4])])).
% 78.92/11.77 thf(f2341,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,sK6(nat),X0)))) ) | (~spl72_4 | ~spl72_61)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2338])).
% 78.92/11.77 thf(f2338,plain,(
% 78.92/11.77 ( ! [X0 : nat] : (($true != $true) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,sK6(nat),X0)))) ) | (~spl72_4 | ~spl72_61)),
% 78.92/11.77 inference(superposition,[],[f2334,f1906])).
% 78.92/11.77 thf(f1906,plain,(
% 78.92/11.77 (no_top(nat) = $true) | ~spl72_4),
% 78.92/11.77 inference(avatar_component_clause,[],[f1904])).
% 78.92/11.77 thf(f16624,plain,(
% 78.92/11.77 spl72_352 | ~spl72_58),
% 78.92/11.77 inference(avatar_split_clause,[],[f2327,f2304,f16622])).
% 78.92/11.77 thf(f16622,plain,(
% 78.92/11.77 spl72_352 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK43,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_352])])).
% 78.92/11.77 thf(f2327,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK43,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1)) ) | ~spl72_58),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2326])).
% 78.92/11.77 thf(f2326,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK43,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl72_58),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2323])).
% 78.92/11.77 thf(f2323,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK43,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl72_58),
% 78.92/11.77 inference(primitive_instantiation,[],[f2305])).
% 78.92/11.77 thf(f16620,plain,(
% 78.92/11.77 spl72_351 | ~spl72_57),
% 78.92/11.77 inference(avatar_split_clause,[],[f2319,f2300,f16618])).
% 78.92/11.77 thf(f16618,plain,(
% 78.92/11.77 spl72_351 <=> ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_351])])).
% 78.92/11.77 thf(f2319,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | (X0 = X1)) ) | ~spl72_57),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2318])).
% 78.92/11.77 thf(f2318,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : ((vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)) != X0) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl72_57),
% 78.92/11.77 inference(equality_proxy_clausification,[],[f2315])).
% 78.92/11.77 thf(f2315,plain,(
% 78.92/11.77 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),vAPP(sTfun(nat,$o),nat,sK42,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),X0),X1))) ) | ~spl72_57),
% 78.92/11.77 inference(primitive_instantiation,[],[f2301])).
% 78.92/11.77 thf(f16193,plain,(
% 78.92/11.77 spl72_350 | ~spl72_28 | ~spl72_56),
% 78.92/11.77 inference(avatar_split_clause,[],[f2295,f2276,f2020,f16191])).
% 78.92/11.77 thf(f16191,plain,(
% 78.92/11.77 spl72_350 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) = $false))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_350])])).
% 78.92/11.77 thf(f2276,plain,(
% 78.92/11.77 spl72_56 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_56])])).
% 78.92/11.77 thf(f2295,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) = $false)) ) | (~spl72_28 | ~spl72_56)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2294])).
% 78.92/11.77 thf(f2294,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) = $false)) ) | (~spl72_28 | ~spl72_56)),
% 78.92/11.77 inference(superposition,[],[f2277,f2021])).
% 78.92/11.77 thf(f2277,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((order(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))) ) | ~spl72_56),
% 78.92/11.77 inference(avatar_component_clause,[],[f2276])).
% 78.92/11.77 thf(f16189,plain,(
% 78.92/11.77 spl72_349 | ~spl72_28 | ~spl72_55),
% 78.92/11.77 inference(avatar_split_clause,[],[f2290,f2272,f2020,f16187])).
% 78.92/11.77 thf(f16187,plain,(
% 78.92/11.77 spl72_349 <=> ! [X0 : $tType,X1 : X0] : ((order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_349])])).
% 78.92/11.77 thf(f2272,plain,(
% 78.92/11.77 spl72_55 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_55])])).
% 78.92/11.77 thf(f2290,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))) ) | (~spl72_28 | ~spl72_55)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2289])).
% 78.92/11.77 thf(f2289,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (order(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))) ) | (~spl72_28 | ~spl72_55)),
% 78.92/11.77 inference(superposition,[],[f2273,f2021])).
% 78.92/11.77 thf(f2273,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true)) ) | ~spl72_55),
% 78.92/11.77 inference(avatar_component_clause,[],[f2272])).
% 78.92/11.77 thf(f16185,plain,(
% 78.92/11.77 spl72_348 | ~spl72_25 | ~spl72_54),
% 78.92/11.77 inference(avatar_split_clause,[],[f2286,f2268,f2008,f16183])).
% 78.92/11.77 thf(f16183,plain,(
% 78.92/11.77 spl72_348 <=> ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_348])])).
% 78.92/11.77 thf(f2008,plain,(
% 78.92/11.77 spl72_25 <=> ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_25])])).
% 78.92/11.77 thf(f2268,plain,(
% 78.92/11.77 spl72_54 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_54])])).
% 78.92/11.77 thf(f2286,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))) ) | (~spl72_25 | ~spl72_54)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2283])).
% 78.92/11.77 thf(f2283,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : set(X0)] : (($true != $true) | ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))) ) | (~spl72_25 | ~spl72_54)),
% 78.92/11.77 inference(superposition,[],[f2269,f2009])).
% 78.92/11.77 thf(f2009,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = preorder(set(X0)))) ) | ~spl72_25),
% 78.92/11.77 inference(avatar_component_clause,[],[f2008])).
% 78.92/11.77 thf(f2269,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((preorder(X0) != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))) ) | ~spl72_54),
% 78.92/11.77 inference(avatar_component_clause,[],[f2268])).
% 78.92/11.77 thf(f16181,plain,(
% 78.92/11.77 spl72_347 | ~spl72_28 | ~spl72_54),
% 78.92/11.77 inference(avatar_split_clause,[],[f2285,f2268,f2020,f16179])).
% 78.92/11.77 thf(f16179,plain,(
% 78.92/11.77 spl72_347 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) = $false))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_347])])).
% 78.92/11.77 thf(f2285,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) = $false)) ) | (~spl72_28 | ~spl72_54)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2284])).
% 78.92/11.77 thf(f2284,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) = $false)) ) | (~spl72_28 | ~spl72_54)),
% 78.92/11.77 inference(superposition,[],[f2269,f2021])).
% 78.92/11.77 thf(f16177,plain,(
% 78.92/11.77 spl72_346 | ~spl72_28 | ~spl72_53),
% 78.92/11.77 inference(avatar_split_clause,[],[f2280,f2264,f2020,f16175])).
% 78.92/11.77 thf(f16175,plain,(
% 78.92/11.77 spl72_346 <=> ! [X0 : $tType,X1 : X0] : ((preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_346])])).
% 78.92/11.77 thf(f2264,plain,(
% 78.92/11.77 spl72_53 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_53])])).
% 78.92/11.77 thf(f2280,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : ((preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))) ) | (~spl72_28 | ~spl72_53)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f2279])).
% 78.92/11.77 thf(f2279,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != $true) | (preorder(X0) != $true) | ($false = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))) ) | (~spl72_28 | ~spl72_53)),
% 78.92/11.77 inference(superposition,[],[f2265,f2021])).
% 78.92/11.77 thf(f2265,plain,(
% 78.92/11.77 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true)) ) | ~spl72_53),
% 78.92/11.77 inference(avatar_component_clause,[],[f2264])).
% 78.92/11.77 thf(f12363,plain,(
% 78.92/11.77 ~spl72_44 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12362])).
% 78.92/11.77 thf(f12362,plain,(
% 78.92/11.77 $false | (~spl72_44 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11826])).
% 78.92/11.77 thf(f11826,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_44 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2150,f11812])).
% 78.92/11.77 thf(f11812,plain,(
% 78.92/11.77 ( ! [X0 : $o] : (($false = X0)) ) | ~spl72_344),
% 78.92/11.77 inference(avatar_component_clause,[],[f11811])).
% 78.92/11.77 thf(f2150,plain,(
% 78.92/11.77 ($true = type(capacity)) | ~spl72_44),
% 78.92/11.77 inference(avatar_component_clause,[],[f2148])).
% 78.92/11.77 thf(f2148,plain,(
% 78.92/11.77 spl72_44 <=> ($true = type(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_44])])).
% 78.92/11.77 thf(f12361,plain,(
% 78.92/11.77 ~spl72_47 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12360])).
% 78.92/11.77 thf(f12360,plain,(
% 78.92/11.77 $false | (~spl72_47 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11827])).
% 78.92/11.77 thf(f11827,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_47 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2211,f11812])).
% 78.92/11.77 thf(f2211,plain,(
% 78.92/11.77 ($true = type(a)) | ~spl72_47),
% 78.92/11.77 inference(avatar_component_clause,[],[f2209])).
% 78.92/11.77 thf(f2209,plain,(
% 78.92/11.77 spl72_47 <=> ($true = type(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_47])])).
% 78.92/11.77 thf(f12359,plain,(
% 78.92/11.77 ~spl72_9 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12358])).
% 78.92/11.77 thf(f12358,plain,(
% 78.92/11.77 $false | (~spl72_9 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11828])).
% 78.92/11.77 thf(f11828,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_9 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1931,f11812])).
% 78.92/11.77 thf(f1931,plain,(
% 78.92/11.77 (size(nat) = $true) | ~spl72_9),
% 78.92/11.77 inference(avatar_component_clause,[],[f1929])).
% 78.92/11.77 thf(f1929,plain,(
% 78.92/11.77 spl72_9 <=> (size(nat) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_9])])).
% 78.92/11.77 thf(f12357,plain,(
% 78.92/11.77 ~spl72_24 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12356])).
% 78.92/11.77 thf(f12356,plain,(
% 78.92/11.77 $false | (~spl72_24 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11829])).
% 78.92/11.77 thf(f11829,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_24 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2005,f11812])).
% 78.92/11.77 thf(f2005,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = size(list(X0)))) ) | ~spl72_24),
% 78.92/11.77 inference(avatar_component_clause,[],[f2004])).
% 78.92/11.77 thf(f2004,plain,(
% 78.92/11.77 spl72_24 <=> ! [X0 : $tType] : ($true = size(list(X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_24])])).
% 78.92/11.77 thf(f12355,plain,(
% 78.92/11.77 ~spl72_29 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12354])).
% 78.92/11.77 thf(f12354,plain,(
% 78.92/11.77 $false | (~spl72_29 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11830])).
% 78.92/11.77 thf(f11830,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_29 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2025,f11812])).
% 78.92/11.77 thf(f2025,plain,(
% 78.92/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = size(product_prod(X0,X1)))) ) | ~spl72_29),
% 78.92/11.77 inference(avatar_component_clause,[],[f2024])).
% 78.92/11.77 thf(f2024,plain,(
% 78.92/11.77 spl72_29 <=> ! [X1 : $tType,X0 : $tType] : ($true = size(product_prod(X0,X1)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_29])])).
% 78.92/11.77 thf(f12353,plain,(
% 78.92/11.77 ~spl72_20 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12352])).
% 78.92/11.77 thf(f12352,plain,(
% 78.92/11.77 $false | (~spl72_20 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11833])).
% 78.92/11.77 thf(f11833,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_20 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1986,f11812])).
% 78.92/11.77 thf(f12351,plain,(
% 78.92/11.77 ~spl72_21 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12350])).
% 78.92/11.77 thf(f12350,plain,(
% 78.92/11.77 $false | (~spl72_21 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11834])).
% 78.92/11.77 thf(f11834,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_21 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1991,f11812])).
% 78.92/11.77 thf(f12349,plain,(
% 78.92/11.77 ~spl72_308 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12348])).
% 78.92/11.77 thf(f12348,plain,(
% 78.92/11.77 $false | (~spl72_308 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11835])).
% 78.92/11.77 thf(f11835,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_308 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f6965,f11812])).
% 78.92/11.77 thf(f12347,plain,(
% 78.92/11.77 ~spl72_307 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12346])).
% 78.92/11.77 thf(f12346,plain,(
% 78.92/11.77 $false | (~spl72_307 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11836])).
% 78.92/11.77 thf(f11836,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_307 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f6961,f11812])).
% 78.92/11.77 thf(f12345,plain,(
% 78.92/11.77 ~spl72_312 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12344])).
% 78.92/11.77 thf(f12344,plain,(
% 78.92/11.77 $false | (~spl72_312 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11837])).
% 78.92/11.77 thf(f11837,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_312 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f7021,f11812])).
% 78.92/11.77 thf(f12343,plain,(
% 78.92/11.77 ~spl72_26 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12342])).
% 78.92/11.77 thf(f12342,plain,(
% 78.92/11.77 $false | (~spl72_26 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11838])).
% 78.92/11.77 thf(f11838,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_26 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2013,f11812])).
% 78.92/11.77 thf(f2013,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = ord(set(X0)))) ) | ~spl72_26),
% 78.92/11.77 inference(avatar_component_clause,[],[f2012])).
% 78.92/11.77 thf(f2012,plain,(
% 78.92/11.77 spl72_26 <=> ! [X0 : $tType] : ($true = ord(set(X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_26])])).
% 78.92/11.77 thf(f12341,plain,(
% 78.92/11.77 ~spl72_189 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12340])).
% 78.92/11.77 thf(f12340,plain,(
% 78.92/11.77 $false | (~spl72_189 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11839])).
% 78.92/11.77 thf(f11839,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_189 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f4157,f11812])).
% 78.92/11.77 thf(f4157,plain,(
% 78.92/11.77 ($true = ord(capacity)) | ~spl72_189),
% 78.92/11.77 inference(avatar_component_clause,[],[f4155])).
% 78.92/11.77 thf(f4155,plain,(
% 78.92/11.77 spl72_189 <=> ($true = ord(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_189])])).
% 78.92/11.77 thf(f12339,plain,(
% 78.92/11.77 ~spl72_196 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12338])).
% 78.92/11.77 thf(f12338,plain,(
% 78.92/11.77 $false | (~spl72_196 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11840])).
% 78.92/11.77 thf(f11840,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_196 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f4267,f11812])).
% 78.92/11.77 thf(f4267,plain,(
% 78.92/11.77 ($true = ord(a)) | ~spl72_196),
% 78.92/11.77 inference(avatar_component_clause,[],[f4265])).
% 78.92/11.77 thf(f4265,plain,(
% 78.92/11.77 spl72_196 <=> ($true = ord(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_196])])).
% 78.92/11.77 thf(f12337,plain,(
% 78.92/11.77 ~spl72_22 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12336])).
% 78.92/11.77 thf(f12336,plain,(
% 78.92/11.77 $false | (~spl72_22 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11847])).
% 78.92/11.77 thf(f11847,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_22 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1996,f11812])).
% 78.92/11.77 thf(f1996,plain,(
% 78.92/11.77 (order($o) = $true) | ~spl72_22),
% 78.92/11.77 inference(avatar_component_clause,[],[f1994])).
% 78.92/11.77 thf(f1994,plain,(
% 78.92/11.77 spl72_22 <=> (order($o) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_22])])).
% 78.92/11.77 thf(f12335,plain,(
% 78.92/11.77 ~spl72_23 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12334])).
% 78.92/11.77 thf(f12334,plain,(
% 78.92/11.77 $false | (~spl72_23 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11848])).
% 78.92/11.77 thf(f11848,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_23 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2001,f11812])).
% 78.92/11.77 thf(f12333,plain,(
% 78.92/11.77 ~spl72_310 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12332])).
% 78.92/11.77 thf(f12332,plain,(
% 78.92/11.77 $false | (~spl72_310 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11849])).
% 78.92/11.77 thf(f11849,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_310 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f6973,f11812])).
% 78.92/11.77 thf(f12331,plain,(
% 78.92/11.77 ~spl72_309 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12330])).
% 78.92/11.77 thf(f12330,plain,(
% 78.92/11.77 $false | (~spl72_309 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11850])).
% 78.92/11.77 thf(f11850,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_309 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f6969,f11812])).
% 78.92/11.77 thf(f12329,plain,(
% 78.92/11.77 ~spl72_313 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12328])).
% 78.92/11.77 thf(f12328,plain,(
% 78.92/11.77 $false | (~spl72_313 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11851])).
% 78.92/11.77 thf(f11851,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_313 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f7025,f11812])).
% 78.92/11.77 thf(f12327,plain,(
% 78.92/11.77 ~spl72_27 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12326])).
% 78.92/11.77 thf(f12326,plain,(
% 78.92/11.77 $false | (~spl72_27 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11852])).
% 78.92/11.77 thf(f11852,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_27 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2017,f11812])).
% 78.92/11.77 thf(f2017,plain,(
% 78.92/11.77 ( ! [X0 : $tType] : (($true = order(set(X0)))) ) | ~spl72_27),
% 78.92/11.77 inference(avatar_component_clause,[],[f2016])).
% 78.92/11.77 thf(f2016,plain,(
% 78.92/11.77 spl72_27 <=> ! [X0 : $tType] : ($true = order(set(X0)))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_27])])).
% 78.92/11.77 thf(f12325,plain,(
% 78.92/11.77 ~spl72_202 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12324])).
% 78.92/11.77 thf(f12324,plain,(
% 78.92/11.77 $false | (~spl72_202 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11853])).
% 78.92/11.77 thf(f11853,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_202 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f4362,f11812])).
% 78.92/11.77 thf(f4362,plain,(
% 78.92/11.77 ($true = order(capacity)) | ~spl72_202),
% 78.92/11.77 inference(avatar_component_clause,[],[f4360])).
% 78.92/11.77 thf(f4360,plain,(
% 78.92/11.77 spl72_202 <=> ($true = order(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_202])])).
% 78.92/11.77 thf(f12323,plain,(
% 78.92/11.77 ~spl72_207 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12322])).
% 78.92/11.77 thf(f12322,plain,(
% 78.92/11.77 $false | (~spl72_207 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11854])).
% 78.92/11.77 thf(f11854,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_207 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f4615,f11812])).
% 78.92/11.77 thf(f4615,plain,(
% 78.92/11.77 ($true = order(a)) | ~spl72_207),
% 78.92/11.77 inference(avatar_component_clause,[],[f4613])).
% 78.92/11.77 thf(f4613,plain,(
% 78.92/11.77 spl72_207 <=> ($true = order(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_207])])).
% 78.92/11.77 thf(f12321,plain,(
% 78.92/11.77 ~spl72_66 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12320])).
% 78.92/11.77 thf(f12320,plain,(
% 78.92/11.77 $false | (~spl72_66 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11855])).
% 78.92/11.77 thf(f11855,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_66 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2361,f11812])).
% 78.92/11.77 thf(f2361,plain,(
% 78.92/11.77 ($true = group_add(capacity)) | ~spl72_66),
% 78.92/11.77 inference(avatar_component_clause,[],[f2359])).
% 78.92/11.77 thf(f2359,plain,(
% 78.92/11.77 spl72_66 <=> ($true = group_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_66])])).
% 78.92/11.77 thf(f12319,plain,(
% 78.92/11.77 ~spl72_71 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12318])).
% 78.92/11.77 thf(f12318,plain,(
% 78.92/11.77 $false | (~spl72_71 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11856])).
% 78.92/11.77 thf(f11856,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_71 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2445,f11812])).
% 78.92/11.77 thf(f2445,plain,(
% 78.92/11.77 ($true = group_add(a)) | ~spl72_71),
% 78.92/11.77 inference(avatar_component_clause,[],[f2443])).
% 78.92/11.77 thf(f2443,plain,(
% 78.92/11.77 spl72_71 <=> ($true = group_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_71])])).
% 78.92/11.77 thf(f12317,plain,(
% 78.92/11.77 ~spl72_4 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12316])).
% 78.92/11.77 thf(f12316,plain,(
% 78.92/11.77 $false | (~spl72_4 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11858])).
% 78.92/11.77 thf(f11858,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_4 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1906,f11812])).
% 78.92/11.77 thf(f12315,plain,(
% 78.92/11.77 ~spl72_16 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12314])).
% 78.92/11.77 thf(f12314,plain,(
% 78.92/11.77 $false | (~spl72_16 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11864])).
% 78.92/11.77 thf(f11864,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_16 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1966,f11812])).
% 78.92/11.77 thf(f12313,plain,(
% 78.92/11.77 ~spl72_17 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12312])).
% 78.92/11.77 thf(f12312,plain,(
% 78.92/11.77 $false | (~spl72_17 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11865])).
% 78.92/11.77 thf(f11865,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_17 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1971,f11812])).
% 78.92/11.77 thf(f12311,plain,(
% 78.92/11.77 ~spl72_168 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12310])).
% 78.92/11.77 thf(f12310,plain,(
% 78.92/11.77 $false | (~spl72_168 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11866])).
% 78.92/11.77 thf(f11866,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_168 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3779,f11812])).
% 78.92/11.77 thf(f3779,plain,(
% 78.92/11.77 ($true = linorder(capacity)) | ~spl72_168),
% 78.92/11.77 inference(avatar_component_clause,[],[f3777])).
% 78.92/11.77 thf(f3777,plain,(
% 78.92/11.77 spl72_168 <=> ($true = linorder(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_168])])).
% 78.92/11.77 thf(f12309,plain,(
% 78.92/11.77 ~spl72_171 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12308])).
% 78.92/11.77 thf(f12308,plain,(
% 78.92/11.77 $false | (~spl72_171 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11867])).
% 78.92/11.77 thf(f11867,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_171 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3874,f11812])).
% 78.92/11.77 thf(f3874,plain,(
% 78.92/11.77 ($true = linorder(a)) | ~spl72_171),
% 78.92/11.77 inference(avatar_component_clause,[],[f3872])).
% 78.92/11.77 thf(f3872,plain,(
% 78.92/11.77 spl72_171 <=> ($true = linorder(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_171])])).
% 78.92/11.77 thf(f12307,plain,(
% 78.92/11.77 ~spl72_18 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12306])).
% 78.92/11.77 thf(f12306,plain,(
% 78.92/11.77 $false | (~spl72_18 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11870])).
% 78.92/11.77 thf(f11870,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_18 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1976,f11812])).
% 78.92/11.77 thf(f1976,plain,(
% 78.92/11.77 (preorder($o) = $true) | ~spl72_18),
% 78.92/11.77 inference(avatar_component_clause,[],[f1974])).
% 78.92/11.77 thf(f1974,plain,(
% 78.92/11.77 spl72_18 <=> (preorder($o) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_18])])).
% 78.92/11.77 thf(f12305,plain,(
% 78.92/11.77 ~spl72_19 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12304])).
% 78.92/11.77 thf(f12304,plain,(
% 78.92/11.77 $false | (~spl72_19 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11871])).
% 78.92/11.77 thf(f11871,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_19 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1981,f11812])).
% 78.92/11.77 thf(f12303,plain,(
% 78.92/11.77 ~spl72_306 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12302])).
% 78.92/11.77 thf(f12302,plain,(
% 78.92/11.77 $false | (~spl72_306 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11872])).
% 78.92/11.77 thf(f11872,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_306 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f6957,f11812])).
% 78.92/11.77 thf(f12301,plain,(
% 78.92/11.77 ~spl72_305 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12300])).
% 78.92/11.77 thf(f12300,plain,(
% 78.92/11.77 $false | (~spl72_305 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11873])).
% 78.92/11.77 thf(f11873,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_305 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f6953,f11812])).
% 78.92/11.77 thf(f12299,plain,(
% 78.92/11.77 ~spl72_311 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12298])).
% 78.92/11.77 thf(f12298,plain,(
% 78.92/11.77 $false | (~spl72_311 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11874])).
% 78.92/11.77 thf(f11874,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_311 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f7017,f11812])).
% 78.92/11.77 thf(f12297,plain,(
% 78.92/11.77 ~spl72_25 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12296])).
% 78.92/11.77 thf(f12296,plain,(
% 78.92/11.77 $false | (~spl72_25 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11875])).
% 78.92/11.77 thf(f11875,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_25 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2009,f11812])).
% 78.92/11.77 thf(f12295,plain,(
% 78.92/11.77 ~spl72_179 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12294])).
% 78.92/11.77 thf(f12294,plain,(
% 78.92/11.77 $false | (~spl72_179 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11876])).
% 78.92/11.77 thf(f11876,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_179 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f4003,f11812])).
% 78.92/11.77 thf(f4003,plain,(
% 78.92/11.77 ($true = preorder(capacity)) | ~spl72_179),
% 78.92/11.77 inference(avatar_component_clause,[],[f4001])).
% 78.92/11.77 thf(f4001,plain,(
% 78.92/11.77 spl72_179 <=> ($true = preorder(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_179])])).
% 78.92/11.77 thf(f12293,plain,(
% 78.92/11.77 ~spl72_183 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12292])).
% 78.92/11.77 thf(f12292,plain,(
% 78.92/11.77 $false | (~spl72_183 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11877])).
% 78.92/11.77 thf(f11877,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_183 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f4064,f11812])).
% 78.92/11.77 thf(f4064,plain,(
% 78.92/11.77 ($true = preorder(a)) | ~spl72_183),
% 78.92/11.77 inference(avatar_component_clause,[],[f4062])).
% 78.92/11.77 thf(f4062,plain,(
% 78.92/11.77 spl72_183 <=> ($true = preorder(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_183])])).
% 78.92/11.77 thf(f12291,plain,(
% 78.92/11.77 ~spl72_14 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12290])).
% 78.92/11.77 thf(f12290,plain,(
% 78.92/11.77 $false | (~spl72_14 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11878])).
% 78.92/11.77 thf(f11878,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_14 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1956,f11812])).
% 78.92/11.77 thf(f12289,plain,(
% 78.92/11.77 spl72_341 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12288])).
% 78.92/11.77 thf(f12288,plain,(
% 78.92/11.77 $false | (spl72_341 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11880])).
% 78.92/11.77 thf(f11880,plain,(
% 78.92/11.77 ($false != $false) | (spl72_341 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f7909,f11812])).
% 78.92/11.77 thf(f7909,plain,(
% 78.92/11.77 ($false != wellorder($o)) | spl72_341),
% 78.92/11.77 inference(avatar_component_clause,[],[f7908])).
% 78.92/11.77 thf(f7908,plain,(
% 78.92/11.77 spl72_341 <=> ($false = wellorder($o))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_341])])).
% 78.92/11.77 thf(f12287,plain,(
% 78.92/11.77 ~spl72_337 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12286])).
% 78.92/11.77 thf(f12286,plain,(
% 78.92/11.77 $false | (~spl72_337 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11881])).
% 78.92/11.77 thf(f11881,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_337 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f7889,f11812])).
% 78.92/11.77 thf(f12285,plain,(
% 78.92/11.77 ~spl72_6 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12284])).
% 78.92/11.77 thf(f12284,plain,(
% 78.92/11.77 $false | (~spl72_6 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11883])).
% 78.92/11.77 thf(f11883,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_6 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1916,f11812])).
% 78.92/11.77 thf(f12283,plain,(
% 78.92/11.77 ~spl72_52 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12282])).
% 78.92/11.77 thf(f12282,plain,(
% 78.92/11.77 $false | (~spl72_52 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11884])).
% 78.92/11.77 thf(f11884,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_52 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2261,f11812])).
% 78.92/11.77 thf(f2261,plain,(
% 78.92/11.77 ($true = semigroup_add(capacity)) | ~spl72_52),
% 78.92/11.77 inference(avatar_component_clause,[],[f2259])).
% 78.92/11.77 thf(f2259,plain,(
% 78.92/11.77 spl72_52 <=> ($true = semigroup_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_52])])).
% 78.92/11.77 thf(f12281,plain,(
% 78.92/11.77 ~spl72_59 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12280])).
% 78.92/11.77 thf(f12280,plain,(
% 78.92/11.77 $false | (~spl72_59 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11885])).
% 78.92/11.77 thf(f11885,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_59 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2310,f11812])).
% 78.92/11.77 thf(f2310,plain,(
% 78.92/11.77 ($true = semigroup_add(a)) | ~spl72_59),
% 78.92/11.77 inference(avatar_component_clause,[],[f2308])).
% 78.92/11.77 thf(f2308,plain,(
% 78.92/11.77 spl72_59 <=> ($true = semigroup_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_59])])).
% 78.92/11.77 thf(f12279,plain,(
% 78.92/11.77 ~spl72_2 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12278])).
% 78.92/11.77 thf(f12278,plain,(
% 78.92/11.77 $false | (~spl72_2 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11886])).
% 78.92/11.77 thf(f11886,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_2 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1896,f11812])).
% 78.92/11.77 thf(f12277,plain,(
% 78.92/11.77 ~spl72_3 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12276])).
% 78.92/11.77 thf(f12276,plain,(
% 78.92/11.77 $false | (~spl72_3 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11887])).
% 78.92/11.77 thf(f11887,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_3 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1901,f11812])).
% 78.92/11.77 thf(f12275,plain,(
% 78.92/11.77 ~spl72_8 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12274])).
% 78.92/11.77 thf(f12274,plain,(
% 78.92/11.77 $false | (~spl72_8 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11913])).
% 78.92/11.77 thf(f11913,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_8 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1926,f11812])).
% 78.92/11.77 thf(f1926,plain,(
% 78.92/11.77 (comm_monoid_add(nat) = $true) | ~spl72_8),
% 78.92/11.77 inference(avatar_component_clause,[],[f1924])).
% 78.92/11.77 thf(f1924,plain,(
% 78.92/11.77 spl72_8 <=> (comm_monoid_add(nat) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_8])])).
% 78.92/11.77 thf(f12273,plain,(
% 78.92/11.77 ~spl72_89 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12272])).
% 78.92/11.77 thf(f12272,plain,(
% 78.92/11.77 $false | (~spl72_89 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11914])).
% 78.92/11.77 thf(f11914,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_89 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2691,f11812])).
% 78.92/11.77 thf(f2691,plain,(
% 78.92/11.77 ($true = comm_monoid_add(capacity)) | ~spl72_89),
% 78.92/11.77 inference(avatar_component_clause,[],[f2689])).
% 78.92/11.77 thf(f2689,plain,(
% 78.92/11.77 spl72_89 <=> ($true = comm_monoid_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_89])])).
% 78.92/11.77 thf(f12271,plain,(
% 78.92/11.77 ~spl72_94 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12270])).
% 78.92/11.77 thf(f12270,plain,(
% 78.92/11.77 $false | (~spl72_94 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11915])).
% 78.92/11.77 thf(f11915,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_94 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2740,f11812])).
% 78.92/11.77 thf(f2740,plain,(
% 78.92/11.77 ($true = comm_monoid_add(a)) | ~spl72_94),
% 78.92/11.77 inference(avatar_component_clause,[],[f2738])).
% 78.92/11.77 thf(f2738,plain,(
% 78.92/11.77 spl72_94 <=> ($true = comm_monoid_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_94])])).
% 78.92/11.77 thf(f12269,plain,(
% 78.92/11.77 ~spl72_10 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12268])).
% 78.92/11.77 thf(f12268,plain,(
% 78.92/11.77 $false | (~spl72_10 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11919])).
% 78.92/11.77 thf(f11919,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_10 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1936,f11812])).
% 78.92/11.77 thf(f12267,plain,(
% 78.92/11.77 ~spl72_105 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12266])).
% 78.92/11.77 thf(f12266,plain,(
% 78.92/11.77 $false | (~spl72_105 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11920])).
% 78.92/11.77 thf(f11920,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_105 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2785,f11812])).
% 78.92/11.77 thf(f2785,plain,(
% 78.92/11.77 ($true = ab_semigroup_add(capacity)) | ~spl72_105),
% 78.92/11.77 inference(avatar_component_clause,[],[f2783])).
% 78.92/11.77 thf(f2783,plain,(
% 78.92/11.77 spl72_105 <=> ($true = ab_semigroup_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_105])])).
% 78.92/11.77 thf(f12265,plain,(
% 78.92/11.77 ~spl72_106 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12264])).
% 78.92/11.77 thf(f12264,plain,(
% 78.92/11.77 $false | (~spl72_106 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11921])).
% 78.92/11.77 thf(f11921,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_106 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2862,f11812])).
% 78.92/11.77 thf(f2862,plain,(
% 78.92/11.77 ($true = ab_semigroup_add(a)) | ~spl72_106),
% 78.92/11.77 inference(avatar_component_clause,[],[f2860])).
% 78.92/11.77 thf(f2860,plain,(
% 78.92/11.77 spl72_106 <=> ($true = ab_semigroup_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_106])])).
% 78.92/11.77 thf(f12263,plain,(
% 78.92/11.77 ~spl72_11 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12262])).
% 78.92/11.77 thf(f12262,plain,(
% 78.92/11.77 $false | (~spl72_11 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11922])).
% 78.92/11.77 thf(f11922,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_11 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1941,f11812])).
% 78.92/11.77 thf(f1941,plain,(
% 78.92/11.77 (cancel_semigroup_add(nat) = $true) | ~spl72_11),
% 78.92/11.77 inference(avatar_component_clause,[],[f1939])).
% 78.92/11.77 thf(f1939,plain,(
% 78.92/11.77 spl72_11 <=> (cancel_semigroup_add(nat) = $true)),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_11])])).
% 78.92/11.77 thf(f12261,plain,(
% 78.92/11.77 ~spl72_117 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12260])).
% 78.92/11.77 thf(f12260,plain,(
% 78.92/11.77 $false | (~spl72_117 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11923])).
% 78.92/11.77 thf(f11923,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_117 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f2977,f11812])).
% 78.92/11.77 thf(f2977,plain,(
% 78.92/11.77 ($true = cancel_semigroup_add(capacity)) | ~spl72_117),
% 78.92/11.77 inference(avatar_component_clause,[],[f2975])).
% 78.92/11.77 thf(f2975,plain,(
% 78.92/11.77 spl72_117 <=> ($true = cancel_semigroup_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_117])])).
% 78.92/11.77 thf(f12259,plain,(
% 78.92/11.77 ~spl72_123 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12258])).
% 78.92/11.77 thf(f12258,plain,(
% 78.92/11.77 $false | (~spl72_123 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11924])).
% 78.92/11.77 thf(f11924,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_123 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3059,f11812])).
% 78.92/11.77 thf(f3059,plain,(
% 78.92/11.77 ($true = cancel_semigroup_add(a)) | ~spl72_123),
% 78.92/11.77 inference(avatar_component_clause,[],[f3057])).
% 78.92/11.77 thf(f3057,plain,(
% 78.92/11.77 spl72_123 <=> ($true = cancel_semigroup_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_123])])).
% 78.92/11.77 thf(f12257,plain,(
% 78.92/11.77 ~spl72_12 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12256])).
% 78.92/11.77 thf(f12256,plain,(
% 78.92/11.77 $false | (~spl72_12 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11925])).
% 78.92/11.77 thf(f11925,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_12 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1946,f11812])).
% 78.92/11.77 thf(f12255,plain,(
% 78.92/11.77 ~spl72_131 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12254])).
% 78.92/11.77 thf(f12254,plain,(
% 78.92/11.77 $false | (~spl72_131 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11926])).
% 78.92/11.77 thf(f11926,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_131 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3135,f11812])).
% 78.92/11.77 thf(f3135,plain,(
% 78.92/11.77 ($true = ordere779506340up_add(capacity)) | ~spl72_131),
% 78.92/11.77 inference(avatar_component_clause,[],[f3133])).
% 78.92/11.77 thf(f3133,plain,(
% 78.92/11.77 spl72_131 <=> ($true = ordere779506340up_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_131])])).
% 78.92/11.77 thf(f12253,plain,(
% 78.92/11.77 ~spl72_136 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12252])).
% 78.92/11.77 thf(f12252,plain,(
% 78.92/11.77 $false | (~spl72_136 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11927])).
% 78.92/11.77 thf(f11927,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_136 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3217,f11812])).
% 78.92/11.77 thf(f3217,plain,(
% 78.92/11.77 ($true = ordere779506340up_add(a)) | ~spl72_136),
% 78.92/11.77 inference(avatar_component_clause,[],[f3215])).
% 78.92/11.77 thf(f3215,plain,(
% 78.92/11.77 spl72_136 <=> ($true = ordere779506340up_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_136])])).
% 78.92/11.77 thf(f12251,plain,(
% 78.92/11.77 ~spl72_7 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12250])).
% 78.92/11.77 thf(f12250,plain,(
% 78.92/11.77 $false | (~spl72_7 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11928])).
% 78.92/11.77 thf(f11928,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_7 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1921,f11812])).
% 78.92/11.77 thf(f12249,plain,(
% 78.92/11.77 ~spl72_13 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12248])).
% 78.92/11.77 thf(f12248,plain,(
% 78.92/11.77 $false | (~spl72_13 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11930])).
% 78.92/11.77 thf(f11930,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_13 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1951,f11812])).
% 78.92/11.77 thf(f12247,plain,(
% 78.92/11.77 ~spl72_143 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12246])).
% 78.92/11.77 thf(f12246,plain,(
% 78.92/11.77 $false | (~spl72_143 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11931])).
% 78.92/11.77 thf(f11931,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_143 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3269,f11812])).
% 78.92/11.77 thf(f3269,plain,(
% 78.92/11.77 ($true = ordere236663937imp_le(capacity)) | ~spl72_143),
% 78.92/11.77 inference(avatar_component_clause,[],[f3267])).
% 78.92/11.77 thf(f3267,plain,(
% 78.92/11.77 spl72_143 <=> ($true = ordere236663937imp_le(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_143])])).
% 78.92/11.77 thf(f12245,plain,(
% 78.92/11.77 ~spl72_148 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12244])).
% 78.92/11.77 thf(f12244,plain,(
% 78.92/11.77 $false | (~spl72_148 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11932])).
% 78.92/11.77 thf(f11932,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_148 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3476,f11812])).
% 78.92/11.77 thf(f3476,plain,(
% 78.92/11.77 ($true = ordere236663937imp_le(a)) | ~spl72_148),
% 78.92/11.77 inference(avatar_component_clause,[],[f3474])).
% 78.92/11.77 thf(f3474,plain,(
% 78.92/11.77 spl72_148 <=> ($true = ordere236663937imp_le(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_148])])).
% 78.92/11.77 thf(f12243,plain,(
% 78.92/11.77 ~spl72_15 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12242])).
% 78.92/11.77 thf(f12242,plain,(
% 78.92/11.77 $false | (~spl72_15 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11933])).
% 78.92/11.77 thf(f11933,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_15 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1961,f11812])).
% 78.92/11.77 thf(f12241,plain,(
% 78.92/11.77 ~spl72_155 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12240])).
% 78.92/11.77 thf(f12240,plain,(
% 78.92/11.77 $false | (~spl72_155 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11934])).
% 78.92/11.77 thf(f11934,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_155 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3626,f11812])).
% 78.92/11.77 thf(f3626,plain,(
% 78.92/11.77 ($true = ordere223160158up_add(capacity)) | ~spl72_155),
% 78.92/11.77 inference(avatar_component_clause,[],[f3624])).
% 78.92/11.77 thf(f3624,plain,(
% 78.92/11.77 spl72_155 <=> ($true = ordere223160158up_add(capacity))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_155])])).
% 78.92/11.77 thf(f12239,plain,(
% 78.92/11.77 ~spl72_160 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12238])).
% 78.92/11.77 thf(f12238,plain,(
% 78.92/11.77 $false | (~spl72_160 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11935])).
% 78.92/11.77 thf(f11935,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_160 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f3681,f11812])).
% 78.92/11.77 thf(f3681,plain,(
% 78.92/11.77 ($true = ordere223160158up_add(a)) | ~spl72_160),
% 78.92/11.77 inference(avatar_component_clause,[],[f3679])).
% 78.92/11.77 thf(f3679,plain,(
% 78.92/11.77 spl72_160 <=> ($true = ordere223160158up_add(a))),
% 78.92/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_160])])).
% 78.92/11.77 thf(f12237,plain,(
% 78.92/11.77 ~spl72_5 | ~spl72_344),
% 78.92/11.77 inference(avatar_contradiction_clause,[],[f12236])).
% 78.92/11.77 thf(f12236,plain,(
% 78.92/11.77 $false | (~spl72_5 | ~spl72_344)),
% 78.92/11.77 inference(trivial_inequality_removal,[],[f11936])).
% 78.92/11.77 thf(f11936,plain,(
% 78.92/11.77 ($true = $false) | (~spl72_5 | ~spl72_344)),
% 78.92/11.77 inference(superposition,[],[f1911,f11812])).
% 78.92/11.77 thf(f1911,plain,(
% 78.92/11.77 (strict2144017051up_add(nat) = $true) | ~spl72_5),
% 78.92/11.77 inference(avatar_component_clause,[],[f1909])).
% 79.42/11.77 thf(f1909,plain,(
% 79.42/11.77 spl72_5 <=> (strict2144017051up_add(nat) = $true)),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_5])])).
% 79.42/11.77 thf(f12235,plain,(
% 79.42/11.77 ~spl72_76 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12234])).
% 79.42/11.77 thf(f12234,plain,(
% 79.42/11.77 $false | (~spl72_76 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f11937])).
% 79.42/11.77 thf(f11937,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_76 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f2497,f11812])).
% 79.42/11.77 thf(f2497,plain,(
% 79.42/11.77 ($true = strict2144017051up_add(capacity)) | ~spl72_76),
% 79.42/11.77 inference(avatar_component_clause,[],[f2495])).
% 79.42/11.77 thf(f2495,plain,(
% 79.42/11.77 spl72_76 <=> ($true = strict2144017051up_add(capacity))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_76])])).
% 79.42/11.77 thf(f12233,plain,(
% 79.42/11.77 ~spl72_82 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12232])).
% 79.42/11.77 thf(f12232,plain,(
% 79.42/11.77 $false | (~spl72_82 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f11938])).
% 79.42/11.77 thf(f11938,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_82 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f2613,f11812])).
% 79.42/11.77 thf(f2613,plain,(
% 79.42/11.77 ($true = strict2144017051up_add(a)) | ~spl72_82),
% 79.42/11.77 inference(avatar_component_clause,[],[f2611])).
% 79.42/11.77 thf(f2611,plain,(
% 79.42/11.77 spl72_82 <=> ($true = strict2144017051up_add(a))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_82])])).
% 79.42/11.77 thf(f12231,plain,(
% 79.42/11.77 ~spl72_50 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12230])).
% 79.42/11.77 thf(f12230,plain,(
% 79.42/11.77 $false | (~spl72_50 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12024])).
% 79.42/11.77 thf(f12024,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_50 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f2247,f11812])).
% 79.42/11.77 thf(f12229,plain,(
% 79.42/11.77 ~spl72_67 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12228])).
% 79.42/11.77 thf(f12228,plain,(
% 79.42/11.77 $false | (~spl72_67 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12025])).
% 79.42/11.77 thf(f12025,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_67 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f2365,f11812])).
% 79.42/11.77 thf(f12227,plain,(
% 79.42/11.77 ~spl72_68 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12226])).
% 79.42/11.77 thf(f12226,plain,(
% 79.42/11.77 $false | (~spl72_68 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12026])).
% 79.42/11.77 thf(f12026,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_68 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f2369,f11812])).
% 79.42/11.77 thf(f12223,plain,(
% 79.42/11.77 ~spl72_72 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12222])).
% 79.42/11.77 thf(f12222,plain,(
% 79.42/11.77 $false | (~spl72_72 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12084])).
% 79.42/11.77 thf(f12084,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_72 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f2450,f11812])).
% 79.42/11.77 thf(f12221,plain,(
% 79.42/11.77 ~spl72_141 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12220])).
% 79.42/11.77 thf(f12220,plain,(
% 79.42/11.77 $false | (~spl72_141 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12086])).
% 79.42/11.77 thf(f12086,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_141 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3251,f11812])).
% 79.42/11.77 thf(f12219,plain,(
% 79.42/11.77 ~spl72_142 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12218])).
% 79.42/11.77 thf(f12218,plain,(
% 79.42/11.77 $false | (~spl72_142 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12092])).
% 79.42/11.77 thf(f12092,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_142 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3256,f11812])).
% 79.42/11.77 thf(f12216,plain,(
% 79.42/11.77 ~spl72_124 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12215])).
% 79.42/11.77 thf(f12215,plain,(
% 79.42/11.77 $false | (~spl72_124 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12113])).
% 79.42/11.77 thf(f12113,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_124 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3064,f11812])).
% 79.42/11.77 thf(f12214,plain,(
% 79.42/11.77 ~spl72_125 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12213])).
% 79.42/11.77 thf(f12213,plain,(
% 79.42/11.77 $false | (~spl72_125 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12114])).
% 79.42/11.77 thf(f12114,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_125 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3069,f11812])).
% 79.42/11.77 thf(f12212,plain,(
% 79.42/11.77 ~spl72_126 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12211])).
% 79.42/11.77 thf(f12211,plain,(
% 79.42/11.77 $false | (~spl72_126 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12115])).
% 79.42/11.77 thf(f12115,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_126 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3074,f11812])).
% 79.42/11.77 thf(f12210,plain,(
% 79.42/11.77 ~spl72_127 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12209])).
% 79.42/11.77 thf(f12209,plain,(
% 79.42/11.77 $false | (~spl72_127 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12116])).
% 79.42/11.77 thf(f12116,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_127 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3079,f11812])).
% 79.42/11.77 thf(f12208,plain,(
% 79.42/11.77 ~spl72_128 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12207])).
% 79.42/11.77 thf(f12207,plain,(
% 79.42/11.77 $false | (~spl72_128 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12117])).
% 79.42/11.77 thf(f12117,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_128 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3084,f11812])).
% 79.42/11.77 thf(f12206,plain,(
% 79.42/11.77 ~spl72_129 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12205])).
% 79.42/11.77 thf(f12205,plain,(
% 79.42/11.77 $false | (~spl72_129 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12118])).
% 79.42/11.77 thf(f12118,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_129 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3089,f11812])).
% 79.42/11.77 thf(f12204,plain,(
% 79.42/11.77 ~spl72_130 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12203])).
% 79.42/11.77 thf(f12203,plain,(
% 79.42/11.77 $false | (~spl72_130 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12119])).
% 79.42/11.77 thf(f12119,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_130 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f3094,f11812])).
% 79.42/11.77 thf(f12202,plain,(
% 79.42/11.77 spl72_1 | ~spl72_344),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f12201])).
% 79.42/11.77 thf(f12201,plain,(
% 79.42/11.77 $false | (spl72_1 | ~spl72_344)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f12121])).
% 79.42/11.77 thf(f12121,plain,(
% 79.42/11.77 ($false != $false) | (spl72_1 | ~spl72_344)),
% 79.42/11.77 inference(superposition,[],[f1891,f11812])).
% 79.42/11.77 thf(f1891,plain,(
% 79.42/11.77 ($true != $false) | spl72_1),
% 79.42/11.77 inference(avatar_component_clause,[],[f1889])).
% 79.42/11.77 thf(f1889,plain,(
% 79.42/11.77 spl72_1 <=> ($true = $false)),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_1])])).
% 79.42/11.77 thf(f11817,plain,(
% 79.42/11.77 spl72_344 | spl72_345 | ~spl72_63 | ~spl72_337),
% 79.42/11.77 inference(avatar_split_clause,[],[f8312,f7888,f2347,f11814,f11811])).
% 79.42/11.77 thf(f11814,plain,(
% 79.42/11.77 spl72_345 <=> ($true = vAPP(sTfun($o,$o),$o,sK8($o),vNOT))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_345])])).
% 79.42/11.77 thf(f8312,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK8($o),vNOT)) | ($false = X0)) ) | (~spl72_63 | ~spl72_337)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f8311])).
% 79.42/11.77 thf(f8311,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true != $true) | ($true = vAPP(sTfun($o,$o),$o,sK8($o),vNOT)) | ($false = X0)) ) | (~spl72_63 | ~spl72_337)),
% 79.42/11.77 inference(forward_demodulation,[],[f2412,f7889])).
% 79.42/11.77 thf(f2412,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK8($o),vNOT)) | ($false = X0) | ($true != wellorder($o))) ) | ~spl72_63),
% 79.42/11.77 inference(not_proxy_clausification,[],[f2411])).
% 79.42/11.77 thf(f2411,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = vAPP(sTfun($o,$o),$o,sK8($o),vNOT)) | ($true = vAPP($o,$o,vNOT,X0)) | ($true != wellorder($o))) ) | ~spl72_63),
% 79.42/11.77 inference(not_proxy_clausification,[],[f2407])).
% 79.42/11.77 thf(f2407,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,sK8($o),vNOT))) | ($true = vAPP($o,$o,vNOT,X0)) | ($true != wellorder($o))) ) | ~spl72_63),
% 79.42/11.77 inference(primitive_instantiation,[],[f2348])).
% 79.42/11.77 thf(f11809,plain,(
% 79.42/11.77 spl72_343 | ~spl72_48 | ~spl72_207),
% 79.42/11.77 inference(avatar_split_clause,[],[f6945,f4613,f2214,f11807])).
% 79.42/11.77 thf(f6945,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,a)))) ) | (~spl72_48 | ~spl72_207)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f6944])).
% 79.42/11.77 thf(f6944,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,a)))) ) | (~spl72_48 | ~spl72_207)),
% 79.42/11.77 inference(superposition,[],[f2215,f4615])).
% 79.42/11.77 thf(f11437,plain,(
% 79.42/11.77 spl72_342 | ~spl72_48 | ~spl72_202),
% 79.42/11.77 inference(avatar_split_clause,[],[f6933,f4360,f2214,f11435])).
% 79.42/11.77 thf(f6933,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,capacity)))) ) | (~spl72_48 | ~spl72_202)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f6932])).
% 79.42/11.77 thf(f6932,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,capacity)))) ) | (~spl72_48 | ~spl72_202)),
% 79.42/11.77 inference(superposition,[],[f2215,f4362])).
% 79.42/11.77 thf(f7990,plain,(
% 79.42/11.77 ~spl72_335 | ~spl72_339),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f7989])).
% 79.42/11.77 thf(f7989,plain,(
% 79.42/11.77 $false | (~spl72_335 | ~spl72_339)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f7950])).
% 79.42/11.77 thf(f7950,plain,(
% 79.42/11.77 ($true = $false) | (~spl72_335 | ~spl72_339)),
% 79.42/11.77 inference(superposition,[],[f7629,f7897])).
% 79.42/11.77 thf(f7897,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = X0)) ) | ~spl72_339),
% 79.42/11.77 inference(avatar_component_clause,[],[f7896])).
% 79.42/11.77 thf(f7629,plain,(
% 79.42/11.77 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | ~spl72_335),
% 79.42/11.77 inference(avatar_component_clause,[],[f7628])).
% 79.42/11.77 thf(f7628,plain,(
% 79.42/11.77 spl72_335 <=> ! [X0 : nat] : ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_335])])).
% 79.42/11.77 thf(f7988,plain,(
% 79.42/11.77 ~spl72_49 | ~spl72_339),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f7987])).
% 79.42/11.77 thf(f7987,plain,(
% 79.42/11.77 $false | (~spl72_49 | ~spl72_339)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f7951])).
% 79.42/11.77 thf(f7951,plain,(
% 79.42/11.77 ($true != $true) | (~spl72_49 | ~spl72_339)),
% 79.42/11.77 inference(superposition,[],[f2243,f7897])).
% 79.42/11.77 thf(f2243,plain,(
% 79.42/11.77 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | ~spl72_49),
% 79.42/11.77 inference(avatar_component_clause,[],[f2242])).
% 79.42/11.77 thf(f2242,plain,(
% 79.42/11.77 spl72_49 <=> ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_49])])).
% 79.42/11.77 thf(f7975,plain,(
% 79.42/11.77 spl72_51 | ~spl72_339),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f7974])).
% 79.42/11.77 thf(f7974,plain,(
% 79.42/11.77 $false | (spl72_51 | ~spl72_339)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f7963])).
% 79.42/11.77 thf(f7963,plain,(
% 79.42/11.77 ($true != $true) | (spl72_51 | ~spl72_339)),
% 79.42/11.77 inference(superposition,[],[f2254,f7897])).
% 79.42/11.77 thf(f2254,plain,(
% 79.42/11.77 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) != $true) | spl72_51),
% 79.42/11.77 inference(avatar_component_clause,[],[f2252])).
% 79.42/11.77 thf(f2252,plain,(
% 79.42/11.77 spl72_51 <=> (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $true)),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_51])])).
% 79.42/11.77 thf(f7973,plain,(
% 79.42/11.77 ~spl72_64 | ~spl72_339),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f7972])).
% 79.42/11.77 thf(f7972,plain,(
% 79.42/11.77 $false | (~spl72_64 | ~spl72_339)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f7964])).
% 79.42/11.77 thf(f7964,plain,(
% 79.42/11.77 ($true != $true) | (~spl72_64 | ~spl72_339)),
% 79.42/11.77 inference(superposition,[],[f2352,f7897])).
% 79.42/11.77 thf(f7971,plain,(
% 79.42/11.77 ~spl72_65 | ~spl72_339),
% 79.42/11.77 inference(avatar_contradiction_clause,[],[f7970])).
% 79.42/11.77 thf(f7970,plain,(
% 79.42/11.77 $false | (~spl72_65 | ~spl72_339)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f7965])).
% 79.42/11.77 thf(f7965,plain,(
% 79.42/11.77 ($true != $true) | (~spl72_65 | ~spl72_339)),
% 79.42/11.77 inference(superposition,[],[f2356,f7897])).
% 79.42/11.77 thf(f7911,plain,(
% 79.42/11.77 spl72_341 | ~spl72_28 | spl72_337),
% 79.42/11.77 inference(avatar_split_clause,[],[f7900,f7888,f2020,f7908])).
% 79.42/11.77 thf(f7900,plain,(
% 79.42/11.77 ($false = wellorder($o)) | (~spl72_28 | spl72_337)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f7899])).
% 79.42/11.77 thf(f7899,plain,(
% 79.42/11.77 ($true != $true) | ($false = wellorder($o)) | (~spl72_28 | spl72_337)),
% 79.42/11.77 inference(superposition,[],[f7890,f2021])).
% 79.42/11.77 thf(f7890,plain,(
% 79.42/11.77 ($true != wellorder($o)) | spl72_337),
% 79.42/11.77 inference(avatar_component_clause,[],[f7888])).
% 79.42/11.77 thf(f7906,plain,(
% 79.42/11.77 spl72_340 | ~spl72_28 | spl72_51),
% 79.42/11.77 inference(avatar_split_clause,[],[f2257,f2252,f2020,f7903])).
% 79.42/11.77 thf(f2257,plain,(
% 79.42/11.77 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $false) | (~spl72_28 | spl72_51)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2256])).
% 79.42/11.77 thf(f2256,plain,(
% 79.42/11.77 ($true != $true) | (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $false) | (~spl72_28 | spl72_51)),
% 79.42/11.77 inference(superposition,[],[f2254,f2021])).
% 79.42/11.77 thf(f7898,plain,(
% 79.42/11.77 ~spl72_337 | spl72_338 | spl72_339 | ~spl72_62),
% 79.42/11.77 inference(avatar_split_clause,[],[f2384,f2343,f7896,f7892,f7888])).
% 79.42/11.77 thf(f2384,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = X0) | ($false = vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT)) | ($true != wellorder($o))) ) | ~spl72_62),
% 79.42/11.77 inference(not_proxy_clausification,[],[f2383])).
% 79.42/11.77 thf(f2383,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = X0) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_62),
% 79.42/11.77 inference(not_proxy_clausification,[],[f2378])).
% 79.42/11.77 thf(f2378,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true != vAPP($o,$o,vNOT,X0)) | ($true = vAPP($o,$o,vNOT,vAPP(sTfun($o,$o),$o,ord_Least($o),vNOT))) | ($true != wellorder($o))) ) | ~spl72_62),
% 79.42/11.77 inference(primitive_instantiation,[],[f2344])).
% 79.42/11.77 thf(f7634,plain,(
% 79.42/11.77 spl72_336 | ~spl72_18 | ~spl72_54),
% 79.42/11.77 inference(avatar_split_clause,[],[f2288,f2268,f1974,f7632])).
% 79.42/11.77 thf(f7632,plain,(
% 79.42/11.77 spl72_336 <=> ! [X0 : $o] : ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X0))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_336])])).
% 79.42/11.77 thf(f2288,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X0))) ) | (~spl72_18 | ~spl72_54)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2281])).
% 79.42/11.77 thf(f2281,plain,(
% 79.42/11.77 ( ! [X0 : $o] : (($true != $true) | ($true = vAPP($o,$o,vAPP($o,sTfun($o,$o),ord_less_eq($o),X0),X0))) ) | (~spl72_18 | ~spl72_54)),
% 79.42/11.77 inference(superposition,[],[f2269,f1976])).
% 79.42/11.77 thf(f7630,plain,(
% 79.42/11.77 spl72_335 | ~spl72_28 | ~spl72_49),
% 79.42/11.77 inference(avatar_split_clause,[],[f2250,f2242,f2020,f7628])).
% 79.42/11.77 thf(f2250,plain,(
% 79.42/11.77 ( ! [X0 : nat] : (($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | (~spl72_28 | ~spl72_49)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2249])).
% 79.42/11.77 thf(f2249,plain,(
% 79.42/11.77 ( ! [X0 : nat] : (($true != $true) | ($false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) ) | (~spl72_28 | ~spl72_49)),
% 79.42/11.77 inference(superposition,[],[f2243,f2021])).
% 79.42/11.77 thf(f7610,plain,(
% 79.42/11.77 spl72_334 | ~spl72_46 | ~spl72_196),
% 79.42/11.77 inference(avatar_split_clause,[],[f6925,f4265,f2205,f7608])).
% 79.42/11.77 thf(f6925,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,a)))) ) | (~spl72_46 | ~spl72_196)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f6924])).
% 79.42/11.77 thf(f6924,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X0,a)))) ) | (~spl72_46 | ~spl72_196)),
% 79.42/11.77 inference(superposition,[],[f2206,f4267])).
% 79.42/11.77 thf(f7602,plain,(
% 79.42/11.77 spl72_333 | ~spl72_28 | ~spl72_48),
% 79.42/11.77 inference(avatar_split_clause,[],[f2237,f2214,f2020,f7600])).
% 79.42/11.77 thf(f7600,plain,(
% 79.42/11.77 spl72_333 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,X0))) | (order(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_333])])).
% 79.42/11.77 thf(f2237,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,X0))) | (order(X0) = $false)) ) | (~spl72_28 | ~spl72_48)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2236])).
% 79.42/11.77 thf(f2236,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,X0))) | (order(X0) = $false)) ) | (~spl72_28 | ~spl72_48)),
% 79.42/11.77 inference(superposition,[],[f2215,f2021])).
% 79.42/11.77 thf(f7598,plain,(
% 79.42/11.77 spl72_332 | ~spl72_28 | ~spl72_46),
% 79.42/11.77 inference(avatar_split_clause,[],[f2229,f2205,f2020,f7596])).
% 79.42/11.77 thf(f2229,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,X0))) | (ord(X0) = $false)) ) | (~spl72_28 | ~spl72_46)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2228])).
% 79.42/11.77 thf(f2228,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,X0))) | (ord(X0) = $false)) ) | (~spl72_28 | ~spl72_46)),
% 79.42/11.77 inference(superposition,[],[f2206,f2021])).
% 79.42/11.77 thf(f7594,plain,(
% 79.42/11.77 spl72_331 | ~spl72_28 | ~spl72_45),
% 79.42/11.77 inference(avatar_split_clause,[],[f2221,f2201,f2020,f7592])).
% 79.42/11.77 thf(f2221,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,X0))) | (preorder(X0) = $false)) ) | (~spl72_28 | ~spl72_45)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2220])).
% 79.42/11.77 thf(f2220,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,X0))) | (preorder(X0) = $false)) ) | (~spl72_28 | ~spl72_45)),
% 79.42/11.77 inference(superposition,[],[f2202,f2021])).
% 79.42/11.77 thf(f7386,plain,(
% 79.42/11.77 spl72_330 | ~spl72_46 | ~spl72_189),
% 79.42/11.77 inference(avatar_split_clause,[],[f6921,f4155,f2205,f7384])).
% 79.42/11.77 thf(f6921,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,capacity)))) ) | (~spl72_46 | ~spl72_189)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f6920])).
% 79.42/11.77 thf(f6920,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X0,capacity)))) ) | (~spl72_46 | ~spl72_189)),
% 79.42/11.77 inference(superposition,[],[f2206,f4157])).
% 79.42/11.77 thf(f7110,plain,(
% 79.42/11.77 spl72_329 | ~spl72_28 | ~spl72_43),
% 79.42/11.77 inference(avatar_split_clause,[],[f2197,f2108,f2020,f7108])).
% 79.42/11.77 thf(f7108,plain,(
% 79.42/11.77 spl72_329 <=> ! [X0 : $tType] : ((order(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_329])])).
% 79.42/11.77 thf(f2108,plain,(
% 79.42/11.77 spl72_43 <=> ! [X0 : $tType] : ((order(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_43])])).
% 79.42/11.77 thf(f2197,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((order(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_43)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2196])).
% 79.42/11.77 thf(f2196,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (order(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_43)),
% 79.42/11.77 inference(superposition,[],[f2109,f2021])).
% 79.42/11.77 thf(f2109,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (order(X0) = $true)) ) | ~spl72_43),
% 79.42/11.77 inference(avatar_component_clause,[],[f2108])).
% 79.42/11.77 thf(f7106,plain,(
% 79.42/11.77 spl72_328 | ~spl72_28 | ~spl72_42),
% 79.42/11.77 inference(avatar_split_clause,[],[f2191,f2104,f2020,f7104])).
% 79.42/11.77 thf(f7104,plain,(
% 79.42/11.77 spl72_328 <=> ! [X0 : $tType] : ((ord(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_328])])).
% 79.42/11.77 thf(f2104,plain,(
% 79.42/11.77 spl72_42 <=> ! [X0 : $tType] : ((ord(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_42])])).
% 79.42/11.77 thf(f2191,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((ord(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_42)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2190])).
% 79.42/11.77 thf(f2190,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (ord(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_42)),
% 79.42/11.77 inference(superposition,[],[f2105,f2021])).
% 79.42/11.77 thf(f2105,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (ord(X0) = $true)) ) | ~spl72_42),
% 79.42/11.77 inference(avatar_component_clause,[],[f2104])).
% 79.42/11.77 thf(f7102,plain,(
% 79.42/11.77 spl72_327 | ~spl72_45 | ~spl72_183),
% 79.42/11.77 inference(avatar_split_clause,[],[f6917,f4062,f2201,f7100])).
% 79.42/11.77 thf(f6917,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,a)))) ) | (~spl72_45 | ~spl72_183)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f6916])).
% 79.42/11.77 thf(f6916,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,a)))) ) | (~spl72_45 | ~spl72_183)),
% 79.42/11.77 inference(superposition,[],[f2202,f4064])).
% 79.42/11.77 thf(f7098,plain,(
% 79.42/11.77 spl72_326 | ~spl72_28 | ~spl72_41),
% 79.42/11.77 inference(avatar_split_clause,[],[f2185,f2100,f2020,f7096])).
% 79.42/11.77 thf(f7096,plain,(
% 79.42/11.77 spl72_326 <=> ! [X0 : $tType] : ((preorder(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_326])])).
% 79.42/11.77 thf(f2100,plain,(
% 79.42/11.77 spl72_41 <=> ! [X0 : $tType] : ((preorder(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_41])])).
% 79.42/11.77 thf(f2185,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((preorder(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_41)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2184])).
% 79.42/11.77 thf(f2184,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (preorder(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_41)),
% 79.42/11.77 inference(superposition,[],[f2101,f2021])).
% 79.42/11.77 thf(f2101,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (preorder(X0) = $true)) ) | ~spl72_41),
% 79.42/11.77 inference(avatar_component_clause,[],[f2100])).
% 79.42/11.77 thf(f7094,plain,(
% 79.42/11.77 spl72_325 | ~spl72_28 | ~spl72_40),
% 79.42/11.77 inference(avatar_split_clause,[],[f2179,f2096,f2020,f7092])).
% 79.42/11.77 thf(f7092,plain,(
% 79.42/11.77 spl72_325 <=> ! [X0 : $tType] : ((linorder(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_325])])).
% 79.42/11.77 thf(f2096,plain,(
% 79.42/11.77 spl72_40 <=> ! [X0 : $tType] : ((linorder(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_40])])).
% 79.42/11.77 thf(f2179,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linorder(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_40)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2178])).
% 79.42/11.77 thf(f2178,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (linorder(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_40)),
% 79.42/11.77 inference(superposition,[],[f2097,f2021])).
% 79.42/11.77 thf(f2097,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (linorder(X0) = $true)) ) | ~spl72_40),
% 79.42/11.77 inference(avatar_component_clause,[],[f2096])).
% 79.42/11.77 thf(f7090,plain,(
% 79.42/11.77 spl72_324 | ~spl72_28 | ~spl72_39),
% 79.42/11.77 inference(avatar_split_clause,[],[f2173,f2092,f2020,f7088])).
% 79.42/11.77 thf(f7088,plain,(
% 79.42/11.77 spl72_324 <=> ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_324])])).
% 79.42/11.77 thf(f2092,plain,(
% 79.42/11.77 spl72_39 <=> ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_39])])).
% 79.42/11.77 thf(f2173,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_39)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2172])).
% 79.42/11.77 thf(f2172,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (ordere223160158up_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_39)),
% 79.42/11.77 inference(superposition,[],[f2093,f2021])).
% 79.42/11.77 thf(f2093,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (ordere223160158up_add(X0) = $true)) ) | ~spl72_39),
% 79.42/11.77 inference(avatar_component_clause,[],[f2092])).
% 79.42/11.77 thf(f7086,plain,(
% 79.42/11.77 spl72_323 | ~spl72_28 | ~spl72_38),
% 79.42/11.77 inference(avatar_split_clause,[],[f2167,f2088,f2020,f7084])).
% 79.42/11.77 thf(f7084,plain,(
% 79.42/11.77 spl72_323 <=> ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_323])])).
% 79.42/11.77 thf(f2088,plain,(
% 79.42/11.77 spl72_38 <=> ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_38])])).
% 79.42/11.77 thf(f2167,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_38)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2166])).
% 79.42/11.77 thf(f2166,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (ordere236663937imp_le(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_38)),
% 79.42/11.77 inference(superposition,[],[f2089,f2021])).
% 79.42/11.77 thf(f2089,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (ordere236663937imp_le(X0) = $true)) ) | ~spl72_38),
% 79.42/11.77 inference(avatar_component_clause,[],[f2088])).
% 79.42/11.77 thf(f7082,plain,(
% 79.42/11.77 spl72_322 | ~spl72_28 | ~spl72_37),
% 79.42/11.77 inference(avatar_split_clause,[],[f2161,f2084,f2020,f7080])).
% 79.42/11.77 thf(f7080,plain,(
% 79.42/11.77 spl72_322 <=> ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_322])])).
% 79.42/11.77 thf(f2084,plain,(
% 79.42/11.77 spl72_37 <=> ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_37])])).
% 79.42/11.77 thf(f2161,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_37)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2160])).
% 79.42/11.77 thf(f2160,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (ordere779506340up_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_37)),
% 79.42/11.77 inference(superposition,[],[f2085,f2021])).
% 79.42/11.77 thf(f2085,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (ordere779506340up_add(X0) = $true)) ) | ~spl72_37),
% 79.42/11.77 inference(avatar_component_clause,[],[f2084])).
% 79.42/11.77 thf(f7078,plain,(
% 79.42/11.77 spl72_321 | ~spl72_28 | ~spl72_36),
% 79.42/11.77 inference(avatar_split_clause,[],[f2155,f2080,f2020,f7076])).
% 79.42/11.77 thf(f7076,plain,(
% 79.42/11.77 spl72_321 <=> ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_321])])).
% 79.42/11.77 thf(f2080,plain,(
% 79.42/11.77 spl72_36 <=> ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_36])])).
% 79.42/11.77 thf(f2155,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_36)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2154])).
% 79.42/11.77 thf(f2154,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (cancel_semigroup_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_36)),
% 79.42/11.77 inference(superposition,[],[f2081,f2021])).
% 79.42/11.77 thf(f2081,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (cancel_semigroup_add(X0) = $true)) ) | ~spl72_36),
% 79.42/11.77 inference(avatar_component_clause,[],[f2080])).
% 79.42/11.77 thf(f7074,plain,(
% 79.42/11.77 spl72_320 | ~spl72_28 | ~spl72_35),
% 79.42/11.77 inference(avatar_split_clause,[],[f2144,f2076,f2020,f7072])).
% 79.42/11.77 thf(f7072,plain,(
% 79.42/11.77 spl72_320 <=> ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_320])])).
% 79.42/11.77 thf(f2076,plain,(
% 79.42/11.77 spl72_35 <=> ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_35])])).
% 79.42/11.77 thf(f2144,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_35)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2143])).
% 79.42/11.77 thf(f2143,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (ab_semigroup_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_35)),
% 79.42/11.77 inference(superposition,[],[f2077,f2021])).
% 79.42/11.77 thf(f2077,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (ab_semigroup_add(X0) = $true)) ) | ~spl72_35),
% 79.42/11.77 inference(avatar_component_clause,[],[f2076])).
% 79.42/11.77 thf(f7070,plain,(
% 79.42/11.77 spl72_319 | ~spl72_28 | ~spl72_34),
% 79.42/11.77 inference(avatar_split_clause,[],[f2138,f2072,f2020,f7068])).
% 79.42/11.77 thf(f7068,plain,(
% 79.42/11.77 spl72_319 <=> ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_319])])).
% 79.42/11.77 thf(f2072,plain,(
% 79.42/11.77 spl72_34 <=> ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_34])])).
% 79.42/11.77 thf(f2138,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_34)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2137])).
% 79.42/11.77 thf(f2137,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (comm_monoid_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_34)),
% 79.42/11.77 inference(superposition,[],[f2073,f2021])).
% 79.42/11.77 thf(f2073,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (comm_monoid_add(X0) = $true)) ) | ~spl72_34),
% 79.42/11.77 inference(avatar_component_clause,[],[f2072])).
% 79.42/11.77 thf(f7066,plain,(
% 79.42/11.77 spl72_318 | ~spl72_28 | ~spl72_33),
% 79.42/11.77 inference(avatar_split_clause,[],[f2132,f2068,f2020,f7064])).
% 79.42/11.77 thf(f7064,plain,(
% 79.42/11.77 spl72_318 <=> ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_318])])).
% 79.42/11.77 thf(f2068,plain,(
% 79.42/11.77 spl72_33 <=> ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_33])])).
% 79.42/11.77 thf(f2132,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_33)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2131])).
% 79.42/11.77 thf(f2131,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (strict2144017051up_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_33)),
% 79.42/11.77 inference(superposition,[],[f2069,f2021])).
% 79.42/11.77 thf(f2069,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (strict2144017051up_add(X0) = $true)) ) | ~spl72_33),
% 79.42/11.77 inference(avatar_component_clause,[],[f2068])).
% 79.42/11.77 thf(f7062,plain,(
% 79.42/11.77 spl72_317 | ~spl72_28 | ~spl72_32),
% 79.42/11.77 inference(avatar_split_clause,[],[f2126,f2064,f2020,f7060])).
% 79.42/11.77 thf(f7060,plain,(
% 79.42/11.77 spl72_317 <=> ! [X0 : $tType] : ((group_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_317])])).
% 79.42/11.77 thf(f2064,plain,(
% 79.42/11.77 spl72_32 <=> ! [X0 : $tType] : ((group_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_32])])).
% 79.42/11.77 thf(f2126,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((group_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_32)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2125])).
% 79.42/11.77 thf(f2125,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (group_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_32)),
% 79.42/11.77 inference(superposition,[],[f2065,f2021])).
% 79.42/11.77 thf(f2065,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (group_add(X0) = $true)) ) | ~spl72_32),
% 79.42/11.77 inference(avatar_component_clause,[],[f2064])).
% 79.42/11.77 thf(f7058,plain,(
% 79.42/11.77 spl72_316 | ~spl72_45 | ~spl72_179),
% 79.42/11.77 inference(avatar_split_clause,[],[f6913,f4001,f2201,f7056])).
% 79.42/11.77 thf(f6913,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,capacity)))) ) | (~spl72_45 | ~spl72_179)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f6912])).
% 79.42/11.77 thf(f6912,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,capacity)))) ) | (~spl72_45 | ~spl72_179)),
% 79.42/11.77 inference(superposition,[],[f2202,f4003])).
% 79.42/11.77 thf(f7054,plain,(
% 79.42/11.77 spl72_315 | ~spl72_28 | ~spl72_31),
% 79.42/11.77 inference(avatar_split_clause,[],[f2120,f2060,f2020,f7052])).
% 79.42/11.77 thf(f7052,plain,(
% 79.42/11.77 spl72_315 <=> ! [X0 : $tType] : ((semigroup_add(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_315])])).
% 79.42/11.77 thf(f2060,plain,(
% 79.42/11.77 spl72_31 <=> ! [X0 : $tType] : ((semigroup_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_31])])).
% 79.42/11.77 thf(f2120,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((semigroup_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_31)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2119])).
% 79.42/11.77 thf(f2119,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (semigroup_add(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_31)),
% 79.42/11.77 inference(superposition,[],[f2061,f2021])).
% 79.42/11.77 thf(f2061,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (semigroup_add(X0) = $true)) ) | ~spl72_31),
% 79.42/11.77 inference(avatar_component_clause,[],[f2060])).
% 79.42/11.77 thf(f7050,plain,(
% 79.42/11.77 spl72_314 | ~spl72_28 | ~spl72_30),
% 79.42/11.77 inference(avatar_split_clause,[],[f2114,f2056,f2020,f7048])).
% 79.42/11.77 thf(f7048,plain,(
% 79.42/11.77 spl72_314 <=> ! [X0 : $tType] : ((type(X0) = $true) | (linordered_idom(X0) = $false))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_314])])).
% 79.42/11.77 thf(f2056,plain,(
% 79.42/11.77 spl72_30 <=> ! [X0 : $tType] : ((type(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_30])])).
% 79.42/11.77 thf(f2114,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((type(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_30)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2113])).
% 79.42/11.77 thf(f2113,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | (type(X0) = $true) | (linordered_idom(X0) = $false)) ) | (~spl72_28 | ~spl72_30)),
% 79.42/11.77 inference(superposition,[],[f2057,f2021])).
% 79.42/11.77 thf(f2057,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((linordered_idom(X0) != $true) | (type(X0) = $true)) ) | ~spl72_30),
% 79.42/11.77 inference(avatar_component_clause,[],[f2056])).
% 79.42/11.77 thf(f7026,plain,(
% 79.42/11.77 spl72_313 | ~spl72_27 | ~spl72_48),
% 79.42/11.77 inference(avatar_split_clause,[],[f2238,f2214,f2016,f7024])).
% 79.42/11.77 thf(f2238,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,set(X0))))) ) | (~spl72_27 | ~spl72_48)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2235])).
% 79.42/11.77 thf(f2235,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,set(X0))))) ) | (~spl72_27 | ~spl72_48)),
% 79.42/11.77 inference(superposition,[],[f2215,f2017])).
% 79.42/11.77 thf(f7022,plain,(
% 79.42/11.77 spl72_312 | ~spl72_26 | ~spl72_46),
% 79.42/11.77 inference(avatar_split_clause,[],[f2230,f2205,f2012,f7020])).
% 79.42/11.77 thf(f2230,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,set(X0))))) ) | (~spl72_26 | ~spl72_46)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2227])).
% 79.42/11.77 thf(f2227,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,set(X0))))) ) | (~spl72_26 | ~spl72_46)),
% 79.42/11.77 inference(superposition,[],[f2206,f2013])).
% 79.42/11.77 thf(f7018,plain,(
% 79.42/11.77 spl72_311 | ~spl72_25 | ~spl72_45),
% 79.42/11.77 inference(avatar_split_clause,[],[f2222,f2201,f2008,f7016])).
% 79.42/11.77 thf(f2222,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,set(X0))))) ) | (~spl72_25 | ~spl72_45)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2219])).
% 79.42/11.77 thf(f2219,plain,(
% 79.42/11.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,set(X0))))) ) | (~spl72_25 | ~spl72_45)),
% 79.42/11.77 inference(superposition,[],[f2202,f2009])).
% 79.42/11.77 thf(f6974,plain,(
% 79.42/11.77 spl72_310 | ~spl72_22 | ~spl72_48),
% 79.42/11.77 inference(avatar_split_clause,[],[f2240,f2214,f1994,f6972])).
% 79.42/11.77 thf(f2240,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,$o)))) ) | (~spl72_22 | ~spl72_48)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2233])).
% 79.42/11.77 thf(f2233,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,$o)))) ) | (~spl72_22 | ~spl72_48)),
% 79.42/11.77 inference(superposition,[],[f2215,f1996])).
% 79.42/11.77 thf(f6970,plain,(
% 79.42/11.77 spl72_309 | ~spl72_23 | ~spl72_48),
% 79.42/11.77 inference(avatar_split_clause,[],[f2239,f2214,f1999,f6968])).
% 79.42/11.77 thf(f2239,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,nat)))) ) | (~spl72_23 | ~spl72_48)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2234])).
% 79.42/11.77 thf(f2234,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,nat)))) ) | (~spl72_23 | ~spl72_48)),
% 79.42/11.77 inference(superposition,[],[f2215,f2001])).
% 79.42/11.77 thf(f6966,plain,(
% 79.42/11.77 spl72_308 | ~spl72_20 | ~spl72_46),
% 79.42/11.77 inference(avatar_split_clause,[],[f2232,f2205,f1984,f6964])).
% 79.42/11.77 thf(f2232,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,$o)))) ) | (~spl72_20 | ~spl72_46)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2225])).
% 79.42/11.77 thf(f2225,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X0,$o)))) ) | (~spl72_20 | ~spl72_46)),
% 79.42/11.77 inference(superposition,[],[f2206,f1986])).
% 79.42/11.77 thf(f6962,plain,(
% 79.42/11.77 spl72_307 | ~spl72_21 | ~spl72_46),
% 79.42/11.77 inference(avatar_split_clause,[],[f2231,f2205,f1989,f6960])).
% 79.42/11.77 thf(f2231,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,nat)))) ) | (~spl72_21 | ~spl72_46)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2226])).
% 79.42/11.77 thf(f2226,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X0,nat)))) ) | (~spl72_21 | ~spl72_46)),
% 79.42/11.77 inference(superposition,[],[f2206,f1991])).
% 79.42/11.77 thf(f6958,plain,(
% 79.42/11.77 spl72_306 | ~spl72_18 | ~spl72_45),
% 79.42/11.77 inference(avatar_split_clause,[],[f2224,f2201,f1974,f6956])).
% 79.42/11.77 thf(f2224,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,$o)))) ) | (~spl72_18 | ~spl72_45)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2217])).
% 79.42/11.77 thf(f2217,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,$o)))) ) | (~spl72_18 | ~spl72_45)),
% 79.42/11.77 inference(superposition,[],[f2202,f1976])).
% 79.42/11.77 thf(f6954,plain,(
% 79.42/11.77 spl72_305 | ~spl72_19 | ~spl72_45),
% 79.42/11.77 inference(avatar_split_clause,[],[f2223,f2201,f1979,f6952])).
% 79.42/11.77 thf(f2223,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,nat)))) ) | (~spl72_19 | ~spl72_45)),
% 79.42/11.77 inference(trivial_inequality_removal,[],[f2218])).
% 79.42/11.77 thf(f2218,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,nat)))) ) | (~spl72_19 | ~spl72_45)),
% 79.42/11.77 inference(superposition,[],[f2202,f1981])).
% 79.42/11.77 thf(f6888,plain,(
% 79.42/11.77 spl72_304),
% 79.42/11.77 inference(avatar_split_clause,[],[f1487,f6886])).
% 79.42/11.77 thf(f6886,plain,(
% 79.42/11.77 spl72_304 <=> ! [X0 : $tType] : ((isShortestPath(X0) = 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| (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_304])])).
% 79.42/11.77 thf(f1487,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((isShortestPath(X0) = 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| (linordered_idom(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f1071])).
% 79.42/11.77 thf(f1071,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((isShortestPath(X0) = 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fun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,cCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),bCOMB,vIMP)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))))))),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(list(product_prod(nat,nat)),$o)),vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(list(product_prod(nat,nat)),$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,ord_less_eq(nat)),size_size(list(product_prod(nat,nat)))))),size_size(list(product_prod(nat,nat)))))))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f540])).
% 79.42/11.77 thf(f540,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isPath(X0)))))),vAPP(sTfun(sTfun(product_prod(n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fun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,cCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),bCOMB,vIMP)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))))))),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(list(product_prod(nat,nat)),$o)),vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(list(product_prod(nat,nat)),$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,ord_less_eq(nat)),size_size(list(product_prod(nat,nat)))))),size_size(list(product_prod(nat,nat)))))))))),
% 79.42/11.77 inference(fool_elimination,[],[f539])).
% 79.42/11.77 thf(f539,plain,(
% 79.42/11.77 ! [X0 : $tType] : (linordered_idom(X0) => (isShortestPath(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : list(product_prod(nat,nat)), X4 : nat] : (! [X5 : list(product_prod(nat,nat))] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X5),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X5))) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)))))),
% 79.42/11.77 inference(rectify,[],[f121])).
% 79.42/11.77 thf(f121,axiom,(
% 79.42/11.77 ! [X1 : $tType] : (linordered_idom(X1) => (isShortestPath(X1) = (^[X35 : product_prod(nat,nat) > X1, X57 : nat, X17 : list(product_prod(nat,nat)), X58 : nat] : (! [X23 : list(product_prod(nat,nat))] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X35),X57),X23),X58) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X17)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X23))) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X35),X57),X17),X58)))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_120_Graph_OisShortestPath__def)).
% 79.42/11.77 thf(f6878,plain,(
% 79.42/11.77 spl72_303),
% 79.42/11.77 inference(avatar_split_clause,[],[f1491,f6876])).
% 79.42/11.77 thf(f6876,plain,(
% 79.42/11.77 spl72_303 <=> ! [X0 : $tType] : ((dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat))))))),vAPP(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),cCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,vAPP(sTfun(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,bCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,cCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),bCOMB,vAND)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))))))),vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_303])])).
% 79.42/11.77 thf(f1491,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat))))))),vAPP(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),cCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,vAPP(sTfun(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,bCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,n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| (linordered_idom(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f1075])).
% 79.42/11.77 thf(f1075,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat))))))),vAPP(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),cCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,vAPP(sTfun(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,bCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,cCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),bCOMB,vAND)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))))))),vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f548])).
% 79.42/11.77 thf(f548,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat))))))),vAPP(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),cCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,cCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))))),bCOMB,vAPP(sTfun(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,bCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,cCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(nat,sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(list(product_prod(nat,nat)),$o),sTfun(list(product_prod(nat,nat)),sTfun($o,$o))),bCOMB,vAND)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))))))),vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))))),
% 79.42/11.77 inference(fool_elimination,[],[f547])).
% 79.42/11.77 thf(f547,plain,(
% 79.42/11.77 ! [X0 : $tType] : (linordered_idom(X0) => (dist(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : nat, X4 : nat] : (? [X5 : list(product_prod(nat,nat))] : ((vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X5) = X3) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X5),X4))))))),
% 79.42/11.77 inference(rectify,[],[f124])).
% 79.42/11.77 thf(f124,axiom,(
% 79.42/11.77 ! [X1 : $tType] : (linordered_idom(X1) => (dist(X1) = (^[X35 : product_prod(nat,nat) > X1, X58 : nat, X20 : nat, X59 : nat] : (? [X17 : list(product_prod(nat,nat))] : ((vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X17) = X20) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X35),X58),X17),X59))))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_123_Graph_Odist__def)).
% 79.42/11.77 thf(f6862,plain,(
% 79.42/11.77 spl72_302),
% 79.42/11.77 inference(avatar_split_clause,[],[f1486,f6860])).
% 79.42/11.77 thf(f6860,plain,(
% 79.42/11.77 spl72_302 <=> ! [X0 : $tType] : ((isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isPath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_302])])).
% 79.42/11.77 thf(f1486,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isPath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))) | (linordered_idom(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f1070])).
% 79.42/11.77 thf(f1070,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isPath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f538])).
% 79.42/11.77 thf(f538,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isPath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))))),
% 79.42/11.77 inference(fool_elimination,[],[f537])).
% 79.42/11.77 thf(f537,plain,(
% 79.42/11.77 ! [X0 : $tType] : (linordered_idom(X0) => (isShortestPath(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : list(product_prod(nat,nat)), X4 : nat] : ((vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)))))),
% 79.42/11.77 inference(rectify,[],[f120])).
% 79.42/11.77 thf(f120,axiom,(
% 79.42/11.77 ! [X1 : $tType] : (linordered_idom(X1) => (isShortestPath(X1) = (^[X35 : product_prod(nat,nat) > X1, X57 : nat, X17 : list(product_prod(nat,nat)), X58 : nat] : ((vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X17) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X35),X57),X58)) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X35),X57),X17),X58)))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_Graph_OisShortestPath__min__dist__def)).
% 79.42/11.77 thf(f6858,plain,(
% 79.42/11.77 spl72_301),
% 79.42/11.77 inference(avatar_split_clause,[],[f1485,f6856])).
% 79.42/11.77 thf(f6856,plain,(
% 79.42/11.77 spl72_301 <=> ! [X0 : $tType] : ((isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isSimplePath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_301])])).
% 79.42/11.77 thf(f1485,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isSimplePath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))) | (linordered_idom(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f1069])).
% 79.42/11.77 thf(f1069,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isSimplePath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f536])).
% 79.42/11.77 thf(f536,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (isShortestPath(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sCOMB,vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,sCOMB),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(nat,sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,sCOMB)),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)))),isSimplePath(X0)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),bCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(nat,nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),cCOMB,vAPP(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(sTfun(nat,nat),sTfun(nat,$o))),sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(list(product_prod(nat,nat)),sTfun(sTfun(nat,nat),sTfun(nat,$o)))),bCOMB,bCOMB),vAPP(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(list(product_prod(nat,nat)),nat),sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),bCOMB,vEQ(nat)),size_size(list(product_prod(nat,nat)))))))),min_dist(X0)))))),
% 79.42/11.77 inference(fool_elimination,[],[f535])).
% 79.42/11.77 thf(f535,plain,(
% 79.42/11.77 ! [X0 : $tType] : (linordered_idom(X0) => (isShortestPath(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : list(product_prod(nat,nat)), X4 : nat] : ((vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X3),X4)))))),
% 79.42/11.77 inference(rectify,[],[f136])).
% 79.42/11.77 thf(f136,axiom,(
% 79.42/11.77 ! [X1 : $tType] : (linordered_idom(X1) => (isShortestPath(X1) = (^[X35 : product_prod(nat,nat) > X1, X57 : nat, X17 : list(product_prod(nat,nat)), X58 : nat] : ((vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X17) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X35),X57),X58)) & vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X1),X35),X57),X17),X58)))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_135_Graph_OisShortestPath__alt)).
% 79.42/11.77 thf(f6850,plain,(
% 79.42/11.77 spl72_300),
% 79.42/11.77 inference(avatar_split_clause,[],[f1390,f6848])).
% 79.42/11.77 thf(f6848,plain,(
% 79.42/11.77 spl72_300 <=> ! [X0 : $tType] : ((vSIGMA(X0) = vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sCOMB,vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)))))) | (wellorder(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_300])])).
% 79.42/11.77 thf(f1390,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((vSIGMA(X0) = vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sCOMB,vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)))))) | (wellorder(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f965])).
% 79.42/11.77 thf(f965,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((vSIGMA(X0) = vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sCOMB,vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)))))) | (wellorder(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f386])).
% 79.42/11.77 thf(f386,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((wellorder(X0) = $true) => (vSIGMA(X0) = vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o),vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),$o)),bCOMB,vSIGMA(X0)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sCOMB,vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vPI(X0))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,$o),sTfun(X0,sTfun(X0,$o))),cCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vIMP)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less(X0)))))),vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)))))))),
% 79.42/11.77 inference(fool_elimination,[],[f385])).
% 79.42/11.77 thf(f385,plain,(
% 79.42/11.77 ! [X0 : $tType] : (wellorder(X0) => ((^[X1 : X0 > $o] : (? [X2 : X0] : vAPP(X0,$o,X1,X2))) = (^[X3 : X0 > $o] : (? [X4 : X0] : (! [X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X4) => ~vAPP(X0,$o,X3,X5)) & vAPP(X0,$o,X3,X4))))))),
% 79.42/11.77 inference(rectify,[],[f217])).
% 79.42/11.77 thf(f217,axiom,(
% 79.42/11.77 ! [X0 : $tType] : (wellorder(X0) => ((^[X70 : X0 > $o] : (? [X71 : X0] : vAPP(X0,$o,X70,X71))) = (^[X72 : X0 > $o] : (? [X46 : X0] : (! [X45 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X45),X46) => ~vAPP(X0,$o,X72,X45)) & vAPP(X0,$o,X72,X46))))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_216_exists__least__iff)).
% 79.42/11.77 thf(f6840,plain,(
% 79.42/11.77 spl72_299),
% 79.42/11.77 inference(avatar_split_clause,[],[f1489,f6838])).
% 79.42/11.77 thf(f6838,plain,(
% 79.42/11.77 spl72_299 <=> ! [X0 : $tType] : ((connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_299])])).
% 79.42/11.77 thf(f1489,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))) | (linordered_idom(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f1073])).
% 79.42/11.77 thf(f1073,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f544])).
% 79.42/11.77 thf(f544,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),$o),$o),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)),sTfun(nat,$o)),bCOMB,vSIGMA(list(product_prod(nat,nat)))))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),vAPP(sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))))),bCOMB,vAPP(sTfun(sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),sTfun(nat,sTfun(list(product_prod(nat,nat)),$o))),sTfun(sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(list(product_prod(nat,nat)),$o)))),bCOMB,cCOMB)),isPath(X0)))))),
% 79.42/11.77 inference(fool_elimination,[],[f543])).
% 79.42/11.77 thf(f543,plain,(
% 79.42/11.77 ! [X0 : $tType] : (linordered_idom(X0) => (connected(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : nat] : (? [X4 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X4),X3)))))),
% 79.42/11.77 inference(rectify,[],[f144])).
% 79.42/11.77 thf(f144,axiom,(
% 79.42/11.77 ! [X1 : $tType] : (linordered_idom(X1) => (connected(X1) = (^[X35 : product_prod(nat,nat) > X1, X57 : nat, X58 : nat] : (? [X17 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X35),X57),X17),X58)))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_143_Graph_Oconnected__def)).
% 79.42/11.77 thf(f6824,plain,(
% 79.42/11.77 spl72_298),
% 79.42/11.77 inference(avatar_split_clause,[],[f1490,f6822])).
% 79.42/11.77 thf(f6822,plain,(
% 79.42/11.77 spl72_298 <=> ! [X0 : $tType] : ((min_dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),bCOMB,vAPP(sTfun(sTfun(nat,$o),nat),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),bCOMB,ord_Least(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 introduced(avatar_definition,[new_symbols(naming,[spl72_298])])).
% 79.42/11.77 thf(f1490,plain,(
% 79.42/11.77 ( ! [X0 : $tType] : ((min_dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),bCOMB,vAPP(sTfun(sTfun(nat,$o),nat),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),bCOMB,ord_Least(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))) | (linordered_idom(X0) != $true)) )),
% 79.42/11.77 inference(cnf_transformation,[],[f1074])).
% 79.42/11.77 thf(f1074,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((min_dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),bCOMB,vAPP(sTfun(sTfun(nat,$o),nat),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),bCOMB,ord_Least(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.77 inference(ennf_transformation,[],[f546])).
% 79.42/11.77 thf(f546,plain,(
% 79.42/11.77 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (min_dist(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,nat))),bCOMB,vAPP(sTfun(sTfun(nat,$o),nat),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,nat)),bCOMB,ord_Least(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))))),
% 79.42/11.77 inference(fool_elimination,[],[f545])).
% 79.42/11.77 thf(f545,plain,(
% 79.42/11.77 ! [X0 : $tType] : (linordered_idom(X0) => (min_dist(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : nat] : (vAPP(sTfun(nat,$o),nat,ord_Least(nat),(^[X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X4),X3))))))))),
% 79.42/11.77 inference(rectify,[],[f135])).
% 79.42/11.77 thf(f135,axiom,(
% 79.42/11.77 ! [X1 : $tType] : (linordered_idom(X1) => (min_dist(X1) = (^[X35 : product_prod(nat,nat) > X1, X58 : nat, X59 : nat] : (vAPP(sTfun(nat,$o),nat,ord_Least(nat),(^[X20 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X35),X58),X20),X59))))))))),
% 79.42/11.77 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_134_Graph_Omin__dist__def)).
% 79.42/11.77 thf(f6820,plain,(
% 79.42/11.77 spl72_297),
% 79.42/11.77 inference(avatar_split_clause,[],[f1488,f6818])).
% 79.42/11.77 thf(f6818,plain,(
% 79.42/11.77 spl72_297 <=> ! [X0 : $tType] : ((connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_297])])).
% 79.42/11.78 thf(f1488,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1072])).
% 79.42/11.78 thf(f1072,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f542])).
% 79.42/11.78 thf(f542,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (connected(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat)))),vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),vAPP(sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))))),bCOMB,vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB)),dist(X0)))))),
% 79.42/11.78 inference(fool_elimination,[],[f541])).
% 79.42/11.78 thf(f541,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => (connected(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat, X3 : nat] : (? [X4 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X4),X3)))))),
% 79.42/11.78 inference(rectify,[],[f146])).
% 79.42/11.78 thf(f146,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => (connected(X1) = (^[X35 : product_prod(nat,nat) > X1, X58 : nat, X59 : nat] : (? [X20 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X35),X58),X20),X59)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_145_Graph_Oconnected__by__dist)).
% 79.42/11.78 thf(f6808,plain,(
% 79.42/11.78 spl72_296),
% 79.42/11.78 inference(avatar_split_clause,[],[f1455,f6806])).
% 79.42/11.78 thf(f6806,plain,(
% 79.42/11.78 spl72_296 <=> ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0)))) | (order(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_296])])).
% 79.42/11.78 thf(f1455,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0)))) | (order(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1031])).
% 79.42/11.78 thf(f1031,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0)))) | (order(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f476])).
% 79.42/11.78 thf(f476,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((order(X0) = $true) => (ord_less(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(X0,$o),sTfun(X0,$o)),bCOMB,vNOT)),vEQ(X0)))))),
% 79.42/11.78 inference(fool_elimination,[],[f475])).
% 79.42/11.78 thf(f475,plain,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => (ord_less(X0) = (^[X1 : X0, X2 : X0] : ((X1 != X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))))),
% 79.42/11.78 inference(rectify,[],[f254])).
% 79.42/11.78 thf(f254,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => (ord_less(X0) = (^[X34 : X0, X33 : X0] : ((X33 != X34) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X34),X33)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_253_dual__order_Ostrict__iff__order)).
% 79.42/11.78 thf(f6750,plain,(
% 79.42/11.78 spl72_295),
% 79.42/11.78 inference(avatar_split_clause,[],[f1350,f6747])).
% 79.42/11.78 thf(f6747,plain,(
% 79.42/11.78 spl72_295 <=> (ord_less(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(nat)))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_295])])).
% 79.42/11.78 thf(f1350,plain,(
% 79.42/11.78 (ord_less(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(nat)))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))))),
% 79.42/11.78 inference(cnf_transformation,[],[f312])).
% 79.42/11.78 thf(f312,plain,(
% 79.42/11.78 (ord_less(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(nat)))),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun($o,$o),sTfun(sTfun(nat,$o),sTfun(nat,$o)),bCOMB,vNOT)),vEQ(nat))))),
% 79.42/11.78 inference(fool_elimination,[],[f311])).
% 79.42/11.78 thf(f311,plain,(
% 79.42/11.78 (ord_less(nat) = (^[X0 : nat, X1 : nat] : ((X0 != X1) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))))),
% 79.42/11.78 inference(rectify,[],[f62])).
% 79.42/11.78 thf(f62,axiom,(
% 79.42/11.78 (ord_less(nat) = (^[X45 : nat, X46 : nat] : ((X45 != X46) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X45),X46))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_nat__less__le)).
% 79.42/11.78 thf(f6737,plain,(
% 79.42/11.78 spl72_294),
% 79.42/11.78 inference(avatar_split_clause,[],[f1574,f6735])).
% 79.42/11.78 thf(f6735,plain,(
% 79.42/11.78 spl72_294 <=> ! [X1 : $tType,X0 : $tType] : ((ord_less_eq(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o)),vAPP(sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),sTfun(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),bCOMB,vPI(X1))),vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),vAPP(sTfun(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))))) | (ord(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_294])])).
% 79.42/11.78 thf(f1574,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType] : ((ord_less_eq(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o)),vAPP(sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),sTfun(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),bCOMB,vPI(X1))),vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),vAPP(sTfun(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))))) | (ord(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1138])).
% 79.42/11.78 thf(f1138,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord_less_eq(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o)),vAPP(sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),sTfun(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),bCOMB,vPI(X1))),vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),vAPP(sTfun(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))))) | (ord(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f678])).
% 79.42/11.78 thf(f678,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord(X0) = $true) => (ord_less_eq(sTfun(X1,X0)) = vAPP(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o)),vAPP(sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),sTfun(sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o))),bCOMB,vAPP(sTfun(sTfun(X1,$o),$o),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,$o)),sTfun(sTfun(X1,X0),$o)),bCOMB,vPI(X1))),vAPP(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o))),vAPP(sTfun(sTfun(X1,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,$o))),sTfun(sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),sTfun(sTfun(X1,X0),sTfun(sTfun(X1,X0),sTfun(X1,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X1,X0),sTfun(X1,sTfun(X0,$o))),bCOMB,ord_less_eq(X0))))))),
% 79.42/11.78 inference(fool_elimination,[],[f677])).
% 79.42/11.78 thf(f677,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (ord(X0) => (ord_less_eq(sTfun(X1,X0)) = (^[X2 : X1 > X0, X3 : X1 > X0] : (! [X4 : X1] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))))))),
% 79.42/11.78 inference(rectify,[],[f189])).
% 79.42/11.78 thf(f189,axiom,(
% 79.42/11.78 ! [X38 : $tType,X0 : $tType] : (ord(X38) => (ord_less_eq(sTfun(X0,X38)) = (^[X61 : X0 > X38, X62 : X0 > X38] : (! [X37 : X0] : vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),vAPP(X0,X38,X61,X37)),vAPP(X0,X38,X62,X37))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_188_le__fun__def)).
% 79.42/11.78 thf(f6729,plain,(
% 79.42/11.78 spl72_293),
% 79.42/11.78 inference(avatar_split_clause,[],[f1359,f6727])).
% 79.42/11.78 thf(f6727,plain,(
% 79.42/11.78 spl72_293 <=> ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))) | (canoni770627133id_add(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_293])])).
% 79.42/11.78 thf(f1359,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))) | (canoni770627133id_add(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f928])).
% 79.42/11.78 thf(f928,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))) | (canoni770627133id_add(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f324])).
% 79.42/11.78 thf(f324,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => (ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,$o))),bCOMB,vAPP(sTfun(sTfun(X0,$o),$o),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),bCOMB,vSIGMA(X0))),vAPP(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun(X0,$o))),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,cCOMB),vAPP(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,X0)),sTfun(X0,sTfun(X0,sTfun(X0,$o)))),bCOMB,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,X0),sTfun(X0,sTfun(X0,$o))),bCOMB,vEQ(X0))),plus_plus(X0))))))),
% 79.42/11.78 inference(fool_elimination,[],[f323])).
% 79.42/11.78 thf(f323,plain,(
% 79.42/11.78 ! [X0 : $tType] : (canoni770627133id_add(X0) => (ord_less_eq(X0) = (^[X1 : X0, X2 : X0] : (? [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2)))))),
% 79.42/11.78 inference(rectify,[],[f45])).
% 79.42/11.78 thf(f45,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (canoni770627133id_add(X0) => (ord_less_eq(X0) = (^[X33 : X0, X34 : X0] : (? [X35 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X33),X35) = X34)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_le__iff__add)).
% 79.42/11.78 thf(f6697,plain,(
% 79.42/11.78 spl72_292),
% 79.42/11.78 inference(avatar_split_clause,[],[f1352,f6694])).
% 79.42/11.78 thf(f6694,plain,(
% 79.42/11.78 spl72_292 <=> (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus(nat)))))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_292])])).
% 79.42/11.78 thf(f1352,plain,(
% 79.42/11.78 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus(nat)))))),
% 79.42/11.78 inference(cnf_transformation,[],[f316])).
% 79.42/11.78 thf(f316,plain,(
% 79.42/11.78 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,$o))),bCOMB,vAPP(sTfun(sTfun(nat,$o),$o),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,$o)),bCOMB,vSIGMA(nat))),vAPP(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun(nat,$o))),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,cCOMB),vAPP(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,nat)),sTfun(nat,sTfun(nat,sTfun(nat,$o)))),bCOMB,vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(sTfun(nat,nat),sTfun(nat,sTfun(nat,$o))),bCOMB,vEQ(nat))),plus_plus(nat)))))),
% 79.42/11.78 inference(fool_elimination,[],[f315])).
% 79.42/11.78 thf(f315,plain,(
% 79.42/11.78 (ord_less_eq(nat) = (^[X0 : nat, X1 : nat] : (? [X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) = X1))))),
% 79.42/11.78 inference(rectify,[],[f63])).
% 79.42/11.78 thf(f63,axiom,(
% 79.42/11.78 (ord_less_eq(nat) = (^[X45 : nat, X46 : nat] : (? [X47 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X45),X47) = X46))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_nat__le__iff__add)).
% 79.42/11.78 thf(f6676,plain,(
% 79.42/11.78 spl72_291),
% 79.42/11.78 inference(avatar_split_clause,[],[f1453,f6674])).
% 79.42/11.78 thf(f6674,plain,(
% 79.42/11.78 spl72_291 <=> ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))) | (order(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_291])])).
% 79.42/11.78 thf(f1453,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))) | (order(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1029])).
% 79.42/11.78 thf(f1029,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))) | (order(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f472])).
% 79.42/11.78 thf(f472,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((order(X0) = $true) => (vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),ord_less_eq(X0)))),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0)))))),
% 79.42/11.78 inference(fool_elimination,[],[f471])).
% 79.42/11.78 thf(f471,plain,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => ((^[X1 : X0, X2 : X0] : ((X1 = X2))) = (^[X3 : X0, X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X3) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)))))),
% 79.42/11.78 inference(rectify,[],[f194])).
% 79.42/11.78 thf(f194,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => ((^[X64 : X0, X65 : X0] : ((X64 = X65))) = (^[X37 : X0, X66 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X66),X37) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X37),X66)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_193_eq__iff)).
% 79.42/11.78 thf(f6672,plain,(
% 79.42/11.78 spl72_290),
% 79.42/11.78 inference(avatar_split_clause,[],[f1452,f6670])).
% 79.42/11.78 thf(f6670,plain,(
% 79.42/11.78 spl72_290 <=> ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0))))),ord_less_eq(X0))) | (order(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_290])])).
% 79.42/11.78 thf(f1452,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0))))),ord_less_eq(X0))) | (order(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1028])).
% 79.42/11.78 thf(f1028,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0))))),ord_less_eq(X0))) | (order(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f470])).
% 79.42/11.78 thf(f470,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((order(X0) = $true) => (vEQ(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vAND)),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),cCOMB,ord_less_eq(X0))))),ord_less_eq(X0))))),
% 79.42/11.78 inference(fool_elimination,[],[f469])).
% 79.42/11.78 thf(f469,plain,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => ((^[X1 : X0, X2 : X0] : ((X1 = X2))) = (^[X3 : X0, X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X3)))))),
% 79.42/11.78 inference(rectify,[],[f210])).
% 79.42/11.78 thf(f210,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => ((^[X64 : X0, X65 : X0] : ((X64 = X65))) = (^[X33 : X0, X34 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X33),X34) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X34),X33)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_209_dual__order_Oeq__iff)).
% 79.42/11.78 thf(f6660,plain,(
% 79.42/11.78 spl72_289),
% 79.42/11.78 inference(avatar_split_clause,[],[f1456,f6658])).
% 79.42/11.78 thf(f6658,plain,(
% 79.42/11.78 spl72_289 <=> ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vOR)),ord_less(X0)))),vEQ(X0))) | (order(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_289])])).
% 79.42/11.78 thf(f1456,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vOR)),ord_less(X0)))),vEQ(X0))) | (order(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1032])).
% 79.42/11.78 thf(f1032,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vOR)),ord_less(X0)))),vEQ(X0))) | (order(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f478])).
% 79.42/11.78 thf(f478,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((order(X0) = $true) => (ord_less_eq(X0) = vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o)),vAPP(sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,$o))),sCOMB,vAPP(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o))),vAPP(sTfun(sTfun(X0,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,$o))),sTfun(sTfun(X0,sTfun(X0,sTfun($o,$o))),sTfun(X0,sTfun(sTfun(X0,$o),sTfun(X0,$o)))),bCOMB,sCOMB),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o))),vAPP(sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,sTfun(X0,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(X0,$o),sTfun(X0,sTfun($o,$o))),bCOMB,vOR)),ord_less(X0)))),vEQ(X0))))),
% 79.42/11.78 inference(fool_elimination,[],[f477])).
% 79.42/11.78 thf(f477,plain,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => (ord_less_eq(X0) = (^[X1 : X0, X2 : X0] : ((X1 = X2) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))))),
% 79.42/11.78 inference(rectify,[],[f255])).
% 79.42/11.78 thf(f255,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (order(X0) => (ord_less_eq(X0) = (^[X34 : X0, X33 : X0] : ((X33 = X34) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X34),X33)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_254_dual__order_Oorder__iff__strict)).
% 79.42/11.78 thf(f6604,plain,(
% 79.42/11.78 spl72_288),
% 79.42/11.78 inference(avatar_split_clause,[],[f1351,f6601])).
% 79.42/11.78 thf(f6601,plain,(
% 79.42/11.78 spl72_288 <=> (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less(nat)))),vEQ(nat)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_288])])).
% 79.42/11.78 thf(f1351,plain,(
% 79.42/11.78 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less(nat)))),vEQ(nat)))),
% 79.42/11.78 inference(cnf_transformation,[],[f314])).
% 79.42/11.78 thf(f314,plain,(
% 79.42/11.78 (ord_less_eq(nat) = vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o))),sCOMB,vAPP(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o))),vAPP(sTfun(sTfun(nat,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,$o))),sTfun(sTfun(nat,sTfun(nat,sTfun($o,$o))),sTfun(nat,sTfun(sTfun(nat,$o),sTfun(nat,$o)))),bCOMB,sCOMB),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o))),vAPP(sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,sTfun($o,$o)))),bCOMB,vAPP(sTfun($o,sTfun($o,$o)),sTfun(sTfun(nat,$o),sTfun(nat,sTfun($o,$o))),bCOMB,vOR)),ord_less(nat)))),vEQ(nat)))),
% 79.42/11.78 inference(fool_elimination,[],[f313])).
% 79.42/11.78 thf(f313,plain,(
% 79.42/11.78 (ord_less_eq(nat) = (^[X0 : nat, X1 : nat] : ((X0 = X1) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))))),
% 79.42/11.78 inference(rectify,[],[f60])).
% 79.42/11.78 thf(f60,axiom,(
% 79.42/11.78 (ord_less_eq(nat) = (^[X45 : nat, X46 : nat] : ((X45 = X46) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X45),X46))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_le__eq__less__or__eq)).
% 79.42/11.78 thf(f6597,plain,(
% 79.42/11.78 spl72_287),
% 79.42/11.78 inference(avatar_split_clause,[],[f1496,f6595])).
% 79.42/11.78 thf(f6595,plain,(
% 79.42/11.78 spl72_287 <=> ! [X0 : $tType,X6 : nat,X4 : nat > $o,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_287])])).
% 79.42/11.78 thf(f1496,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X6 : nat,X4 : nat > $o] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1265])).
% 79.42/11.78 thf(f1265,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat > $o] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | (($true != vAPP(nat,$o,X4,vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1))) & ! [X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f1080,f1264])).
% 79.42/11.78 thf(f1264,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat > $o] : (? [X5 : nat] : (($true != vAPP(nat,$o,X4,X5)) & ! [X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X3))) => (($true != vAPP(nat,$o,X4,vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1))) & ! [X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X3))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1080,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat > $o] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ? [X5 : nat] : (($true != vAPP(nat,$o,X4,X5)) & ! [X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1079])).
% 79.42/11.78 thf(f1079,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat > $o] : ((($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ? [X5 : nat] : ((($true != vAPP(nat,$o,X4,X5)) & ! [X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f556])).
% 79.42/11.78 thf(f556,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) => (! [X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X3)) => (! [X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X6))) => ($true = vAPP(nat,$o,X4,X5)))) => ($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))))))),
% 79.42/11.78 inference(fool_elimination,[],[f555])).
% 79.42/11.78 thf(f555,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3) => (! [X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X3) => (! [X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X6),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X6)) => vAPP(nat,$o,X4,X5))) => vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)))))),
% 79.42/11.78 inference(rectify,[],[f122])).
% 79.42/11.78 thf(f122,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X12 : nat,X19 : nat,X24 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X12),X19) => (! [X25 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),X25),X19) => (! [X26 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),X26),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X25),X26)) => vAPP(nat,$o,X24,X25))) => vAPP(nat,$o,X24,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X12),X19)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_121_Graph_Omin__distI2)).
% 79.42/11.78 thf(f6591,plain,(
% 79.42/11.78 spl72_286),
% 79.42/11.78 inference(avatar_split_clause,[],[f1500,f6589])).
% 79.42/11.78 thf(f6589,plain,(
% 79.42/11.78 spl72_286 <=> ! [X0 : $tType,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_286])])).
% 79.42/11.78 thf(f1500,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1269])).
% 79.42/11.78 thf(f1269,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1)),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f1084,f1268])).
% 79.42/11.78 thf(f1268,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X4))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1)),X4))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1084,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | ? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1083])).
% 79.42/11.78 thf(f1083,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | ? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X4)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f560])).
% 79.42/11.78 thf(f560,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) => (! [X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5))) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f559])).
% 79.42/11.78 thf(f559,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4) => (! [X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X5),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X5)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3))))),
% 79.42/11.78 inference(rectify,[],[f151])).
% 79.42/11.78 thf(f151,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),X14),X19) => (! [X22 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),X22),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X14),X22)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X12),X19) = X14))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_150_Graph_Omin__distI__eq)).
% 79.42/11.78 thf(f6581,plain,(
% 79.42/11.78 spl72_285),
% 79.42/11.78 inference(avatar_split_clause,[],[f1495,f6579])).
% 79.42/11.78 thf(f6579,plain,(
% 79.42/11.78 spl72_285 <=> ! [X0 : $tType,X4 : nat > $o,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_285])])).
% 79.42/11.78 thf(f1495,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat > $o] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1265])).
% 79.42/11.78 thf(f6575,plain,(
% 79.42/11.78 spl72_284),
% 79.42/11.78 inference(avatar_split_clause,[],[f1511,f6573])).
% 79.42/11.78 thf(f6573,plain,(
% 79.42/11.78 spl72_284 <=> ! [X0 : $tType,X5 : nat,X3 : nat,X4 : nat,X2 : nat,X6 : nat,X1 : product_prod(nat,nat) > X0] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X4),X6) = X5) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_284])])).
% 79.42/11.78 thf(f1511,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X6 : nat,X4 : nat,X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X4),X6) = X5) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1096])).
% 79.42/11.78 thf(f1096,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X4),X6) = X5) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1095])).
% 79.42/11.78 thf(f1095,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : ((((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X4),X6) = X5) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f578])).
% 79.42/11.78 thf(f578,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X4),X6) = X5)))))),
% 79.42/11.78 inference(fool_elimination,[],[f577])).
% 79.42/11.78 thf(f577,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X4),X6) = X5)))))),
% 79.42/11.78 inference(rectify,[],[f153])).
% 79.42/11.78 thf(f153,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X10),X11),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X8),X12)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X10),X12) = X11)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_152_Graph_Omin__dist__split_I2_J)).
% 79.42/11.78 thf(f6571,plain,(
% 79.42/11.78 spl72_283),
% 79.42/11.78 inference(avatar_split_clause,[],[f1510,f6569])).
% 79.42/11.78 thf(f6569,plain,(
% 79.42/11.78 spl72_283 <=> ! [X0 : $tType,X5 : nat,X6 : nat,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_283])])).
% 79.42/11.78 thf(f1510,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X6 : nat,X4 : nat,X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1094])).
% 79.42/11.78 thf(f1094,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1093])).
% 79.42/11.78 thf(f1093,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : ((((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f576])).
% 79.42/11.78 thf(f576,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3)))))),
% 79.42/11.78 inference(fool_elimination,[],[f575])).
% 79.42/11.78 thf(f575,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3)))))),
% 79.42/11.78 inference(rectify,[],[f127])).
% 79.42/11.78 thf(f127,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X10),X11),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X8),X12)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X8),X10) = X9)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_126_Graph_Omin__dist__split_I1_J)).
% 79.42/11.78 thf(f6563,plain,(
% 79.42/11.78 spl72_282),
% 79.42/11.78 inference(avatar_split_clause,[],[f1673,f6561])).
% 79.42/11.78 thf(f6561,plain,(
% 79.42/11.78 spl72_282 <=> ! [X4 : nat,X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_282])])).
% 79.42/11.78 thf(f1673,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1222])).
% 79.42/11.78 thf(f1222,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1221])).
% 79.42/11.78 thf(f1221,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f824])).
% 79.42/11.78 thf(f824,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X4) = X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f823])).
% 79.42/11.78 thf(f823,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X2),X4) = X3))))),
% 79.42/11.78 inference(rectify,[],[f9])).
% 79.42/11.78 thf(f9,axiom,(
% 79.42/11.78 ! [X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X10),X11),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X8),X12) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X10),X12) = X11))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_min__dist__split_I2_J)).
% 79.42/11.78 thf(f6559,plain,(
% 79.42/11.78 spl72_281),
% 79.42/11.78 inference(avatar_split_clause,[],[f1672,f6557])).
% 79.42/11.78 thf(f6557,plain,(
% 79.42/11.78 spl72_281 <=> ! [X4 : nat,X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_281])])).
% 79.42/11.78 thf(f1672,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1220])).
% 79.42/11.78 thf(f1220,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1219])).
% 79.42/11.78 thf(f1219,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f822])).
% 79.42/11.78 thf(f822,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1))))),
% 79.42/11.78 inference(fool_elimination,[],[f821])).
% 79.42/11.78 thf(f821,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1))))),
% 79.42/11.78 inference(rectify,[],[f10])).
% 79.42/11.78 thf(f10,axiom,(
% 79.42/11.78 ! [X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X10),X11),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X8),X12) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X8),X10) = X9))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_min__dist__split_I1_J)).
% 79.42/11.78 thf(f6555,plain,(
% 79.42/11.78 spl72_280),
% 79.42/11.78 inference(avatar_split_clause,[],[f1670,f6553])).
% 79.42/11.78 thf(f6553,plain,(
% 79.42/11.78 spl72_280 <=> ! [X4 : nat,X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_280])])).
% 79.42/11.78 thf(f1670,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1216])).
% 79.42/11.78 thf(f1216,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1215])).
% 79.42/11.78 thf(f1215,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X4) = X3) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f818])).
% 79.42/11.78 thf(f818,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X4) = X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f817])).
% 79.42/11.78 thf(f817,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X2),X4) = X3))))),
% 79.42/11.78 inference(rectify,[],[f168])).
% 79.42/11.78 thf(f168,axiom,(
% 79.42/11.78 ! [X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X10),X11),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X8),X12)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X10),X12) = X11))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_167_g_H_Omin__dist__split_I2_J)).
% 79.42/11.78 thf(f6551,plain,(
% 79.42/11.78 spl72_279),
% 79.42/11.78 inference(avatar_split_clause,[],[f1669,f6549])).
% 79.42/11.78 thf(f6549,plain,(
% 79.42/11.78 spl72_279 <=> ! [X4 : nat,X0 : nat,X3 : nat,X2 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_279])])).
% 79.42/11.78 thf(f1669,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1214])).
% 79.42/11.78 thf(f1214,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1213])).
% 79.42/11.78 thf(f1213,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f816])).
% 79.42/11.78 thf(f816,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1))))),
% 79.42/11.78 inference(fool_elimination,[],[f815])).
% 79.42/11.78 thf(f815,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1))))),
% 79.42/11.78 inference(rectify,[],[f169])).
% 79.42/11.78 thf(f169,axiom,(
% 79.42/11.78 ! [X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X10),X11),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X8),X12)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X8),X10) = X9))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_168_g_H_Omin__dist__split_I1_J)).
% 79.42/11.78 thf(f6521,plain,(
% 79.42/11.78 spl72_278),
% 79.42/11.78 inference(avatar_split_clause,[],[f1506,f6519])).
% 79.42/11.78 thf(f6519,plain,(
% 79.42/11.78 spl72_278 <=> ! [X0 : $tType,X2 : nat,X4 : nat,X3 : list(product_prod(nat,nat)),X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK24(X0),X4),X2),X1)),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_278])])).
% 79.42/11.78 thf(f1506,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : list(product_prod(nat,nat)),X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK24(X0),X4),X2),X1)),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1271])).
% 79.42/11.78 thf(f1271,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK24(X0),X4),X2),X1)),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f1089,f1270])).
% 79.42/11.78 thf(f1270,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : product_prod(nat,nat) > X0,X2 : nat,X4 : nat] : (? [X5 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X5),X4)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK24(X0),X4),X2),X1)),X4)))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1089,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (? [X5 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X5),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f570])).
% 79.42/11.78 thf(f570,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) => ? [X5 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X5),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f569])).
% 79.42/11.78 thf(f569,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4) => ? [X5 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X5),X4)))),
% 79.42/11.78 inference(rectify,[],[f132])).
% 79.42/11.78 thf(f132,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X54 : nat,X18 : list(product_prod(nat,nat)),X55 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X5),X54),X18),X55) => ? [X60 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X1),X5),X54),X60),X55)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_131_Graph_OisSPath__pathLE)).
% 79.42/11.78 thf(f6508,plain,(
% 79.42/11.78 spl72_277),
% 79.42/11.78 inference(avatar_split_clause,[],[f1668,f6506])).
% 79.42/11.78 thf(f6506,plain,(
% 79.42/11.78 spl72_277 <=> ! [X0 : $tType,X4 : nat,X7 : X0,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X7)) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_277])])).
% 79.42/11.78 thf(f1668,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X7 : X0,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X7)) | ($true != vAPP(X0,$o,X1,X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1345])).
% 79.42/11.78 thf(f1345,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : ((($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1)))) | (! [X7 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X7))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f1342,f1344,f1343])).
% 79.42/11.78 thf(f1343,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : (? [X5 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X5)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,X5))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1344,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X3 : X0 > nat] : (? [X6 : X0] : (! [X7 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,X6))) | ($true != vAPP(X0,$o,X1,X7))) & ($true = vAPP(X0,$o,X1,X6))) => (! [X7 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X7))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1342,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : (? [X5 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X5)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,X5))) | ? [X6 : X0] : (! [X7 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,X6))) | ($true != vAPP(X0,$o,X1,X7))) & ($true = vAPP(X0,$o,X1,X6))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 inference(rectify,[],[f1212])).
% 79.42/11.78 thf(f1212,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : (? [X7 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,X7))) | ? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X6)),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X6))) & ($true = vAPP(X0,$o,X1,X5))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 inference(flattening,[],[f1211])).
% 79.42/11.78 thf(f1211,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : ((? [X7 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,X7))) | ? [X5 : X0] : (! [X6 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X6)),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X6))) & ($true = vAPP(X0,$o,X1,X5)))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f924])).
% 79.42/11.78 thf(f924,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : (($true = vAPP(X0,$o,X1,X2)) => (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) => ? [X6 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X6)),vAPP(X0,nat,X3,X5))) & ($true = vAPP(X0,$o,X1,X6)))) => ? [X7 : X0] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,X7)))))),
% 79.42/11.78 inference(flattening,[],[f814])).
% 79.42/11.78 thf(f814,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : (($true = vAPP(X0,$o,X1,X2)) => (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) => ? [X6 : X0] : (~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X6)),vAPP(X0,nat,X3,X5))) & ($true = vAPP(X0,$o,X1,X6)))) => ? [X7 : X0] : (~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) & ($true = vAPP(X0,$o,X1,X7)))))),
% 79.42/11.78 inference(fool_elimination,[],[f813])).
% 79.42/11.78 thf(f813,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat,X4 : nat] : (vAPP(X0,$o,X1,X2) => (! [X5 : X0] : (vAPP(X0,$o,X1,X5) => ? [X6 : X0] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X6)),vAPP(X0,nat,X3,X5)) & vAPP(X0,$o,X1,X6))) => ? [X7 : X0] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,X7)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4)) & vAPP(X0,$o,X1,X7))))),
% 79.42/11.78 inference(rectify,[],[f155])).
% 79.42/11.78 thf(f155,axiom,(
% 79.42/11.78 ! [X0 : $tType,X29 : X0 > $o,X2 : X0,X39 : X0 > nat,X4 : nat] : (vAPP(X0,$o,X29,X2) => (! [X31 : X0] : (vAPP(X0,$o,X29,X31) => ? [X32 : X0] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X39,X32)),vAPP(X0,nat,X39,X31)) & vAPP(X0,$o,X29,X32))) => ? [X30 : X0] : (~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X39,X30)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X39,X2)),X4)) & vAPP(X0,$o,X29,X30))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_154_ex__has__greatest__nat__lemma)).
% 79.42/11.78 thf(f6500,plain,(
% 79.42/11.78 spl72_276),
% 79.42/11.78 inference(avatar_split_clause,[],[f1633,f6498])).
% 79.42/11.78 thf(f6498,plain,(
% 79.42/11.78 spl72_276 <=> ! [X4 : nat,X0 : nat,X2 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_276])])).
% 79.42/11.78 thf(f1633,plain,(
% 79.42/11.78 ( ! [X2 : nat > $o,X0 : nat,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1321])).
% 79.42/11.78 thf(f1321,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0))) & ! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK59])],[f1179,f1320])).
% 79.42/11.78 thf(f1320,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & ! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X1))) => (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0))) & ! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X1))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1179,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & ! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1178])).
% 79.42/11.78 thf(f1178,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : ((($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ? [X3 : nat] : ((($true != vAPP(nat,$o,X2,X3)) & ! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f768])).
% 79.42/11.78 thf(f768,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) => (! [X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X1)) => (! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1)) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true)) => ($true = vAPP(nat,$o,X2,X3)))) => ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)))))),
% 79.42/11.78 inference(fool_elimination,[],[f767])).
% 79.42/11.78 thf(f767,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) => (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X1) => (! [X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X4),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4)) => vAPP(nat,$o,X2,X3))) => vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))))),
% 79.42/11.78 inference(rectify,[],[f28])).
% 79.42/11.78 thf(f28,axiom,(
% 79.42/11.78 ! [X12 : nat,X19 : nat,X24 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X12),X19) => (! [X25 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X25),X19) => (! [X26 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X26),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X25),X26)) => vAPP(nat,$o,X24,X25))) => vAPP(nat,$o,X24,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X12),X19))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_min__distI2)).
% 79.42/11.78 thf(f6496,plain,(
% 79.42/11.78 spl72_275),
% 79.42/11.78 inference(avatar_split_clause,[],[f1628,f6494])).
% 79.42/11.78 thf(f6494,plain,(
% 79.42/11.78 spl72_275 <=> ! [X4 : nat,X0 : nat,X2 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_275])])).
% 79.42/11.78 thf(f1628,plain,(
% 79.42/11.78 ( ! [X2 : nat > $o,X0 : nat,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1317])).
% 79.42/11.78 thf(f1317,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0))) & ! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f1175,f1316])).
% 79.42/11.78 thf(f1316,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & ! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X1))) => (($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0))) & ! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X1))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1175,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ? [X3 : nat] : (($true != vAPP(nat,$o,X2,X3)) & ! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1174])).
% 79.42/11.78 thf(f1174,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : ((($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ? [X3 : nat] : ((($true != vAPP(nat,$o,X2,X3)) & ! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f764])).
% 79.42/11.78 thf(f764,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) => (! [X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X1)) => (! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1)) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) = $true)) => ($true = vAPP(nat,$o,X2,X3)))) => ($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)))))),
% 79.42/11.78 inference(fool_elimination,[],[f763])).
% 79.42/11.78 thf(f763,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) => (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X1) => (! [X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X4),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4)) => vAPP(nat,$o,X2,X3))) => vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))))),
% 79.42/11.78 inference(rectify,[],[f164])).
% 79.42/11.78 thf(f164,axiom,(
% 79.42/11.78 ! [X12 : nat,X19 : nat,X24 : nat > $o] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X12),X19) => (! [X25 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X25),X19) => (! [X26 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X26),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X25),X26)) => vAPP(nat,$o,X24,X25))) => vAPP(nat,$o,X24,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X12),X19))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_163_g_H_Omin__distI2)).
% 79.42/11.78 thf(f6488,plain,(
% 79.42/11.78 spl72_274),
% 79.42/11.78 inference(avatar_split_clause,[],[f1501,f6486])).
% 79.42/11.78 thf(f6486,plain,(
% 79.42/11.78 spl72_274 <=> ! [X0 : $tType,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_274])])).
% 79.42/11.78 thf(f1501,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(nat,sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK23(X0),X4),X3),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1269])).
% 79.42/11.78 thf(f6460,plain,(
% 79.42/11.78 spl72_273),
% 79.42/11.78 inference(avatar_split_clause,[],[f1727,f6458])).
% 79.42/11.78 thf(f6458,plain,(
% 79.42/11.78 spl72_273 <=> ! [X0 : $tType,X3 : nat,X5 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_273])])).
% 79.42/11.78 thf(f1727,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(equality_resolution,[],[f1508])).
% 79.42/11.78 thf(f1508,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat,X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) != X4) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1273])).
% 79.42/11.78 thf(f1273,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)) = X5) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) != X4) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f1092,f1272])).
% 79.42/11.78 thf(f1272,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : product_prod(nat,nat) > X0,X2 : nat,X5 : nat] : (? [X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = X5) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X6))) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)) = X5) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1092,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat] : (? [X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = X5) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X6))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) != X4) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1091])).
% 79.42/11.78 thf(f1091,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat] : (((? [X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = X5) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X6))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4))) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) != X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f574])).
% 79.42/11.78 thf(f574,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) = X4) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4)) => ? [X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = X5) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X6)))))))),
% 79.42/11.78 inference(fool_elimination,[],[f573])).
% 79.42/11.78 thf(f573,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) = X4) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4) => ? [X6 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X6) = X5) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X6))))))),
% 79.42/11.78 inference(rectify,[],[f149])).
% 79.42/11.78 thf(f149,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X13 : nat,X12 : nat,X14 : nat,X15 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X13),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X13),X12) = X14) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X15),X14) => ? [X16 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X13),X16) = X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X13),X16))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_Graph_Omin__dist__less)).
% 79.42/11.78 thf(f6456,plain,(
% 79.42/11.78 spl72_272),
% 79.42/11.78 inference(avatar_split_clause,[],[f1726,f6454])).
% 79.42/11.78 thf(f6454,plain,(
% 79.42/11.78 spl72_272 <=> ! [X0 : $tType,X3 : nat,X5 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)) = X5) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_272])])).
% 79.42/11.78 thf(f1726,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)) = X5) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(equality_resolution,[],[f1509])).
% 79.42/11.78 thf(f1509,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat,X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK25(X0),X5),X2),X1)) = X5) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X5),X4)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3) != X4) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1273])).
% 79.42/11.78 thf(f6452,plain,(
% 79.42/11.78 spl72_271),
% 79.42/11.78 inference(avatar_split_clause,[],[f1499,f6450])).
% 79.42/11.78 thf(f6450,plain,(
% 79.42/11.78 spl72_271 <=> ! [X0 : $tType,X2 : nat,X4 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1)) = X4) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_271])])).
% 79.42/11.78 thf(f1499,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1)) = X4) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1267])).
% 79.42/11.78 thf(f1267,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1)) = X4) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f1082,f1266])).
% 79.42/11.78 thf(f1266,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : product_prod(nat,nat) > X0,X2 : nat,X4 : nat] : (? [X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X5) = X4) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X5))) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1)) = X4) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1082,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (? [X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X5) = X4) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X5))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1081])).
% 79.42/11.78 thf(f1081,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : ((? [X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X5) = X4) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X5))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f558])).
% 79.42/11.78 thf(f558,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) => ? [X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X5) = X4) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X5))))))),
% 79.42/11.78 inference(fool_elimination,[],[f557])).
% 79.42/11.78 thf(f557,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)) => ? [X5 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X5) = X4) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X5)))))),
% 79.42/11.78 inference(rectify,[],[f150])).
% 79.42/11.78 thf(f150,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X13 : nat,X12 : nat,X15 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X13),X12) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X15),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X13),X12)) => ? [X16 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X13),X16) = X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X13),X16)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_149_Graph_Omin__dist__le)).
% 79.42/11.78 thf(f6448,plain,(
% 79.42/11.78 spl72_270),
% 79.42/11.78 inference(avatar_split_clause,[],[f1498,f6446])).
% 79.42/11.78 thf(f6446,plain,(
% 79.42/11.78 spl72_270 <=> ! [X0 : $tType,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_270])])).
% 79.42/11.78 thf(f1498,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),sK22(X0),X4),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1267])).
% 79.42/11.78 thf(f6442,plain,(
% 79.42/11.78 spl72_269),
% 79.42/11.78 inference(avatar_split_clause,[],[f1512,f6440])).
% 79.42/11.78 thf(f6440,plain,(
% 79.42/11.78 spl72_269 <=> ! [X0 : $tType,X5 : nat,X3 : nat,X4 : nat,X6 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_269])])).
% 79.42/11.78 thf(f1512,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X6 : nat,X4 : nat,X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1098])).
% 79.42/11.78 thf(f1098,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1097])).
% 79.42/11.78 thf(f1097,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X6)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f580])).
% 79.42/11.78 thf(f580,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X6)))))),
% 79.42/11.78 inference(fool_elimination,[],[f579])).
% 79.42/11.78 thf(f579,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat,X5 : nat,X6 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X4),X5),X6) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X5)),X6))))),
% 79.42/11.78 inference(rectify,[],[f143])).
% 79.42/11.78 thf(f143,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X10),X11),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X8),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11)),X12))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_142_Graph_Odist__trans)).
% 79.42/11.78 thf(f6432,plain,(
% 79.42/11.78 spl72_268),
% 79.42/11.78 inference(avatar_split_clause,[],[f1428,f6430])).
% 79.42/11.78 thf(f6430,plain,(
% 79.42/11.78 spl72_268 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_268])])).
% 79.42/11.78 thf(f1428,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1229])).
% 79.42/11.78 thf(f1229,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(definition_folding,[],[f1002,f1228,f1227,f1226,f1225])).
% 79.42/11.78 thf(f1225,plain,(
% 79.42/11.78 ! [X3 : X0,X2 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)))),
% 79.42/11.78 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 79.42/11.78 thf(f1226,plain,(
% 79.42/11.78 ! [X3 : X0,X1 : X0,X0 : $tType,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)))),
% 79.42/11.78 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 79.42/11.78 thf(f1227,plain,(
% 79.42/11.78 ! [X2 : X0,X3 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)))),
% 79.42/11.78 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 79.42/11.78 thf(f1228,plain,(
% 79.42/11.78 ! [X1 : X0,X2 : X0,X0 : $tType,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) | ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)))),
% 79.42/11.78 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 79.42/11.78 thf(f1002,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1001])).
% 79.42/11.78 thf(f1001,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)))) | (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f899])).
% 79.42/11.78 thf(f899,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) => ~(($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))))))))),
% 79.42/11.78 inference(flattening,[],[f436])).
% 79.42/11.78 thf(f436,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) => ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) => ~(($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))))))))),
% 79.42/11.78 inference(fool_elimination,[],[f435])).
% 79.42/11.78 thf(f435,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ~(vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))))))))),
% 79.42/11.78 inference(rectify,[],[f200])).
% 79.42/11.78 thf(f200,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (linorder(X0) => ! [X51 : X0,X52 : X0,X67 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X52) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X67)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X51) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X67)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X67) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X67),X52)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X67),X52) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X51)) => ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X67) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X67),X51)) => ~(vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X67),X51) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X52))))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_199_le__cases3)).
% 79.42/11.78 thf(f6424,plain,(
% 79.42/11.78 spl72_267),
% 79.42/11.78 inference(avatar_split_clause,[],[f1674,f6422])).
% 79.42/11.78 thf(f6422,plain,(
% 79.42/11.78 spl72_267 <=> ! [X2 : nat,X4 : nat,X0 : nat,X3 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_267])])).
% 79.42/11.78 thf(f1674,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1224])).
% 79.42/11.78 thf(f1224,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1223])).
% 79.42/11.78 thf(f1223,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f826])).
% 79.42/11.78 thf(f826,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f825])).
% 79.42/11.78 thf(f825,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X2),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)))),
% 79.42/11.78 inference(rectify,[],[f15])).
% 79.42/11.78 thf(f15,axiom,(
% 79.42/11.78 ! [X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X10),X11),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X8),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11)),X12)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_dist__trans)).
% 79.42/11.78 thf(f6420,plain,(
% 79.42/11.78 spl72_266),
% 79.42/11.78 inference(avatar_split_clause,[],[f1671,f6418])).
% 79.42/11.78 thf(f6418,plain,(
% 79.42/11.78 spl72_266 <=> ! [X2 : nat,X4 : nat,X0 : nat,X3 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_266])])).
% 79.42/11.78 thf(f1671,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1218])).
% 79.42/11.78 thf(f1218,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1217])).
% 79.42/11.78 thf(f1217,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f820])).
% 79.42/11.78 thf(f820,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f819])).
% 79.42/11.78 thf(f819,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X2),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)),X4)))),
% 79.42/11.78 inference(rectify,[],[f170])).
% 79.42/11.78 thf(f170,axiom,(
% 79.42/11.78 ! [X8 : nat,X9 : nat,X10 : nat,X11 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X8),X9),X10) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X10),X11),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X8),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X9),X11)),X12)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_169_g_H_Odist__trans)).
% 79.42/11.78 thf(f6412,plain,(
% 79.42/11.78 spl72_265),
% 79.42/11.78 inference(avatar_split_clause,[],[f1641,f6410])).
% 79.42/11.78 thf(f6410,plain,(
% 79.42/11.78 spl72_265 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_265])])).
% 79.42/11.78 thf(f1641,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1327])).
% 79.42/11.78 thf(f1327,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0)),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK62])],[f1187,f1326])).
% 79.42/11.78 thf(f1326,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X2))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0)),X2))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1187,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1186])).
% 79.42/11.78 thf(f1186,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f778])).
% 79.42/11.78 thf(f778,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) => (! [X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3))) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f777])).
% 79.42/11.78 thf(f777,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2) => (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X3),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1)))),
% 79.42/11.78 inference(rectify,[],[f22])).
% 79.42/11.78 thf(f22,axiom,(
% 79.42/11.78 ! [X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X14),X19) => (! [X22 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X22),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X14),X22)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X12),X19) = X14)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_min__distI__eq)).
% 79.42/11.78 thf(f6408,plain,(
% 79.42/11.78 spl72_264),
% 79.42/11.78 inference(avatar_split_clause,[],[f1637,f6406])).
% 79.42/11.78 thf(f6406,plain,(
% 79.42/11.78 spl72_264 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_264])])).
% 79.42/11.78 thf(f1637,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1325])).
% 79.42/11.78 thf(f1325,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0)),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f1183,f1324])).
% 79.42/11.78 thf(f1324,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X2))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0)),X2))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1183,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(flattening,[],[f1182])).
% 79.42/11.78 thf(f1182,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f772])).
% 79.42/11.78 thf(f772,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) => (! [X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3))) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f771])).
% 79.42/11.78 thf(f771,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2) => (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X3),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X3)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1)))),
% 79.42/11.78 inference(rectify,[],[f165])).
% 79.42/11.78 thf(f165,axiom,(
% 79.42/11.78 ! [X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X14),X19) => (! [X22 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X22),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X14),X22)) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X12),X19) = X14)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_g_H_Omin__distI__eq)).
% 79.42/11.78 thf(f6398,plain,(
% 79.42/11.78 spl72_263),
% 79.42/11.78 inference(avatar_split_clause,[],[f1493,f6396])).
% 79.42/11.78 thf(f6396,plain,(
% 79.42/11.78 spl72_263 <=> ! [X0 : $tType,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK20(X0),X3),X2),X1)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_263])])).
% 79.42/11.78 thf(f1493,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK20(X0),X3),X2),X1)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1263])).
% 79.42/11.78 thf(f1263,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK20(X0),X3),X2),X1)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f1077,f1262])).
% 79.42/11.78 thf(f1262,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (? [X4 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X4),X3)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),vAPP(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)),vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat))),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),list(product_prod(nat,nat)))),sK20(X0),X3),X2),X1)),X3)))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1077,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (? [X4 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X4),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f908])).
% 79.42/11.78 thf(f908,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) => ~! [X4 : list(product_prod(nat,nat))] : ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X4),X3))))),
% 79.42/11.78 inference(flattening,[],[f552])).
% 79.42/11.78 thf(f552,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) => ~! [X4 : list(product_prod(nat,nat))] : ~($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X4),X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f551])).
% 79.42/11.78 thf(f551,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3) => ~! [X4 : list(product_prod(nat,nat))] : ~vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X4),X3)))),
% 79.42/11.78 inference(rectify,[],[f148])).
% 79.42/11.78 thf(f148,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X8 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X8),X12) => ~! [X21 : list(product_prod(nat,nat))] : ~vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X1),X5),X8),X21),X12)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_147_Graph_Oobtain__shortest__path)).
% 79.42/11.78 thf(f6372,plain,(
% 79.42/11.78 spl72_262),
% 79.42/11.78 inference(avatar_split_clause,[],[f1497,f6370])).
% 79.42/11.78 thf(f6370,plain,(
% 79.42/11.78 spl72_262 <=> ! [X0 : $tType,X4 : nat > $o,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,X4,vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_262])])).
% 79.42/11.78 thf(f1497,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat > $o] : (($true = vAPP(nat,$o,X4,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3))) | ($true != vAPP(nat,$o,X4,vAPP(sTfun(product_prod(nat,nat),X0),nat,vAPP(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat),vAPP(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat)),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,sTfun(sTfun(product_prod(nat,nat),X0),nat))),sK21(X0),X4),X3),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1265])).
% 79.42/11.78 thf(f6368,plain,(
% 79.42/11.78 spl72_261),
% 79.42/11.78 inference(avatar_split_clause,[],[f1484,f6366])).
% 79.42/11.78 thf(f6366,plain,(
% 79.42/11.78 spl72_261 <=> ! [X0 : $tType] : ((reachableNodes(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat)))),bCOMB,vAPP(sTfun(sTfun(nat,$o),set(nat)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),bCOMB,collect(nat))),connected(X0))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_261])])).
% 79.42/11.78 thf(f1484,plain,(
% 79.42/11.78 ( ! [X0 : $tType] : ((reachableNodes(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat)))),bCOMB,vAPP(sTfun(sTfun(nat,$o),set(nat)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),bCOMB,collect(nat))),connected(X0))) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1068])).
% 79.42/11.78 thf(f1068,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((reachableNodes(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat)))),bCOMB,vAPP(sTfun(sTfun(nat,$o),set(nat)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),bCOMB,collect(nat))),connected(X0))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f534])).
% 79.42/11.78 thf(f534,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (reachableNodes(X0) = vAPP(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat))),vAPP(sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),sTfun(sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o))),sTfun(sTfun(product_prod(nat,nat),X0),sTfun(nat,set(nat)))),bCOMB,vAPP(sTfun(sTfun(nat,$o),set(nat)),sTfun(sTfun(nat,sTfun(nat,$o)),sTfun(nat,set(nat))),bCOMB,collect(nat))),connected(X0))))),
% 79.42/11.78 inference(fool_elimination,[],[f533])).
% 79.42/11.78 thf(f533,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => (reachableNodes(X0) = (^[X1 : product_prod(nat,nat) > X0, X2 : nat] : (vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2))))))),
% 79.42/11.78 inference(rectify,[],[f134])).
% 79.42/11.78 thf(f134,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => (reachableNodes(X1) = (^[X35 : product_prod(nat,nat) > X1, X57 : nat] : (vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X35),X57))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_133_Graph_OreachableNodes__def)).
% 79.42/11.78 thf(f6358,plain,(
% 79.42/11.78 spl72_260),
% 79.42/11.78 inference(avatar_split_clause,[],[f1632,f6356])).
% 79.42/11.78 thf(f6356,plain,(
% 79.42/11.78 spl72_260 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_260])])).
% 79.42/11.78 thf(f1632,plain,(
% 79.42/11.78 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1321])).
% 79.42/11.78 thf(f6354,plain,(
% 79.42/11.78 spl72_259),
% 79.42/11.78 inference(avatar_split_clause,[],[f1627,f6352])).
% 79.42/11.78 thf(f6352,plain,(
% 79.42/11.78 spl72_259 <=> ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_259])])).
% 79.42/11.78 thf(f1627,plain,(
% 79.42/11.78 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1317])).
% 79.42/11.78 thf(f6259,plain,(
% 79.42/11.78 spl72_258),
% 79.42/11.78 inference(avatar_split_clause,[],[f1432,f6257])).
% 79.42/11.78 thf(f1432,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1257])).
% 79.42/11.78 thf(f1257,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12,sK13,sK14,sK15])],[f1253,f1256,f1255,f1254])).
% 79.42/11.78 thf(f1254,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1255,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X6 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X6)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1256,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X7 : X0,X8 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X8)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X8))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1253,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) | ? [X6 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X6)) | ? [X7 : X0,X8 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X8)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X8)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(rectify,[],[f1004])).
% 79.42/11.78 thf(f1004,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X7 : X0,X8 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X8)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X8),X7))) | ? [X6 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X6)) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X5)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1003])).
% 79.42/11.78 thf(f1003,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X7 : X0,X8 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X8)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X8),X7)))) | ? [X6 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X6))) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X5)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f438])).
% 79.42/11.78 thf(f438,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X5)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) => (! [X6 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X6)) => (! [X7 : X0,X8 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X8),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X8))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))))),
% 79.42/11.78 inference(fool_elimination,[],[f437])).
% 79.42/11.78 thf(f437,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (! [X4 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X5) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) => (! [X6 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X6) => (! [X7 : X0,X8 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X8),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X8)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 79.42/11.78 inference(rectify,[],[f216])).
% 79.42/11.78 thf(f216,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (linorder(X0) => ! [X29 : X0 > X0 > $o,X6 : X0,X7 : X0] : (! [X68 : X0,X69 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X68),X69) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X68),X69)) => (! [X68 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X68),X68) => (! [X68 : X0,X69 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X69),X68) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X68),X69)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X6),X7)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_215_linorder__less__wlog)).
% 79.42/11.78 thf(f6255,plain,(
% 79.42/11.78 spl72_257),
% 79.42/11.78 inference(avatar_split_clause,[],[f1430,f6253])).
% 79.42/11.78 thf(f1430,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1257])).
% 79.42/11.78 thf(f6124,plain,(
% 79.42/11.78 spl72_256),
% 79.42/11.78 inference(avatar_split_clause,[],[f1433,f6122])).
% 79.42/11.78 thf(f1433,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1257])).
% 79.42/11.78 thf(f6120,plain,(
% 79.42/11.78 spl72_255),
% 79.42/11.78 inference(avatar_split_clause,[],[f1431,f6118])).
% 79.42/11.78 thf(f1431,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK12(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK11(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK13(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK14(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK15(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1257])).
% 79.42/11.78 thf(f6094,plain,(
% 79.42/11.78 spl72_254),
% 79.42/11.78 inference(avatar_split_clause,[],[f1831,f6092])).
% 79.42/11.78 thf(f6092,plain,(
% 79.42/11.78 spl72_254 <=> ! [X0 : $tType,X3 : X0,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_254])])).
% 79.42/11.78 thf(f1831,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(duplicate_literal_removal,[],[f1427])).
% 79.42/11.78 thf(f1427,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1229])).
% 79.42/11.78 thf(f6086,plain,(
% 79.42/11.78 spl72_253),
% 79.42/11.78 inference(avatar_split_clause,[],[f1651,f6084])).
% 79.42/11.78 thf(f1651,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,X2),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1331])).
% 79.42/11.78 thf(f1331,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,X2),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK64])],[f1196,f1330])).
% 79.42/11.78 thf(f1330,plain,(
% 79.42/11.78 ! [X0 : nat,X2 : nat] : (? [X3 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X3),X2)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK64,X2),X0)),X2)))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1196,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (? [X3 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X3),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f796])).
% 79.42/11.78 thf(f796,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) => ? [X3 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X3),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f795])).
% 79.42/11.78 thf(f795,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2) => ? [X3 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X3),X2))),
% 79.42/11.78 inference(rectify,[],[f128])).
% 79.42/11.78 thf(f128,axiom,(
% 79.42/11.78 ! [X54 : nat,X18 : list(product_prod(nat,nat)),X55 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X54),X18),X55) => ? [X60 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X54),X60),X55))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_127_isSPath__pathLE)).
% 79.42/11.78 thf(f6082,plain,(
% 79.42/11.78 spl72_252),
% 79.42/11.78 inference(avatar_split_clause,[],[f1647,f6080])).
% 79.42/11.78 thf(f1647,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,X2),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1329])).
% 79.42/11.78 thf(f1329,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,X2),X0)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK63])],[f1192,f1328])).
% 79.42/11.78 thf(f1328,plain,(
% 79.42/11.78 ! [X0 : nat,X2 : nat] : (? [X3 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X3),X2)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK63,X2),X0)),X2)))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1192,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (? [X3 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X3),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f788])).
% 79.42/11.78 thf(f788,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) => ? [X3 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X3),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f787])).
% 79.42/11.78 thf(f787,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2) => ? [X3 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X3),X2))),
% 79.42/11.78 inference(rectify,[],[f172])).
% 79.42/11.78 thf(f172,axiom,(
% 79.42/11.78 ! [X54 : nat,X18 : list(product_prod(nat,nat)),X55 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X54),X18),X55) => ? [X60 : list(product_prod(nat,nat))] : vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X54),X60),X55))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_171_g_H_OisSPath__pathLE)).
% 79.42/11.78 thf(f6068,plain,(
% 79.42/11.78 spl72_251),
% 79.42/11.78 inference(avatar_split_clause,[],[f1667,f6066])).
% 79.42/11.78 thf(f6066,plain,(
% 79.42/11.78 spl72_251 <=> ! [X0 : $tType,X4 : nat,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_251])])).
% 79.42/11.78 thf(f1667,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(X0,nat,X3,X2)),X4))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1345])).
% 79.42/11.78 thf(f5990,plain,(
% 79.42/11.78 spl72_250),
% 79.42/11.78 inference(avatar_split_clause,[],[f1666,f5988])).
% 79.42/11.78 thf(f5988,plain,(
% 79.42/11.78 spl72_250 <=> ! [X0 : $tType,X4 : nat,X7 : X0,X3 : X0 > nat,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X7)) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_250])])).
% 79.42/11.78 thf(f1666,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X7 : X0,X4 : nat] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X7)),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X7)) | ($true != vAPP(X0,$o,X1,X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1345])).
% 79.42/11.78 thf(f5934,plain,(
% 79.42/11.78 spl72_249),
% 79.42/11.78 inference(avatar_split_clause,[],[f1743,f5932])).
% 79.42/11.78 thf(f5932,plain,(
% 79.42/11.78 spl72_249 <=> ! [X0 : nat,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_249])])).
% 79.42/11.78 thf(f1743,plain,(
% 79.42/11.78 ( ! [X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1663])).
% 79.42/11.78 thf(f1663,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1341])).
% 79.42/11.78 thf(f1341,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f1210,f1340])).
% 79.42/11.78 thf(f1340,plain,(
% 79.42/11.78 ! [X0 : nat,X3 : nat] : (? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X4))) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1210,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1209])).
% 79.42/11.78 thf(f1209,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) != X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f812])).
% 79.42/11.78 thf(f812,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) = X2) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) => ? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X4))))))),
% 79.42/11.78 inference(fool_elimination,[],[f811])).
% 79.42/11.78 thf(f811,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) = X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => ? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X4) = X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X4)))))),
% 79.42/11.78 inference(rectify,[],[f11])).
% 79.42/11.78 thf(f11,axiom,(
% 79.42/11.78 ! [X13 : nat,X12 : nat,X14 : nat,X15 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X13),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X13),X12) = X14) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X15),X14) => ? [X16 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X13),X16) = X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X13),X16)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_min__dist__less)).
% 79.42/11.78 thf(f5930,plain,(
% 79.42/11.78 spl72_248),
% 79.42/11.78 inference(avatar_split_clause,[],[f1742,f5928])).
% 79.42/11.78 thf(f5928,plain,(
% 79.42/11.78 spl72_248 <=> ! [X0 : nat,X1 : nat,X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_248])])).
% 79.42/11.78 thf(f1742,plain,(
% 79.42/11.78 ( ! [X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1664])).
% 79.42/11.78 thf(f1664,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK69,X3),X0)) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1341])).
% 79.42/11.78 thf(f5926,plain,(
% 79.42/11.78 spl72_247),
% 79.42/11.78 inference(avatar_split_clause,[],[f1741,f5924])).
% 79.42/11.78 thf(f5924,plain,(
% 79.42/11.78 spl72_247 <=> ! [X0 : nat,X1 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_247])])).
% 79.42/11.78 thf(f1741,plain,(
% 79.42/11.78 ( ! [X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1661])).
% 79.42/11.78 thf(f1661,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1339])).
% 79.42/11.78 thf(f1339,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK68])],[f1208,f1338])).
% 79.42/11.78 thf(f1338,plain,(
% 79.42/11.78 ! [X0 : nat,X3 : nat] : (? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X4))) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1208,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1207])).
% 79.42/11.78 thf(f1207,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X4))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) != X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f810])).
% 79.42/11.78 thf(f810,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) = X2) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) => ? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4) = X3) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X4))))))),
% 79.42/11.78 inference(fool_elimination,[],[f809])).
% 79.42/11.78 thf(f809,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) = X2) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => ? [X4 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X4) = X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X4)))))),
% 79.42/11.78 inference(rectify,[],[f163])).
% 79.42/11.78 thf(f163,axiom,(
% 79.42/11.78 ! [X13 : nat,X12 : nat,X14 : nat,X15 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X13),X12) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X13),X12) = X14) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X15),X14) => ? [X16 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X13),X16) = X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X13),X16)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_162_g_H_Omin__dist__less)).
% 79.42/11.78 thf(f5922,plain,(
% 79.42/11.78 spl72_246),
% 79.42/11.78 inference(avatar_split_clause,[],[f1740,f5920])).
% 79.42/11.78 thf(f5920,plain,(
% 79.42/11.78 spl72_246 <=> ! [X0 : nat,X1 : nat,X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_246])])).
% 79.42/11.78 thf(f1740,plain,(
% 79.42/11.78 ( ! [X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1662])).
% 79.42/11.78 thf(f1662,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK68,X3),X0)) = X3) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) != X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1339])).
% 79.42/11.78 thf(f5918,plain,(
% 79.42/11.78 spl72_245),
% 79.42/11.78 inference(avatar_split_clause,[],[f1636,f5916])).
% 79.42/11.78 thf(f5916,plain,(
% 79.42/11.78 spl72_245 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0)) = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_245])])).
% 79.42/11.78 thf(f1636,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0)) = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1323])).
% 79.42/11.78 thf(f1323,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0)) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK60])],[f1181,f1322])).
% 79.42/11.78 thf(f1322,plain,(
% 79.42/11.78 ! [X0 : nat,X2 : nat] : (? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X3))) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0)) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1181,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1180])).
% 79.42/11.78 thf(f1180,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f770])).
% 79.42/11.78 thf(f770,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) => ? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X3)))))),
% 79.42/11.78 inference(fool_elimination,[],[f769])).
% 79.42/11.78 thf(f769,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)) => ? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X3) = X2) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X3))))),
% 79.42/11.78 inference(rectify,[],[f20])).
% 79.42/11.78 thf(f20,axiom,(
% 79.42/11.78 ! [X13 : nat,X12 : nat,X15 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X13),X12) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X15),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X13),X12)) => ? [X16 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X13),X16) = X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X13),X16))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_min__dist__le)).
% 79.42/11.78 thf(f5914,plain,(
% 79.42/11.78 spl72_244),
% 79.42/11.78 inference(avatar_split_clause,[],[f1635,f5912])).
% 79.42/11.78 thf(f5912,plain,(
% 79.42/11.78 spl72_244 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_244])])).
% 79.42/11.78 thf(f1635,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK60,X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1323])).
% 79.42/11.78 thf(f5910,plain,(
% 79.42/11.78 spl72_243),
% 79.42/11.78 inference(avatar_split_clause,[],[f1631,f5908])).
% 79.42/11.78 thf(f5908,plain,(
% 79.42/11.78 spl72_243 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0)) = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_243])])).
% 79.42/11.78 thf(f1631,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0)) = X2) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1319])).
% 79.42/11.78 thf(f1319,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0)) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK58])],[f1177,f1318])).
% 79.42/11.78 thf(f1318,plain,(
% 79.42/11.78 ! [X0 : nat,X2 : nat] : (? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X3))) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0)) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1177,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1176])).
% 79.42/11.78 thf(f1176,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : ((? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f766])).
% 79.42/11.78 thf(f766,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) => ? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X3) = X2) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X3)))))),
% 79.42/11.78 inference(fool_elimination,[],[f765])).
% 79.42/11.78 thf(f765,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)) => ? [X3 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X3) = X2) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X3))))),
% 79.42/11.78 inference(rectify,[],[f166])).
% 79.42/11.78 thf(f166,axiom,(
% 79.42/11.78 ! [X13 : nat,X12 : nat,X15 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X13),X12) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X15),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X13),X12)) => ? [X16 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X13),X16) = X15) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X13),X16))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_165_g_H_Omin__dist__le)).
% 79.42/11.78 thf(f5906,plain,(
% 79.42/11.78 spl72_242),
% 79.42/11.78 inference(avatar_split_clause,[],[f1630,f5904])).
% 79.42/11.78 thf(f5904,plain,(
% 79.42/11.78 spl72_242 <=> ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_242])])).
% 79.42/11.78 thf(f1630,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK58,X2),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1319])).
% 79.42/11.78 thf(f5684,plain,(
% 79.42/11.78 spl72_241),
% 79.42/11.78 inference(avatar_split_clause,[],[f1562,f5682])).
% 79.42/11.78 thf(f5682,plain,(
% 79.42/11.78 spl72_241 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_241])])).
% 79.42/11.78 thf(f1562,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1289])).
% 79.42/11.78 thf(f1289,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41])],[f1131,f1288])).
% 79.42/11.78 thf(f1288,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X3 : X1 > X0] : (? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1131,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(flattening,[],[f1130])).
% 79.42/11.78 thf(f1130,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)))) | ((order(X0) != $true) | ($true != order(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f664])).
% 79.42/11.78 thf(f664,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((order(X0) = $true) & ($true = order(X1))) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) => (! [X6 : X1,X7 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5)))))))),
% 79.42/11.78 inference(fool_elimination,[],[f663])).
% 79.42/11.78 thf(f663,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4)) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5) => (! [X6 : X1,X7 : X1] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))))))),
% 79.42/11.78 inference(rectify,[],[f190])).
% 79.42/11.78 thf(f190,axiom,(
% 79.42/11.78 ! [X0 : $tType,X38 : $tType] : ((order(X0) & order(X38)) => ! [X6 : X0,X39 : X38 > X0,X7 : X38,X5 : X38] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),vAPP(X38,X0,X39,X7)) => (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),X7),X5) => (! [X31 : X38,X30 : X38] : (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),X31),X30) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X38,X0,X39,X31)),vAPP(X38,X0,X39,X30))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),vAPP(X38,X0,X39,X5))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_189_order__subst1)).
% 79.42/11.78 thf(f5680,plain,(
% 79.42/11.78 spl72_240),
% 79.42/11.78 inference(avatar_split_clause,[],[f1560,f5678])).
% 79.42/11.78 thf(f5678,plain,(
% 79.42/11.78 spl72_240 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_240])])).
% 79.42/11.78 thf(f1560,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1287])).
% 79.42/11.78 thf(f1287,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4)))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f1129,f1286])).
% 79.42/11.78 thf(f1286,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X3 : X1 > X0] : (? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1129,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4)))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(flattening,[],[f1128])).
% 79.42/11.78 thf(f1128,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4)))) | ((order(X0) != $true) | ($true != order(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f662])).
% 79.42/11.78 thf(f662,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((order(X0) = $true) & ($true = order(X1))) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4))) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) => (! [X6 : X1,X7 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5)))))))),
% 79.42/11.78 inference(fool_elimination,[],[f661])).
% 79.42/11.78 thf(f661,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4)) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5) => (! [X6 : X1,X7 : X1] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))))))),
% 79.42/11.78 inference(rectify,[],[f244])).
% 79.42/11.78 thf(f244,axiom,(
% 79.42/11.78 ! [X0 : $tType,X38 : $tType] : ((order(X0) & order(X38)) => ! [X6 : X0,X39 : X38 > X0,X7 : X38,X5 : X38] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),vAPP(X38,X0,X39,X7)) => (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),X7),X5) => (! [X31 : X38,X30 : X38] : (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),X31),X30) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X38,X0,X39,X31)),vAPP(X38,X0,X39,X30))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),vAPP(X38,X0,X39,X5))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_243_order__less__subst1)).
% 79.42/11.78 thf(f5676,plain,(
% 79.42/11.78 spl72_239),
% 79.42/11.78 inference(avatar_split_clause,[],[f1558,f5674])).
% 79.42/11.78 thf(f5674,plain,(
% 79.42/11.78 spl72_239 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X4 : X0 > X1,X5 : X1,X2 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_239])])).
% 79.42/11.78 thf(f1558,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1285])).
% 79.42/11.78 thf(f1285,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK36,sK37])],[f1127,f1284])).
% 79.42/11.78 thf(f1284,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X4 : X0 > X1] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true)) => (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1127,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(flattening,[],[f1126])).
% 79.42/11.78 thf(f1126,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (((($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ((order(X0) != $true) | ($true != order(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f660])).
% 79.42/11.78 thf(f660,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((order(X0) = $true) & ($true = order(X1))) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) => (! [X6 : X0,X7 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7)))) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5))))))),
% 79.42/11.78 inference(fool_elimination,[],[f659])).
% 79.42/11.78 thf(f659,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)))))),
% 79.42/11.78 inference(rectify,[],[f191])).
% 79.42/11.78 thf(f191,axiom,(
% 79.42/11.78 ! [X0 : $tType,X63 : $tType] : ((order(X0) & order(X63)) => ! [X6 : X0,X7 : X0,X39 : X0 > X63,X5 : X63] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => (vAPP(X63,$o,vAPP(X63,sTfun(X63,$o),ord_less_eq(X63),vAPP(X0,X63,X39,X7)),X5) => (! [X31 : X0,X30 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X31),X30) => vAPP(X63,$o,vAPP(X63,sTfun(X63,$o),ord_less_eq(X63),vAPP(X0,X63,X39,X31)),vAPP(X0,X63,X39,X30))) => vAPP(X63,$o,vAPP(X63,sTfun(X63,$o),ord_less_eq(X63),vAPP(X0,X63,X39,X6)),X5)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_190_order__subst2)).
% 79.42/11.78 thf(f5672,plain,(
% 79.42/11.78 spl72_238),
% 79.42/11.78 inference(avatar_split_clause,[],[f1556,f5670])).
% 79.42/11.78 thf(f5670,plain,(
% 79.42/11.78 spl72_238 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X4 : X0 > X1,X5 : X1,X2 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_238])])).
% 79.42/11.78 thf(f1556,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1283])).
% 79.42/11.78 thf(f1283,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35])],[f1125,f1282])).
% 79.42/11.78 thf(f1282,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X4 : X0 > X1] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true)) => (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1125,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 inference(flattening,[],[f1124])).
% 79.42/11.78 thf(f1124,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (((($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | ((order(X0) != $true) | ($true != order(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f658])).
% 79.42/11.78 thf(f658,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((order(X0) = $true) & ($true = order(X1))) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) => (! [X6 : X0,X7 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7)))) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5))))))),
% 79.42/11.78 inference(fool_elimination,[],[f657])).
% 79.42/11.78 thf(f657,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((order(X0) & order(X1)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)))))),
% 79.42/11.78 inference(rectify,[],[f243])).
% 79.42/11.78 thf(f243,axiom,(
% 79.42/11.78 ! [X0 : $tType,X63 : $tType] : ((order(X0) & order(X63)) => ! [X6 : X0,X7 : X0,X39 : X0 > X63,X5 : X63] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => (vAPP(X63,$o,vAPP(X63,sTfun(X63,$o),ord_less(X63),vAPP(X0,X63,X39,X7)),X5) => (! [X31 : X0,X30 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X31),X30) => vAPP(X63,$o,vAPP(X63,sTfun(X63,$o),ord_less(X63),vAPP(X0,X63,X39,X31)),vAPP(X0,X63,X39,X30))) => vAPP(X63,$o,vAPP(X63,sTfun(X63,$o),ord_less(X63),vAPP(X0,X63,X39,X6)),X5)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_242_order__less__subst2)).
% 79.42/11.78 thf(f5668,plain,(
% 79.42/11.78 spl72_237),
% 79.42/11.78 inference(avatar_split_clause,[],[f1507,f5666])).
% 79.42/11.78 thf(f5666,plain,(
% 79.42/11.78 spl72_237 <=> ! [X0 : $tType,X4 : nat,X3 : list(product_prod(nat,nat)),X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_237])])).
% 79.42/11.78 thf(f1507,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : list(product_prod(nat,nat)),X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1090])).
% 79.42/11.78 thf(f1090,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3)),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f572])).
% 79.42/11.78 thf(f572,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3)),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f571])).
% 79.42/11.78 thf(f571,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X3)),X4)))),
% 79.42/11.78 inference(rectify,[],[f125])).
% 79.42/11.78 thf(f125,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X8 : nat,X18 : list(product_prod(nat,nat)),X12 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X5),X8),X18),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X8),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X18)),X12)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_124_Graph_OisPath__distD)).
% 79.42/11.78 thf(f5652,plain,(
% 79.42/11.78 spl72_236),
% 79.42/11.78 inference(avatar_split_clause,[],[f1642,f5650])).
% 79.42/11.78 thf(f5650,plain,(
% 79.42/11.78 spl72_236 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_236])])).
% 79.42/11.78 thf(f1642,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK62,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1327])).
% 79.42/11.78 thf(f5648,plain,(
% 79.42/11.78 spl72_235),
% 79.42/11.78 inference(avatar_split_clause,[],[f1638,f5646])).
% 79.42/11.78 thf(f5646,plain,(
% 79.42/11.78 spl72_235 <=> ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_235])])).
% 79.42/11.78 thf(f1638,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(nat,sTfun(nat,sTfun(nat,nat)),sK61,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1325])).
% 79.42/11.78 thf(f5644,plain,(
% 79.42/11.78 spl72_234),
% 79.42/11.78 inference(avatar_split_clause,[],[f1505,f5642])).
% 79.42/11.78 thf(f5642,plain,(
% 79.42/11.78 spl72_234 <=> ! [X0 : $tType,X4 : nat,X3 : list(product_prod(nat,nat)),X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_234])])).
% 79.42/11.78 thf(f1505,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : list(product_prod(nat,nat)),X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1088])).
% 79.42/11.78 thf(f1088,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f568])).
% 79.42/11.78 thf(f568,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f567])).
% 79.42/11.78 thf(f567,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X0),X1),X2),X3),X4)))),
% 79.42/11.78 inference(rectify,[],[f145])).
% 79.42/11.78 thf(f145,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X8 : nat,X18 : list(product_prod(nat,nat)),X12 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X1),X5),X8),X18),X12) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(X1),X5),X8),X18),X12)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_144_Graph_OshortestPath__is__path)).
% 79.42/11.78 thf(f5640,plain,(
% 79.42/11.78 spl72_233),
% 79.42/11.78 inference(avatar_split_clause,[],[f1504,f5638])).
% 79.42/11.78 thf(f5638,plain,(
% 79.42/11.78 spl72_233 <=> ! [X0 : $tType,X4 : nat,X3 : list(product_prod(nat,nat)),X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_233])])).
% 79.42/11.78 thf(f1504,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : list(product_prod(nat,nat)),X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1087])).
% 79.42/11.78 thf(f1087,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X3),X4)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f566])).
% 79.42/11.78 thf(f566,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X3),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f565])).
% 79.42/11.78 thf(f565,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : list(product_prod(nat,nat)),X4 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X0),X1),X2),X3),X4) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X0),X1),X2),X3),X4)))),
% 79.42/11.78 inference(rectify,[],[f133])).
% 79.42/11.78 thf(f133,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X54 : nat,X18 : list(product_prod(nat,nat)),X55 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(X1),X5),X54),X18),X55) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(X1),X5),X54),X18),X55)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_132_Graph_OshortestPath__is__simple)).
% 79.42/11.78 thf(f5620,plain,(
% 79.42/11.78 spl72_232),
% 79.42/11.78 inference(avatar_split_clause,[],[f1652,f5618])).
% 79.42/11.78 thf(f1652,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1197])).
% 79.42/11.78 thf(f1197,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f798])).
% 79.42/11.78 thf(f798,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f797])).
% 79.42/11.78 thf(f797,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2))),
% 79.42/11.78 inference(rectify,[],[f23])).
% 79.42/11.78 thf(f23,axiom,(
% 79.42/11.78 ! [X8 : nat,X18 : list(product_prod(nat,nat)),X12 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X8),X18),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X8),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X18)),X12))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_isPath__distD)).
% 79.42/11.78 thf(f5616,plain,(
% 79.42/11.78 spl72_231),
% 79.42/11.78 inference(avatar_split_clause,[],[f1648,f5614])).
% 79.42/11.78 thf(f1648,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1193])).
% 79.42/11.78 thf(f1193,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f790])).
% 79.42/11.78 thf(f790,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f789])).
% 79.42/11.78 thf(f789,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X1)),X2))),
% 79.42/11.78 inference(rectify,[],[f177])).
% 79.42/11.78 thf(f177,axiom,(
% 79.42/11.78 ! [X8 : nat,X18 : list(product_prod(nat,nat)),X12 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X8),X18),X12) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X8),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),X18)),X12))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_176_g_H_OisPath__distD)).
% 79.42/11.78 thf(f5600,plain,(
% 79.42/11.78 spl72_230),
% 79.42/11.78 inference(avatar_split_clause,[],[f1650,f5598])).
% 79.42/11.78 thf(f1650,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1195])).
% 79.42/11.78 thf(f1195,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f794])).
% 79.42/11.78 thf(f794,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f793])).
% 79.42/11.78 thf(f793,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X0),X1),X2))),
% 79.42/11.78 inference(rectify,[],[f17])).
% 79.42/11.78 thf(f17,axiom,(
% 79.42/11.78 ! [X8 : nat,X18 : list(product_prod(nat,nat)),X12 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X8),X18),X12) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),X8),X18),X12))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_shortestPath__is__path)).
% 79.42/11.78 thf(f5596,plain,(
% 79.42/11.78 spl72_229),
% 79.42/11.78 inference(avatar_split_clause,[],[f1649,f5594])).
% 79.42/11.78 thf(f1649,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1194])).
% 79.42/11.78 thf(f1194,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f792])).
% 79.42/11.78 thf(f792,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f791])).
% 79.42/11.78 thf(f791,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X1),X2) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X0),X1),X2))),
% 79.42/11.78 inference(rectify,[],[f129])).
% 79.42/11.78 thf(f129,axiom,(
% 79.42/11.78 ! [X54 : nat,X18 : list(product_prod(nat,nat)),X55 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X54),X18),X55) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(capacity),c),X54),X18),X55))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_128_shortestPath__is__simple)).
% 79.42/11.78 thf(f5592,plain,(
% 79.42/11.78 spl72_228),
% 79.42/11.78 inference(avatar_split_clause,[],[f1646,f5590])).
% 79.42/11.78 thf(f5590,plain,(
% 79.42/11.78 spl72_228 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_228])])).
% 79.42/11.78 thf(f1646,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1191])).
% 79.42/11.78 thf(f1191,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f786])).
% 79.42/11.78 thf(f786,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f785])).
% 79.42/11.78 thf(f785,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X0),X1),X2))),
% 79.42/11.78 inference(rectify,[],[f173])).
% 79.42/11.78 thf(f173,axiom,(
% 79.42/11.78 ! [X8 : nat,X18 : list(product_prod(nat,nat)),X12 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X8),X18),X12) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),X8),X18),X12))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_172_g_H_OshortestPath__is__path)).
% 79.42/11.78 thf(f5588,plain,(
% 79.42/11.78 spl72_227),
% 79.42/11.78 inference(avatar_split_clause,[],[f1645,f5586])).
% 79.42/11.78 thf(f5586,plain,(
% 79.42/11.78 spl72_227 <=> ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_227])])).
% 79.42/11.78 thf(f1645,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : list(product_prod(nat,nat))] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1190])).
% 79.42/11.78 thf(f1190,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X1),X2)) | ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f784])).
% 79.42/11.78 thf(f784,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f783])).
% 79.42/11.78 thf(f783,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : list(product_prod(nat,nat)),X2 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X1),X2) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X0),X1),X2))),
% 79.42/11.78 inference(rectify,[],[f161])).
% 79.42/11.78 thf(f161,axiom,(
% 79.42/11.78 ! [X54 : nat,X18 : list(product_prod(nat,nat)),X55 : nat] : (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X54),X18),X55) => vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isSimplePath(a),c2),X54),X18),X55))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_160_g_H_OshortestPath__is__simple)).
% 79.42/11.78 thf(f5580,plain,(
% 79.42/11.78 spl72_226),
% 79.42/11.78 inference(avatar_split_clause,[],[f1494,f5578])).
% 79.42/11.78 thf(f5578,plain,(
% 79.42/11.78 spl72_226 <=> ! [X0 : $tType,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_226])])).
% 79.42/11.78 thf(f1494,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1078])).
% 79.42/11.78 thf(f1078,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f554])).
% 79.42/11.78 thf(f554,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)),X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f553])).
% 79.42/11.78 thf(f553,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X3)),X3)))),
% 79.42/11.78 inference(rectify,[],[f126])).
% 79.42/11.78 thf(f126,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X12 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X12),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X12),X19)),X19)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_125_Graph_Omin__dist__is__dist)).
% 79.42/11.78 thf(f5073,plain,(
% 79.42/11.78 spl72_225),
% 79.42/11.78 inference(avatar_split_clause,[],[f1561,f5071])).
% 79.42/11.78 thf(f1561,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK40(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK41(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1289])).
% 79.42/11.78 thf(f5069,plain,(
% 79.42/11.78 spl72_224),
% 79.42/11.78 inference(avatar_split_clause,[],[f1559,f5067])).
% 79.42/11.78 thf(f5067,plain,(
% 79.42/11.78 spl72_224 <=> ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_224])])).
% 79.42/11.78 thf(f1559,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK38(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK39(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X4))) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1287])).
% 79.42/11.78 thf(f5063,plain,(
% 79.42/11.78 spl72_223),
% 79.42/11.78 inference(avatar_split_clause,[],[f1557,f5061])).
% 79.42/11.78 thf(f1557,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK36(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK37(X0,X1),X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1285])).
% 79.42/11.78 thf(f5059,plain,(
% 79.42/11.78 spl72_222),
% 79.42/11.78 inference(avatar_split_clause,[],[f1555,f5057])).
% 79.42/11.78 thf(f5057,plain,(
% 79.42/11.78 spl72_222 <=> ! [X1 : $tType,X0 : $tType,X3 : X0,X4 : X0 > X1,X5 : X1,X2 : X0] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_222])])).
% 79.42/11.78 thf(f1555,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK34(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK35(X0,X1),X4))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X3)),X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (order(X0) != $true) | ($true != order(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1283])).
% 79.42/11.78 thf(f5049,plain,(
% 79.42/11.78 spl72_221),
% 79.42/11.78 inference(avatar_split_clause,[],[f1588,f5047])).
% 79.42/11.78 thf(f1588,plain,(
% 79.42/11.78 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1305])).
% 79.42/11.78 thf(f1305,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK49])],[f1154,f1304])).
% 79.42/11.78 thf(f1304,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (? [X2 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X2),X1)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK49,X1),X0)),X1)))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1154,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (? [X2 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f914])).
% 79.42/11.78 thf(f914,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) => ~! [X2 : list(product_prod(nat,nat))] : ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X2),X1)))),
% 79.42/11.78 inference(flattening,[],[f706])).
% 79.42/11.78 thf(f706,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) => ~! [X2 : list(product_prod(nat,nat))] : ~($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X2),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f705])).
% 79.42/11.78 thf(f705,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) => ~! [X2 : list(product_prod(nat,nat))] : ~vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X0),X2),X1))),
% 79.42/11.78 inference(rectify,[],[f19])).
% 79.42/11.78 thf(f19,axiom,(
% 79.42/11.78 ! [X8 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X8),X12) => ~! [X21 : list(product_prod(nat,nat))] : ~vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),X8),X21),X12))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_obtain__shortest__path)).
% 79.42/11.78 thf(f5045,plain,(
% 79.42/11.78 spl72_220),
% 79.42/11.78 inference(avatar_split_clause,[],[f1586,f5043])).
% 79.42/11.78 thf(f5043,plain,(
% 79.42/11.78 spl72_220 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK48,X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_220])])).
% 79.42/11.78 thf(f1586,plain,(
% 79.42/11.78 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK48,X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1303])).
% 79.42/11.78 thf(f1303,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK48,X1),X0)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK48])],[f1152,f1302])).
% 79.42/11.78 thf(f1302,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (? [X2 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X2),X1)) => ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),vAPP(nat,list(product_prod(nat,nat)),vAPP(nat,sTfun(nat,list(product_prod(nat,nat))),sK48,X1),X0)),X1)))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1152,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (? [X2 : list(product_prod(nat,nat))] : ($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X2),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f913])).
% 79.42/11.78 thf(f913,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) => ~! [X2 : list(product_prod(nat,nat))] : ($true != vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X2),X1)))),
% 79.42/11.78 inference(flattening,[],[f702])).
% 79.42/11.78 thf(f702,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) => ~! [X2 : list(product_prod(nat,nat))] : ~($true = vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X2),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f701])).
% 79.42/11.78 thf(f701,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) => ~! [X2 : list(product_prod(nat,nat))] : ~vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X0),X2),X1))),
% 79.42/11.78 inference(rectify,[],[f160])).
% 79.42/11.78 thf(f160,axiom,(
% 79.42/11.78 ! [X8 : nat,X12 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X8),X12) => ~! [X21 : list(product_prod(nat,nat))] : ~vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(a),c2),X8),X21),X12))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_159_g_H_Oobtain__shortest__path)).
% 79.42/11.78 thf(f5035,plain,(
% 79.42/11.78 spl72_219),
% 79.42/11.78 inference(avatar_split_clause,[],[f1589,f5033])).
% 79.42/11.78 thf(f1589,plain,(
% 79.42/11.78 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1155])).
% 79.42/11.78 thf(f1155,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f708])).
% 79.42/11.78 thf(f708,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f707])).
% 79.42/11.78 thf(f707,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1)),X1))),
% 79.42/11.78 inference(rectify,[],[f26])).
% 79.42/11.78 thf(f26,axiom,(
% 79.42/11.78 ! [X12 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X12),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X12),X19)),X19))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_min__dist__is__dist)).
% 79.42/11.78 thf(f5031,plain,(
% 79.42/11.78 spl72_218),
% 79.42/11.78 inference(avatar_split_clause,[],[f1587,f5029])).
% 79.42/11.78 thf(f5029,plain,(
% 79.42/11.78 spl72_218 <=> ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_218])])).
% 79.42/11.78 thf(f1587,plain,(
% 79.42/11.78 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1153])).
% 79.42/11.78 thf(f1153,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f704])).
% 79.42/11.78 thf(f704,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f703])).
% 79.42/11.78 thf(f703,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1)),X1))),
% 79.42/11.78 inference(rectify,[],[f159])).
% 79.42/11.78 thf(f159,axiom,(
% 79.42/11.78 ! [X12 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X12),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X12),X19)),X19))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_158_g_H_Omin__dist__is__dist)).
% 79.42/11.78 thf(f4972,plain,(
% 79.42/11.78 spl72_217),
% 79.42/11.78 inference(avatar_split_clause,[],[f1575,f4970])).
% 79.42/11.78 thf(f1575,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2)))) | (ord(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1299])).
% 79.42/11.78 thf(f1299,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))))) | (ord(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK46])],[f1139,f1298])).
% 79.42/11.78 thf(f1298,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (? [X4 : X1] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK46(X0,X1),X3),X2)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1139,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > X0] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | ? [X4 : X1] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4)))) | (ord(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f680])).
% 79.42/11.78 thf(f680,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord(X0) = $true) => ! [X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) => ($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f679])).
% 79.42/11.78 thf(f679,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (ord(X0) => ! [X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4)) => vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)))),
% 79.42/11.78 inference(rectify,[],[f188])).
% 79.42/11.78 thf(f188,axiom,(
% 79.42/11.78 ! [X38 : $tType,X0 : $tType] : (ord(X38) => ! [X39 : X0 > X38,X40 : X0 > X38] : (! [X31 : X0] : vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),vAPP(X0,X38,X39,X31)),vAPP(X0,X38,X40,X31)) => vAPP(sTfun(X0,X38),$o,vAPP(sTfun(X0,X38),sTfun(sTfun(X0,X38),$o),ord_less_eq(sTfun(X0,X38)),X39),X40)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_187_le__funI)).
% 79.42/11.78 thf(f4904,plain,(
% 79.42/11.78 spl72_216),
% 79.42/11.78 inference(avatar_split_clause,[],[f1634,f4902])).
% 79.42/11.78 thf(f1634,plain,(
% 79.42/11.78 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1))) | ($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK59,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1321])).
% 79.42/11.78 thf(f4900,plain,(
% 79.42/11.78 spl72_215),
% 79.42/11.78 inference(avatar_split_clause,[],[f1629,f4898])).
% 79.42/11.78 thf(f1629,plain,(
% 79.42/11.78 ( ! [X2 : nat > $o,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1))) | ($true != vAPP(nat,$o,X2,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(nat,$o),sTfun(nat,sTfun(nat,nat)),sK57,X2),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1317])).
% 79.42/11.78 thf(f4896,plain,(
% 79.42/11.78 spl72_214),
% 79.42/11.78 inference(avatar_split_clause,[],[f1349,f4893])).
% 79.42/11.78 thf(f1349,plain,(
% 79.42/11.78 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),
% 79.42/11.78 inference(cnf_transformation,[],[f1])).
% 79.42/11.78 thf(f1,axiom,(
% 79.42/11.78 (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__092_060open_062min__dist_As_At_A_061_Amin__dist_As_Au_A_L_Amin__dist_Au_At_092_060close_062)).
% 79.42/11.78 thf(f4687,plain,(
% 79.42/11.78 spl72_213),
% 79.42/11.78 inference(avatar_split_clause,[],[f1735,f4685])).
% 79.42/11.78 thf(f1735,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1554])).
% 79.42/11.78 thf(f1554,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1281])).
% 79.42/11.78 thf(f1281,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f1123,f1280])).
% 79.42/11.78 thf(f1280,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X4 : X0 > X1] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true)) => (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1123,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true)) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(flattening,[],[f1122])).
% 79.42/11.78 thf(f1122,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (((($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true))) | (vAPP(X0,X1,X4,X3) != X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f656])).
% 79.42/11.78 thf(f656,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ((vAPP(X0,X1,X4,X3) = X5) => (! [X6 : X0,X7 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7)))) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5))))))),
% 79.42/11.78 inference(fool_elimination,[],[f655])).
% 79.42/11.78 thf(f655,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => ((vAPP(X0,X1,X4,X3) = X5) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)))))),
% 79.42/11.78 inference(rectify,[],[f193])).
% 79.42/11.78 thf(f193,axiom,(
% 79.42/11.78 ! [X0 : $tType,X38 : $tType] : ((ord(X0) & ord(X38)) => ! [X6 : X0,X7 : X0,X39 : X0 > X38,X5 : X38] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => ((vAPP(X0,X38,X39,X7) = X5) => (! [X31 : X0,X30 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X31),X30) => vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),vAPP(X0,X38,X39,X31)),vAPP(X0,X38,X39,X30))) => vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),vAPP(X0,X38,X39,X6)),X5)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_192_ord__le__eq__subst)).
% 79.42/11.78 thf(f4683,plain,(
% 79.42/11.78 spl72_212),
% 79.42/11.78 inference(avatar_split_clause,[],[f1733,f4681])).
% 79.42/11.78 thf(f1733,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1552])).
% 79.42/11.78 thf(f1552,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1279])).
% 79.42/11.78 thf(f1279,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31])],[f1121,f1278])).
% 79.42/11.78 thf(f1278,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X4 : X0 > X1] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true)) => (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4))),vAPP(X0,X1,X4,vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1121,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true)) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(flattening,[],[f1120])).
% 79.42/11.78 thf(f1120,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (((($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true))) | (vAPP(X0,X1,X4,X3) != X5)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f654])).
% 79.42/11.78 thf(f654,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) => ((vAPP(X0,X1,X4,X3) = X5) => (! [X6 : X0,X7 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) = $true) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7)))) => ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5))))))),
% 79.42/11.78 inference(fool_elimination,[],[f653])).
% 79.42/11.78 thf(f653,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => ((vAPP(X0,X1,X4,X3) = X5) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X6)),vAPP(X0,X1,X4,X7))) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)))))),
% 79.42/11.78 inference(rectify,[],[f245])).
% 79.42/11.78 thf(f245,axiom,(
% 79.42/11.78 ! [X0 : $tType,X38 : $tType] : ((ord(X0) & ord(X38)) => ! [X6 : X0,X7 : X0,X39 : X0 > X38,X5 : X38] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => ((vAPP(X0,X38,X39,X7) = X5) => (! [X31 : X0,X30 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X31),X30) => vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),vAPP(X0,X38,X39,X31)),vAPP(X0,X38,X39,X30))) => vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),vAPP(X0,X38,X39,X6)),X5)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_244_ord__less__eq__subst)).
% 79.42/11.78 thf(f4679,plain,(
% 79.42/11.78 spl72_211),
% 79.42/11.78 inference(avatar_split_clause,[],[f1731,f4677])).
% 79.42/11.78 thf(f1731,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1550])).
% 79.42/11.78 thf(f1550,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1277])).
% 79.42/11.78 thf(f1277,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f1119,f1276])).
% 79.42/11.78 thf(f1276,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X3 : X1 > X0] : (? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1119,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(flattening,[],[f1118])).
% 79.42/11.78 thf(f1118,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5))) | (vAPP(X1,X0,X3,X4) != X2)) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f652])).
% 79.42/11.78 thf(f652,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : ((vAPP(X1,X0,X3,X4) = X2) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) => (! [X6 : X1,X7 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5)))))))),
% 79.42/11.78 inference(fool_elimination,[],[f651])).
% 79.42/11.78 thf(f651,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : ((vAPP(X1,X0,X3,X4) = X2) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5) => (! [X6 : X1,X7 : X1] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))))))),
% 79.42/11.78 inference(rectify,[],[f192])).
% 79.42/11.78 thf(f192,axiom,(
% 79.42/11.78 ! [X0 : $tType,X38 : $tType] : ((ord(X0) & ord(X38)) => ! [X6 : X0,X39 : X38 > X0,X7 : X38,X5 : X38] : ((vAPP(X38,X0,X39,X7) = X6) => (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),X7),X5) => (! [X31 : X38,X30 : X38] : (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),X31),X30) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X38,X0,X39,X31)),vAPP(X38,X0,X39,X30))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),vAPP(X38,X0,X39,X5))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_191_ord__eq__le__subst)).
% 79.42/11.78 thf(f4675,plain,(
% 79.42/11.78 spl72_210),
% 79.42/11.78 inference(avatar_split_clause,[],[f1729,f4673])).
% 79.42/11.78 thf(f1729,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1548])).
% 79.42/11.78 thf(f1548,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1275])).
% 79.42/11.78 thf(f1275,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26,sK27])],[f1117,f1274])).
% 79.42/11.78 thf(f1274,plain,(
% 79.42/11.78 ! [X1 : $tType,X0 : $tType,X3 : X1 > X0] : (? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3))),vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1117,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2)) | (ord(X0) != $true) | ($true != ord(X1)))),
% 79.42/11.78 inference(flattening,[],[f1116])).
% 79.42/11.78 thf(f1116,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ? [X6 : X1,X7 : X1] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) & ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7)))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5))) | (vAPP(X1,X0,X3,X4) != X2)) | ((ord(X0) != $true) | ($true != ord(X1))))),
% 79.42/11.78 inference(ennf_transformation,[],[f650])).
% 79.42/11.78 thf(f650,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : (((ord(X0) = $true) & ($true = ord(X1))) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : ((vAPP(X1,X0,X3,X4) = X2) => (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) => (! [X6 : X1,X7 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7)))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5)))))))),
% 79.42/11.78 inference(fool_elimination,[],[f649])).
% 79.42/11.78 thf(f649,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : $tType] : ((ord(X0) & ord(X1)) => ! [X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : ((vAPP(X1,X0,X3,X4) = X2) => (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5) => (! [X6 : X1,X7 : X1] : (vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X6)),vAPP(X1,X0,X3,X7))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))))))),
% 79.42/11.78 inference(rectify,[],[f246])).
% 79.42/11.78 thf(f246,axiom,(
% 79.42/11.78 ! [X0 : $tType,X38 : $tType] : ((ord(X0) & ord(X38)) => ! [X6 : X0,X39 : X38 > X0,X7 : X38,X5 : X38] : ((vAPP(X38,X0,X39,X7) = X6) => (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),X7),X5) => (! [X31 : X38,X30 : X38] : (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),X31),X30) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X38,X0,X39,X31)),vAPP(X38,X0,X39,X30))) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),vAPP(X38,X0,X39,X5))))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_245_ord__eq__less__subst)).
% 79.42/11.78 thf(f4624,plain,(
% 79.42/11.78 spl72_209),
% 79.42/11.78 inference(avatar_split_clause,[],[f1436,f4622])).
% 79.42/11.78 thf(f1436,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1261])).
% 79.42/11.78 thf(f1261,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16,sK17,sK18,sK19])],[f1258,f1260,f1259])).
% 79.42/11.78 thf(f1259,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1260,plain,(
% 79.42/11.78 ! [X0 : $tType,X1 : X0 > X0 > $o] : (? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true)) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1258,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X5),X4))) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) = $true))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(rectify,[],[f1006])).
% 79.42/11.78 thf(f1006,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6))) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X5)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f1005])).
% 79.42/11.78 thf(f1005,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ? [X6 : X0,X7 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6)))) | ? [X4 : X0,X5 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X5)))) | (linorder(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f440])).
% 79.42/11.78 thf(f440,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (! [X4 : X0,X5 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X5)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5))) => (! [X6 : X0,X7 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)))))),
% 79.42/11.78 inference(fool_elimination,[],[f439])).
% 79.42/11.78 thf(f439,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0 > X0 > $o,X2 : X0,X3 : X0] : (! [X4 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X4),X5) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X5)) => (! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X7),X6) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X6),X7)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3))))),
% 79.42/11.78 inference(rectify,[],[f208])).
% 79.42/11.78 thf(f208,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (linorder(X0) => ! [X29 : X0 > X0 > $o,X6 : X0,X7 : X0] : (! [X68 : X0,X69 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X68),X69) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X68),X69)) => (! [X68 : X0,X69 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X69),X68) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X68),X69)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X29,X6),X7))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_207_linorder__wlog)).
% 79.42/11.78 thf(f4620,plain,(
% 79.42/11.78 spl72_208),
% 79.42/11.78 inference(avatar_split_clause,[],[f1434,f4618])).
% 79.42/11.78 thf(f1434,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1261])).
% 79.42/11.78 thf(f4616,plain,(
% 79.42/11.78 spl72_207 | ~spl72_2 | ~spl72_43),
% 79.42/11.78 inference(avatar_split_clause,[],[f2199,f2108,f1894,f4613])).
% 79.42/11.78 thf(f2199,plain,(
% 79.42/11.78 ($true = order(a)) | (~spl72_2 | ~spl72_43)),
% 79.42/11.78 inference(trivial_inequality_removal,[],[f2194])).
% 79.42/11.78 thf(f2194,plain,(
% 79.42/11.78 ($true != $true) | ($true = order(a)) | (~spl72_2 | ~spl72_43)),
% 79.42/11.78 inference(superposition,[],[f2109,f1896])).
% 79.42/11.78 thf(f4423,plain,(
% 79.42/11.78 spl72_206),
% 79.42/11.78 inference(avatar_split_clause,[],[f1665,f4421])).
% 79.42/11.78 thf(f1665,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X4 : nat] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(X0,sTfun(sTfun(X0,$o),X0),vAPP(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0)),vAPP(nat,sTfun(sTfun(X0,nat),sTfun(X0,sTfun(sTfun(X0,$o),X0))),sK70(X0),X4),X3),X2),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK71(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1345])).
% 79.42/11.78 thf(f4419,plain,(
% 79.42/11.78 spl72_205),
% 79.42/11.78 inference(avatar_split_clause,[],[f1437,f4417])).
% 79.42/11.78 thf(f1437,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1261])).
% 79.42/11.78 thf(f4415,plain,(
% 79.42/11.78 spl72_204),
% 79.42/11.78 inference(avatar_split_clause,[],[f1435,f4413])).
% 79.42/11.78 thf(f1435,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X2),X3)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK17(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK16(X0),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK18(X0),X1)),vAPP(sTfun(X0,sTfun(X0,$o)),X0,sK19(X0),X1))) | (linorder(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1261])).
% 79.42/11.78 thf(f4409,plain,(
% 79.42/11.78 spl72_203),
% 79.42/11.78 inference(avatar_split_clause,[],[f1610,f4407])).
% 79.42/11.78 thf(f4407,plain,(
% 79.42/11.78 spl72_203 <=> ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK53,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK54,X0)))))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_203])])).
% 79.42/11.78 thf(f1610,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK53,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK54,X0))))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1311])).
% 79.42/11.78 thf(f1311,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK53,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK54,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK53,sK54])],[f1159,f1310])).
% 79.42/11.78 thf(f1310,plain,(
% 79.42/11.78 ! [X0 : nat > nat] : (? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true)) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK53,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK54,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1159,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true)))),
% 79.42/11.78 inference(ennf_transformation,[],[f738])).
% 79.42/11.78 thf(f738,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (! [X3 : nat,X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))))),
% 79.42/11.78 inference(fool_elimination,[],[f737])).
% 79.42/11.78 thf(f737,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (! [X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 79.42/11.78 inference(rectify,[],[f101])).
% 79.42/11.78 thf(f101,axiom,(
% 79.42/11.78 ! [X39 : nat > nat,X3 : nat,X2 : nat] : (! [X56 : nat,X48 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X56),X48) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X39,X56)),vAPP(nat,nat,X39,X48))) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X39,X3)),X2)),vAPP(nat,nat,X39,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_100_mono__nat__linear__lb)).
% 79.42/11.78 thf(f4363,plain,(
% 79.42/11.78 spl72_202 | ~spl72_3 | ~spl72_43),
% 79.42/11.78 inference(avatar_split_clause,[],[f2198,f2108,f1899,f4360])).
% 79.42/11.78 thf(f2198,plain,(
% 79.42/11.78 ($true = order(capacity)) | (~spl72_3 | ~spl72_43)),
% 79.42/11.78 inference(trivial_inequality_removal,[],[f2195])).
% 79.42/11.78 thf(f2195,plain,(
% 79.42/11.78 ($true != $true) | ($true = order(capacity)) | (~spl72_3 | ~spl72_43)),
% 79.42/11.78 inference(superposition,[],[f2109,f1901])).
% 79.42/11.78 thf(f4356,plain,(
% 79.42/11.78 spl72_201),
% 79.42/11.78 inference(avatar_split_clause,[],[f1542,f4354])).
% 79.42/11.78 thf(f4354,plain,(
% 79.42/11.78 spl72_201 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_201])])).
% 79.42/11.78 thf(f1542,plain,(
% 79.42/11.78 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1)))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f640])).
% 79.42/11.78 thf(f640,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0)),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f639])).
% 79.42/11.78 thf(f639,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),(^[X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X2),X1)))))),
% 79.42/11.78 inference(rectify,[],[f119])).
% 79.42/11.78 thf(f119,axiom,(
% 79.42/11.78 ! [X12 : nat,X19 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X12),X19) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),(^[X20 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X20),X19)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_118_min__dist__def)).
% 79.42/11.78 thf(f4352,plain,(
% 79.42/11.78 spl72_200),
% 79.42/11.78 inference(avatar_split_clause,[],[f1541,f4350])).
% 79.42/11.78 thf(f4350,plain,(
% 79.42/11.78 spl72_200 <=> ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1)))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_200])])).
% 79.42/11.78 thf(f1541,plain,(
% 79.42/11.78 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1)))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f638])).
% 79.42/11.78 thf(f638,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(nat,sTfun(nat,$o)),sTfun(nat,sTfun(nat,$o)),cCOMB,vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0)),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f637])).
% 79.42/11.78 thf(f637,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X1) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),(^[X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X2),X1)))))),
% 79.42/11.78 inference(rectify,[],[f175])).
% 79.42/11.78 thf(f175,axiom,(
% 79.42/11.78 ! [X12 : nat,X19 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X12),X19) = vAPP(sTfun(nat,$o),nat,ord_Least(nat),(^[X20 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X20),X19)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_174_g_H_Omin__dist__def)).
% 79.42/11.78 thf(f4348,plain,(
% 79.42/11.78 spl72_199),
% 79.42/11.78 inference(avatar_split_clause,[],[f1503,f4346])).
% 79.42/11.78 thf(f4346,plain,(
% 79.42/11.78 spl72_199 <=> ! [X0 : $tType,X4 : nat,X3 : nat,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true))),
% 79.42/11.78 introduced(avatar_definition,[new_symbols(naming,[spl72_199])])).
% 79.42/11.78 thf(f1503,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1086])).
% 79.42/11.78 thf(f1086,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f564])).
% 79.42/11.78 thf(f564,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)),X3))))),
% 79.42/11.78 inference(fool_elimination,[],[f563])).
% 79.42/11.78 thf(f563,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,nat)),min_dist(X0),X1),X2),X4)),X3)))),
% 79.42/11.78 inference(rectify,[],[f152])).
% 79.42/11.78 thf(f152,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),X14),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,nat)),min_dist(X1),X5),X12),X19)),X14)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Graph_Omin__dist__minD)).
% 79.42/11.78 thf(f4276,plain,(
% 79.42/11.78 spl72_198),
% 79.42/11.78 inference(avatar_split_clause,[],[f1736,f4274])).
% 79.42/11.78 thf(f1736,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1553])).
% 79.42/11.78 thf(f1553,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,X1),X0,sK32(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK33(X0,X1),X4))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1281])).
% 79.42/11.78 thf(f4272,plain,(
% 79.42/11.78 spl72_197),
% 79.42/11.78 inference(avatar_split_clause,[],[f1734,f4270])).
% 79.42/11.78 thf(f1734,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),vAPP(X0,X1,X4,X3))) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1551])).
% 79.42/11.78 thf(f1551,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0,X4 : X0 > X1,X5 : X1] : (($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(X0,X1,X4,X2)),X5)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(sTfun(X0,X1),X0,sK30(X0,X1),X4)),vAPP(sTfun(X0,X1),X0,sK31(X0,X1),X4))) | (vAPP(X0,X1,X4,X3) != X5) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1279])).
% 79.42/11.78 thf(f4268,plain,(
% 79.42/11.78 spl72_196 | ~spl72_2 | ~spl72_42),
% 79.42/11.78 inference(avatar_split_clause,[],[f2193,f2104,f1894,f4265])).
% 79.42/11.78 thf(f2193,plain,(
% 79.42/11.78 ($true = ord(a)) | (~spl72_2 | ~spl72_42)),
% 79.42/11.78 inference(trivial_inequality_removal,[],[f2188])).
% 79.42/11.78 thf(f2188,plain,(
% 79.42/11.78 ($true != $true) | ($true = ord(a)) | (~spl72_2 | ~spl72_42)),
% 79.42/11.78 inference(superposition,[],[f2105,f1896])).
% 79.42/11.78 thf(f4263,plain,(
% 79.42/11.78 spl72_195),
% 79.42/11.78 inference(avatar_split_clause,[],[f1732,f4261])).
% 79.42/11.78 thf(f1732,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1549])).
% 79.42/11.78 thf(f1549,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(sTfun(X1,X0),X1,sK28(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK29(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1277])).
% 79.42/11.78 thf(f4259,plain,(
% 79.42/11.78 spl72_194),
% 79.42/11.78 inference(avatar_split_clause,[],[f1730,f4257])).
% 79.42/11.78 thf(f1730,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X3,X4)),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(equality_resolution,[],[f1547])).
% 79.42/11.78 thf(f1547,plain,(
% 79.42/11.78 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1,X5 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(X1,X0,X3,X5))) | ($true = vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),vAPP(sTfun(X1,X0),X1,sK26(X0,X1),X3)),vAPP(sTfun(X1,X0),X1,sK27(X0,X1),X3))) | ($true != vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less(X1),X4),X5)) | (vAPP(X1,X0,X3,X4) != X2) | (ord(X0) != $true) | ($true != ord(X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1275])).
% 79.42/11.78 thf(f4251,plain,(
% 79.42/11.78 spl72_193),
% 79.42/11.78 inference(avatar_split_clause,[],[f1644,f4249])).
% 79.42/11.78 thf(f1644,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1189])).
% 79.42/11.78 thf(f1189,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f782])).
% 79.42/11.78 thf(f782,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f781])).
% 79.42/11.78 thf(f781,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X0),X2)),X1))),
% 79.42/11.78 inference(rectify,[],[f21])).
% 79.42/11.78 thf(f21,axiom,(
% 79.42/11.78 ! [X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X14),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),X12),X19)),X14))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_min__dist__minD)).
% 79.42/11.78 thf(f4247,plain,(
% 79.42/11.78 spl72_192),
% 79.42/11.78 inference(avatar_split_clause,[],[f1640,f4245])).
% 79.42/11.78 thf(f1640,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1185])).
% 79.42/11.78 thf(f1185,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f776])).
% 79.42/11.78 thf(f776,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1)))),
% 79.42/11.78 inference(fool_elimination,[],[f775])).
% 79.42/11.78 thf(f775,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X0),X2)),X1))),
% 79.42/11.78 inference(rectify,[],[f167])).
% 79.42/11.78 thf(f167,axiom,(
% 79.42/11.78 ! [X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X14),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,nat)),min_dist(a),c2),X12),X19)),X14))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_166_g_H_Omin__dist__minD)).
% 79.42/11.78 thf(f4166,plain,(
% 79.42/11.78 spl72_191),
% 79.42/11.78 inference(avatar_split_clause,[],[f1609,f4164])).
% 79.42/11.78 thf(f1609,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(nat,nat,X0,X1)),X2)),vAPP(nat,nat,X0,vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK53,X0)),vAPP(sTfun(nat,nat),nat,sK54,X0)))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1311])).
% 79.42/11.78 thf(f4162,plain,(
% 79.42/11.78 spl72_190),
% 79.42/11.78 inference(avatar_split_clause,[],[f1608,f4160])).
% 79.42/11.78 thf(f1608,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0))))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1309])).
% 79.42/11.78 thf(f1309,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X0)),vAPP(sTfun(nat,nat),nat,sK52,X0)))))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK51,sK52])],[f1158,f1308])).
% 79.42/11.78 thf(f1308,plain,(
% 79.42/11.78 ! [X0 : nat > nat] : (? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true)) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK51,X0))),vAPP(nat,nat,X0,vAPP(sTfun(nat,nat),nat,sK52,X0)))) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X0)),vAPP(sTfun(nat,nat),nat,sK52,X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1158,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true)))),
% 79.42/11.78 inference(flattening,[],[f1157])).
% 79.42/11.78 thf(f1157,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) | ? [X3 : nat,X4 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) & (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true)))),
% 79.42/11.78 inference(ennf_transformation,[],[f736])).
% 79.42/11.78 thf(f736,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (! [X3 : nat,X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) = $true) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4)))) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2)))))),
% 79.42/11.78 inference(fool_elimination,[],[f735])).
% 79.42/11.78 thf(f735,plain,(
% 79.42/11.78 ! [X0 : nat > nat,X1 : nat,X2 : nat] : (! [X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X0,X3)),vAPP(nat,nat,X0,X4))) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))))),
% 79.42/11.78 inference(rectify,[],[f57])).
% 79.42/11.78 thf(f57,axiom,(
% 79.42/11.78 ! [X39 : nat > nat,X27 : nat,X28 : nat] : (! [X43 : nat,X44 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X43),X44) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,X39,X43)),vAPP(nat,nat,X39,X44))) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X39,X27)),vAPP(nat,nat,X39,X28))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_less__mono__imp__le__mono)).
% 79.42/11.78 thf(f4158,plain,(
% 79.42/11.78 spl72_189 | ~spl72_3 | ~spl72_42),
% 79.42/11.78 inference(avatar_split_clause,[],[f2192,f2104,f1899,f4155])).
% 79.42/11.78 thf(f2192,plain,(
% 79.42/11.78 ($true = ord(capacity)) | (~spl72_3 | ~spl72_42)),
% 79.42/11.78 inference(trivial_inequality_removal,[],[f2189])).
% 79.42/11.78 thf(f2189,plain,(
% 79.42/11.78 ($true != $true) | ($true = ord(capacity)) | (~spl72_3 | ~spl72_42)),
% 79.42/11.78 inference(superposition,[],[f2105,f1901])).
% 79.42/11.78 thf(f4085,plain,(
% 79.42/11.78 spl72_188),
% 79.42/11.78 inference(avatar_split_clause,[],[f1407,f4083])).
% 79.42/11.78 thf(f1407,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f986])).
% 79.42/11.78 thf(f986,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f985])).
% 79.42/11.78 thf(f985,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f414])).
% 79.42/11.78 thf(f414,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4)))))),
% 79.42/11.78 inference(fool_elimination,[],[f413])).
% 79.42/11.78 thf(f413,plain,(
% 79.42/11.78 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))))),
% 79.42/11.78 inference(rectify,[],[f100])).
% 79.42/11.78 thf(f100,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X27 : X0,X28 : X0,X2 : X0,X42 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X42) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X27),X28)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X27),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X28),X42))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_add__mono__thms__linordered__field_I4_J)).
% 79.42/11.78 thf(f4081,plain,(
% 79.42/11.78 spl72_187),
% 79.42/11.78 inference(avatar_split_clause,[],[f1406,f4079])).
% 79.42/11.78 thf(f1406,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f984])).
% 79.42/11.78 thf(f984,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f983])).
% 79.42/11.78 thf(f983,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f412])).
% 79.42/11.78 thf(f412,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4)))))),
% 79.42/11.78 inference(fool_elimination,[],[f411])).
% 79.42/11.78 thf(f411,plain,(
% 79.42/11.78 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))))),
% 79.42/11.78 inference(rectify,[],[f99])).
% 79.42/11.78 thf(f99,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X27 : X0,X28 : X0,X2 : X0,X42 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X42) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X27),X28)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X27),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X28),X42))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_add__mono__thms__linordered__field_I3_J)).
% 79.42/11.78 thf(f4077,plain,(
% 79.42/11.78 spl72_186),
% 79.42/11.78 inference(avatar_split_clause,[],[f1405,f4075])).
% 79.42/11.78 thf(f1405,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f982])).
% 79.42/11.78 thf(f982,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f981])).
% 79.42/11.78 thf(f981,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f410])).
% 79.42/11.78 thf(f410,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4)))))),
% 79.42/11.78 inference(fool_elimination,[],[f409])).
% 79.42/11.78 thf(f409,plain,(
% 79.42/11.78 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))))),
% 79.42/11.78 inference(rectify,[],[f109])).
% 79.42/11.78 thf(f109,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X27 : X0,X28 : X0,X2 : X0,X42 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X42) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X27),X28)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X27),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X28),X42))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_108_add__mono__thms__linordered__field_I5_J)).
% 79.42/11.78 thf(f4073,plain,(
% 79.42/11.78 spl72_185),
% 79.42/11.78 inference(avatar_split_clause,[],[f1380,f4071])).
% 79.42/11.78 thf(f1380,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f954])).
% 79.42/11.78 thf(f954,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere779506340up_add(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f953])).
% 79.42/11.78 thf(f953,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4))) | (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))) | (ordere779506340up_add(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f366])).
% 79.42/11.78 thf(f366,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4)))))),
% 79.42/11.78 inference(fool_elimination,[],[f365])).
% 79.42/11.78 thf(f365,plain,(
% 79.42/11.78 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X4) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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),X4))))),
% 79.42/11.78 inference(rectify,[],[f54])).
% 79.42/11.78 thf(f54,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X27 : X0,X28 : X0,X2 : X0,X42 : X0] : ((vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X42) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X27),X28)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X27),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X28),X42))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_add__mono__thms__linordered__semiring_I1_J)).
% 79.42/11.78 thf(f4069,plain,(
% 79.42/11.78 spl72_184),
% 79.42/11.78 inference(avatar_split_clause,[],[f1364,f4067])).
% 79.42/11.78 thf(f1364,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (strict2144017051up_add(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f934])).
% 79.42/11.78 thf(f934,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (strict2144017051up_add(X0) != $true))),
% 79.42/11.78 inference(flattening,[],[f933])).
% 79.42/11.78 thf(f933,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (strict2144017051up_add(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f334])).
% 79.42/11.78 thf(f334,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4))))))),
% 79.42/11.78 inference(fool_elimination,[],[f333])).
% 79.42/11.78 thf(f333,plain,(
% 79.42/11.78 ! [X0 : $tType] : (strict2144017051up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X4) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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),X4)))))),
% 79.42/11.78 inference(rectify,[],[f106])).
% 79.42/11.78 thf(f106,axiom,(
% 79.42/11.78 ! [X0 : $tType] : (strict2144017051up_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0,X14 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X14) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X14)))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_add__strict__mono)).
% 79.42/11.78 thf(f4065,plain,(
% 79.42/11.78 spl72_183 | ~spl72_2 | ~spl72_41),
% 79.42/11.78 inference(avatar_split_clause,[],[f2187,f2100,f1894,f4062])).
% 79.42/11.78 thf(f2187,plain,(
% 79.42/11.78 ($true = preorder(a)) | (~spl72_2 | ~spl72_41)),
% 79.42/11.78 inference(trivial_inequality_removal,[],[f2182])).
% 79.42/11.78 thf(f2182,plain,(
% 79.42/11.78 ($true != $true) | ($true = preorder(a)) | (~spl72_2 | ~spl72_41)),
% 79.42/11.78 inference(superposition,[],[f2101,f1896])).
% 79.42/11.78 thf(f4058,plain,(
% 79.42/11.78 spl72_182),
% 79.42/11.78 inference(avatar_split_clause,[],[f1502,f4056])).
% 79.42/11.78 thf(f1502,plain,(
% 79.42/11.78 ( ! [X0 : $tType,X2 : nat,X3 : nat,X1 : product_prod(nat,nat) > X0,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1085])).
% 79.42/11.78 thf(f1085,plain,(
% 79.42/11.78 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4))) | (linordered_idom(X0) != $true))),
% 79.42/11.78 inference(ennf_transformation,[],[f562])).
% 79.42/11.78 thf(f562,plain,(
% 79.42/11.78 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4))))),
% 79.42/11.78 inference(fool_elimination,[],[f561])).
% 79.42/11.78 thf(f561,plain,(
% 79.42/11.78 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X0),X1),X2),X3),X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X4)))),
% 79.42/11.78 inference(rectify,[],[f147])).
% 79.42/11.78 thf(f147,axiom,(
% 79.42/11.78 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(X1),X5),X12),X14),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X12),X19)))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_146_Graph_Oconnected__distI)).
% 79.42/11.78 thf(f4036,plain,(
% 79.42/11.78 spl72_181),
% 79.42/11.78 inference(avatar_split_clause,[],[f1660,f4034])).
% 79.42/11.78 thf(f1660,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1206])).
% 79.42/11.78 thf(f1206,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1205])).
% 79.42/11.78 thf(f1205,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f808])).
% 79.42/11.78 thf(f808,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))))),
% 79.42/11.78 inference(fool_elimination,[],[f807])).
% 79.42/11.78 thf(f807,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))),
% 79.42/11.78 inference(rectify,[],[f67])).
% 79.42/11.78 thf(f67,axiom,(
% 79.42/11.78 ! [X27 : nat,X28 : nat,X2 : nat,X42 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X28) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X42) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X27),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X42))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_add__le__mono)).
% 79.42/11.78 thf(f4032,plain,(
% 79.42/11.78 spl72_180),
% 79.42/11.78 inference(avatar_split_clause,[],[f1659,f4030])).
% 79.42/11.78 thf(f1659,plain,(
% 79.42/11.78 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1204])).
% 79.42/11.78 thf(f1204,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.78 inference(flattening,[],[f1203])).
% 79.42/11.78 thf(f1203,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.78 inference(ennf_transformation,[],[f806])).
% 79.42/11.78 thf(f806,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3)))))),
% 79.42/11.78 inference(fool_elimination,[],[f805])).
% 79.42/11.78 thf(f805,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X3))))),
% 79.42/11.78 inference(rectify,[],[f116])).
% 79.42/11.78 thf(f116,axiom,(
% 79.42/11.78 ! [X27 : nat,X28 : nat,X2 : nat,X42 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X42) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X27),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X42))))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_115_add__less__mono)).
% 79.42/11.78 thf(f4004,plain,(
% 79.42/11.78 spl72_179 | ~spl72_3 | ~spl72_41),
% 79.42/11.78 inference(avatar_split_clause,[],[f2186,f2100,f1899,f4001])).
% 79.42/11.78 thf(f2186,plain,(
% 79.42/11.78 ($true = preorder(capacity)) | (~spl72_3 | ~spl72_41)),
% 79.42/11.78 inference(trivial_inequality_removal,[],[f2183])).
% 79.42/11.78 thf(f2183,plain,(
% 79.42/11.78 ($true != $true) | ($true = preorder(capacity)) | (~spl72_3 | ~spl72_41)),
% 79.42/11.78 inference(superposition,[],[f2101,f1901])).
% 79.42/11.78 thf(f3999,plain,(
% 79.42/11.78 spl72_178),
% 79.42/11.78 inference(avatar_split_clause,[],[f1643,f3997])).
% 79.42/11.78 thf(f1643,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1188])).
% 79.42/11.78 thf(f1188,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f780])).
% 79.42/11.78 thf(f780,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f779])).
% 79.42/11.78 thf(f779,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X0),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X2))),
% 79.42/11.78 inference(rectify,[],[f36])).
% 79.42/11.78 thf(f36,axiom,(
% 79.42/11.78 ! [X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(capacity),c),X12),X14),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X12),X19))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_connected__distI)).
% 79.42/11.78 thf(f3995,plain,(
% 79.42/11.78 spl72_177),
% 79.42/11.78 inference(avatar_split_clause,[],[f1639,f3993])).
% 79.42/11.78 thf(f1639,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1184])).
% 79.42/11.78 thf(f1184,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)))),
% 79.42/11.78 inference(ennf_transformation,[],[f774])).
% 79.42/11.78 thf(f774,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2)))),
% 79.42/11.78 inference(fool_elimination,[],[f773])).
% 79.42/11.78 thf(f773,plain,(
% 79.42/11.78 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X0),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X2))),
% 79.42/11.78 inference(rectify,[],[f183])).
% 79.42/11.78 thf(f183,axiom,(
% 79.42/11.78 ! [X12 : nat,X14 : nat,X19 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(nat,sTfun(nat,sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,sTfun(nat,$o))),dist(a),c2),X12),X14),X19) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X12),X19))),
% 79.42/11.78 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_182_g_H_Oconnected__distI)).
% 79.42/11.78 thf(f3991,plain,(
% 79.42/11.78 spl72_176),
% 79.42/11.78 inference(avatar_split_clause,[],[f1614,f3989])).
% 79.42/11.78 thf(f1614,plain,(
% 79.42/11.78 ( ! [X2 : nat,X0 : nat > $o,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1))) )),
% 79.42/11.78 inference(cnf_transformation,[],[f1315])).
% 79.42/11.78 thf(f1315,plain,(
% 79.42/11.78 ! [X0 : nat > $o,X1 : nat,X2 : nat] : ((! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0)))) | (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 79.42/11.78 inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f1312,f1314,f1313])).
% 79.42/11.78 thf(f1313,plain,(
% 79.42/11.78 ! [X0 : nat > $o] : (? [X3 : nat] : (! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) = $true) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,X3))) => (! [X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0)))))),
% 79.42/11.78 introduced(choice_axiom,[])).
% 79.42/11.78 thf(f1314,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X2 : nat] : (? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X2)) & ($true = vAPP(nat,$o,X0,X5))) => (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) & ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1312,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (? [X3 : nat] : (! [X4 : nat] : ((vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) = $true) | ($true != vAPP(nat,$o,X0,X4))) & ($true = vAPP(nat,$o,X0,X3))) | ? [X5 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X2)) & ($true = vAPP(nat,$o,X0,X5))) | ($true != vAPP(nat,$o,X0,X1)))),
% 79.42/11.79 inference(rectify,[],[f1161])).
% 79.42/11.79 thf(f1161,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (? [X4 : nat] : (! [X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4)) | ($true != vAPP(nat,$o,X0,X5))) & ($true = vAPP(nat,$o,X0,X4))) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2)) & ($true = vAPP(nat,$o,X0,X3))) | ($true != vAPP(nat,$o,X0,X1)))),
% 79.42/11.79 inference(flattening,[],[f1160])).
% 79.42/11.79 thf(f1160,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat,X2 : nat] : ((? [X4 : nat] : (! [X5 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4)) | ($true != vAPP(nat,$o,X0,X5))) & ($true = vAPP(nat,$o,X0,X4))) | ? [X3 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2)) & ($true = vAPP(nat,$o,X0,X3)))) | ($true != vAPP(nat,$o,X0,X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f740])).
% 79.42/11.79 thf(f740,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,X0,X1)) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2))) => ? [X4 : nat] : (! [X5 : nat] : (($true = vAPP(nat,$o,X0,X5)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4))) & ($true = vAPP(nat,$o,X0,X4)))))),
% 79.42/11.79 inference(fool_elimination,[],[f739])).
% 79.42/11.79 thf(f739,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat,X2 : nat] : (vAPP(nat,$o,X0,X1) => (! [X3 : nat] : (vAPP(nat,$o,X0,X3) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X2)) => ? [X4 : nat] : (! [X5 : nat] : (vAPP(nat,$o,X0,X5) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X5),X4)) & vAPP(nat,$o,X0,X4))))),
% 79.42/11.79 inference(rectify,[],[f42])).
% 79.42/11.79 thf(f42,axiom,(
% 79.42/11.79 ! [X29 : nat > $o,X2 : nat,X7 : nat] : (vAPP(nat,$o,X29,X2) => (! [X30 : nat] : (vAPP(nat,$o,X29,X30) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X30),X7)) => ? [X31 : nat] : (! [X32 : nat] : (vAPP(nat,$o,X29,X32) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X32),X31)) & vAPP(nat,$o,X29,X31))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_Nat_Oex__has__greatest__nat)).
% 79.42/11.79 thf(f3987,plain,(
% 79.42/11.79 spl72_175),
% 79.42/11.79 inference(avatar_split_clause,[],[f1607,f3985])).
% 79.42/11.79 thf(f1607,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat > nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,X0,X1)),vAPP(nat,nat,X0,X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(sTfun(nat,nat),nat,sK51,X0)),vAPP(sTfun(nat,nat),nat,sK52,X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1309])).
% 79.42/11.79 thf(f3927,plain,(
% 79.42/11.79 spl72_174),
% 79.42/11.79 inference(avatar_split_clause,[],[f1571,f3925])).
% 79.42/11.79 thf(f1571,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2)))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1297])).
% 79.42/11.79 thf(f1297,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2))))))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1136,f1296])).
% 79.42/11.79 thf(f1296,plain,(
% 79.42/11.79 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o] : (? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))))) => (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2)))))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1136,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)))))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f674])).
% 79.42/11.79 thf(f674,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : ((wellorder(X0) = $true) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))) => ($true = vAPP(X1,$o,X3,X6))) => ($true = vAPP(X1,$o,X3,X5))) => ($true = vAPP(X1,$o,X3,X4))))),
% 79.42/11.79 inference(fool_elimination,[],[f673])).
% 79.42/11.79 thf(f673,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (wellorder(X0) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)) => vAPP(X1,$o,X3,X6)) => vAPP(X1,$o,X3,X5)) => vAPP(X1,$o,X3,X4)))),
% 79.42/11.79 inference(rectify,[],[f75])).
% 79.42/11.79 thf(f75,axiom,(
% 79.42/11.79 ! [X38 : $tType,X0 : $tType] : (wellorder(X38) => ! [X39 : X0 > X38,X29 : X0 > $o,X6 : X0] : (! [X31 : X0] : (! [X32 : X0] : (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),vAPP(X0,X38,X39,X32)),vAPP(X0,X38,X39,X31)) => vAPP(X0,$o,X29,X32)) => vAPP(X0,$o,X29,X31)) => vAPP(X0,$o,X29,X6)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_measure__induct)).
% 79.42/11.79 thf(f3923,plain,(
% 79.42/11.79 spl72_173),
% 79.42/11.79 inference(avatar_split_clause,[],[f1569,f3921])).
% 79.42/11.79 thf(f1569,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X6 : X1,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2)))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1295])).
% 79.42/11.79 thf(f1295,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2))))))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1135,f1294])).
% 79.42/11.79 thf(f1294,plain,(
% 79.42/11.79 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o] : (? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))))) => (($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2))) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2)))))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1135,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ? [X5 : X1] : (($true != vAPP(X1,$o,X3,X5)) & ! [X6 : X1] : (($true = vAPP(X1,$o,X3,X6)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)))))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f672])).
% 79.42/11.79 thf(f672,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : ((wellorder(X0) = $true) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5))) => ($true = vAPP(X1,$o,X3,X6))) => ($true = vAPP(X1,$o,X3,X5))) => ($true = vAPP(X1,$o,X3,X4))))),
% 79.42/11.79 inference(fool_elimination,[],[f671])).
% 79.42/11.79 thf(f671,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (wellorder(X0) => ! [X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (! [X5 : X1] : (! [X6 : X1] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X1,X0,X2,X6)),vAPP(X1,X0,X2,X5)) => vAPP(X1,$o,X3,X6)) => vAPP(X1,$o,X3,X5)) => vAPP(X1,$o,X3,X4)))),
% 79.42/11.79 inference(rectify,[],[f74])).
% 79.42/11.79 thf(f74,axiom,(
% 79.42/11.79 ! [X38 : $tType,X0 : $tType] : (wellorder(X38) => ! [X39 : X0 > X38,X29 : X0 > $o,X6 : X0] : (! [X31 : X0] : (! [X32 : X0] : (vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less(X38),vAPP(X0,X38,X39,X32)),vAPP(X0,X38,X39,X31)) => vAPP(X0,$o,X29,X32)) => vAPP(X0,$o,X29,X31)) => vAPP(X0,$o,X29,X6)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_measure__induct__rule)).
% 79.42/11.79 thf(f3879,plain,(
% 79.42/11.79 spl72_172),
% 79.42/11.79 inference(avatar_split_clause,[],[f1613,f3877])).
% 79.42/11.79 thf(f1613,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat > $o,X1 : nat,X4 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,X0,X4)) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1315])).
% 79.42/11.79 thf(f3875,plain,(
% 79.42/11.79 spl72_171 | ~spl72_2 | ~spl72_40),
% 79.42/11.79 inference(avatar_split_clause,[],[f2181,f2096,f1894,f3872])).
% 79.42/11.79 thf(f2181,plain,(
% 79.42/11.79 ($true = linorder(a)) | (~spl72_2 | ~spl72_40)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2176])).
% 79.42/11.79 thf(f2176,plain,(
% 79.42/11.79 ($true != $true) | ($true = linorder(a)) | (~spl72_2 | ~spl72_40)),
% 79.42/11.79 inference(superposition,[],[f2097,f1896])).
% 79.42/11.79 thf(f3788,plain,(
% 79.42/11.79 spl72_170),
% 79.42/11.79 inference(avatar_split_clause,[],[f1402,f3786])).
% 79.42/11.79 thf(f1402,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f976])).
% 79.42/11.79 thf(f976,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f404])).
% 79.42/11.79 thf(f404,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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)))))),
% 79.42/11.79 inference(fool_elimination,[],[f403])).
% 79.42/11.79 thf(f403,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))))),
% 79.42/11.79 inference(rectify,[],[f104])).
% 79.42/11.79 thf(f104,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_103_add__strict__right__mono)).
% 79.42/11.79 thf(f3784,plain,(
% 79.42/11.79 spl72_169),
% 79.42/11.79 inference(avatar_split_clause,[],[f1401,f3782])).
% 79.42/11.79 thf(f1401,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (ordere223160158up_add(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f975])).
% 79.42/11.79 thf(f975,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (ordere223160158up_add(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f402])).
% 79.42/11.79 thf(f402,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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)))))),
% 79.42/11.79 inference(fool_elimination,[],[f401])).
% 79.42/11.79 thf(f401,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))))),
% 79.42/11.79 inference(rectify,[],[f105])).
% 79.42/11.79 thf(f105,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere223160158up_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X7))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_add__strict__left__mono)).
% 79.42/11.79 thf(f3780,plain,(
% 79.42/11.79 spl72_168 | ~spl72_3 | ~spl72_40),
% 79.42/11.79 inference(avatar_split_clause,[],[f2180,f2096,f1899,f3777])).
% 79.42/11.79 thf(f2180,plain,(
% 79.42/11.79 ($true = linorder(capacity)) | (~spl72_3 | ~spl72_40)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2177])).
% 79.42/11.79 thf(f2177,plain,(
% 79.42/11.79 ($true != $true) | ($true = linorder(capacity)) | (~spl72_3 | ~spl72_40)),
% 79.42/11.79 inference(superposition,[],[f2097,f1901])).
% 79.42/11.79 thf(f3775,plain,(
% 79.42/11.79 spl72_167),
% 79.42/11.79 inference(avatar_split_clause,[],[f1389,f3773])).
% 79.42/11.79 thf(f1389,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f964])).
% 79.42/11.79 thf(f964,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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)))) | (ordere236663937imp_le(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f384])).
% 79.42/11.79 thf(f384,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))))),
% 79.42/11.79 inference(fool_elimination,[],[f383])).
% 79.42/11.79 thf(f383,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 79.42/11.79 inference(rectify,[],[f43])).
% 79.42/11.79 thf(f43,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X6 : X0,X5 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_add__le__imp__le__right)).
% 79.42/11.79 thf(f3771,plain,(
% 79.42/11.79 spl72_166),
% 79.42/11.79 inference(avatar_split_clause,[],[f1388,f3769])).
% 79.42/11.79 thf(f1388,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | (ordere236663937imp_le(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f963])).
% 79.42/11.79 thf(f963,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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)))) | (ordere236663937imp_le(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f382])).
% 79.42/11.79 thf(f382,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))))),
% 79.42/11.79 inference(fool_elimination,[],[f381])).
% 79.42/11.79 thf(f381,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)))),
% 79.42/11.79 inference(rectify,[],[f44])).
% 79.42/11.79 thf(f44,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X5 : X0,X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X7)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_add__le__imp__le__left)).
% 79.42/11.79 thf(f3767,plain,(
% 79.42/11.79 spl72_165),
% 79.42/11.79 inference(avatar_split_clause,[],[f1387,f3765])).
% 79.42/11.79 thf(f1387,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f962])).
% 79.42/11.79 thf(f962,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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)))) | (ordere236663937imp_le(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f380])).
% 79.42/11.79 thf(f380,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))))),
% 79.42/11.79 inference(fool_elimination,[],[f379])).
% 79.42/11.79 thf(f379,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)))),
% 79.42/11.79 inference(rectify,[],[f103])).
% 79.42/11.79 thf(f103,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X5 : X0,X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X7)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_102_add__less__imp__less__left)).
% 79.42/11.79 thf(f3763,plain,(
% 79.42/11.79 spl72_164),
% 79.42/11.79 inference(avatar_split_clause,[],[f1386,f3761])).
% 79.42/11.79 thf(f1386,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) | (ordere236663937imp_le(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f961])).
% 79.42/11.79 thf(f961,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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)))) | (ordere236663937imp_le(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f378])).
% 79.42/11.79 thf(f378,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(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))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 79.42/11.79 inference(fool_elimination,[],[f377])).
% 79.42/11.79 thf(f377,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X2)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X3),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))),
% 79.42/11.79 inference(rectify,[],[f102])).
% 79.42/11.79 thf(f102,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere236663937imp_le(X0) => ! [X6 : X0,X5 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_101_add__less__imp__less__right)).
% 79.42/11.79 thf(f3759,plain,(
% 79.42/11.79 spl72_163),
% 79.42/11.79 inference(avatar_split_clause,[],[f1376,f3757])).
% 79.42/11.79 thf(f1376,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f946])).
% 79.42/11.79 thf(f946,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere779506340up_add(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f358])).
% 79.42/11.79 thf(f358,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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)))))),
% 79.42/11.79 inference(fool_elimination,[],[f357])).
% 79.42/11.79 thf(f357,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))))),
% 79.42/11.79 inference(rectify,[],[f50])).
% 79.42/11.79 thf(f50,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X5)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_add__right__mono)).
% 79.42/11.79 thf(f3755,plain,(
% 79.42/11.79 spl72_162),
% 79.42/11.79 inference(avatar_split_clause,[],[f1375,f3753])).
% 79.42/11.79 thf(f1375,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (ordere779506340up_add(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f945])).
% 79.42/11.79 thf(f945,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (ordere779506340up_add(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f356])).
% 79.42/11.79 thf(f356,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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)))))),
% 79.42/11.79 inference(fool_elimination,[],[f355])).
% 79.42/11.79 thf(f355,plain,(
% 79.42/11.79 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(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))))),
% 79.42/11.79 inference(rectify,[],[f52])).
% 79.42/11.79 thf(f52,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ordere779506340up_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X6)),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X5),X7))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__left__mono)).
% 79.42/11.79 thf(f3686,plain,(
% 79.42/11.79 spl72_161),
% 79.42/11.79 inference(avatar_split_clause,[],[f1658,f3684])).
% 79.42/11.79 thf(f3684,plain,(
% 79.42/11.79 spl72_161 <=> ! [X0 : nat,X3 : nat,X2 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 introduced(avatar_definition,[new_symbols(naming,[spl72_161])])).
% 79.42/11.79 thf(f1658,plain,(
% 79.42/11.79 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1202])).
% 79.42/11.79 thf(f1202,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 inference(flattening,[],[f1201])).
% 79.42/11.79 thf(f1201,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)) | (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) != vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f804])).
% 79.42/11.79 thf(f804,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3))))),
% 79.42/11.79 inference(fool_elimination,[],[f803])).
% 79.42/11.79 thf(f803,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X3)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X3)))),
% 79.42/11.79 inference(rectify,[],[f110])).
% 79.42/11.79 thf(f110,axiom,(
% 79.42/11.79 ! [X2 : nat,X42 : nat,X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X42) => ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X4) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X42)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_109_less__add__eq__less)).
% 79.42/11.79 thf(f3682,plain,(
% 79.42/11.79 spl72_160 | ~spl72_2 | ~spl72_39),
% 79.42/11.79 inference(avatar_split_clause,[],[f2175,f2092,f1894,f3679])).
% 79.42/11.79 thf(f2175,plain,(
% 79.42/11.79 ($true = ordere223160158up_add(a)) | (~spl72_2 | ~spl72_39)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2170])).
% 79.42/11.79 thf(f2170,plain,(
% 79.42/11.79 ($true != $true) | ($true = ordere223160158up_add(a)) | (~spl72_2 | ~spl72_39)),
% 79.42/11.79 inference(superposition,[],[f2093,f1896])).
% 79.42/11.79 thf(f3677,plain,(
% 79.42/11.79 spl72_159),
% 79.42/11.79 inference(avatar_split_clause,[],[f1657,f3675])).
% 79.42/11.79 thf(f1657,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o,X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X5)) | ($true != vAPP(X0,$o,X1,X2))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1337])).
% 79.42/11.79 thf(f1337,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat] : ((! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X5))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f1200,f1336])).
% 79.42/11.79 thf(f1336,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X3 : X0 > nat] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X4)),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X5))) & ($true = vAPP(X0,$o,X1,X4))) => (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X5))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1200,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X4)),vAPP(X0,nat,X3,X5))) | ($true != vAPP(X0,$o,X1,X5))) & ($true = vAPP(X0,$o,X1,X4))) | ($true != vAPP(X0,$o,X1,X2)))),
% 79.42/11.79 inference(ennf_transformation,[],[f802])).
% 79.42/11.79 thf(f802,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat] : (($true = vAPP(X0,$o,X1,X2)) => ? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X4)),vAPP(X0,nat,X3,X5)))) & ($true = vAPP(X0,$o,X1,X4))))),
% 79.42/11.79 inference(fool_elimination,[],[f801])).
% 79.42/11.79 thf(f801,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > nat] : (vAPP(X0,$o,X1,X2) => ? [X4 : X0] : (! [X5 : X0] : (vAPP(X0,$o,X1,X5) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X4)),vAPP(X0,nat,X3,X5))) & vAPP(X0,$o,X1,X4)))),
% 79.42/11.79 inference(rectify,[],[f247])).
% 79.42/11.79 thf(f247,axiom,(
% 79.42/11.79 ! [X0 : $tType,X29 : X0 > $o,X2 : X0,X3 : X0 > nat] : (vAPP(X0,$o,X29,X2) => ? [X31 : X0] : (! [X32 : X0] : (vAPP(X0,$o,X29,X32) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(X0,nat,X3,X31)),vAPP(X0,nat,X3,X32))) & vAPP(X0,$o,X29,X31)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_246_ex__has__least__nat)).
% 79.42/11.79 thf(f3673,plain,(
% 79.42/11.79 spl72_158),
% 79.42/11.79 inference(avatar_split_clause,[],[f1655,f3671])).
% 79.42/11.79 thf(f1655,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o,X5 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1))))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1335])).
% 79.42/11.79 thf(f1335,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1))))) & ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f1199,f1334])).
% 79.42/11.79 thf(f1334,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat] : (? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) & ($true != vAPP(X0,$o,X1,X4))) => (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1))))) & ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1199,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) | ? [X4 : X0] : (! [X5 : X0] : (($true = vAPP(X0,$o,X1,X5)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) & ($true != vAPP(X0,$o,X1,X4))))),
% 79.42/11.79 inference(ennf_transformation,[],[f923])).
% 79.42/11.79 thf(f923,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (($true != vAPP(X0,$o,X1,X4)) => ? [X5 : X0] : (($true != vAPP(X0,$o,X1,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4))))) => ($true = vAPP(X0,$o,X1,X3)))),
% 79.42/11.79 inference(flattening,[],[f800])).
% 79.42/11.79 thf(f800,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (~($true = vAPP(X0,$o,X1,X4)) => ? [X5 : X0] : (~($true = vAPP(X0,$o,X1,X5)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4))))) => ($true = vAPP(X0,$o,X1,X3)))),
% 79.42/11.79 inference(fool_elimination,[],[f799])).
% 79.42/11.79 thf(f799,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > nat,X3 : X0] : (! [X4 : X0] : (~vAPP(X0,$o,X1,X4) => ? [X5 : X0] : (~vAPP(X0,$o,X1,X5) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X2,X5)),vAPP(X0,nat,X2,X4)))) => vAPP(X0,$o,X1,X3))),
% 79.42/11.79 inference(rectify,[],[f87])).
% 79.42/11.79 thf(f87,axiom,(
% 79.42/11.79 ! [X0 : $tType,X29 : X0 > $o,X50 : X0 > nat,X51 : X0] : (! [X31 : X0] : (~vAPP(X0,$o,X29,X31) => ? [X32 : X0] : (~vAPP(X0,$o,X29,X32) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(X0,nat,X50,X32)),vAPP(X0,nat,X50,X31)))) => vAPP(X0,$o,X29,X51))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_infinite__descent__measure)).
% 79.42/11.79 thf(f3655,plain,(
% 79.42/11.79 spl72_157),
% 79.42/11.79 inference(avatar_split_clause,[],[f1653,f3653])).
% 79.42/11.79 thf(f1653,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1333])).
% 79.42/11.79 thf(f1333,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2))))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f1198,f1332])).
% 79.42/11.79 thf(f1332,plain,(
% 79.42/11.79 ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (? [X4 : X1] : (vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4)) => (vAPP(X1,X0,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK65(X0,X1),X3),X2))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1198,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | ? [X4 : X1] : (vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4)))),
% 79.42/11.79 inference(ennf_transformation,[],[f922])).
% 79.42/11.79 thf(f922,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : (vAPP(X1,X0,X3,X4) = vAPP(X1,X0,X2,X4)) => (X2 = X3))),
% 79.42/11.79 inference(rectify,[],[f49])).
% 79.42/11.79 thf(f49,axiom,(
% 79.42/11.79 ! [X38 : $tType,X0 : $tType,X39 : X0 > X38,X40 : X0 > X38] : (! [X31 : X0] : (vAPP(X0,X38,X39,X31) = vAPP(X0,X38,X40,X31)) => (X39 = X40))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_ext)).
% 79.42/11.79 thf(f3631,plain,(
% 79.42/11.79 spl72_156),
% 79.42/11.79 inference(avatar_split_clause,[],[f1709,f3629])).
% 79.42/11.79 thf(f1709,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(equality_resolution,[],[f1367])).
% 79.42/11.79 thf(f1367,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f937])).
% 79.42/11.79 thf(f937,plain,(
% 79.42/11.79 ! [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))),
% 79.42/11.79 inference(ennf_transformation,[],[f340])).
% 79.42/11.79 thf(f340,plain,(
% 79.42/11.79 ! [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))))),
% 79.42/11.79 inference(fool_elimination,[],[f339])).
% 79.42/11.79 thf(f339,plain,(
% 79.42/11.79 ! [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))))),
% 79.42/11.79 inference(rectify,[],[f84])).
% 79.42/11.79 thf(f84,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X36 : X0,X2 : X0,X6 : X0,X7 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X6) = X36) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X36),X7))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_group__cancel_Oadd1)).
% 79.42/11.79 thf(f3627,plain,(
% 79.42/11.79 spl72_155 | ~spl72_3 | ~spl72_39),
% 79.42/11.79 inference(avatar_split_clause,[],[f2174,f2092,f1899,f3624])).
% 79.42/11.79 thf(f2174,plain,(
% 79.42/11.79 ($true = ordere223160158up_add(capacity)) | (~spl72_3 | ~spl72_39)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2171])).
% 79.42/11.79 thf(f2171,plain,(
% 79.42/11.79 ($true != $true) | ($true = ordere223160158up_add(capacity)) | (~spl72_3 | ~spl72_39)),
% 79.42/11.79 inference(superposition,[],[f2093,f1901])).
% 79.42/11.79 thf(f3622,plain,(
% 79.42/11.79 spl72_154),
% 79.42/11.79 inference(avatar_split_clause,[],[f1708,f3620])).
% 79.42/11.79 thf(f1708,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(equality_resolution,[],[f1366])).
% 79.42/11.79 thf(f1366,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f936])).
% 79.42/11.79 thf(f936,plain,(
% 79.42/11.79 ! [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))),
% 79.42/11.79 inference(ennf_transformation,[],[f338])).
% 79.42/11.79 thf(f338,plain,(
% 79.42/11.79 ! [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)))))),
% 79.42/11.79 inference(fool_elimination,[],[f337])).
% 79.42/11.79 thf(f337,plain,(
% 79.42/11.79 ! [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)))))),
% 79.42/11.79 inference(rectify,[],[f83])).
% 79.42/11.79 thf(f83,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (comm_monoid_add(X0) => ! [X49 : X0,X2 : X0,X7 : X0,X6 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),X7) = X49) => (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X49) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_group__cancel_Oadd2)).
% 79.42/11.79 thf(f3618,plain,(
% 79.42/11.79 spl72_153),
% 79.42/11.79 inference(avatar_split_clause,[],[f1370,f3616])).
% 79.42/11.79 thf(f1370,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f940])).
% 79.42/11.79 thf(f940,plain,(
% 79.42/11.79 ! [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))),
% 79.42/11.79 inference(ennf_transformation,[],[f346])).
% 79.42/11.79 thf(f346,plain,(
% 79.42/11.79 ! [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)))),
% 79.42/11.79 inference(fool_elimination,[],[f345])).
% 79.42/11.79 thf(f345,plain,(
% 79.42/11.79 ! [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)))),
% 79.42/11.79 inference(rectify,[],[f86])).
% 79.42/11.79 thf(f86,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X6 : X0,X7 : X0,X5 : 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),X5)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X5)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_ab__semigroup__add__class_Oadd__ac_I1_J)).
% 79.42/11.79 thf(f3614,plain,(
% 79.42/11.79 spl72_152),
% 79.42/11.79 inference(avatar_split_clause,[],[f1369,f3612])).
% 79.42/11.79 thf(f1369,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f939])).
% 79.42/11.79 thf(f939,plain,(
% 79.42/11.79 ! [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))),
% 79.42/11.79 inference(ennf_transformation,[],[f344])).
% 79.42/11.79 thf(f344,plain,(
% 79.42/11.79 ! [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))))),
% 79.42/11.79 inference(fool_elimination,[],[f343])).
% 79.42/11.79 thf(f343,plain,(
% 79.42/11.79 ! [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))))),
% 79.42/11.79 inference(rectify,[],[f78])).
% 79.42/11.79 thf(f78,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ab_semigroup_add(X0) => ! [X7 : X0,X6 : X0,X5 : 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),X5)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_add_Oleft__commute)).
% 79.42/11.79 thf(f3610,plain,(
% 79.42/11.79 spl72_151),
% 79.42/11.79 inference(avatar_split_clause,[],[f1361,f3608])).
% 79.42/11.79 thf(f1361,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f930])).
% 79.42/11.79 thf(f930,plain,(
% 79.42/11.79 ! [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))),
% 79.42/11.79 inference(ennf_transformation,[],[f328])).
% 79.42/11.79 thf(f328,plain,(
% 79.42/11.79 ! [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)))),
% 79.42/11.79 inference(fool_elimination,[],[f327])).
% 79.42/11.79 thf(f327,plain,(
% 79.42/11.79 ! [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)))),
% 79.42/11.79 inference(rectify,[],[f82])).
% 79.42/11.79 thf(f82,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (semigroup_add(X0) => ! [X6 : X0,X7 : X0,X5 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X7),X5)) = vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X7)),X5)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_add_Oassoc)).
% 79.42/11.79 thf(f3588,plain,(
% 79.42/11.79 spl72_150),
% 79.42/11.79 inference(avatar_split_clause,[],[f1621,f3586])).
% 79.42/11.79 thf(f1621,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1169])).
% 79.42/11.79 thf(f1169,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f754])).
% 79.42/11.79 thf(f754,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f753])).
% 79.42/11.79 thf(f753,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f66])).
% 79.42/11.79 thf(f66,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X27),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X2)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_add__le__mono1)).
% 79.42/11.79 thf(f3584,plain,(
% 79.42/11.79 spl72_149),
% 79.42/11.79 inference(avatar_split_clause,[],[f1617,f3582])).
% 79.42/11.79 thf(f1617,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1164])).
% 79.42/11.79 thf(f1164,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f746])).
% 79.42/11.79 thf(f746,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f745])).
% 79.42/11.79 thf(f745,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f113])).
% 79.42/11.79 thf(f113,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X27),X2)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X2)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_112_add__less__mono1)).
% 79.42/11.79 thf(f3477,plain,(
% 79.42/11.79 spl72_148 | ~spl72_2 | ~spl72_38),
% 79.42/11.79 inference(avatar_split_clause,[],[f2169,f2088,f1894,f3474])).
% 79.42/11.79 thf(f2169,plain,(
% 79.42/11.79 ($true = ordere236663937imp_le(a)) | (~spl72_2 | ~spl72_38)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2164])).
% 79.42/11.79 thf(f2164,plain,(
% 79.42/11.79 ($true != $true) | ($true = ordere236663937imp_le(a)) | (~spl72_2 | ~spl72_38)),
% 79.42/11.79 inference(superposition,[],[f2089,f1896])).
% 79.42/11.79 thf(f3369,plain,(
% 79.42/11.79 spl72_147),
% 79.42/11.79 inference(avatar_split_clause,[],[f1400,f3367])).
% 79.42/11.79 thf(f1400,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1244])).
% 79.42/11.79 thf(f1244,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (($true != vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1)))) | ($true != vAPP(X0,$o,X1,X2))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f974,f1243])).
% 79.42/11.79 thf(f1243,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X3 : X0 > $o] : (? [X4 : X0] : (($true != vAPP(X0,$o,X3,X4)) & ($true = vAPP(X0,$o,X1,X4))) => (($true != vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f974,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X3,X4)) & ($true = vAPP(X0,$o,X1,X4))) | ($true != vAPP(X0,$o,X1,X2))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f973])).
% 79.42/11.79 thf(f973,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : ((($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X3,X4)) & ($true = vAPP(X0,$o,X1,X4)))) | ($true != vAPP(X0,$o,X1,X2))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f400])).
% 79.42/11.79 thf(f400,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) => (! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) => ($true = vAPP(X0,$o,X3,X4))) => ($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))))))),
% 79.42/11.79 inference(fool_elimination,[],[f399])).
% 79.42/11.79 thf(f399,plain,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (vAPP(X0,$o,X1,X2) => (! [X4 : X0] : (vAPP(X0,$o,X1,X4) => vAPP(X0,$o,X3,X4)) => vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))))),
% 79.42/11.79 inference(rectify,[],[f248])).
% 79.42/11.79 thf(f248,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X29 : X0 > $o,X6 : X0,X24 : X0 > $o] : (vAPP(X0,$o,X29,X6) => (! [X31 : X0] : (vAPP(X0,$o,X29,X31) => vAPP(X0,$o,X24,X31)) => vAPP(X0,$o,X24,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X29)))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_247_LeastI2)).
% 79.42/11.79 thf(f3365,plain,(
% 79.42/11.79 spl72_146),
% 79.42/11.79 inference(avatar_split_clause,[],[f1399,f3363])).
% 79.42/11.79 thf(f1399,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK10(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1244])).
% 79.42/11.79 thf(f3361,plain,(
% 79.42/11.79 spl72_145),
% 79.42/11.79 inference(avatar_split_clause,[],[f1395,f3359])).
% 79.42/11.79 thf(f1395,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X4)) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1242])).
% 79.42/11.79 thf(f1242,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1)))) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f1240,f1241])).
% 79.42/11.79 thf(f1241,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) => (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1240,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))) | ! [X4 : X0] : ($true != vAPP(X0,$o,X1,X4))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(rectify,[],[f969])).
% 79.42/11.79 thf(f969,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true = vAPP(X0,$o,X1,X4))) | ! [X3 : X0] : ($true != vAPP(X0,$o,X1,X3))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f968])).
% 79.42/11.79 thf(f968,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0 > $o] : ((($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ? [X4 : X0] : (($true != vAPP(X0,$o,X2,X4)) & ($true = vAPP(X0,$o,X1,X4)))) | ! [X3 : X0] : ($true != vAPP(X0,$o,X1,X3))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f392])).
% 79.42/11.79 thf(f392,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : ($true = vAPP(X0,$o,X1,X3)) => (! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) => ($true = vAPP(X0,$o,X2,X4))) => ($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))))))),
% 79.42/11.79 inference(fool_elimination,[],[f391])).
% 79.42/11.79 thf(f391,plain,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X1 : X0 > $o,X2 : X0 > $o] : (? [X3 : X0] : vAPP(X0,$o,X1,X3) => (! [X4 : X0] : (vAPP(X0,$o,X1,X4) => vAPP(X0,$o,X2,X4)) => vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))))),
% 79.42/11.79 inference(rectify,[],[f250])).
% 79.42/11.79 thf(f250,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X29 : X0 > $o,X24 : X0 > $o] : (? [X75 : X0] : vAPP(X0,$o,X29,X75) => (! [X31 : X0] : (vAPP(X0,$o,X29,X31) => vAPP(X0,$o,X24,X31)) => vAPP(X0,$o,X24,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X29)))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_249_LeastI2__ex)).
% 79.42/11.79 thf(f3357,plain,(
% 79.42/11.79 spl72_144),
% 79.42/11.79 inference(avatar_split_clause,[],[f1394,f3355])).
% 79.42/11.79 thf(f1394,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK9(X0),X2),X1))) | ($true != vAPP(X0,$o,X1,X4)) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1242])).
% 79.42/11.79 thf(f3270,plain,(
% 79.42/11.79 spl72_143 | ~spl72_3 | ~spl72_38),
% 79.42/11.79 inference(avatar_split_clause,[],[f2168,f2088,f1899,f3267])).
% 79.42/11.79 thf(f2168,plain,(
% 79.42/11.79 ($true = ordere236663937imp_le(capacity)) | (~spl72_3 | ~spl72_38)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2165])).
% 79.42/11.79 thf(f2165,plain,(
% 79.42/11.79 ($true != $true) | ($true = ordere236663937imp_le(capacity)) | (~spl72_3 | ~spl72_38)),
% 79.42/11.79 inference(superposition,[],[f2089,f1901])).
% 79.42/11.79 thf(f3257,plain,(
% 79.42/11.79 spl72_142),
% 79.42/11.79 inference(avatar_split_clause,[],[f1706,f3254])).
% 79.42/11.79 thf(f1706,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f890])).
% 79.42/11.79 thf(f890,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f889])).
% 79.42/11.79 thf(f889,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))),
% 79.42/11.79 inference(rectify,[],[f3])).
% 79.42/11.79 thf(f3,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),ua),t)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__092_060open_062min__dist_Au_At_A_092_060le_062_Alength_Ap2_H_092_060close_062)).
% 79.42/11.79 thf(f3252,plain,(
% 79.42/11.79 spl72_141),
% 79.42/11.79 inference(avatar_split_clause,[],[f1705,f3249])).
% 79.42/11.79 thf(f1705,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f888])).
% 79.42/11.79 thf(f888,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f887])).
% 79.42/11.79 thf(f887,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))),
% 79.42/11.79 inference(rectify,[],[f2])).
% 79.42/11.79 thf(f2,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),ua)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__092_060open_062min__dist_As_Au_A_060_Alength_Ap1_092_060close_062)).
% 79.42/11.79 thf(f3247,plain,(
% 79.42/11.79 spl72_140),
% 79.42/11.79 inference(avatar_split_clause,[],[f1612,f3245])).
% 79.42/11.79 thf(f1612,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0)),X2)) | ($true != vAPP(nat,$o,X0,X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1315])).
% 79.42/11.79 thf(f3243,plain,(
% 79.42/11.79 spl72_139),
% 79.42/11.79 inference(avatar_split_clause,[],[f1576,f3241])).
% 79.42/11.79 thf(f1576,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) | (ord(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1140])).
% 79.42/11.79 thf(f1140,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (! [X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))) | ($true != vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3))) | (ord(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f682])).
% 79.42/11.79 thf(f682,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : ((ord(X0) = $true) => ! [X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (($true = vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4)))))),
% 79.42/11.79 inference(fool_elimination,[],[f681])).
% 79.42/11.79 thf(f681,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (ord(X0) => ! [X2 : X1 > X0,X3 : X1 > X0,X4 : X1] : (vAPP(sTfun(X1,X0),$o,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),$o),ord_less_eq(sTfun(X1,X0)),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X1,X0,X2,X4)),vAPP(X1,X0,X3,X4))))),
% 79.42/11.79 inference(rectify,[],[f187])).
% 79.42/11.79 thf(f187,axiom,(
% 79.42/11.79 ! [X38 : $tType,X0 : $tType] : (ord(X38) => ! [X39 : X0 > X38,X40 : X0 > X38,X51 : X0] : (vAPP(sTfun(X0,X38),$o,vAPP(sTfun(X0,X38),sTfun(sTfun(X0,X38),$o),ord_less_eq(sTfun(X0,X38)),X39),X40) => vAPP(X38,$o,vAPP(X38,sTfun(X38,$o),ord_less_eq(X38),vAPP(X0,X38,X39,X51)),vAPP(X0,X38,X40,X51))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_186_le__funE)).
% 79.42/11.79 thf(f3239,plain,(
% 79.42/11.79 spl72_138),
% 79.42/11.79 inference(avatar_split_clause,[],[f1354,f3237])).
% 79.42/11.79 thf(f1354,plain,(
% 79.42/11.79 ( ! [X0 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f893])).
% 79.42/11.79 thf(f893,plain,(
% 79.42/11.79 ! [X0 : nat] : (vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0)))),
% 79.42/11.79 inference(rectify,[],[f118])).
% 79.42/11.79 thf(f118,axiom,(
% 79.42/11.79 ! [X8 : nat] : (vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,set(nat)),reachableNodes(capacity),c),X8) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X8)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_117_reachableNodes__def)).
% 79.42/11.79 thf(f3235,plain,(
% 79.42/11.79 spl72_137),
% 79.42/11.79 inference(avatar_split_clause,[],[f1353,f3233])).
% 79.42/11.79 thf(f1353,plain,(
% 79.42/11.79 ( ! [X0 : nat] : ((vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f892])).
% 79.42/11.79 thf(f892,plain,(
% 79.42/11.79 ! [X0 : nat] : (vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X0) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0)))),
% 79.42/11.79 inference(rectify,[],[f162])).
% 79.42/11.79 thf(f162,axiom,(
% 79.42/11.79 ! [X8 : nat] : (vAPP(nat,set(nat),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,set(nat)),reachableNodes(a),c2),X8) = vAPP(sTfun(nat,$o),set(nat),collect(nat),vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X8)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_161_g_H_OreachableNodes__def)).
% 79.42/11.79 thf(f3218,plain,(
% 79.42/11.79 spl72_136 | ~spl72_2 | ~spl72_37),
% 79.42/11.79 inference(avatar_split_clause,[],[f2163,f2084,f1894,f3215])).
% 79.42/11.79 thf(f2163,plain,(
% 79.42/11.79 ($true = ordere779506340up_add(a)) | (~spl72_2 | ~spl72_37)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2158])).
% 79.42/11.79 thf(f2158,plain,(
% 79.42/11.79 ($true != $true) | ($true = ordere779506340up_add(a)) | (~spl72_2 | ~spl72_37)),
% 79.42/11.79 inference(superposition,[],[f2085,f1896])).
% 79.42/11.79 thf(f3200,plain,(
% 79.42/11.79 spl72_135),
% 79.42/11.79 inference(avatar_split_clause,[],[f1475,f3198])).
% 79.42/11.79 thf(f1475,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1058])).
% 79.42/11.79 thf(f1058,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f1057])).
% 79.42/11.79 thf(f1057,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f516])).
% 79.42/11.79 thf(f516,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)))))),
% 79.42/11.79 inference(fool_elimination,[],[f515])).
% 79.42/11.79 thf(f515,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))))),
% 79.42/11.79 inference(rectify,[],[f209])).
% 79.42/11.79 thf(f209,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X7 : X0,X6 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X7),X6) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X6))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_208_dual__order_Otrans)).
% 79.42/11.79 thf(f3196,plain,(
% 79.42/11.79 spl72_134),
% 79.42/11.79 inference(avatar_split_clause,[],[f1473,f3194])).
% 79.42/11.79 thf(f1473,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1054])).
% 79.42/11.79 thf(f1054,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f1053])).
% 79.42/11.79 thf(f1053,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f512])).
% 79.42/11.79 thf(f512,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)))))),
% 79.42/11.79 inference(fool_elimination,[],[f511])).
% 79.42/11.79 thf(f511,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))))),
% 79.42/11.79 inference(rectify,[],[f215])).
% 79.42/11.79 thf(f215,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X7 : X0,X6 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X6) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X6))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_214_dual__order_Ostrict__trans)).
% 79.42/11.79 thf(f3192,plain,(
% 79.42/11.79 spl72_133),
% 79.42/11.79 inference(avatar_split_clause,[],[f1447,f3190])).
% 79.42/11.79 thf(f1447,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (preorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1019])).
% 79.42/11.79 thf(f1019,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (preorder(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f1018])).
% 79.42/11.79 thf(f1018,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (preorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f460])).
% 79.42/11.79 thf(f460,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))))),
% 79.42/11.79 inference(fool_elimination,[],[f459])).
% 79.42/11.79 thf(f459,plain,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))))),
% 79.42/11.79 inference(rectify,[],[f206])).
% 79.42/11.79 thf(f206,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X51 : X0,X52 : X0,X67 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X52) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X67) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X67))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_205_order__trans)).
% 79.42/11.79 thf(f3188,plain,(
% 79.42/11.79 spl72_132),
% 79.42/11.79 inference(avatar_split_clause,[],[f1446,f3186])).
% 79.42/11.79 thf(f1446,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1017])).
% 79.42/11.79 thf(f1017,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (preorder(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f1016])).
% 79.42/11.79 thf(f1016,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (preorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f458])).
% 79.42/11.79 thf(f458,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))))),
% 79.42/11.79 inference(fool_elimination,[],[f457])).
% 79.42/11.79 thf(f457,plain,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0,X2 : X0,X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 79.42/11.79 inference(rectify,[],[f233])).
% 79.42/11.79 thf(f233,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X51 : X0,X52 : X0,X67 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X52) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X52),X67) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X67))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_232_less__trans)).
% 79.42/11.79 thf(f3136,plain,(
% 79.42/11.79 spl72_131 | ~spl72_3 | ~spl72_37),
% 79.42/11.79 inference(avatar_split_clause,[],[f2162,f2084,f1899,f3133])).
% 79.42/11.79 thf(f2162,plain,(
% 79.42/11.79 ($true = ordere779506340up_add(capacity)) | (~spl72_3 | ~spl72_37)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2159])).
% 79.42/11.79 thf(f2159,plain,(
% 79.42/11.79 ($true != $true) | ($true = ordere779506340up_add(capacity)) | (~spl72_3 | ~spl72_37)),
% 79.42/11.79 inference(superposition,[],[f2085,f1901])).
% 79.42/11.79 thf(f3095,plain,(
% 79.42/11.79 spl72_130),
% 79.42/11.79 inference(avatar_split_clause,[],[f1703,f3092])).
% 79.42/11.79 thf(f1703,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a),va) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f884])).
% 79.42/11.79 thf(f884,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a),va) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f883])).
% 79.42/11.79 thf(f883,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a),va)),
% 79.42/11.79 inference(rectify,[],[f34])).
% 79.42/11.79 thf(f34,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1a),va)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_P1)).
% 79.42/11.79 thf(f3090,plain,(
% 79.42/11.79 spl72_129),
% 79.42/11.79 inference(avatar_split_clause,[],[f1702,f3087])).
% 79.42/11.79 thf(f1702,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1),v) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f882])).
% 79.42/11.79 thf(f882,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1),v) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f881])).
% 79.42/11.79 thf(f881,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1),v)),
% 79.42/11.79 inference(rectify,[],[f25])).
% 79.42/11.79 thf(f25,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),s),p1),v)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24__092_060open_062isPath_As_Ap1_____Av_____092_060close_062)).
% 79.42/11.79 thf(f3085,plain,(
% 79.42/11.79 spl72_128),
% 79.42/11.79 inference(avatar_split_clause,[],[f1701,f3082])).
% 79.42/11.79 thf(f1701,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a),t) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f880])).
% 79.42/11.79 thf(f880,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a),t) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f879])).
% 79.42/11.79 thf(f879,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a),t)),
% 79.42/11.79 inference(rectify,[],[f14])).
% 79.42/11.79 thf(f14,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(capacity),c),ua),p2_a),t)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13__092_060open_062isPath_Au_Ap2_H_At_092_060close_062)).
% 79.42/11.79 thf(f3080,plain,(
% 79.42/11.79 spl72_127),
% 79.42/11.79 inference(avatar_split_clause,[],[f1700,f3077])).
% 79.42/11.79 thf(f1700,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p),t) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f878])).
% 79.42/11.79 thf(f878,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p),t) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f877])).
% 79.42/11.79 thf(f877,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p),t)),
% 79.42/11.79 inference(rectify,[],[f8])).
% 79.42/11.79 thf(f8,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isShortestPath(capacity),c),s),p),t)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_SP)).
% 79.42/11.79 thf(f3075,plain,(
% 79.42/11.79 spl72_126),
% 79.42/11.79 inference(avatar_split_clause,[],[f1699,f3072])).
% 79.42/11.79 thf(f1699,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3),t) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f876])).
% 79.42/11.79 thf(f876,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3),t) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f875])).
% 79.42/11.79 thf(f875,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3),t)),
% 79.42/11.79 inference(rectify,[],[f181])).
% 79.42/11.79 thf(f181,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),s),p3),t)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_180_assms_I5_J)).
% 79.42/11.79 thf(f3070,plain,(
% 79.42/11.79 spl72_125),
% 79.42/11.79 inference(avatar_split_clause,[],[f1697,f3067])).
% 79.42/11.79 thf(f1697,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a),t) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f872])).
% 79.42/11.79 thf(f872,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a),t) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f871])).
% 79.42/11.79 thf(f871,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a),t)),
% 79.42/11.79 inference(rectify,[],[f154])).
% 79.42/11.79 thf(f154,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),ua),p2_a),t)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_153__C1_Oprems_C_I3_J)).
% 79.42/11.79 thf(f3065,plain,(
% 79.42/11.79 spl72_124),
% 79.42/11.79 inference(avatar_split_clause,[],[f1696,f3062])).
% 79.42/11.79 thf(f1696,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2),t) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f870])).
% 79.42/11.79 thf(f870,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2),t) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f869])).
% 79.42/11.79 thf(f869,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2),t)),
% 79.42/11.79 inference(rectify,[],[f182])).
% 79.42/11.79 thf(f182,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(list(product_prod(nat,nat)),sTfun(nat,$o),vAPP(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o)),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(list(product_prod(nat,nat)),sTfun(nat,$o))),isPath(a),c2),u),p2),t)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_181__092_060open_062g_H_OisPath_Au_____Ap2_H_____At_092_060close_062)).
% 79.42/11.79 thf(f3060,plain,(
% 79.42/11.79 spl72_123 | ~spl72_2 | ~spl72_36),
% 79.42/11.79 inference(avatar_split_clause,[],[f2157,f2080,f1894,f3057])).
% 79.42/11.79 thf(f2157,plain,(
% 79.42/11.79 ($true = cancel_semigroup_add(a)) | (~spl72_2 | ~spl72_36)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2152])).
% 79.42/11.79 thf(f2152,plain,(
% 79.42/11.79 ($true != $true) | ($true = cancel_semigroup_add(a)) | (~spl72_2 | ~spl72_36)),
% 79.42/11.79 inference(superposition,[],[f2081,f1896])).
% 79.42/11.79 thf(f3031,plain,(
% 79.42/11.79 spl72_122),
% 79.42/11.79 inference(avatar_split_clause,[],[f1360,f3029])).
% 79.42/11.79 thf(f1360,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK7(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (canoni770627133id_add(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1237])).
% 79.42/11.79 thf(f1237,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK7(X0),X2),X1)) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (canoni770627133id_add(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f929,f1236])).
% 79.42/11.79 thf(f1236,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0,X2 : X0] : (? [X3 : 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),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK7(X0),X2),X1)) = X2))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f929,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (? [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (canoni770627133id_add(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f326])).
% 79.42/11.79 thf(f326,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((canoni770627133id_add(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ~! [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2)))),
% 79.42/11.79 inference(fool_elimination,[],[f325])).
% 79.42/11.79 thf(f325,plain,(
% 79.42/11.79 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => ~! [X3 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X1),X3) != X2)))),
% 79.42/11.79 inference(rectify,[],[f51])).
% 79.42/11.79 thf(f51,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (canoni770627133id_add(X0) => ! [X6 : X0,X7 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => ~! [X41 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X6),X41) != X7)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_less__eqE)).
% 79.42/11.79 thf(f3027,plain,(
% 79.42/11.79 spl72_121),
% 79.42/11.79 inference(avatar_split_clause,[],[f1357,f3025])).
% 79.42/11.79 thf(f1357,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1233])).
% 79.42/11.79 thf(f1233,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (dense_order(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f926,f1232])).
% 79.42/11.79 thf(f1232,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0,X2 : X0] : (? [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f926,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (? [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (dense_order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f320])).
% 79.42/11.79 thf(f320,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((dense_order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ? [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))))),
% 79.42/11.79 inference(fool_elimination,[],[f319])).
% 79.42/11.79 thf(f319,plain,(
% 79.42/11.79 ! [X0 : $tType] : (dense_order(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => ? [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 79.42/11.79 inference(rectify,[],[f237])).
% 79.42/11.79 thf(f237,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (dense_order(X0) => ! [X51 : X0,X52 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X52) => ? [X73 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X73),X52) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X73))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_236_dense)).
% 79.42/11.79 thf(f3023,plain,(
% 79.42/11.79 spl72_120),
% 79.42/11.79 inference(avatar_split_clause,[],[f1356,f3021])).
% 79.42/11.79 thf(f1356,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK5(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1233])).
% 79.42/11.79 thf(f3008,plain,(
% 79.42/11.79 spl72_119),
% 79.42/11.79 inference(avatar_split_clause,[],[f1618,f3006])).
% 79.42/11.79 thf(f1618,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1166])).
% 79.42/11.79 thf(f1166,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(flattening,[],[f1165])).
% 79.42/11.79 thf(f1165,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f748])).
% 79.42/11.79 thf(f748,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f747])).
% 79.42/11.79 thf(f747,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)))),
% 79.42/11.79 inference(rectify,[],[f38])).
% 79.42/11.79 thf(f38,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X28) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X28),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X2)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_le__trans)).
% 79.42/11.79 thf(f2982,plain,(
% 79.42/11.79 spl72_118),
% 79.42/11.79 inference(avatar_split_clause,[],[f1611,f2980])).
% 79.42/11.79 thf(f1611,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK55,X0))) | ($true = vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,vAPP(nat,sTfun(sTfun(nat,$o),nat),sK56,X2),X0))) | ($true != vAPP(nat,$o,X0,X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1315])).
% 79.42/11.79 thf(f2978,plain,(
% 79.42/11.79 spl72_117 | ~spl72_3 | ~spl72_36),
% 79.42/11.79 inference(avatar_split_clause,[],[f2156,f2080,f1899,f2975])).
% 79.42/11.79 thf(f2156,plain,(
% 79.42/11.79 ($true = cancel_semigroup_add(capacity)) | (~spl72_3 | ~spl72_36)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2153])).
% 79.42/11.79 thf(f2153,plain,(
% 79.42/11.79 ($true != $true) | ($true = cancel_semigroup_add(capacity)) | (~spl72_3 | ~spl72_36)),
% 79.42/11.79 inference(superposition,[],[f2081,f1901])).
% 79.42/11.79 thf(f2916,plain,(
% 79.42/11.79 spl72_116),
% 79.42/11.79 inference(avatar_split_clause,[],[f1624,f2914])).
% 79.42/11.79 thf(f1624,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1171])).
% 79.42/11.79 thf(f1171,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 79.42/11.79 inference(ennf_transformation,[],[f921])).
% 79.42/11.79 thf(f921,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) => ~(($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) => ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))))),
% 79.42/11.79 inference(flattening,[],[f758])).
% 79.42/11.79 thf(f758,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) => ~(($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) => ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f757])).
% 79.42/11.79 thf(f757,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2) => ~(vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2) => ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f73])).
% 79.42/11.79 thf(f73,axiom,(
% 79.42/11.79 ! [X3 : nat,X2 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X2)),X4) => ~(vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) => ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X4)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_add__leE)).
% 79.42/11.79 thf(f2912,plain,(
% 79.42/11.79 spl72_115),
% 79.42/11.79 inference(avatar_split_clause,[],[f1623,f2910])).
% 79.42/11.79 thf(f1623,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1171])).
% 79.42/11.79 thf(f2908,plain,(
% 79.42/11.79 spl72_114),
% 79.42/11.79 inference(avatar_split_clause,[],[f1622,f2906])).
% 79.42/11.79 thf(f1622,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1170])).
% 79.42/11.79 thf(f1170,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)))),
% 79.42/11.79 inference(ennf_transformation,[],[f756])).
% 79.42/11.79 thf(f756,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2)))),
% 79.42/11.79 inference(fool_elimination,[],[f755])).
% 79.42/11.79 thf(f755,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X2))),
% 79.42/11.79 inference(rectify,[],[f117])).
% 79.42/11.79 thf(f117,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X27),X28)),X2) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X2))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_116_add__lessD1)).
% 79.42/11.79 thf(f2904,plain,(
% 79.42/11.79 spl72_113),
% 79.42/11.79 inference(avatar_split_clause,[],[f1620,f2902])).
% 79.42/11.79 thf(f1620,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1168])).
% 79.42/11.79 thf(f1168,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f752])).
% 79.42/11.79 thf(f752,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f751])).
% 79.42/11.79 thf(f751,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 79.42/11.79 inference(rectify,[],[f64])).
% 79.42/11.79 thf(f64,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X28)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_trans__le__add2)).
% 79.42/11.79 thf(f2900,plain,(
% 79.42/11.79 spl72_112),
% 79.42/11.79 inference(avatar_split_clause,[],[f1619,f2898])).
% 79.42/11.79 thf(f1619,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1167])).
% 79.42/11.79 thf(f1167,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f750])).
% 79.42/11.79 thf(f750,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f749])).
% 79.42/11.79 thf(f749,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f65])).
% 79.42/11.79 thf(f65,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X27),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X3)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_trans__le__add1)).
% 79.42/11.79 thf(f2896,plain,(
% 79.42/11.79 spl72_111),
% 79.42/11.79 inference(avatar_split_clause,[],[f1616,f2894])).
% 79.42/11.79 thf(f1616,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1163])).
% 79.42/11.79 thf(f1163,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f744])).
% 79.42/11.79 thf(f744,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f743])).
% 79.42/11.79 thf(f743,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X1)))),
% 79.42/11.79 inference(rectify,[],[f111])).
% 79.42/11.79 thf(f111,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X28)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_110_trans__less__add2)).
% 79.42/11.79 thf(f2892,plain,(
% 79.42/11.79 spl72_110),
% 79.42/11.79 inference(avatar_split_clause,[],[f1615,f2890])).
% 79.42/11.79 thf(f1615,plain,(
% 79.42/11.79 ( ! [X2 : nat,X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1162])).
% 79.42/11.79 thf(f1162,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f742])).
% 79.42/11.79 thf(f742,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f741])).
% 79.42/11.79 thf(f741,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat,X2 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f112])).
% 79.42/11.79 thf(f112,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat,X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),X28) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X27),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X3)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_111_trans__less__add1)).
% 79.42/11.79 thf(f2888,plain,(
% 79.42/11.79 spl72_109),
% 79.42/11.79 inference(avatar_split_clause,[],[f1392,f2886])).
% 79.42/11.79 thf(f1392,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,X1,X2)) | ($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1239])).
% 79.42/11.79 thf(f1239,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,X1,X2)) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) & ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),vAPP(sTfun(X0,$o),X0,sK8(X0),X1)))))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f967,f1238])).
% 79.42/11.79 thf(f1238,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0 > $o] : (? [X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) & ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X3)))) => (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) & ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),vAPP(sTfun(X0,$o),X0,sK8(X0),X1))))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f967,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,X1,X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X1,X3)) & ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X3))))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f390])).
% 79.42/11.79 thf(f390,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (! [X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X3)) => ($true = vAPP(X0,$o,X1,X4))) => ($true = vAPP(X0,$o,X1,X3))) => ($true = vAPP(X0,$o,X1,X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f389])).
% 79.42/11.79 thf(f389,plain,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X1 : X0 > $o,X2 : X0] : (! [X3 : X0] : (! [X4 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),X3) => vAPP(X0,$o,X1,X4)) => vAPP(X0,$o,X1,X3)) => vAPP(X0,$o,X1,X2)))),
% 79.42/11.79 inference(rectify,[],[f225])).
% 79.42/11.79 thf(f225,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X29 : X0 > $o,X6 : X0] : (! [X31 : X0] : (! [X32 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X32),X31) => vAPP(X0,$o,X29,X32)) => vAPP(X0,$o,X29,X31)) => vAPP(X0,$o,X29,X6)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_224_less__induct)).
% 79.42/11.79 thf(f2871,plain,(
% 79.42/11.79 spl72_108),
% 79.42/11.79 inference(avatar_split_clause,[],[f1585,f2869])).
% 79.42/11.79 thf(f1585,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1301])).
% 79.42/11.79 thf(f1301,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ((vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK47])],[f1151,f1300])).
% 79.42/11.79 thf(f1300,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (? [X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) = X1) => (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),sK47,X1),X0)) = X1))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1151,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (? [X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f700])).
% 79.42/11.79 thf(f700,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ? [X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) = X1))),
% 79.42/11.79 inference(fool_elimination,[],[f699])).
% 79.42/11.79 thf(f699,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => ? [X2 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X2) = X1))),
% 79.42/11.79 inference(rectify,[],[f68])).
% 79.42/11.79 thf(f68,axiom,(
% 79.42/11.79 ! [X2 : nat,X42 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X42) => ? [X48 : nat] : (vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X2),X48) = X42))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_le__Suc__ex)).
% 79.42/11.79 thf(f2867,plain,(
% 79.42/11.79 spl72_107),
% 79.42/11.79 inference(avatar_split_clause,[],[f1543,f2865])).
% 79.42/11.79 thf(f1543,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f642])).
% 79.42/11.79 thf(f642,plain,(
% 79.42/11.79 ! [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)),
% 79.42/11.79 inference(fool_elimination,[],[f641])).
% 79.42/11.79 thf(f641,plain,(
% 79.42/11.79 ! [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)),
% 79.42/11.79 inference(rectify,[],[f47])).
% 79.42/11.79 thf(f47,axiom,(
% 79.42/11.79 ! [X0 : $tType,X36 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X37 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X37),X36)))) = X36)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)).
% 79.42/11.79 thf(f2863,plain,(
% 79.42/11.79 spl72_106 | ~spl72_2 | ~spl72_35),
% 79.42/11.79 inference(avatar_split_clause,[],[f2146,f2076,f1894,f2860])).
% 79.42/11.79 thf(f2146,plain,(
% 79.42/11.79 ($true = ab_semigroup_add(a)) | (~spl72_2 | ~spl72_35)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2141])).
% 79.42/11.79 thf(f2141,plain,(
% 79.42/11.79 ($true != $true) | ($true = ab_semigroup_add(a)) | (~spl72_2 | ~spl72_35)),
% 79.42/11.79 inference(superposition,[],[f2077,f1896])).
% 79.42/11.79 thf(f2786,plain,(
% 79.42/11.79 spl72_105 | ~spl72_3 | ~spl72_35),
% 79.42/11.79 inference(avatar_split_clause,[],[f2145,f2076,f1899,f2783])).
% 79.42/11.79 thf(f2145,plain,(
% 79.42/11.79 ($true = ab_semigroup_add(capacity)) | (~spl72_3 | ~spl72_35)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2142])).
% 79.42/11.79 thf(f2142,plain,(
% 79.42/11.79 ($true != $true) | ($true = ab_semigroup_add(capacity)) | (~spl72_3 | ~spl72_35)),
% 79.42/11.79 inference(superposition,[],[f2077,f1901])).
% 79.42/11.79 thf(f2781,plain,(
% 79.42/11.79 spl72_104),
% 79.42/11.79 inference(avatar_split_clause,[],[f1572,f2779])).
% 79.42/11.79 thf(f1572,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK45(X0,X1),X3),X2))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1297])).
% 79.42/11.79 thf(f2777,plain,(
% 79.42/11.79 spl72_103),
% 79.42/11.79 inference(avatar_split_clause,[],[f1570,f2775])).
% 79.42/11.79 thf(f1570,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : X1 > $o,X4 : X1] : (($true = vAPP(X1,$o,X3,X4)) | ($true != vAPP(X1,$o,X3,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,$o),sTfun(sTfun(X1,X0),X1),sK44(X0,X1),X3),X2))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1295])).
% 79.42/11.79 thf(f2773,plain,(
% 79.42/11.79 spl72_102),
% 79.42/11.79 inference(avatar_split_clause,[],[f1425,f2771])).
% 79.42/11.79 thf(f1425,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1252])).
% 79.42/11.79 thf(f1252,plain,(
% 79.42/11.79 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0)))),
% 79.42/11.79 inference(rectify,[],[f1251])).
% 79.42/11.79 thf(f1251,plain,(
% 79.42/11.79 ! [X3 : X0,X2 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP0(X0),X1),X2),X3)))),
% 79.42/11.79 inference(nnf_transformation,[],[f1225])).
% 79.42/11.79 thf(f2769,plain,(
% 79.42/11.79 spl72_101),
% 79.42/11.79 inference(avatar_split_clause,[],[f1424,f2767])).
% 79.42/11.79 thf(f1424,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP0(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1252])).
% 79.42/11.79 thf(f2765,plain,(
% 79.42/11.79 spl72_100),
% 79.42/11.79 inference(avatar_split_clause,[],[f1423,f2763])).
% 79.42/11.79 thf(f1423,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1250])).
% 79.42/11.79 thf(f1250,plain,(
% 79.42/11.79 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0)))),
% 79.42/11.79 inference(rectify,[],[f1249])).
% 79.42/11.79 thf(f1249,plain,(
% 79.42/11.79 ! [X3 : X0,X1 : X0,X0 : $tType,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP1(X0),X2),X1),X3)))),
% 79.42/11.79 inference(nnf_transformation,[],[f1226])).
% 79.42/11.79 thf(f2761,plain,(
% 79.42/11.79 spl72_99),
% 79.42/11.79 inference(avatar_split_clause,[],[f1422,f2759])).
% 79.42/11.79 thf(f1422,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP1(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1250])).
% 79.42/11.79 thf(f2757,plain,(
% 79.42/11.79 spl72_98),
% 79.42/11.79 inference(avatar_split_clause,[],[f1421,f2755])).
% 79.42/11.79 thf(f1421,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1248])).
% 79.42/11.79 thf(f1248,plain,(
% 79.42/11.79 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0)))),
% 79.42/11.79 inference(rectify,[],[f1247])).
% 79.42/11.79 thf(f1247,plain,(
% 79.42/11.79 ! [X2 : X0,X3 : X0,X0 : $tType,X1 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP2(X0),X1),X3),X2)))),
% 79.42/11.79 inference(nnf_transformation,[],[f1227])).
% 79.42/11.79 thf(f2753,plain,(
% 79.42/11.79 spl72_97),
% 79.42/11.79 inference(avatar_split_clause,[],[f1420,f2751])).
% 79.42/11.79 thf(f1420,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP2(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1248])).
% 79.42/11.79 thf(f2749,plain,(
% 79.42/11.79 spl72_96),
% 79.42/11.79 inference(avatar_split_clause,[],[f1419,f2747])).
% 79.42/11.79 thf(f1419,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1246])).
% 79.42/11.79 thf(f1246,plain,(
% 79.42/11.79 ! [X0 : X2,X1 : X2,X2 : $tType,X3 : X2] : ((($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X1),X0)) & ($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1))) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0)))),
% 79.42/11.79 inference(rectify,[],[f1245])).
% 79.42/11.79 thf(f1245,plain,(
% 79.42/11.79 ! [X1 : X0,X2 : X0,X0 : $tType,X3 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),vAPP(X0,sTfun(X0,sTfun(X0,$o)),sP3(X0),X3),X2),X1)))),
% 79.42/11.79 inference(nnf_transformation,[],[f1228])).
% 79.42/11.79 thf(f2745,plain,(
% 79.42/11.79 spl72_95),
% 79.42/11.79 inference(avatar_split_clause,[],[f1418,f2743])).
% 79.42/11.79 thf(f1418,plain,(
% 79.42/11.79 ( ! [X2 : $tType,X3 : X2,X0 : X2,X1 : X2] : (($true = vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),ord_less_eq(X2),X3),X1)) | ($true != vAPP(X2,$o,vAPP(X2,sTfun(X2,$o),vAPP(X2,sTfun(X2,sTfun(X2,$o)),sP3(X2),X3),X1),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1246])).
% 79.42/11.79 thf(f2741,plain,(
% 79.42/11.79 spl72_94 | ~spl72_2 | ~spl72_34),
% 79.42/11.79 inference(avatar_split_clause,[],[f2140,f2072,f1894,f2738])).
% 79.42/11.79 thf(f2140,plain,(
% 79.42/11.79 ($true = comm_monoid_add(a)) | (~spl72_2 | ~spl72_34)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2135])).
% 79.42/11.79 thf(f2135,plain,(
% 79.42/11.79 ($true != $true) | ($true = comm_monoid_add(a)) | (~spl72_2 | ~spl72_34)),
% 79.42/11.79 inference(superposition,[],[f2073,f1896])).
% 79.42/11.79 thf(f2716,plain,(
% 79.42/11.79 spl72_93),
% 79.42/11.79 inference(avatar_split_clause,[],[f1470,f2714])).
% 79.42/11.79 thf(f2714,plain,(
% 79.42/11.79 spl72_93 <=> ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true))),
% 79.42/11.79 introduced(avatar_definition,[new_symbols(naming,[spl72_93])])).
% 79.42/11.79 thf(f1470,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1048])).
% 79.42/11.79 thf(f1048,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f1047])).
% 79.42/11.79 thf(f1047,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((X1 = X2) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f506])).
% 79.42/11.79 thf(f506,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) => (X1 = X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f505])).
% 79.42/11.79 thf(f505,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) => (X1 = X2))))),
% 79.42/11.79 inference(rectify,[],[f211])).
% 79.42/11.79 thf(f211,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X7 : X0,X6 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X7),X6) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => (X6 = X7))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_210_dual__order_Oantisym)).
% 79.42/11.79 thf(f2712,plain,(
% 79.42/11.79 spl72_92),
% 79.42/11.79 inference(avatar_split_clause,[],[f1459,f2710])).
% 79.42/11.79 thf(f1459,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (X1 = X2) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1036])).
% 79.42/11.79 thf(f1036,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (X1 = X2)) | (order(X0) != $true))),
% 79.42/11.79 inference(flattening,[],[f1035])).
% 79.42/11.79 thf(f1035,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : ((($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (X1 = X2)) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f484])).
% 79.42/11.79 thf(f484,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : ((X1 != X2) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))))),
% 79.42/11.79 inference(fool_elimination,[],[f483])).
% 79.42/11.79 thf(f483,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0] : ((X1 != X2) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))))),
% 79.42/11.79 inference(rectify,[],[f252])).
% 79.42/11.79 thf(f252,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X6 : X0,X7 : X0] : ((X6 != X7) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X7) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_251_order_Onot__eq__order__implies__strict)).
% 79.42/11.79 thf(f2704,plain,(
% 79.42/11.79 spl72_91),
% 79.42/11.79 inference(avatar_split_clause,[],[f1567,f2702])).
% 79.42/11.79 thf(f1567,plain,(
% 79.42/11.79 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK43,X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1293])).
% 79.42/11.79 thf(f1293,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0))) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK43,X0))))))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f1134,f1292])).
% 79.42/11.79 thf(f1292,plain,(
% 79.42/11.79 ! [X0 : nat > $o] : (? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => (($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0))) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK43,X0))))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1134,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) & ! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))))),
% 79.42/11.79 inference(ennf_transformation,[],[f670])).
% 79.42/11.79 thf(f670,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)) => ($true = vAPP(nat,$o,X0,X3))) => ($true = vAPP(nat,$o,X0,X2))) => ($true = vAPP(nat,$o,X0,X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f669])).
% 79.42/11.79 thf(f669,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (! [X3 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2) => vAPP(nat,$o,X0,X3)) => vAPP(nat,$o,X0,X2)) => vAPP(nat,$o,X0,X1))),
% 79.42/11.79 inference(rectify,[],[f90])).
% 79.42/11.79 thf(f90,axiom,(
% 79.42/11.79 ! [X29 : nat > $o,X4 : nat] : (! [X48 : nat] : (! [X53 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X53),X48) => vAPP(nat,$o,X29,X53)) => vAPP(nat,$o,X29,X48)) => vAPP(nat,$o,X29,X4))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_nat__less__induct)).
% 79.42/11.79 thf(f2700,plain,(
% 79.42/11.79 spl72_90),
% 79.42/11.79 inference(avatar_split_clause,[],[f1566,f2698])).
% 79.42/11.79 thf(f1566,plain,(
% 79.42/11.79 ( ! [X3 : nat,X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK42,X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1291])).
% 79.42/11.79 thf(f1291,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK42,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)))))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f1133,f1290])).
% 79.42/11.79 thf(f1290,plain,(
% 79.42/11.79 ! [X0 : nat > $o] : (? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2))) => (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),vAPP(sTfun(nat,$o),nat,sK42,X0)))) & ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f1133,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ? [X2 : nat] : (! [X3 : nat] : (($true = vAPP(nat,$o,X0,X3)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) & ($true != vAPP(nat,$o,X0,X2))))),
% 79.42/11.79 inference(ennf_transformation,[],[f912])).
% 79.42/11.79 thf(f912,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (($true != vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (($true != vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => ($true = vAPP(nat,$o,X0,X1)))),
% 79.42/11.79 inference(flattening,[],[f668])).
% 79.42/11.79 thf(f668,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (~($true = vAPP(nat,$o,X0,X2)) => ? [X3 : nat] : (~($true = vAPP(nat,$o,X0,X3)) & ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2)))) => ($true = vAPP(nat,$o,X0,X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f667])).
% 79.42/11.79 thf(f667,plain,(
% 79.42/11.79 ! [X0 : nat > $o,X1 : nat] : (! [X2 : nat] : (~vAPP(nat,$o,X0,X2) => ? [X3 : nat] : (~vAPP(nat,$o,X0,X3) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X2))) => vAPP(nat,$o,X0,X1))),
% 79.42/11.79 inference(rectify,[],[f89])).
% 79.42/11.79 thf(f89,axiom,(
% 79.42/11.79 ! [X29 : nat > $o,X4 : nat] : (! [X48 : nat] : (~vAPP(nat,$o,X29,X48) => ? [X53 : nat] : (~vAPP(nat,$o,X29,X53) & vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X53),X48))) => vAPP(nat,$o,X29,X4))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_infinite__descent)).
% 79.42/11.79 thf(f2692,plain,(
% 79.42/11.79 spl72_89 | ~spl72_3 | ~spl72_34),
% 79.42/11.79 inference(avatar_split_clause,[],[f2139,f2072,f1899,f2689])).
% 79.42/11.79 thf(f2139,plain,(
% 79.42/11.79 ($true = comm_monoid_add(capacity)) | (~spl72_3 | ~spl72_34)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2136])).
% 79.42/11.79 thf(f2136,plain,(
% 79.42/11.79 ($true != $true) | ($true = comm_monoid_add(capacity)) | (~spl72_3 | ~spl72_34)),
% 79.42/11.79 inference(superposition,[],[f2073,f1901])).
% 79.42/11.79 thf(f2638,plain,(
% 79.42/11.79 spl72_88),
% 79.42/11.79 inference(avatar_split_clause,[],[f1467,f2636])).
% 79.42/11.79 thf(f1467,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1044])).
% 79.42/11.79 thf(f1044,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f500])).
% 79.42/11.79 thf(f500,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f499])).
% 79.42/11.79 thf(f499,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f253])).
% 79.42/11.79 thf(f253,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X7 : X0,X6 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X6) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X7),X6)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_252_dual__order_Ostrict__implies__order)).
% 79.42/11.79 thf(f2634,plain,(
% 79.42/11.79 spl72_87),
% 79.42/11.79 inference(avatar_split_clause,[],[f1465,f2632])).
% 79.42/11.79 thf(f1465,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1042])).
% 79.42/11.79 thf(f1042,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f906])).
% 79.42/11.79 thf(f906,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))))),
% 79.42/11.79 inference(flattening,[],[f496])).
% 79.42/11.79 thf(f496,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f495])).
% 79.42/11.79 thf(f495,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))),
% 79.42/11.79 inference(rectify,[],[f228])).
% 79.42/11.79 thf(f228,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X7 : X0,X6 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X7),X6) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X7)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_227_dual__order_Oasym)).
% 79.42/11.79 thf(f2630,plain,(
% 79.42/11.79 spl72_86),
% 79.42/11.79 inference(avatar_split_clause,[],[f1441,f2628])).
% 79.42/11.79 thf(f1441,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1010])).
% 79.42/11.79 thf(f1010,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (preorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f901])).
% 79.42/11.79 thf(f901,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))))),
% 79.42/11.79 inference(flattening,[],[f448])).
% 79.42/11.79 thf(f448,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f447])).
% 79.42/11.79 thf(f447,plain,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))),
% 79.42/11.79 inference(rectify,[],[f226])).
% 79.42/11.79 thf(f226,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X51 : X0,X52 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X52) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X52),X51)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_225_less__not__sym)).
% 79.42/11.79 thf(f2626,plain,(
% 79.42/11.79 spl72_85),
% 79.42/11.79 inference(avatar_split_clause,[],[f1413,f2624])).
% 79.42/11.79 thf(f1413,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | (linorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f994])).
% 79.42/11.79 thf(f994,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))) | (linorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f426])).
% 79.42/11.79 thf(f426,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f425])).
% 79.42/11.79 thf(f425,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0,X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 79.42/11.79 inference(rectify,[],[f196])).
% 79.42/11.79 thf(f196,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linorder(X0) => ! [X51 : X0,X52 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X52),X51) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X52)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_195_linear)).
% 79.42/11.79 thf(f2622,plain,(
% 79.42/11.79 spl72_84),
% 79.42/11.79 inference(avatar_split_clause,[],[f1398,f2620])).
% 79.42/11.79 thf(f1398,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (($true != vAPP(X0,$o,X2,X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f972])).
% 79.42/11.79 thf(f972,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0,X2 : X0 > $o] : (($true != vAPP(X0,$o,X2,X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2)))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f894])).
% 79.42/11.79 thf(f894,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0,X2 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) => ($true != vAPP(X0,$o,X2,X1))))),
% 79.42/11.79 inference(flattening,[],[f398])).
% 79.42/11.79 thf(f398,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0,X2 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2))) => ~($true = vAPP(X0,$o,X2,X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f397])).
% 79.42/11.79 thf(f397,plain,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X1 : X0,X2 : X0 > $o] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X2)) => ~vAPP(X0,$o,X2,X1)))),
% 79.42/11.79 inference(rectify,[],[f156])).
% 79.42/11.79 thf(f156,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X2 : X0,X29 : X0 > $o] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X29)) => ~vAPP(X0,$o,X29,X2)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_155_not__less__Least)).
% 79.42/11.79 thf(f2618,plain,(
% 79.42/11.79 spl72_83),
% 79.42/11.79 inference(avatar_split_clause,[],[f1397,f2616])).
% 79.42/11.79 thf(f1397,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f971])).
% 79.42/11.79 thf(f971,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)) | ($true != vAPP(X0,$o,X1,X2))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f396])).
% 79.42/11.79 thf(f396,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,X1,X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2))))),
% 79.42/11.79 inference(fool_elimination,[],[f395])).
% 79.42/11.79 thf(f395,plain,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X1 : X0 > $o,X2 : X0] : (vAPP(X0,$o,X1,X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)),X2)))),
% 79.42/11.79 inference(rectify,[],[f157])).
% 79.42/11.79 thf(f157,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X29 : X0 > $o,X2 : X0] : (vAPP(X0,$o,X29,X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(sTfun(X0,$o),X0,ord_Least(X0),X29)),X2)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_156_Least__le)).
% 79.42/11.79 thf(f2614,plain,(
% 79.42/11.79 spl72_82 | ~spl72_2 | ~spl72_33),
% 79.42/11.79 inference(avatar_split_clause,[],[f2134,f2068,f1894,f2611])).
% 79.42/11.79 thf(f2134,plain,(
% 79.42/11.79 ($true = strict2144017051up_add(a)) | (~spl72_2 | ~spl72_33)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2129])).
% 79.42/11.79 thf(f2129,plain,(
% 79.42/11.79 ($true != $true) | ($true = strict2144017051up_add(a)) | (~spl72_2 | ~spl72_33)),
% 79.42/11.79 inference(superposition,[],[f2069,f1896])).
% 79.42/11.79 thf(f2524,plain,(
% 79.42/11.79 spl72_81),
% 79.42/11.79 inference(avatar_split_clause,[],[f1656,f2522])).
% 79.42/11.79 thf(f1656,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X3 : X0 > nat,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK67(X0),X3),X1))) | ($true != vAPP(X0,$o,X1,X2))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1337])).
% 79.42/11.79 thf(f2520,plain,(
% 79.42/11.79 spl72_80),
% 79.42/11.79 inference(avatar_split_clause,[],[f1654,f2518])).
% 79.42/11.79 thf(f1654,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0 > nat,X3 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X3)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,nat),sTfun(sTfun(X0,$o),X0),sK66(X0),X2),X1)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1335])).
% 79.42/11.79 thf(f2516,plain,(
% 79.42/11.79 spl72_79),
% 79.42/11.79 inference(avatar_split_clause,[],[f1584,f2514])).
% 79.42/11.79 thf(f1584,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1150])).
% 79.42/11.79 thf(f1150,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(flattening,[],[f1149])).
% 79.42/11.79 thf(f1149,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0))) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f698])).
% 79.42/11.79 thf(f698,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) => (X0 = X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f697])).
% 79.42/11.79 thf(f697,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) => (X0 = X1)))),
% 79.42/11.79 inference(rectify,[],[f40])).
% 79.42/11.79 thf(f40,axiom,(
% 79.42/11.79 ! [X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) => (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) => (X3 = X4)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__antisym)).
% 79.42/11.79 thf(f2512,plain,(
% 79.42/11.79 spl72_78),
% 79.42/11.79 inference(avatar_split_clause,[],[f1583,f2510])).
% 79.42/11.79 thf(f1583,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1148])).
% 79.42/11.79 thf(f1148,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(flattening,[],[f1147])).
% 79.42/11.79 thf(f1147,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ((($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) | (X0 = X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f696])).
% 79.42/11.79 thf(f696,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) => ((X0 != X1) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f695])).
% 79.42/11.79 thf(f695,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) => ((X0 != X1) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)))),
% 79.42/11.79 inference(rectify,[],[f58])).
% 79.42/11.79 thf(f58,axiom,(
% 79.42/11.79 ! [X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4) => ((X3 != X4) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_le__neq__implies__less)).
% 79.42/11.79 thf(f2502,plain,(
% 79.42/11.79 spl72_77),
% 79.42/11.79 inference(avatar_split_clause,[],[f1492,f2500])).
% 79.42/11.79 thf(f1492,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : nat,X1 : product_prod(nat,nat) > X0] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1076])).
% 79.42/11.79 thf(f1076,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : product_prod(nat,nat) > X0,X2 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f550])).
% 79.42/11.79 thf(f550,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2)))),
% 79.42/11.79 inference(fool_elimination,[],[f549])).
% 79.42/11.79 thf(f549,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ! [X1 : product_prod(nat,nat) > X0,X2 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X0),sTfun(nat,sTfun(nat,$o)),connected(X0),X1),X2),X2))),
% 79.42/11.79 inference(rectify,[],[f139])).
% 79.42/11.79 thf(f139,axiom,(
% 79.42/11.79 ! [X1 : $tType] : (linordered_idom(X1) => ! [X5 : product_prod(nat,nat) > X1,X12 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),X1),sTfun(nat,sTfun(nat,$o)),connected(X1),X5),X12),X12))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_138_Graph_Oconnected__refl)).
% 79.42/11.79 thf(f2498,plain,(
% 79.42/11.79 spl72_76 | ~spl72_3 | ~spl72_33),
% 79.42/11.79 inference(avatar_split_clause,[],[f2133,f2068,f1899,f2495])).
% 79.42/11.79 thf(f2133,plain,(
% 79.42/11.79 ($true = strict2144017051up_add(capacity)) | (~spl72_3 | ~spl72_33)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2130])).
% 79.42/11.79 thf(f2130,plain,(
% 79.42/11.79 ($true != $true) | ($true = strict2144017051up_add(capacity)) | (~spl72_3 | ~spl72_33)),
% 79.42/11.79 inference(superposition,[],[f2069,f1901])).
% 79.42/11.79 thf(f2473,plain,(
% 79.42/11.79 spl72_75),
% 79.42/11.79 inference(avatar_split_clause,[],[f1563,f2471])).
% 79.42/11.79 thf(f1563,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1132])).
% 79.42/11.79 thf(f1132,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)) | ((X0 != X1) & ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))))),
% 79.42/11.79 inference(ennf_transformation,[],[f666])).
% 79.42/11.79 thf(f666,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (((X0 = X1) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1))) => ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f665])).
% 79.42/11.79 thf(f665,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (((X0 = X1) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))),
% 79.42/11.79 inference(rectify,[],[f59])).
% 79.42/11.79 thf(f59,axiom,(
% 79.42/11.79 ! [X3 : nat,X4 : nat] : (((X3 = X4) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X3),X4)) => vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_less__or__eq__imp__le)).
% 79.42/11.79 thf(f2469,plain,(
% 79.42/11.79 spl72_74),
% 79.42/11.79 inference(avatar_split_clause,[],[f1544,f2467])).
% 79.42/11.79 thf(f1544,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f644])).
% 79.42/11.79 thf(f644,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)) | ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f643])).
% 79.42/11.79 thf(f643,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1))),
% 79.42/11.79 inference(rectify,[],[f41])).
% 79.42/11.79 thf(f41,axiom,(
% 79.42/11.79 ! [X3 : nat,X4 : nat] : (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X3) | vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X3),X4))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_nat__le__linear)).
% 79.42/11.79 thf(f2465,plain,(
% 79.42/11.79 spl72_73),
% 79.42/11.79 inference(avatar_split_clause,[],[f1368,f2463])).
% 79.42/11.79 thf(f1368,plain,(
% 79.42/11.79 ( ! [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)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f938])).
% 79.42/11.79 thf(f938,plain,(
% 79.42/11.79 ! [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))),
% 79.42/11.79 inference(ennf_transformation,[],[f342])).
% 79.42/11.79 thf(f342,plain,(
% 79.42/11.79 ! [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))))),
% 79.42/11.79 inference(fool_elimination,[],[f341])).
% 79.42/11.79 thf(f341,plain,(
% 79.42/11.79 ! [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)))))),
% 79.42/11.79 inference(rectify,[],[f79])).
% 79.42/11.79 thf(f79,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (ab_semigroup_add(X0) => (plus_plus(X0) = (^[X33 : X0, X34 : X0] : (vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),plus_plus(X0),X34),X33)))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_add_Ocommute)).
% 79.42/11.79 thf(f2451,plain,(
% 79.42/11.79 spl72_72),
% 79.42/11.79 inference(avatar_split_clause,[],[f1695,f2448])).
% 79.42/11.79 thf(f1695,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s),ua) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f868])).
% 79.42/11.79 thf(f868,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s),ua) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f867])).
% 79.42/11.79 thf(f867,plain,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s),ua)),
% 79.42/11.79 inference(rectify,[],[f30])).
% 79.42/11.79 thf(f30,axiom,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),s),ua)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29__092_060open_062connected_As_Au_092_060close_062)).
% 79.42/11.79 thf(f2446,plain,(
% 79.42/11.79 spl72_71 | ~spl72_2 | ~spl72_32),
% 79.42/11.79 inference(avatar_split_clause,[],[f2128,f2064,f1894,f2443])).
% 79.42/11.79 thf(f2128,plain,(
% 79.42/11.79 ($true = group_add(a)) | (~spl72_2 | ~spl72_32)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2123])).
% 79.42/11.79 thf(f2123,plain,(
% 79.42/11.79 ($true != $true) | ($true = group_add(a)) | (~spl72_2 | ~spl72_32)),
% 79.42/11.79 inference(superposition,[],[f2065,f1896])).
% 79.42/11.79 thf(f2441,plain,(
% 79.42/11.79 spl72_70),
% 79.42/11.79 inference(avatar_split_clause,[],[f1535,f2439])).
% 79.42/11.79 thf(f2439,plain,(
% 79.42/11.79 spl72_70 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X0))),
% 79.42/11.79 introduced(avatar_definition,[new_symbols(naming,[spl72_70])])).
% 79.42/11.79 thf(f1535,plain,(
% 79.42/11.79 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f626])).
% 79.42/11.79 thf(f626,plain,(
% 79.42/11.79 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X0))),
% 79.42/11.79 inference(fool_elimination,[],[f625])).
% 79.42/11.79 thf(f625,plain,(
% 79.42/11.79 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X0),X0)),
% 79.42/11.79 inference(rectify,[],[f35])).
% 79.42/11.79 thf(f35,axiom,(
% 79.42/11.79 ! [X12 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,$o)),connected(capacity),c),X12),X12)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_connected__refl)).
% 79.42/11.79 thf(f2437,plain,(
% 79.42/11.79 spl72_69),
% 79.42/11.79 inference(avatar_split_clause,[],[f1534,f2435])).
% 79.42/11.79 thf(f2435,plain,(
% 79.42/11.79 spl72_69 <=> ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X0))),
% 79.42/11.79 introduced(avatar_definition,[new_symbols(naming,[spl72_69])])).
% 79.42/11.79 thf(f1534,plain,(
% 79.42/11.79 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f624])).
% 79.42/11.79 thf(f624,plain,(
% 79.42/11.79 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X0))),
% 79.42/11.79 inference(fool_elimination,[],[f623])).
% 79.42/11.79 thf(f623,plain,(
% 79.42/11.79 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X0),X0)),
% 79.42/11.79 inference(rectify,[],[f184])).
% 79.42/11.79 thf(f184,axiom,(
% 79.42/11.79 ! [X12 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vAPP(sTfun(product_prod(nat,nat),a),sTfun(nat,sTfun(nat,$o)),connected(a),c2),X12),X12)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_183_g_H_Oconnected__refl)).
% 79.42/11.79 thf(f2370,plain,(
% 79.42/11.79 spl72_68),
% 79.42/11.79 inference(avatar_split_clause,[],[f1594,f2368])).
% 79.42/11.79 thf(f1594,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f718])).
% 79.42/11.79 thf(f718,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f717])).
% 79.42/11.79 thf(f717,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1))),
% 79.42/11.79 inference(rectify,[],[f72])).
% 79.42/11.79 thf(f72,axiom,(
% 79.42/11.79 ! [X4 : nat,X3 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X4),X3))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__add1)).
% 79.42/11.79 thf(f2366,plain,(
% 79.42/11.79 spl72_67),
% 79.42/11.79 inference(avatar_split_clause,[],[f1593,f2364])).
% 79.42/11.79 thf(f1593,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f716])).
% 79.42/11.79 thf(f716,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0)))),
% 79.42/11.79 inference(fool_elimination,[],[f715])).
% 79.42/11.79 thf(f715,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X1),X0))),
% 79.42/11.79 inference(rectify,[],[f71])).
% 79.42/11.79 thf(f71,axiom,(
% 79.42/11.79 ! [X4 : nat,X3 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X3),X4))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__add2)).
% 79.42/11.79 thf(f2362,plain,(
% 79.42/11.79 spl72_66 | ~spl72_3 | ~spl72_32),
% 79.42/11.79 inference(avatar_split_clause,[],[f2127,f2064,f1899,f2359])).
% 79.42/11.79 thf(f2127,plain,(
% 79.42/11.79 ($true = group_add(capacity)) | (~spl72_3 | ~spl72_32)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2124])).
% 79.42/11.79 thf(f2124,plain,(
% 79.42/11.79 ($true != $true) | ($true = group_add(capacity)) | (~spl72_3 | ~spl72_32)),
% 79.42/11.79 inference(superposition,[],[f2065,f1901])).
% 79.42/11.79 thf(f2357,plain,(
% 79.42/11.79 spl72_65),
% 79.42/11.79 inference(avatar_split_clause,[],[f1591,f2355])).
% 79.42/11.79 thf(f1591,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f916])).
% 79.42/11.79 thf(f916,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 79.42/11.79 inference(flattening,[],[f712])).
% 79.42/11.79 thf(f712,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0))),
% 79.42/11.79 inference(fool_elimination,[],[f711])).
% 79.42/11.79 thf(f711,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X0)),
% 79.42/11.79 inference(rectify,[],[f115])).
% 79.42/11.79 thf(f115,axiom,(
% 79.42/11.79 ! [X27 : nat,X28 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X27),X28)),X27)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_114_not__add__less1)).
% 79.42/11.79 thf(f2353,plain,(
% 79.42/11.79 spl72_64),
% 79.42/11.79 inference(avatar_split_clause,[],[f1590,f2351])).
% 79.42/11.79 thf(f1590,plain,(
% 79.42/11.79 ( ! [X0 : nat,X1 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f915])).
% 79.42/11.79 thf(f915,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 79.42/11.79 inference(flattening,[],[f710])).
% 79.42/11.79 thf(f710,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1))),
% 79.42/11.79 inference(fool_elimination,[],[f709])).
% 79.42/11.79 thf(f709,plain,(
% 79.42/11.79 ! [X0 : nat,X1 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X0),X1)),X1)),
% 79.42/11.79 inference(rectify,[],[f114])).
% 79.42/11.79 thf(f114,axiom,(
% 79.42/11.79 ! [X28 : nat,X27 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),X28),X27)),X27)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_113_not__add__less2)).
% 79.42/11.79 thf(f2349,plain,(
% 79.42/11.79 spl72_63),
% 79.42/11.79 inference(avatar_split_clause,[],[f1393,f2347])).
% 79.42/11.79 thf(f1393,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK8(X0),X1))) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1239])).
% 79.42/11.79 thf(f2345,plain,(
% 79.42/11.79 spl72_62),
% 79.42/11.79 inference(avatar_split_clause,[],[f1391,f2343])).
% 79.42/11.79 thf(f1391,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ($true != vAPP(X0,$o,X1,X2)) | (wellorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f966])).
% 79.42/11.79 thf(f966,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))) | ! [X2 : X0] : ($true != vAPP(X0,$o,X1,X2))) | (wellorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f388])).
% 79.42/11.79 thf(f388,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((wellorder(X0) = $true) => ! [X1 : X0 > $o] : (? [X2 : X0] : ($true = vAPP(X0,$o,X1,X2)) => ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1)))))),
% 79.42/11.79 inference(fool_elimination,[],[f387])).
% 79.42/11.79 thf(f387,plain,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X1 : X0 > $o] : (? [X2 : X0] : vAPP(X0,$o,X1,X2) => vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X1))))),
% 79.42/11.79 inference(rectify,[],[f249])).
% 79.42/11.79 thf(f249,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (wellorder(X0) => ! [X29 : X0 > $o] : (? [X75 : X0] : vAPP(X0,$o,X29,X75) => vAPP(X0,$o,X29,vAPP(sTfun(X0,$o),X0,ord_Least(X0),X29))))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_248_LeastI__ex)).
% 79.42/11.79 thf(f2335,plain,(
% 79.42/11.79 spl72_61),
% 79.42/11.79 inference(avatar_split_clause,[],[f1358,f2333])).
% 79.42/11.79 thf(f1358,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))) | (no_top(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1235])).
% 79.42/11.79 thf(f1235,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))) | (no_top(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f927,f1234])).
% 79.42/11.79 thf(f1234,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK6(X0),X1))))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f927,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (no_top(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f322])).
% 79.42/11.79 thf(f322,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((no_top(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 79.42/11.79 inference(fool_elimination,[],[f321])).
% 79.42/11.79 thf(f321,plain,(
% 79.42/11.79 ! [X0 : $tType] : (no_top(X0) => ! [X1 : X0] : ? [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))),
% 79.42/11.79 inference(rectify,[],[f241])).
% 79.42/11.79 thf(f241,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (no_top(X0) => ! [X51 : X0] : ? [X74 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X74))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_240_gt__ex)).
% 79.42/11.79 thf(f2331,plain,(
% 79.42/11.79 spl72_60),
% 79.42/11.79 inference(avatar_split_clause,[],[f1355,f2329])).
% 79.42/11.79 thf(f1355,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)) | (no_bot(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1231])).
% 79.42/11.79 thf(f1231,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)) | (no_bot(X0) != $true))),
% 79.42/11.79 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f925,f1230])).
% 79.42/11.79 thf(f1230,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK4(X0),X1)),X1)))),
% 79.42/11.79 introduced(choice_axiom,[])).
% 79.42/11.79 thf(f925,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (no_bot(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f318])).
% 79.42/11.79 thf(f318,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((no_bot(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f317])).
% 79.42/11.79 thf(f317,plain,(
% 79.42/11.79 ! [X0 : $tType] : (no_bot(X0) => ! [X1 : X0] : ? [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))),
% 79.42/11.79 inference(rectify,[],[f242])).
% 79.42/11.79 thf(f242,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (no_bot(X0) => ! [X51 : X0] : ? [X30 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X30),X51))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_241_lt__ex)).
% 79.42/11.79 thf(f2311,plain,(
% 79.42/11.79 spl72_59 | ~spl72_2 | ~spl72_31),
% 79.42/11.79 inference(avatar_split_clause,[],[f2122,f2060,f1894,f2308])).
% 79.42/11.79 thf(f2122,plain,(
% 79.42/11.79 ($true = semigroup_add(a)) | (~spl72_2 | ~spl72_31)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2117])).
% 79.42/11.79 thf(f2117,plain,(
% 79.42/11.79 ($true != $true) | ($true = semigroup_add(a)) | (~spl72_2 | ~spl72_31)),
% 79.42/11.79 inference(superposition,[],[f2061,f1896])).
% 79.42/11.79 thf(f2306,plain,(
% 79.42/11.79 spl72_58),
% 79.42/11.79 inference(avatar_split_clause,[],[f1568,f2304])).
% 79.42/11.79 thf(f1568,plain,(
% 79.42/11.79 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK43,X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1293])).
% 79.42/11.79 thf(f2302,plain,(
% 79.42/11.79 spl72_57),
% 79.42/11.79 inference(avatar_split_clause,[],[f1565,f2300])).
% 79.42/11.79 thf(f1565,plain,(
% 79.42/11.79 ( ! [X0 : nat > $o,X1 : nat] : (($true = vAPP(nat,$o,X0,X1)) | ($true != vAPP(nat,$o,X0,vAPP(sTfun(nat,$o),nat,sK42,X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1291])).
% 79.42/11.79 thf(f2278,plain,(
% 79.42/11.79 spl72_56),
% 79.42/11.79 inference(avatar_split_clause,[],[f1458,f2276])).
% 79.42/11.79 thf(f1458,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1034])).
% 79.42/11.79 thf(f1034,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f482])).
% 79.42/11.79 thf(f482,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f481])).
% 79.42/11.79 thf(f481,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 79.42/11.79 inference(rectify,[],[f207])).
% 79.42/11.79 thf(f207,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X6 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X6),X6))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_206_dual__order_Orefl)).
% 79.42/11.79 thf(f2274,plain,(
% 79.42/11.79 spl72_55),
% 79.42/11.79 inference(avatar_split_clause,[],[f1457,f2272])).
% 79.42/11.79 thf(f1457,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1033])).
% 79.42/11.79 thf(f1033,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f905])).
% 79.42/11.79 thf(f905,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 79.42/11.79 inference(flattening,[],[f480])).
% 79.42/11.79 thf(f480,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f479])).
% 79.42/11.79 thf(f479,plain,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))),
% 79.42/11.79 inference(rectify,[],[f220])).
% 79.42/11.79 thf(f220,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (order(X0) => ! [X6 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X6),X6))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_219_dual__order_Oirrefl)).
% 79.42/11.79 thf(f2270,plain,(
% 79.42/11.79 spl72_54),
% 79.42/11.79 inference(avatar_split_clause,[],[f1439,f2268])).
% 79.42/11.79 thf(f1439,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1008])).
% 79.42/11.79 thf(f1008,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f444])).
% 79.42/11.79 thf(f444,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f443])).
% 79.42/11.79 thf(f443,plain,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 79.42/11.79 inference(rectify,[],[f179])).
% 79.42/11.79 thf(f179,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X51 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X51),X51))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_178_order__refl)).
% 79.42/11.79 thf(f2266,plain,(
% 79.42/11.79 spl72_53),
% 79.42/11.79 inference(avatar_split_clause,[],[f1438,f2264])).
% 79.42/11.79 thf(f1438,plain,(
% 79.42/11.79 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1007])).
% 79.42/11.79 thf(f1007,plain,(
% 79.42/11.79 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f900])).
% 79.42/11.79 thf(f900,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 79.42/11.79 inference(flattening,[],[f442])).
% 79.42/11.79 thf(f442,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f441])).
% 79.42/11.79 thf(f441,plain,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))),
% 79.42/11.79 inference(rectify,[],[f231])).
% 79.42/11.79 thf(f231,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (preorder(X0) => ! [X51 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X51),X51))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_230_less__irrefl)).
% 79.42/11.79 thf(f2262,plain,(
% 79.42/11.79 spl72_52 | ~spl72_3 | ~spl72_31),
% 79.42/11.79 inference(avatar_split_clause,[],[f2121,f2060,f1899,f2259])).
% 79.42/11.79 thf(f2121,plain,(
% 79.42/11.79 ($true = semigroup_add(capacity)) | (~spl72_3 | ~spl72_31)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2118])).
% 79.42/11.79 thf(f2118,plain,(
% 79.42/11.79 ($true != $true) | ($true = semigroup_add(capacity)) | (~spl72_3 | ~spl72_31)),
% 79.42/11.79 inference(superposition,[],[f2061,f1901])).
% 79.42/11.79 thf(f2255,plain,(
% 79.42/11.79 ~spl72_51),
% 79.42/11.79 inference(avatar_split_clause,[],[f1346,f2252])).
% 79.42/11.79 thf(f1346,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) != $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f891])).
% 79.42/11.79 thf(f891,plain,(
% 79.42/11.79 (vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) != $true)),
% 79.42/11.79 inference(flattening,[],[f306])).
% 79.42/11.79 thf(f306,plain,(
% 79.42/11.79 ~(vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a))) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f305])).
% 79.42/11.79 thf(f305,plain,(
% 79.42/11.79 ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))),
% 79.42/11.79 inference(rectify,[],[f302])).
% 79.42/11.79 thf(f302,negated_conjecture,(
% 79.42/11.79 ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))),
% 79.42/11.79 inference(negated_conjecture,[],[f301])).
% 79.42/11.79 thf(f301,conjecture,(
% 79.42/11.79 vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),vAPP(sTfun(product_prod(nat,nat),capacity),sTfun(nat,sTfun(nat,nat)),min_dist(capacity),c),s),t)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),plus_plus(nat),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p1a)),vAPP(list(product_prod(nat,nat)),nat,size_size(list(product_prod(nat,nat))),p2_a)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
% 79.42/11.79 thf(f2248,plain,(
% 79.42/11.79 spl72_50),
% 79.42/11.79 inference(avatar_split_clause,[],[f1533,f2246])).
% 79.42/11.79 thf(f1533,plain,(
% 79.42/11.79 ( ! [X0 : nat] : (($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f622])).
% 79.42/11.79 thf(f622,plain,(
% 79.42/11.79 ! [X0 : nat] : ($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0))),
% 79.42/11.79 inference(fool_elimination,[],[f621])).
% 79.42/11.79 thf(f621,plain,(
% 79.42/11.79 ! [X0 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X0)),
% 79.42/11.79 inference(rectify,[],[f37])).
% 79.42/11.79 thf(f37,axiom,(
% 79.42/11.79 ! [X4 : nat] : vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X4),X4)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_le__refl)).
% 79.42/11.79 thf(f2244,plain,(
% 79.42/11.79 spl72_49),
% 79.42/11.79 inference(avatar_split_clause,[],[f1527,f2242])).
% 79.42/11.79 thf(f1527,plain,(
% 79.42/11.79 ( ! [X0 : nat] : (($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f909])).
% 79.42/11.79 thf(f909,plain,(
% 79.42/11.79 ! [X0 : nat] : ($true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 79.42/11.79 inference(flattening,[],[f610])).
% 79.42/11.79 thf(f610,plain,(
% 79.42/11.79 ! [X0 : nat] : ~($true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0))),
% 79.42/11.79 inference(fool_elimination,[],[f609])).
% 79.42/11.79 thf(f609,plain,(
% 79.42/11.79 ! [X0 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0)),
% 79.42/11.79 inference(rectify,[],[f91])).
% 79.42/11.79 thf(f91,axiom,(
% 79.42/11.79 ! [X4 : nat] : ~vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X4),X4)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_less__irrefl__nat)).
% 79.42/11.79 thf(f2216,plain,(
% 79.42/11.79 spl72_48),
% 79.42/11.79 inference(avatar_split_clause,[],[f1579,f2214])).
% 79.42/11.79 thf(f1579,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | ($true != order(X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1143])).
% 79.42/11.79 thf(f1143,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (($true = order(sTfun(X0,X1))) | ($true != order(X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f688])).
% 79.42/11.79 thf(f688,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (($true = order(X1)) => ($true = order(sTfun(X0,X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f687])).
% 79.42/11.79 thf(f687,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (order(X1) => order(sTfun(X0,X1)))),
% 79.42/11.79 inference(rectify,[],[f272])).
% 79.42/11.79 thf(f272,axiom,(
% 79.42/11.79 ! [X76 : $tType,X77 : $tType] : (order(X77) => order(sTfun(X76,X77)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder)).
% 79.42/11.79 thf(f2212,plain,(
% 79.42/11.79 spl72_47 | ~spl72_2 | ~spl72_30),
% 79.42/11.79 inference(avatar_split_clause,[],[f2116,f2056,f1894,f2209])).
% 79.42/11.79 thf(f2116,plain,(
% 79.42/11.79 ($true = type(a)) | (~spl72_2 | ~spl72_30)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2111])).
% 79.42/11.79 thf(f2111,plain,(
% 79.42/11.79 ($true != $true) | ($true = type(a)) | (~spl72_2 | ~spl72_30)),
% 79.42/11.79 inference(superposition,[],[f2057,f1896])).
% 79.42/11.79 thf(f2207,plain,(
% 79.42/11.79 spl72_46),
% 79.42/11.79 inference(avatar_split_clause,[],[f1578,f2205])).
% 79.42/11.79 thf(f1578,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X0,X1))) | ($true != ord(X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1142])).
% 79.42/11.79 thf(f1142,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (($true = ord(sTfun(X0,X1))) | ($true != ord(X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f686])).
% 79.42/11.79 thf(f686,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (($true = ord(X1)) => ($true = ord(sTfun(X0,X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f685])).
% 79.42/11.79 thf(f685,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (ord(X1) => ord(sTfun(X0,X1)))),
% 79.42/11.79 inference(rectify,[],[f273])).
% 79.42/11.79 thf(f273,axiom,(
% 79.42/11.79 ! [X76 : $tType,X77 : $tType] : (ord(X77) => ord(sTfun(X76,X77)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord)).
% 79.42/11.79 thf(f2203,plain,(
% 79.42/11.79 spl72_45),
% 79.42/11.79 inference(avatar_split_clause,[],[f1573,f2201])).
% 79.42/11.79 thf(f1573,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1137])).
% 79.42/11.79 thf(f1137,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 79.42/11.79 inference(ennf_transformation,[],[f676])).
% 79.42/11.79 thf(f676,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (($true = preorder(X1)) => ($true = preorder(sTfun(X0,X1))))),
% 79.42/11.79 inference(fool_elimination,[],[f675])).
% 79.42/11.79 thf(f675,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : (preorder(X1) => preorder(sTfun(X0,X1)))),
% 79.42/11.79 inference(rectify,[],[f271])).
% 79.42/11.79 thf(f271,axiom,(
% 79.42/11.79 ! [X76 : $tType,X77 : $tType] : (preorder(X77) => preorder(sTfun(X76,X77)))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder)).
% 79.42/11.79 thf(f2151,plain,(
% 79.42/11.79 spl72_44 | ~spl72_3 | ~spl72_30),
% 79.42/11.79 inference(avatar_split_clause,[],[f2115,f2056,f1899,f2148])).
% 79.42/11.79 thf(f2115,plain,(
% 79.42/11.79 ($true = type(capacity)) | (~spl72_3 | ~spl72_30)),
% 79.42/11.79 inference(trivial_inequality_removal,[],[f2112])).
% 79.42/11.79 thf(f2112,plain,(
% 79.42/11.79 ($true != $true) | ($true = type(capacity)) | (~spl72_3 | ~spl72_30)),
% 79.42/11.79 inference(superposition,[],[f2057,f1901])).
% 79.42/11.79 thf(f2110,plain,(
% 79.42/11.79 spl72_43),
% 79.42/11.79 inference(avatar_split_clause,[],[f1526,f2108])).
% 79.42/11.79 thf(f1526,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((order(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1112])).
% 79.42/11.79 thf(f1112,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((order(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f608])).
% 79.42/11.79 thf(f608,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (order(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f607])).
% 79.42/11.79 thf(f607,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => order(X0))),
% 79.42/11.79 inference(rectify,[],[f259])).
% 79.42/11.79 thf(f259,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => order(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Oorder)).
% 79.42/11.79 thf(f2106,plain,(
% 79.42/11.79 spl72_42),
% 79.42/11.79 inference(avatar_split_clause,[],[f1525,f2104])).
% 79.42/11.79 thf(f1525,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((ord(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1111])).
% 79.42/11.79 thf(f1111,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ord(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f606])).
% 79.42/11.79 thf(f606,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (ord(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f605])).
% 79.42/11.79 thf(f605,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ord(X0))),
% 79.42/11.79 inference(rectify,[],[f258])).
% 79.42/11.79 thf(f258,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ord(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Oord)).
% 79.42/11.79 thf(f2102,plain,(
% 79.42/11.79 spl72_41),
% 79.42/11.79 inference(avatar_split_clause,[],[f1524,f2100])).
% 79.42/11.79 thf(f1524,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((preorder(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1110])).
% 79.42/11.79 thf(f1110,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((preorder(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f604])).
% 79.42/11.79 thf(f604,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (preorder(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f603])).
% 79.42/11.79 thf(f603,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => preorder(X0))),
% 79.42/11.79 inference(rectify,[],[f262])).
% 79.42/11.79 thf(f262,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => preorder(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Opreorder)).
% 79.42/11.79 thf(f2098,plain,(
% 79.42/11.79 spl72_40),
% 79.42/11.79 inference(avatar_split_clause,[],[f1523,f2096])).
% 79.42/11.79 thf(f1523,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((linorder(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1109])).
% 79.42/11.79 thf(f1109,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linorder(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f602])).
% 79.42/11.79 thf(f602,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (linorder(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f601])).
% 79.42/11.79 thf(f601,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => linorder(X0))),
% 79.42/11.79 inference(rectify,[],[f261])).
% 79.42/11.79 thf(f261,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => linorder(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Orderings_Olinorder)).
% 79.42/11.79 thf(f2094,plain,(
% 79.42/11.79 spl72_39),
% 79.42/11.79 inference(avatar_split_clause,[],[f1522,f2092])).
% 79.42/11.79 thf(f1522,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1108])).
% 79.42/11.79 thf(f1108,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere223160158up_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f600])).
% 79.42/11.79 thf(f600,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (ordere223160158up_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f599])).
% 79.42/11.79 thf(f599,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ordere223160158up_add(X0))),
% 79.42/11.79 inference(rectify,[],[f269])).
% 79.42/11.79 thf(f269,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ordere223160158up_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__cancel__ab__semigroup__add)).
% 79.42/11.79 thf(f2090,plain,(
% 79.42/11.79 spl72_38),
% 79.42/11.79 inference(avatar_split_clause,[],[f1521,f2088])).
% 79.42/11.79 thf(f1521,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1107])).
% 79.42/11.79 thf(f1107,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere236663937imp_le(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f598])).
% 79.42/11.79 thf(f598,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (ordere236663937imp_le(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f597])).
% 79.42/11.79 thf(f597,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ordere236663937imp_le(X0))),
% 79.42/11.79 inference(rectify,[],[f268])).
% 79.42/11.79 thf(f268,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ordere236663937imp_le(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add__imp__le)).
% 79.42/11.79 thf(f2086,plain,(
% 79.42/11.79 spl72_37),
% 79.42/11.79 inference(avatar_split_clause,[],[f1520,f2084])).
% 79.42/11.79 thf(f1520,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1106])).
% 79.42/11.79 thf(f1106,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ordere779506340up_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f596])).
% 79.42/11.79 thf(f596,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (ordere779506340up_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f595])).
% 79.42/11.79 thf(f595,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ordere779506340up_add(X0))),
% 79.42/11.79 inference(rectify,[],[f267])).
% 79.42/11.79 thf(f267,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ordere779506340up_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oordered__ab__semigroup__add)).
% 79.42/11.79 thf(f2082,plain,(
% 79.42/11.79 spl72_36),
% 79.42/11.79 inference(avatar_split_clause,[],[f1519,f2080])).
% 79.42/11.79 thf(f1519,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1105])).
% 79.42/11.79 thf(f1105,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((cancel_semigroup_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f594])).
% 79.42/11.79 thf(f594,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (cancel_semigroup_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f593])).
% 79.42/11.79 thf(f593,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => cancel_semigroup_add(X0))),
% 79.42/11.79 inference(rectify,[],[f266])).
% 79.42/11.79 thf(f266,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => cancel_semigroup_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ocancel__semigroup__add)).
% 79.42/11.79 thf(f2078,plain,(
% 79.42/11.79 spl72_35),
% 79.42/11.79 inference(avatar_split_clause,[],[f1518,f2076])).
% 79.42/11.79 thf(f1518,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1104])).
% 79.42/11.79 thf(f1104,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((ab_semigroup_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f592])).
% 79.42/11.79 thf(f592,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (ab_semigroup_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f591])).
% 79.42/11.79 thf(f591,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ab_semigroup_add(X0))),
% 79.42/11.79 inference(rectify,[],[f265])).
% 79.42/11.79 thf(f265,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => ab_semigroup_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Oab__semigroup__add)).
% 79.42/11.79 thf(f2074,plain,(
% 79.42/11.79 spl72_34),
% 79.42/11.79 inference(avatar_split_clause,[],[f1517,f2072])).
% 79.42/11.79 thf(f1517,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1103])).
% 79.42/11.79 thf(f1103,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((comm_monoid_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f590])).
% 79.42/11.79 thf(f590,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (comm_monoid_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f589])).
% 79.42/11.79 thf(f589,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => comm_monoid_add(X0))),
% 79.42/11.79 inference(rectify,[],[f264])).
% 79.42/11.79 thf(f264,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => comm_monoid_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ocomm__monoid__add)).
% 79.42/11.79 thf(f2070,plain,(
% 79.42/11.79 spl72_33),
% 79.42/11.79 inference(avatar_split_clause,[],[f1516,f2068])).
% 79.42/11.79 thf(f1516,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1102])).
% 79.42/11.79 thf(f1102,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((strict2144017051up_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f588])).
% 79.42/11.79 thf(f588,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (strict2144017051up_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f587])).
% 79.42/11.79 thf(f587,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => strict2144017051up_add(X0))),
% 79.42/11.79 inference(rectify,[],[f270])).
% 79.42/11.79 thf(f270,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => strict2144017051up_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ostrict__ordered__ab__semigroup__add)).
% 79.42/11.79 thf(f2066,plain,(
% 79.42/11.79 spl72_32),
% 79.42/11.79 inference(avatar_split_clause,[],[f1515,f2064])).
% 79.42/11.79 thf(f1515,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((group_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1101])).
% 79.42/11.79 thf(f1101,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((group_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f586])).
% 79.42/11.79 thf(f586,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (group_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f585])).
% 79.42/11.79 thf(f585,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => group_add(X0))),
% 79.42/11.79 inference(rectify,[],[f260])).
% 79.42/11.79 thf(f260,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => group_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Ogroup__add)).
% 79.42/11.79 thf(f2062,plain,(
% 79.42/11.79 spl72_31),
% 79.42/11.79 inference(avatar_split_clause,[],[f1514,f2060])).
% 79.42/11.79 thf(f1514,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((semigroup_add(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1100])).
% 79.42/11.79 thf(f1100,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((semigroup_add(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f584])).
% 79.42/11.79 thf(f584,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (semigroup_add(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f583])).
% 79.42/11.79 thf(f583,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => semigroup_add(X0))),
% 79.42/11.79 inference(rectify,[],[f263])).
% 79.42/11.79 thf(f263,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => semigroup_add(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___Groups_Osemigroup__add)).
% 79.42/11.79 thf(f2058,plain,(
% 79.42/11.79 spl72_30),
% 79.42/11.79 inference(avatar_split_clause,[],[f1513,f2056])).
% 79.42/11.79 thf(f1513,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : ((type(X0) = $true) | (linordered_idom(X0) != $true)) )),
% 79.42/11.79 inference(cnf_transformation,[],[f1099])).
% 79.42/11.79 thf(f1099,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((type(X0) = $true) | (linordered_idom(X0) != $true))),
% 79.42/11.79 inference(ennf_transformation,[],[f582])).
% 79.42/11.79 thf(f582,plain,(
% 79.42/11.79 ! [X0 : $tType] : ((linordered_idom(X0) = $true) => (type(X0) = $true))),
% 79.42/11.79 inference(fool_elimination,[],[f581])).
% 79.42/11.79 thf(f581,plain,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => type(X0))),
% 79.42/11.79 inference(rectify,[],[f257])).
% 79.42/11.79 thf(f257,axiom,(
% 79.42/11.79 ! [X0 : $tType] : (linordered_idom(X0) => type(X0))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',subcl_Rings_Olinordered__idom___HOL_Otype)).
% 79.42/11.79 thf(f2026,plain,(
% 79.42/11.79 spl72_29),
% 79.42/11.79 inference(avatar_split_clause,[],[f1592,f2024])).
% 79.42/11.79 thf(f1592,plain,(
% 79.42/11.79 ( ! [X1 : $tType,X0 : $tType] : (($true = size(product_prod(X0,X1)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f714])).
% 79.42/11.79 thf(f714,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : ($true = size(product_prod(X0,X1)))),
% 79.42/11.79 inference(fool_elimination,[],[f713])).
% 79.42/11.79 thf(f713,plain,(
% 79.42/11.79 ! [X0 : $tType,X1 : $tType] : size(product_prod(X0,X1))),
% 79.42/11.79 inference(rectify,[],[f298])).
% 79.42/11.79 thf(f298,axiom,(
% 79.42/11.79 ! [X76 : $tType,X77 : $tType] : size(product_prod(X76,X77))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Product__Type_Oprod___Nat_Osize_12)).
% 79.42/11.79 thf(f2022,plain,(
% 79.42/11.79 spl72_28),
% 79.42/11.79 inference(avatar_split_clause,[],[f304,f2020])).
% 79.42/11.79 thf(f304,plain,(
% 79.42/11.79 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 79.42/11.79 introduced(fool_axiom,[])).
% 79.42/11.79 thf(f2018,plain,(
% 79.42/11.79 spl72_27),
% 79.42/11.79 inference(avatar_split_clause,[],[f1532,f2016])).
% 79.42/11.79 thf(f1532,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : (($true = order(set(X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f620])).
% 79.42/11.79 thf(f620,plain,(
% 79.42/11.79 ! [X0 : $tType] : ($true = order(set(X0)))),
% 79.42/11.79 inference(fool_elimination,[],[f619])).
% 79.42/11.79 thf(f619,plain,(
% 79.42/11.79 ! [X0 : $tType] : order(set(X0))),
% 79.42/11.79 inference(rectify,[],[f291])).
% 79.42/11.79 thf(f291,axiom,(
% 79.42/11.79 ! [X76 : $tType] : order(set(X76))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_5)).
% 79.42/11.79 thf(f2014,plain,(
% 79.42/11.79 spl72_26),
% 79.42/11.79 inference(avatar_split_clause,[],[f1531,f2012])).
% 79.42/11.79 thf(f1531,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : (($true = ord(set(X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f618])).
% 79.42/11.79 thf(f618,plain,(
% 79.42/11.79 ! [X0 : $tType] : ($true = ord(set(X0)))),
% 79.42/11.79 inference(fool_elimination,[],[f617])).
% 79.42/11.79 thf(f617,plain,(
% 79.42/11.79 ! [X0 : $tType] : ord(set(X0))),
% 79.42/11.79 inference(rectify,[],[f292])).
% 79.42/11.79 thf(f292,axiom,(
% 79.42/11.79 ! [X76 : $tType] : ord(set(X76))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_6)).
% 79.42/11.79 thf(f2010,plain,(
% 79.42/11.79 spl72_25),
% 79.42/11.79 inference(avatar_split_clause,[],[f1530,f2008])).
% 79.42/11.79 thf(f1530,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : (($true = preorder(set(X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f616])).
% 79.42/11.79 thf(f616,plain,(
% 79.42/11.79 ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 79.42/11.79 inference(fool_elimination,[],[f615])).
% 79.42/11.79 thf(f615,plain,(
% 79.42/11.79 ! [X0 : $tType] : preorder(set(X0))),
% 79.42/11.79 inference(rectify,[],[f290])).
% 79.42/11.79 thf(f290,axiom,(
% 79.42/11.79 ! [X76 : $tType] : preorder(set(X76))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_4)).
% 79.42/11.79 thf(f2006,plain,(
% 79.42/11.79 spl72_24),
% 79.42/11.79 inference(avatar_split_clause,[],[f1529,f2004])).
% 79.42/11.79 thf(f1529,plain,(
% 79.42/11.79 ( ! [X0 : $tType] : (($true = size(list(X0)))) )),
% 79.42/11.79 inference(cnf_transformation,[],[f614])).
% 79.42/11.79 thf(f614,plain,(
% 79.42/11.79 ! [X0 : $tType] : ($true = size(list(X0)))),
% 79.42/11.79 inference(fool_elimination,[],[f613])).
% 79.42/11.79 thf(f613,plain,(
% 79.42/11.79 ! [X0 : $tType] : size(list(X0))),
% 79.42/11.79 inference(rectify,[],[f297])).
% 79.42/11.79 thf(f297,axiom,(
% 79.42/11.79 ! [X76 : $tType] : size(list(X76))),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_List_Olist___Nat_Osize_11)).
% 79.42/11.79 thf(f2002,plain,(
% 79.42/11.79 spl72_23),
% 79.42/11.79 inference(avatar_split_clause,[],[f1694,f1999])).
% 79.42/11.79 thf(f1694,plain,(
% 79.42/11.79 (order(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f866])).
% 79.42/11.79 thf(f866,plain,(
% 79.42/11.79 (order(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f865])).
% 79.42/11.79 thf(f865,plain,(
% 79.42/11.79 order(nat)),
% 79.42/11.79 inference(rectify,[],[f287])).
% 79.42/11.79 thf(f287,axiom,(
% 79.42/11.79 order(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oorder_2)).
% 79.42/11.79 thf(f1997,plain,(
% 79.42/11.79 spl72_22),
% 79.42/11.79 inference(avatar_split_clause,[],[f1693,f1994])).
% 79.42/11.79 thf(f1693,plain,(
% 79.42/11.79 (order($o) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f864])).
% 79.42/11.79 thf(f864,plain,(
% 79.42/11.79 (order($o) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f863])).
% 79.42/11.79 thf(f863,plain,(
% 79.42/11.79 order($o)),
% 79.42/11.79 inference(rectify,[],[f295])).
% 79.42/11.79 thf(f295,axiom,(
% 79.42/11.79 order($o)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_9)).
% 79.42/11.79 thf(f1992,plain,(
% 79.42/11.79 spl72_21),
% 79.42/11.79 inference(avatar_split_clause,[],[f1692,f1989])).
% 79.42/11.79 thf(f1692,plain,(
% 79.42/11.79 (ord(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f862])).
% 79.42/11.79 thf(f862,plain,(
% 79.42/11.79 (ord(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f861])).
% 79.42/11.79 thf(f861,plain,(
% 79.42/11.79 ord(nat)),
% 79.42/11.79 inference(rectify,[],[f288])).
% 79.42/11.79 thf(f288,axiom,(
% 79.42/11.79 ord(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Oord_3)).
% 79.42/11.79 thf(f1987,plain,(
% 79.42/11.79 spl72_20),
% 79.42/11.79 inference(avatar_split_clause,[],[f1691,f1984])).
% 79.42/11.79 thf(f1691,plain,(
% 79.42/11.79 (ord($o) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f860])).
% 79.42/11.79 thf(f860,plain,(
% 79.42/11.79 (ord($o) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f859])).
% 79.42/11.79 thf(f859,plain,(
% 79.42/11.79 ord($o)),
% 79.42/11.79 inference(rectify,[],[f296])).
% 79.42/11.79 thf(f296,axiom,(
% 79.42/11.79 ord($o)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_10)).
% 79.42/11.79 thf(f1982,plain,(
% 79.42/11.79 spl72_19),
% 79.42/11.79 inference(avatar_split_clause,[],[f1690,f1979])).
% 79.42/11.79 thf(f1690,plain,(
% 79.42/11.79 (preorder(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f858])).
% 79.42/11.79 thf(f858,plain,(
% 79.42/11.79 (preorder(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f857])).
% 79.42/11.79 thf(f857,plain,(
% 79.42/11.79 preorder(nat)),
% 79.42/11.79 inference(rectify,[],[f284])).
% 79.42/11.79 thf(f284,axiom,(
% 79.42/11.79 preorder(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Opreorder_1)).
% 79.42/11.79 thf(f1977,plain,(
% 79.42/11.79 spl72_18),
% 79.42/11.79 inference(avatar_split_clause,[],[f1689,f1974])).
% 79.42/11.79 thf(f1689,plain,(
% 79.42/11.79 (preorder($o) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f856])).
% 79.42/11.79 thf(f856,plain,(
% 79.42/11.79 (preorder($o) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f855])).
% 79.42/11.79 thf(f855,plain,(
% 79.42/11.79 preorder($o)),
% 79.42/11.79 inference(rectify,[],[f293])).
% 79.42/11.79 thf(f293,axiom,(
% 79.42/11.79 preorder($o)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_7)).
% 79.42/11.79 thf(f1972,plain,(
% 79.42/11.79 spl72_17),
% 79.42/11.79 inference(avatar_split_clause,[],[f1688,f1969])).
% 79.42/11.79 thf(f1688,plain,(
% 79.42/11.79 (linorder(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f854])).
% 79.42/11.79 thf(f854,plain,(
% 79.42/11.79 (linorder(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f853])).
% 79.42/11.79 thf(f853,plain,(
% 79.42/11.79 linorder(nat)),
% 79.42/11.79 inference(rectify,[],[f285])).
% 79.42/11.79 thf(f285,axiom,(
% 79.42/11.79 linorder(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Olinorder)).
% 79.42/11.79 thf(f1967,plain,(
% 79.42/11.79 spl72_16),
% 79.42/11.79 inference(avatar_split_clause,[],[f1687,f1964])).
% 79.42/11.79 thf(f1687,plain,(
% 79.42/11.79 (linorder($o) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f852])).
% 79.42/11.79 thf(f852,plain,(
% 79.42/11.79 (linorder($o) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f851])).
% 79.42/11.79 thf(f851,plain,(
% 79.42/11.79 linorder($o)),
% 79.42/11.79 inference(rectify,[],[f294])).
% 79.42/11.79 thf(f294,axiom,(
% 79.42/11.79 linorder($o)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_8)).
% 79.42/11.79 thf(f1962,plain,(
% 79.42/11.79 spl72_15),
% 79.42/11.79 inference(avatar_split_clause,[],[f1686,f1959])).
% 79.42/11.79 thf(f1686,plain,(
% 79.42/11.79 (ordere223160158up_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f850])).
% 79.42/11.79 thf(f850,plain,(
% 79.42/11.79 (ordere223160158up_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f849])).
% 79.42/11.79 thf(f849,plain,(
% 79.42/11.79 ordere223160158up_add(nat)),
% 79.42/11.79 inference(rectify,[],[f275])).
% 79.42/11.79 thf(f275,axiom,(
% 79.42/11.79 ordere223160158up_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add)).
% 79.42/11.79 thf(f1957,plain,(
% 79.42/11.79 spl72_14),
% 79.42/11.79 inference(avatar_split_clause,[],[f1685,f1954])).
% 79.42/11.79 thf(f1685,plain,(
% 79.42/11.79 (wellorder(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f848])).
% 79.42/11.79 thf(f848,plain,(
% 79.42/11.79 (wellorder(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f847])).
% 79.42/11.79 thf(f847,plain,(
% 79.42/11.79 wellorder(nat)),
% 79.42/11.79 inference(rectify,[],[f283])).
% 79.42/11.79 thf(f283,axiom,(
% 79.42/11.79 wellorder(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Owellorder)).
% 79.42/11.79 thf(f1952,plain,(
% 79.42/11.79 spl72_13),
% 79.42/11.79 inference(avatar_split_clause,[],[f1684,f1949])).
% 79.42/11.79 thf(f1684,plain,(
% 79.42/11.79 (ordere236663937imp_le(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f846])).
% 79.42/11.79 thf(f846,plain,(
% 79.42/11.79 (ordere236663937imp_le(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f845])).
% 79.42/11.79 thf(f845,plain,(
% 79.42/11.79 ordere236663937imp_le(nat)),
% 79.42/11.79 inference(rectify,[],[f276])).
% 79.42/11.79 thf(f276,axiom,(
% 79.42/11.79 ordere236663937imp_le(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le)).
% 79.42/11.79 thf(f1947,plain,(
% 79.42/11.79 spl72_12),
% 79.42/11.79 inference(avatar_split_clause,[],[f1683,f1944])).
% 79.42/11.79 thf(f1683,plain,(
% 79.42/11.79 (ordere779506340up_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f844])).
% 79.42/11.79 thf(f844,plain,(
% 79.42/11.79 (ordere779506340up_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f843])).
% 79.42/11.79 thf(f843,plain,(
% 79.42/11.79 ordere779506340up_add(nat)),
% 79.42/11.79 inference(rectify,[],[f278])).
% 79.42/11.79 thf(f278,axiom,(
% 79.42/11.79 ordere779506340up_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add)).
% 79.42/11.79 thf(f1942,plain,(
% 79.42/11.79 spl72_11),
% 79.42/11.79 inference(avatar_split_clause,[],[f1682,f1939])).
% 79.42/11.79 thf(f1682,plain,(
% 79.42/11.79 (cancel_semigroup_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f842])).
% 79.42/11.79 thf(f842,plain,(
% 79.42/11.79 (cancel_semigroup_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f841])).
% 79.42/11.79 thf(f841,plain,(
% 79.42/11.79 cancel_semigroup_add(nat)),
% 79.42/11.79 inference(rectify,[],[f279])).
% 79.42/11.79 thf(f279,axiom,(
% 79.42/11.79 cancel_semigroup_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocancel__semigroup__add)).
% 79.42/11.79 thf(f1937,plain,(
% 79.42/11.79 spl72_10),
% 79.42/11.79 inference(avatar_split_clause,[],[f1681,f1934])).
% 79.42/11.79 thf(f1681,plain,(
% 79.42/11.79 (ab_semigroup_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f840])).
% 79.42/11.79 thf(f840,plain,(
% 79.42/11.79 (ab_semigroup_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f839])).
% 79.42/11.79 thf(f839,plain,(
% 79.42/11.79 ab_semigroup_add(nat)),
% 79.42/11.79 inference(rectify,[],[f280])).
% 79.42/11.79 thf(f280,axiom,(
% 79.42/11.79 ab_semigroup_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Oab__semigroup__add)).
% 79.42/11.79 thf(f1932,plain,(
% 79.42/11.79 spl72_9),
% 79.42/11.79 inference(avatar_split_clause,[],[f1680,f1929])).
% 79.42/11.79 thf(f1680,plain,(
% 79.42/11.79 (size(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f838])).
% 79.42/11.79 thf(f838,plain,(
% 79.42/11.79 (size(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f837])).
% 79.42/11.79 thf(f837,plain,(
% 79.42/11.79 size(nat)),
% 79.42/11.79 inference(rectify,[],[f289])).
% 79.42/11.79 thf(f289,axiom,(
% 79.42/11.79 size(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Nat_Osize)).
% 79.42/11.79 thf(f1927,plain,(
% 79.42/11.79 spl72_8),
% 79.42/11.79 inference(avatar_split_clause,[],[f1679,f1924])).
% 79.42/11.79 thf(f1679,plain,(
% 79.42/11.79 (comm_monoid_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f836])).
% 79.42/11.79 thf(f836,plain,(
% 79.42/11.79 (comm_monoid_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f835])).
% 79.42/11.79 thf(f835,plain,(
% 79.42/11.79 comm_monoid_add(nat)),
% 79.42/11.79 inference(rectify,[],[f281])).
% 79.42/11.79 thf(f281,axiom,(
% 79.42/11.79 comm_monoid_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocomm__monoid__add)).
% 79.42/11.79 thf(f1922,plain,(
% 79.42/11.79 spl72_7),
% 79.42/11.79 inference(avatar_split_clause,[],[f1678,f1919])).
% 79.42/11.79 thf(f1678,plain,(
% 79.42/11.79 (canoni770627133id_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f834])).
% 79.42/11.79 thf(f834,plain,(
% 79.42/11.79 (canoni770627133id_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f833])).
% 79.42/11.79 thf(f833,plain,(
% 79.42/11.79 canoni770627133id_add(nat)),
% 79.42/11.79 inference(rectify,[],[f277])).
% 79.42/11.79 thf(f277,axiom,(
% 79.42/11.79 canoni770627133id_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ocanonically__ordered__monoid__add)).
% 79.42/11.79 thf(f1917,plain,(
% 79.42/11.79 spl72_6),
% 79.42/11.79 inference(avatar_split_clause,[],[f1677,f1914])).
% 79.42/11.79 thf(f1677,plain,(
% 79.42/11.79 (semigroup_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f832])).
% 79.42/11.79 thf(f832,plain,(
% 79.42/11.79 (semigroup_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f831])).
% 79.42/11.79 thf(f831,plain,(
% 79.42/11.79 semigroup_add(nat)),
% 79.42/11.79 inference(rectify,[],[f282])).
% 79.42/11.79 thf(f282,axiom,(
% 79.42/11.79 semigroup_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Osemigroup__add)).
% 79.42/11.79 thf(f1912,plain,(
% 79.42/11.79 spl72_5),
% 79.42/11.79 inference(avatar_split_clause,[],[f1676,f1909])).
% 79.42/11.79 thf(f1676,plain,(
% 79.42/11.79 (strict2144017051up_add(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f830])).
% 79.42/11.79 thf(f830,plain,(
% 79.42/11.79 (strict2144017051up_add(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f829])).
% 79.42/11.79 thf(f829,plain,(
% 79.42/11.79 strict2144017051up_add(nat)),
% 79.42/11.79 inference(rectify,[],[f274])).
% 79.42/11.79 thf(f274,axiom,(
% 79.42/11.79 strict2144017051up_add(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Groups_Ostrict__ordered__ab__semigroup__add)).
% 79.42/11.79 thf(f1907,plain,(
% 79.42/11.79 spl72_4),
% 79.42/11.79 inference(avatar_split_clause,[],[f1675,f1904])).
% 79.42/11.79 thf(f1675,plain,(
% 79.42/11.79 (no_top(nat) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f828])).
% 79.42/11.79 thf(f828,plain,(
% 79.42/11.79 (no_top(nat) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f827])).
% 79.42/11.79 thf(f827,plain,(
% 79.42/11.79 no_top(nat)),
% 79.42/11.79 inference(rectify,[],[f286])).
% 79.42/11.79 thf(f286,axiom,(
% 79.42/11.79 no_top(nat)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tcon_Nat_Onat___Orderings_Ono__top)).
% 79.42/11.79 thf(f1902,plain,(
% 79.42/11.79 spl72_3),
% 79.42/11.79 inference(avatar_split_clause,[],[f1348,f1899])).
% 79.42/11.79 thf(f1348,plain,(
% 79.42/11.79 (linordered_idom(capacity) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f310])).
% 79.42/11.79 thf(f310,plain,(
% 79.42/11.79 (linordered_idom(capacity) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f309])).
% 79.42/11.79 thf(f309,plain,(
% 79.42/11.79 linordered_idom(capacity)),
% 79.42/11.79 inference(rectify,[],[f299])).
% 79.42/11.79 thf(f299,axiom,(
% 79.42/11.79 linordered_idom(capacity)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_0)).
% 79.42/11.79 thf(f1897,plain,(
% 79.42/11.79 spl72_2),
% 79.42/11.79 inference(avatar_split_clause,[],[f1347,f1894])).
% 79.42/11.79 thf(f1347,plain,(
% 79.42/11.79 (linordered_idom(a) = $true)),
% 79.42/11.79 inference(cnf_transformation,[],[f308])).
% 79.42/11.79 thf(f308,plain,(
% 79.42/11.79 (linordered_idom(a) = $true)),
% 79.42/11.79 inference(fool_elimination,[],[f307])).
% 79.42/11.79 thf(f307,plain,(
% 79.42/11.79 linordered_idom(a)),
% 79.42/11.79 inference(rectify,[],[f300])).
% 79.42/11.79 thf(f300,axiom,(
% 79.42/11.79 linordered_idom(a)),
% 79.42/11.79 file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_1)).
% 79.42/11.79 thf(f1892,plain,(
% 79.42/11.79 ~spl72_1),
% 79.42/11.79 inference(avatar_split_clause,[],[f303,f1889])).
% 79.42/11.79 thf(f303,plain,(
% 79.42/11.79 ($true != $false)),
% 79.42/11.79 introduced(fool_axiom,[])).
% 79.42/11.79 % SZS output end Proof for theBenchmark
% 79.42/11.79 % (8919)------------------------------
% 79.42/11.79 % (8919)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 79.42/11.79 % (8919)Termination reason: Refutation
% 79.42/11.79
% 79.42/11.79 % (8919)Memory used [KB]: 34948
% 79.42/11.79 % (8919)Time elapsed: 11.312 s
% 79.42/11.79 % (8919)Instructions burned: 18168 (million)
% 79.42/11.79 % (8914)Success in time 11.401 s
%------------------------------------------------------------------------------