TSTP Solution File: ITP033^2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ITP033^2 : 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 : n004.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 22:48:28 EDT 2024
% Result : Theorem 2.36s 0.77s
% Output : Refutation 2.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : ITP033^2 : TPTP v8.2.0. Released v7.5.0.
% 0.15/0.16 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.16/0.38 % Computer : n004.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Sat May 18 16:47:08 EDT 2024
% 0.16/0.38 % CPUTime :
% 0.16/0.39 % (4171)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.42 % (4174)WARNING: value z3 for option sas not known
% 0.16/0.43 % (4174)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)
% 0.16/0.43 % (4172)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.43 % (4177)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)
% 0.16/0.43 % (4175)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.43 % (4176)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)
% 0.16/0.43 % (4178)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)
% 0.16/0.43 % (4173)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.23/0.47 % (4178)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.23/0.48 % Exception at run slice level
% 0.23/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.48 % Exception at run slice level
% 0.23/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.48 % Exception at run slice level
% 0.23/0.48 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.23/0.50 % (4179)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.23/0.50 % (4180)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)
% 0.23/0.50 % (4181)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)
% 1.09/0.55 % (4179)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.09/0.55 % (4180)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 1.09/0.56 % Exception at run slice level
% 1.09/0.56 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 1.29/0.58 % (4182)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)
% 2.21/0.73 % (4176)First to succeed.
% 2.36/0.76 % (4176)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4171"
% 2.36/0.77 % (4176)Refutation found. Thanks to Tanya!
% 2.36/0.77 % SZS status Theorem for theBenchmark
% 2.36/0.77 % SZS output start Proof for theBenchmark
% 2.36/0.77 thf(type_def_5, type, product_prod: ($tType * $tType) > $tType).
% 2.36/0.77 thf(type_def_6, type, set: $tType > $tType).
% 2.36/0.77 thf(type_def_7, type, sTfun: ($tType * $tType) > $tType).
% 2.36/0.77 thf(type_def_8, type, binary1291135688e_Tree: $tType > $tType).
% 2.36/0.77 thf(type_def_9, type, int: $tType).
% 2.36/0.77 thf(type_def_10, type, a: $tType).
% 2.36/0.77 thf(func_def_0, type, binary1291135688e_Tree: $tType > $tType).
% 2.36/0.77 thf(func_def_1, type, product_prod: ($tType * $tType) > $tType).
% 2.36/0.77 thf(func_def_2, type, set: $tType > $tType).
% 2.36/0.77 thf(func_def_3, type, int: $tType).
% 2.36/0.77 thf(func_def_4, type, a: $tType).
% 2.36/0.77 thf(func_def_5, type, type: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_6, type, bot: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_7, type, ord: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_8, type, order: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_9, type, no_bot: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_10, type, no_top: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_11, type, linorder: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_12, type, preorder: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_13, type, order_bot: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_14, type, wellorder: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_15, type, dense_order: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_16, type, dense_linorder: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_17, type, condit1656338222tinuum: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_18, type, condit1037483654norder: !>[X0: $tType]:($o)).
% 2.36/0.77 thf(func_def_19, type, bNF_Ca1785829860lChain: !>[X0: $tType, X1: $tType]:(set(product_prod(X0,X0)) > (X0 > X1) > $o)).
% 2.36/0.77 thf(func_def_20, type, binary210054475elle_T: !>[X0: $tType]:(binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_21, type, binary1746293266le_Tip: !>[X0: $tType]:(binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_22, type, binary536355927e_Tree: !>[X0: $tType, X1: $tType]:(X0 > (binary1291135688e_Tree(X1) > X1 > binary1291135688e_Tree(X1) > X0) > binary1291135688e_Tree(X1) > X0)).
% 2.36/0.77 thf(func_def_23, type, binary1929596613c_Tree: !>[X0: $tType, X1: $tType]:(X0 > (binary1291135688e_Tree(X1) > X1 > binary1291135688e_Tree(X1) > X0 > X0 > X0) > binary1291135688e_Tree(X1) > X0)).
% 2.36/0.77 thf(func_def_24, type, binary1830089824insert: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree(X0) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_25, type, binary827270440e_memb: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree(X0) > $o)).
% 2.36/0.77 thf(func_def_26, type, binary997842527remove: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree(X0) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_27, type, binary576689334lle_rm: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree(X0) > X0)).
% 2.36/0.77 thf(func_def_28, type, binary1653327646_setOf: !>[X0: $tType]:(binary1291135688e_Tree(X0) > set(X0))).
% 2.36/0.77 thf(func_def_29, type, binary1610619414edTree: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree(X0) > $o)).
% 2.36/0.77 thf(func_def_30, type, binary231205461t_pred: !>[X0: $tType]:((X0 > int) > X0 > X0 > binary1291135688e_Tree(X0) > $o)).
% 2.36/0.77 thf(func_def_31, type, binary213313527le_wrm: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree(X0) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_32, type, binary1271298290_wrmrm: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree(X0) > product_prod(binary1291135688e_Tree(X0),X0))).
% 2.36/0.77 thf(func_def_33, type, bot_bot: !>[X0: $tType]:(X0)).
% 2.36/0.77 thf(func_def_34, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_35, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_36, type, ordering_top: !>[X0: $tType]:((X0 > X0 > $o) > (X0 > X0 > $o) > X0 > $o)).
% 2.36/0.77 thf(func_def_37, type, product_Pair: !>[X0: $tType, X1: $tType]:(X0 > X1 > product_prod(X0,X1))).
% 2.36/0.77 thf(func_def_38, type, product_case_prod: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > product_prod(X0,X1) > X2)).
% 2.36/0.77 thf(func_def_39, type, inv_image: !>[X0: $tType, X1: $tType]:(set(product_prod(X0,X0)) > (X1 > X0) > set(product_prod(X1,X1)))).
% 2.36/0.77 thf(func_def_40, type, collect: !>[X0: $tType]:((X0 > $o) > set(X0))).
% 2.36/0.77 thf(func_def_41, type, is_empty: !>[X0: $tType]:(set(X0) > $o)).
% 2.36/0.77 thf(func_def_42, type, member: !>[X0: $tType]:(X0 > set(X0) > $o)).
% 2.36/0.77 thf(func_def_43, type, h: a > int).
% 2.36/0.77 thf(func_def_44, type, t1: binary1291135688e_Tree(a)).
% 2.36/0.77 thf(func_def_45, type, t2: binary1291135688e_Tree(a)).
% 2.36/0.77 thf(func_def_46, type, x: a).
% 2.36/0.77 thf(func_def_50, type, vEQ: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_51, type, vAND: $o > $o > $o).
% 2.36/0.77 thf(func_def_52, type, bCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X1 > X2) > (X0 > X1) > X0 > X2)).
% 2.36/0.77 thf(func_def_53, type, cCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > X1 > X0 > X2)).
% 2.36/0.77 thf(func_def_54, type, sCOMB: !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > (X0 > X1) > X0 > X2)).
% 2.36/0.77 thf(func_def_55, type, vIMP: $o > $o > $o).
% 2.36/0.77 thf(func_def_56, type, iCOMB: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_57, type, kCOMB: !>[X0: $tType, X1: $tType]:(X0 > X1 > X0)).
% 2.36/0.77 thf(func_def_58, type, vNOT: $o > $o).
% 2.36/0.77 thf(func_def_59, type, vOR: $o > $o > $o).
% 2.36/0.77 thf(func_def_60, type, vPI: !>[X0: $tType]:((X0 > $o) > $o)).
% 2.36/0.77 thf(func_def_61, type, vSIGMA: !>[X0: $tType]:((X0 > $o) > $o)).
% 2.36/0.77 thf(func_def_62, type, sP0: !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 2.36/0.77 thf(func_def_63, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_64, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_65, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_66, type, sP4: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.36/0.77 thf(func_def_67, type, sK5: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_68, type, sK6: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.36/0.77 thf(func_def_69, type, sK7: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_70, type, sK8: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_71, type, sK9: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_72, type, sK10: !>[X0: $tType]:(X0 > X0 > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_73, type, sK11: !>[X0: $tType]:((X0 > $o) > X0 > X0 > X0)).
% 2.36/0.77 thf(func_def_74, type, sK12: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.36/0.77 thf(func_def_75, type, sK13: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.36/0.77 thf(func_def_76, type, sK14: !>[X0: $tType]:(X0 > X0 > X0 > X0)).
% 2.36/0.77 thf(func_def_77, type, sK15: !>[X0: $tType]:(X0 > X0 > X0 > X0)).
% 2.36/0.77 thf(func_def_78, type, sK16: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_79, type, sK17: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_80, type, sK18: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_81, type, sK19: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_82, type, sK20: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_83, type, sK21: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_84, type, sK22: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_85, type, sK23: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_86, type, sK24: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_87, type, sK25: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_88, type, sK26: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_89, type, sK27: !>[X0: $tType]:(X0 > X0)).
% 2.36/0.77 thf(func_def_90, type, sK28: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_91, type, sK29: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_92, type, sK30: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_93, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_94, type, sK32: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_95, type, sK33: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_96, type, sK34: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_97, type, sK35: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_98, type, sK36: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_99, type, sK37: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_100, type, sK38: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_101, type, sK39: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_102, type, sK40: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_103, type, sK41: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_104, type, sK42: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_105, type, sK43: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_106, type, sK44: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_107, type, sK45: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_108, type, sK46: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_109, type, sK47: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_110, type, sK48: !>[X0: $tType]:(X0 > (X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_111, type, sK49: !>[X0: $tType]:(binary1291135688e_Tree(X0) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_112, type, sK50: !>[X0: $tType]:(binary1291135688e_Tree(X0) > X0)).
% 2.36/0.77 thf(func_def_113, type, sK51: !>[X0: $tType]:(binary1291135688e_Tree(X0) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_114, type, sK52: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_115, type, sK53: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_116, type, sK54: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_117, type, sK55: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_118, type, sK56: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_119, type, sK57: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_120, type, sK58: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_121, type, sK59: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_122, type, sK60: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_123, type, sK61: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_124, type, sK62: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_125, type, sK63: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_126, type, sK64: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_127, type, sK65: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_128, type, sK66: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_129, type, sK67: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.36/0.77 thf(func_def_130, type, sK68: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_131, type, sK69: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_132, type, sK70: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_133, type, sK71: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_134, type, sK72: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_135, type, sK73: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_136, type, sK74: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_137, type, sK75: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_138, type, sK76: !>[X0: $tType]:(set(X0) > X0)).
% 2.36/0.77 thf(func_def_139, type, sK77: !>[X0: $tType]:(set(X0) > X0)).
% 2.36/0.77 thf(func_def_140, type, sK78: !>[X0: $tType, X1: $tType]:(X1 > X0)).
% 2.36/0.77 thf(func_def_141, type, sK79: !>[X0: $tType, X1: $tType]:(X1 > X0)).
% 2.36/0.77 thf(func_def_142, type, sK80: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_143, type, sK81: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_144, type, sK82: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_145, type, sK83: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_146, type, sK84: !>[X0: $tType]:(set(X0) > set(X0) > X0)).
% 2.36/0.77 thf(func_def_147, type, sK85: !>[X0: $tType]:((binary1291135688e_Tree(X0) > $o) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_148, type, sK86: !>[X0: $tType]:((binary1291135688e_Tree(X0) > $o) > X0)).
% 2.36/0.77 thf(func_def_149, type, sK87: !>[X0: $tType]:((binary1291135688e_Tree(X0) > $o) > binary1291135688e_Tree(X0))).
% 2.36/0.77 thf(func_def_150, type, sK88: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_151, type, sK89: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod(X1,X0) > X1)).
% 2.36/0.77 thf(func_def_152, type, sK90: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > product_prod(X1,X0) > X0)).
% 2.36/0.77 thf(func_def_153, type, sK91: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X1)).
% 2.36/0.77 thf(func_def_154, type, sK92: !>[X0: $tType, X1: $tType]:((X1 > X0 > $o) > (X1 > X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_155, type, sK93: !>[X0: $tType, X1: $tType]:(set(product_prod(X1,X0)) > set(product_prod(X1,X0)) > X1)).
% 2.36/0.77 thf(func_def_156, type, sK94: !>[X0: $tType, X1: $tType]:(set(product_prod(X1,X0)) > set(product_prod(X1,X0)) > X0)).
% 2.36/0.77 thf(func_def_157, type, sK95: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > (X0 > X1 > $o) > X0)).
% 2.36/0.77 thf(func_def_158, type, sK96: !>[X0: $tType, X1: $tType]:(product_prod(X0,X1) > (X0 > X1 > $o) > X1)).
% 2.36/0.77 thf(func_def_159, type, sK97: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,X1) > X0) > (X2 > X1 > X0) > X2)).
% 2.36/0.77 thf(func_def_160, type, sK98: !>[X0: $tType, X1: $tType, X2: $tType]:((product_prod(X2,X1) > X0) > (X2 > X1 > X0) > X1)).
% 2.36/0.77 thf(func_def_161, type, sK99: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > set(X0) > X0)).
% 2.36/0.77 thf(func_def_162, type, sK100: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod(X0,X1) > X0)).
% 2.36/0.77 thf(func_def_163, type, sK101: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > (X0 > X1 > X2 > $o) > product_prod(X0,X1) > X1)).
% 2.36/0.77 thf(func_def_164, type, sK102: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > set(X0)) > X0 > product_prod(X2,X1) > X2)).
% 2.36/0.77 thf(func_def_165, type, sK103: !>[X0: $tType, X1: $tType, X2: $tType]:((X2 > X1 > set(X0)) > X0 > product_prod(X2,X1) > X1)).
% 2.36/0.77 thf(func_def_166, type, sK104: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,X2) > (X0 > X2 > X1) > (X1 > $o) > X0)).
% 2.36/0.77 thf(func_def_167, type, sK105: !>[X0: $tType, X1: $tType, X2: $tType]:(product_prod(X0,X2) > (X0 > X2 > X1) > (X1 > $o) > X2)).
% 2.36/0.77 thf(func_def_168, type, sK106: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod(X1,X0) > (X1 > X0 > X2 > $o) > X1)).
% 2.36/0.77 thf(func_def_169, type, sK107: !>[X0: $tType, X1: $tType, X2: $tType]:(X2 > product_prod(X1,X0) > (X1 > X0 > X2 > $o) > X0)).
% 2.36/0.77 thf(func_def_171, type, sK109: !>[X0: $tType]:((X0 > int) > X0 > binary1291135688e_Tree(X0) > X0)).
% 2.36/0.77 thf(func_def_172, type, sK110: !>[X0: $tType]:((X0 > int) > binary1291135688e_Tree(X0) > X0 > X0)).
% 2.36/0.77 thf(func_def_173, type, sK111: !>[X0: $tType]:(set(X0) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_174, type, sK112: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_175, type, sK113: !>[X0: $tType]:(set(X0) > X0)).
% 2.36/0.77 thf(func_def_176, type, sK114: !>[X0: $tType]:(set(X0) > X0)).
% 2.36/0.77 thf(func_def_177, type, sK115: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.36/0.77 thf(func_def_178, type, sK116: !>[X0: $tType]:((X0 > $o) > X0)).
% 2.36/0.77 thf(f3834,plain,(
% 2.36/0.77 $false),
% 2.36/0.77 inference(avatar_sat_refutation,[],[f2204,f2209,f2214,f2219,f2224,f2229,f2234,f2239,f2244,f2249,f2254,f2259,f2264,f2269,f2274,f2279,f2283,f2287,f2291,f2295,f2299,f2303,f2337,f2342,f2346,f2350,f2354,f2358,f2398,f2405,f2409,f2413,f2417,f2421,f2425,f2429,f2435,f2459,f2463,f2467,f2482,f2486,f2490,f2496,f2506,f2510,f2514,f2518,f2522,f2526,f2530,f2534,f2538,f2562,f2581,f2613,f2619,f2623,f2627,f2631,f2635,f2639,f2643,f2647,f2665,f2675,f2679,f2683,f2711,f2715,f2719,f2723,f2746,f2750,f2754,f2758,f2762,f2766,f2770,f2774,f2778,f2782,f2786,f2790,f2794,f2798,f2832,f2840,f2844,f2848,f2852,f2856,f2860,f2864,f2912,f2923,f2930,f2938,f2952,f2956,f2965,f2969,f2973,f2979,f2983,f2987,f2991,f3017,f3021,f3026,f3030,f3034,f3038,f3042,f3050,f3054,f3058,f3062,f3066,f3070,f3295,f3299,f3307,f3315,f3319,f3323,f3327,f3349,f3353,f3357,f3361,f3365,f3387,f3394,f3398,f3425,f3429,f3480,f3484,f3488,f3492,f3500,f3525,f3532,f3545,f3553,f3557,f3561,f3794,f3802,f3816,f3820,f3833])).
% 2.36/0.77 thf(f3833,plain,(
% 2.36/0.77 ~spl108_24 | ~spl108_108 | ~spl108_152),
% 2.36/0.77 inference(avatar_contradiction_clause,[],[f3832])).
% 2.36/0.77 thf(f3832,plain,(
% 2.36/0.77 $false | (~spl108_24 | ~spl108_108 | ~spl108_152)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f3831])).
% 2.36/0.77 thf(f3831,plain,(
% 2.36/0.77 ($true = $false) | (~spl108_24 | ~spl108_108 | ~spl108_152)),
% 2.36/0.77 inference(forward_demodulation,[],[f3830,f2341])).
% 2.36/0.77 thf(f2341,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $false) | ~spl108_24),
% 2.36/0.77 inference(avatar_component_clause,[],[f2339])).
% 2.36/0.77 thf(f2339,plain,(
% 2.36/0.77 spl108_24 <=> (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $false)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_24])])).
% 2.36/0.77 thf(f3830,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $true) | (~spl108_108 | ~spl108_152)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f3827])).
% 2.36/0.77 thf(f3827,plain,(
% 2.36/0.77 ($true != $true) | (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $true) | (~spl108_108 | ~spl108_152)),
% 2.36/0.77 inference(superposition,[],[f3815,f3016])).
% 2.36/0.77 thf(f3016,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),vAPP(binary1291135688e_Tree(a),sTfun(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a))),binary210054475elle_T(a),t1),x),t2)) = $true) | ~spl108_108),
% 2.36/0.77 inference(avatar_component_clause,[],[f3014])).
% 2.36/0.77 thf(f3014,plain,(
% 2.36/0.77 spl108_108 <=> (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),vAPP(binary1291135688e_Tree(a),sTfun(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a))),binary210054475elle_T(a),t1),x),t2)) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_108])])).
% 2.36/0.77 thf(f3815,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree(X0)] : (($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))) | ($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X2))) ) | ~spl108_152),
% 2.36/0.77 inference(avatar_component_clause,[],[f3814])).
% 2.36/0.77 thf(f3814,plain,(
% 2.36/0.77 spl108_152 <=> ! [X0 : $tType,X4 : binary1291135688e_Tree(X0),X3 : X0,X2 : binary1291135688e_Tree(X0),X1 : X0 > int] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X2)) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_152])])).
% 2.36/0.77 thf(f3820,plain,(
% 2.36/0.77 spl108_153),
% 2.36/0.77 inference(avatar_split_clause,[],[f1608,f3818])).
% 2.36/0.77 thf(f3818,plain,(
% 2.36/0.77 spl108_153 <=> ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X4 : binary1291135688e_Tree(X0),X3 : X0,X1 : X0 > int] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X4)) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_153])])).
% 2.36/0.77 thf(f1608,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X4)) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1114])).
% 2.36/0.77 thf(f1114,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X4)) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))))),
% 2.36/0.77 inference(ennf_transformation,[],[f741])).
% 2.36/0.77 thf(f741,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))) => ($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X4)))),
% 2.36/0.77 inference(fool_elimination,[],[f740])).
% 2.36/0.77 thf(f740,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4)) => vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X4))),
% 2.36/0.77 inference(rectify,[],[f5])).
% 2.36/0.77 thf(f5,axiom,(
% 2.36/0.77 ! [X0 : $tType,X3 : X0 > int,X4 : binary1291135688e_Tree(X0),X5 : X0,X6 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X3),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),X6)) => vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X3),X6))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_sortLemmaR)).
% 2.36/0.77 thf(f3816,plain,(
% 2.36/0.77 spl108_152),
% 2.36/0.77 inference(avatar_split_clause,[],[f1607,f3814])).
% 2.36/0.77 thf(f1607,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X3 : X0,X1 : X0 > int,X4 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X2)) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1113])).
% 2.36/0.77 thf(f1113,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X2)) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))))),
% 2.36/0.77 inference(ennf_transformation,[],[f739])).
% 2.36/0.77 thf(f739,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4))) => ($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X2)))),
% 2.36/0.77 inference(fool_elimination,[],[f738])).
% 2.36/0.77 thf(f738,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4)) => vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),X2))),
% 2.36/0.77 inference(rectify,[],[f4])).
% 2.36/0.77 thf(f4,axiom,(
% 2.36/0.77 ! [X0 : $tType,X3 : X0 > int,X4 : binary1291135688e_Tree(X0),X5 : X0,X6 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X3),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),X6)) => vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X3),X4))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_sortLemmaL)).
% 2.36/0.77 thf(f3802,plain,(
% 2.36/0.77 spl108_151),
% 2.36/0.77 inference(avatar_split_clause,[],[f1539,f3800])).
% 2.36/0.77 thf(f3800,plain,(
% 2.36/0.77 spl108_151 <=> ! [X0 : $tType,X2 : X0 > int,X1 : binary1291135688e_Tree(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X2),X1)) | (binary1746293266le_Tip(X0) = X1))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_151])])).
% 2.36/0.77 thf(f1539,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > int,X1 : binary1291135688e_Tree(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X2),X1)) | (binary1746293266le_Tip(X0) = X1)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1056])).
% 2.36/0.77 thf(f1056,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X2),X1)) | (binary1746293266le_Tip(X0) = X1))),
% 2.36/0.77 inference(flattening,[],[f1055])).
% 2.36/0.77 thf(f1055,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X1))) | (($true != vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X2),X1)) | (binary1746293266le_Tip(X0) = X1)))),
% 2.36/0.77 inference(ennf_transformation,[],[f647])).
% 2.36/0.77 thf(f647,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int] : ((($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X2),X1)) & (binary1746293266le_Tip(X0) != X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f646])).
% 2.36/0.77 thf(f646,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int] : ((vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X2),X1) & (binary1746293266le_Tip(X0) != X1)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X1)))),
% 2.36/0.77 inference(rectify,[],[f20])).
% 2.36/0.77 thf(f20,axiom,(
% 2.36/0.77 ! [X0 : $tType,X13 : binary1291135688e_Tree(X0),X3 : X0 > int] : ((vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X3),X13) & (binary1746293266le_Tip(X0) != X13)) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X3),X13)),vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),X13)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_rm__set)).
% 2.36/0.77 thf(f3794,plain,(
% 2.36/0.77 spl108_150),
% 2.36/0.77 inference(avatar_split_clause,[],[f1529,f3792])).
% 2.36/0.77 thf(f3792,plain,(
% 2.36/0.77 spl108_150 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > int] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary1830089824insert(X0),X1),X2),binary1746293266le_Tip(X0)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),binary1746293266le_Tip(X0)),X2),binary1746293266le_Tip(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_150])])).
% 2.36/0.77 thf(f1529,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > int] : ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary1830089824insert(X0),X1),X2),binary1746293266le_Tip(X0)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),binary1746293266le_Tip(X0)),X2),binary1746293266le_Tip(X0)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f837])).
% 2.36/0.77 thf(f837,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : X0] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary1830089824insert(X0),X1),X2),binary1746293266le_Tip(X0)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),binary1746293266le_Tip(X0)),X2),binary1746293266le_Tip(X0)))),
% 2.36/0.77 inference(rectify,[],[f16])).
% 2.36/0.77 thf(f16,axiom,(
% 2.36/0.77 ! [X0 : $tType,X3 : X0 > int,X20 : X0] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary1830089824insert(X0),X3),X20),binary1746293266le_Tip(X0)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),binary1746293266le_Tip(X0)),X20),binary1746293266le_Tip(X0)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_binsert_Osimps_I1_J)).
% 2.36/0.77 thf(f3561,plain,(
% 2.36/0.77 spl108_149),
% 2.36/0.77 inference(avatar_split_clause,[],[f1545,f3559])).
% 2.36/0.77 thf(f3559,plain,(
% 2.36/0.77 spl108_149 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_149])])).
% 2.36/0.77 thf(f1545,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1265])).
% 2.36/0.77 thf(f1265,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1)))))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f1061,f1264])).
% 2.36/0.77 thf(f1264,plain,(
% 2.36/0.77 ! [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),sK83(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1061,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))))),
% 2.36/0.77 inference(ennf_transformation,[],[f653])).
% 2.36/0.77 thf(f653,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X2,X3))) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f652])).
% 2.36/0.77 thf(f652,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) => vAPP(X0,$o,X2,X3)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2)))),
% 2.36/0.77 inference(rectify,[],[f121])).
% 2.36/0.77 thf(f121,axiom,(
% 2.36/0.77 ! [X0 : $tType,X21 : X0 > $o,X43 : X0 > $o] : (! [X38 : X0] : (vAPP(X0,$o,X21,X38) => vAPP(X0,$o,X43,X38)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X21)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X43)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_120_Collect__mono)).
% 2.36/0.77 thf(f3557,plain,(
% 2.36/0.77 spl108_148),
% 2.36/0.77 inference(avatar_split_clause,[],[f1544,f3555])).
% 2.36/0.77 thf(f3555,plain,(
% 2.36/0.77 spl108_148 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_148])])).
% 2.36/0.77 thf(f1544,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X1)),vAPP(sTfun(X0,$o),set(X0),collect(X0),X2))) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK83(X0),X2),X1)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1265])).
% 2.36/0.77 thf(f3553,plain,(
% 2.36/0.77 spl108_147 | ~spl108_21 | ~spl108_28),
% 2.36/0.77 inference(avatar_split_clause,[],[f2392,f2356,f2297,f3551])).
% 2.36/0.77 thf(f3551,plain,(
% 2.36/0.77 spl108_147 <=> ! [X1 : $tType,X0 : $tType] : ($true = order(sTfun(X1,set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_147])])).
% 2.36/0.77 thf(f2297,plain,(
% 2.36/0.77 spl108_21 <=> ! [X0 : $tType] : ($true = order(set(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_21])])).
% 2.36/0.77 thf(f2356,plain,(
% 2.36/0.77 spl108_28 <=> ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | (order(X1) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_28])])).
% 2.36/0.77 thf(f2392,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X1,set(X0))))) ) | (~spl108_21 | ~spl108_28)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2389])).
% 2.36/0.77 thf(f2389,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order(sTfun(X1,set(X0))))) ) | (~spl108_21 | ~spl108_28)),
% 2.36/0.77 inference(superposition,[],[f2357,f2298])).
% 2.36/0.77 thf(f2298,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = order(set(X0)))) ) | ~spl108_21),
% 2.36/0.77 inference(avatar_component_clause,[],[f2297])).
% 2.36/0.77 thf(f2357,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : ((order(X1) != $true) | ($true = order(sTfun(X0,X1)))) ) | ~spl108_28),
% 2.36/0.77 inference(avatar_component_clause,[],[f2356])).
% 2.36/0.77 thf(f3545,plain,(
% 2.36/0.77 spl108_16 | ~spl108_145 | spl108_146),
% 2.36/0.77 inference(avatar_split_clause,[],[f1295,f3542,f3538,f2276])).
% 2.36/0.77 thf(f2276,plain,(
% 2.36/0.77 spl108_16 <=> (t2 = binary1746293266le_Tip(a))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_16])])).
% 2.36/0.77 thf(f3538,plain,(
% 2.36/0.77 spl108_145 <=> (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_145])])).
% 2.36/0.77 thf(f3542,plain,(
% 2.36/0.77 spl108_146 <=> (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2)) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_146])])).
% 2.36/0.77 thf(f1295,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2)) = $true) | (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) != $true) | (t2 = binary1746293266le_Tip(a))),
% 2.36/0.77 inference(cnf_transformation,[],[f859])).
% 2.36/0.77 thf(f859,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2)) = $true) | (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) != $true) | (t2 = binary1746293266le_Tip(a))),
% 2.36/0.77 inference(flattening,[],[f858])).
% 2.36/0.77 thf(f858,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2)) = $true) | ((vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) != $true) | (t2 = binary1746293266le_Tip(a)))),
% 2.36/0.77 inference(ennf_transformation,[],[f287])).
% 2.36/0.77 thf(f287,plain,(
% 2.36/0.77 ((vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) = $true) & (t2 != binary1746293266le_Tip(a))) => (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2)) = $true)),
% 2.36/0.77 inference(fool_elimination,[],[f286])).
% 2.36/0.77 thf(f286,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) & (t2 != binary1746293266le_Tip(a))) => vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2))),
% 2.36/0.77 inference(rectify,[],[f12])).
% 2.36/0.77 thf(f12,axiom,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t2) & (t2 != binary1746293266le_Tip(a))) => vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),binary213313527le_wrm(a),h),t2))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_h2)).
% 2.36/0.77 thf(f3532,plain,(
% 2.36/0.77 spl108_144),
% 2.36/0.77 inference(avatar_split_clause,[],[f1622,f3530])).
% 2.36/0.77 thf(f3530,plain,(
% 2.36/0.77 spl108_144 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_144])])).
% 2.36/0.77 thf(f1622,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1120])).
% 2.36/0.77 thf(f1120,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 2.36/0.77 inference(flattening,[],[f1119])).
% 2.36/0.77 thf(f1119,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : ((($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)) | ($true != vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 2.36/0.77 inference(ennf_transformation,[],[f753])).
% 2.36/0.77 thf(f753,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) => (($true = vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5)) => ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4))))),
% 2.36/0.77 inference(fool_elimination,[],[f752])).
% 2.36/0.77 thf(f752,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1,X5 : X0 > X1 > $o] : (vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) => (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X2),X5) => vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X5,X3),X4)))),
% 2.36/0.77 inference(rectify,[],[f243])).
% 2.36/0.77 thf(f243,axiom,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X21 : X0 > X1 > $o,X5 : X0,X26 : X1,X43 : X0 > X1 > $o] : (vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X21,X5),X26) => (vAPP(sTfun(X0,sTfun(X1,$o)),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(sTfun(X0,sTfun(X1,$o)),$o),ord_less_eq(sTfun(X0,sTfun(X1,$o))),X21),X43) => vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X43,X5),X26)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_242_rev__predicate2D)).
% 2.36/0.77 thf(f3525,plain,(
% 2.36/0.77 spl108_143),
% 2.36/0.77 inference(avatar_split_clause,[],[f1477,f3523])).
% 2.36/0.77 thf(f3523,plain,(
% 2.36/0.77 spl108_143 <=> ! [X0 : $tType,X1 : binary1291135688e_Tree(X0)] : ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK49(X0),X1)),vAPP(binary1291135688e_Tree(X0),X0,sK50(X0),X1)),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK51(X0),X1)) = X1) | (binary1746293266le_Tip(X0) = X1))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_143])])).
% 2.36/0.77 thf(f1477,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : binary1291135688e_Tree(X0)] : ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK49(X0),X1)),vAPP(binary1291135688e_Tree(X0),X0,sK50(X0),X1)),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK51(X0),X1)) = X1) | (binary1746293266le_Tip(X0) = X1)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1225])).
% 2.36/0.77 thf(f1225,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0)] : ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK49(X0),X1)),vAPP(binary1291135688e_Tree(X0),X0,sK50(X0),X1)),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK51(X0),X1)) = X1) | (binary1746293266le_Tip(X0) = X1))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51])],[f1007,f1224])).
% 2.36/0.77 thf(f1224,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0)] : (? [X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4) = X1) => (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK49(X0),X1)),vAPP(binary1291135688e_Tree(X0),X0,sK50(X0),X1)),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),sK51(X0),X1)) = X1))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1007,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0)] : (? [X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4) = X1) | (binary1746293266le_Tip(X0) = X1))),
% 2.36/0.77 inference(ennf_transformation,[],[f828])).
% 2.36/0.77 thf(f828,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0)] : ((binary1746293266le_Tip(X0) != X1) => ~! [X2 : binary1291135688e_Tree(X0),X3 : X0,X4 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X2),X3),X4) != X1))),
% 2.36/0.77 inference(rectify,[],[f19])).
% 2.36/0.77 thf(f19,axiom,(
% 2.36/0.77 ! [X0 : $tType,X26 : binary1291135688e_Tree(X0)] : ((binary1746293266le_Tip(X0) != X26) => ~! [X27 : binary1291135688e_Tree(X0),X28 : X0,X29 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X27),X28),X29) != X26))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Tree_Oexhaust)).
% 2.36/0.77 thf(f3500,plain,(
% 2.36/0.77 spl108_142 | ~spl108_20 | ~spl108_27),
% 2.36/0.77 inference(avatar_split_clause,[],[f2384,f2352,f2293,f3498])).
% 2.36/0.77 thf(f3498,plain,(
% 2.36/0.77 spl108_142 <=> ! [X1 : $tType,X0 : $tType] : ($true = ord(sTfun(X1,set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_142])])).
% 2.36/0.77 thf(f2293,plain,(
% 2.36/0.77 spl108_20 <=> ! [X0 : $tType] : ($true = ord(set(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_20])])).
% 2.36/0.77 thf(f2352,plain,(
% 2.36/0.77 spl108_27 <=> ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X0,X1))) | (ord(X1) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_27])])).
% 2.36/0.77 thf(f2384,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X1,set(X0))))) ) | (~spl108_20 | ~spl108_27)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2381])).
% 2.36/0.77 thf(f2381,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X1,set(X0))))) ) | (~spl108_20 | ~spl108_27)),
% 2.36/0.77 inference(superposition,[],[f2353,f2294])).
% 2.36/0.77 thf(f2294,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = ord(set(X0)))) ) | ~spl108_20),
% 2.36/0.77 inference(avatar_component_clause,[],[f2293])).
% 2.36/0.77 thf(f2353,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : ((ord(X1) != $true) | ($true = ord(sTfun(X0,X1)))) ) | ~spl108_27),
% 2.36/0.77 inference(avatar_component_clause,[],[f2352])).
% 2.36/0.77 thf(f3492,plain,(
% 2.36/0.77 spl108_141),
% 2.36/0.77 inference(avatar_split_clause,[],[f1583,f3490])).
% 2.36/0.77 thf(f3490,plain,(
% 2.36/0.77 spl108_141 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_141])])).
% 2.36/0.77 thf(f1583,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1091])).
% 2.36/0.77 thf(f1091,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1090])).
% 2.36/0.77 thf(f1090,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f707])).
% 2.36/0.77 thf(f707,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f706])).
% 2.36/0.77 thf(f706,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f122])).
% 2.36/0.77 thf(f122,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0),X63 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X37),X63) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X63)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_121_subset__trans)).
% 2.36/0.77 thf(f3488,plain,(
% 2.36/0.77 spl108_140),
% 2.36/0.77 inference(avatar_split_clause,[],[f1582,f3486])).
% 2.36/0.77 thf(f3486,plain,(
% 2.36/0.77 spl108_140 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_140])])).
% 2.36/0.77 thf(f1582,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1089])).
% 2.36/0.77 thf(f1089,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1088])).
% 2.36/0.77 thf(f1088,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f705])).
% 2.36/0.77 thf(f705,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f704])).
% 2.36/0.77 thf(f704,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f184])).
% 2.36/0.77 thf(f184,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0),X63 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X37),X63) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X63)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_183_subset__psubset__trans)).
% 2.36/0.77 thf(f3484,plain,(
% 2.36/0.77 spl108_139),
% 2.36/0.77 inference(avatar_split_clause,[],[f1578,f3482])).
% 2.36/0.77 thf(f3482,plain,(
% 2.36/0.77 spl108_139 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_139])])).
% 2.36/0.77 thf(f1578,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1082])).
% 2.36/0.77 thf(f1082,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1081])).
% 2.36/0.77 thf(f1081,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f697])).
% 2.36/0.77 thf(f697,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f696])).
% 2.36/0.77 thf(f696,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X3) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f186])).
% 2.36/0.77 thf(f186,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0),X63 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X37),X63) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X63)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_185_psubset__subset__trans)).
% 2.36/0.77 thf(f3480,plain,(
% 2.36/0.77 spl108_138),
% 2.36/0.77 inference(avatar_split_clause,[],[f1577,f3478])).
% 2.36/0.77 thf(f3478,plain,(
% 2.36/0.77 spl108_138 <=> ! [X0 : $tType,X3 : set(X0),X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_138])])).
% 2.36/0.77 thf(f1577,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X3 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1080])).
% 2.36/0.77 thf(f1080,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1079])).
% 2.36/0.77 thf(f1079,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f695])).
% 2.36/0.77 thf(f695,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f694])).
% 2.36/0.77 thf(f694,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X2),X3) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f217])).
% 2.36/0.77 thf(f217,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0),X63 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X37),X63) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X63)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_216_psubset__trans)).
% 2.36/0.77 thf(f3429,plain,(
% 2.36/0.77 spl108_137),
% 2.36/0.77 inference(avatar_split_clause,[],[f1606,f3427])).
% 2.36/0.77 thf(f3427,plain,(
% 2.36/0.77 spl108_137 <=> ! [X1 : $tType,X0 : $tType,X4 : X1,X3 : X0,X2 : X0 > X1 > $o] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) | ($true != vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_137])])).
% 2.36/0.77 thf(f1606,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) | ($true != vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1112])).
% 2.36/0.77 thf(f1112,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) | ($true != vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))))),
% 2.36/0.77 inference(ennf_transformation,[],[f737])).
% 2.36/0.77 thf(f737,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))) => ($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 2.36/0.77 inference(fool_elimination,[],[f736])).
% 2.36/0.77 thf(f736,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4)) => vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))),
% 2.36/0.77 inference(rectify,[],[f244])).
% 2.36/0.77 thf(f244,axiom,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X41 : X0 > X1 > $o,X18 : X0,X19 : X1] : (vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X41),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X18),X19)) => vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X41,X18),X19))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_243_case__prodD)).
% 2.36/0.77 thf(f3425,plain,(
% 2.36/0.77 spl108_136),
% 2.36/0.77 inference(avatar_split_clause,[],[f1596,f3423])).
% 2.36/0.77 thf(f3423,plain,(
% 2.36/0.77 spl108_136 <=> ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X4 : X1,X3 : X0] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_136])])).
% 2.36/0.77 thf(f1596,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1101])).
% 2.36/0.77 thf(f1101,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))) | ($true != vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)))),
% 2.36/0.77 inference(ennf_transformation,[],[f721])).
% 2.36/0.77 thf(f721,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (($true = vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4)) => ($true = vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4))))),
% 2.36/0.77 inference(fool_elimination,[],[f720])).
% 2.36/0.77 thf(f720,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X0 > X1 > $o,X3 : X0,X4 : X1] : (vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X2,X3),X4) => vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X2),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X3),X4)))),
% 2.36/0.77 inference(rectify,[],[f235])).
% 2.36/0.77 thf(f235,axiom,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X41 : X0 > X1 > $o,X18 : X0,X19 : X1] : (vAPP(X1,$o,vAPP(X0,sTfun(X1,$o),X41,X18),X19) => vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),X41),vAPP(X1,product_prod(X0,X1),vAPP(X0,sTfun(X1,product_prod(X0,X1)),product_Pair(X0,X1),X18),X19)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_234_case__prodI)).
% 2.36/0.77 thf(f3398,plain,(
% 2.36/0.77 spl108_135 | ~spl108_19 | ~spl108_26),
% 2.36/0.77 inference(avatar_split_clause,[],[f2376,f2348,f2289,f3396])).
% 2.36/0.77 thf(f3396,plain,(
% 2.36/0.77 spl108_135 <=> ! [X1 : $tType,X0 : $tType] : ($true = preorder(sTfun(X1,set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_135])])).
% 2.36/0.77 thf(f2289,plain,(
% 2.36/0.77 spl108_19 <=> ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_19])])).
% 2.36/0.77 thf(f2348,plain,(
% 2.36/0.77 spl108_26 <=> ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_26])])).
% 2.36/0.77 thf(f2376,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X1,set(X0))))) ) | (~spl108_19 | ~spl108_26)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2373])).
% 2.36/0.77 thf(f2373,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X1,set(X0))))) ) | (~spl108_19 | ~spl108_26)),
% 2.36/0.77 inference(superposition,[],[f2349,f2290])).
% 2.36/0.77 thf(f2290,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = preorder(set(X0)))) ) | ~spl108_19),
% 2.36/0.77 inference(avatar_component_clause,[],[f2289])).
% 2.36/0.77 thf(f2349,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != preorder(X1)) | ($true = preorder(sTfun(X0,X1)))) ) | ~spl108_26),
% 2.36/0.77 inference(avatar_component_clause,[],[f2348])).
% 2.36/0.77 thf(f3394,plain,(
% 2.36/0.77 spl108_134),
% 2.36/0.77 inference(avatar_split_clause,[],[f1568,f3392])).
% 2.36/0.77 thf(f3392,plain,(
% 2.36/0.77 spl108_134 <=> ! [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),sK88(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK88(X0,X1),X3),X2))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_134])])).
% 2.36/0.77 thf(f1568,plain,(
% 2.36/0.77 ( ! [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),sK88(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK88(X0,X1),X3),X2)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1271])).
% 2.36/0.77 thf(f1271,plain,(
% 2.36/0.77 ! [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),sK88(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK88(X0,X1),X3),X2))))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK88])],[f1071,f1270])).
% 2.36/0.77 thf(f1270,plain,(
% 2.36/0.77 ! [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),sK88(X0,X1),X3),X2)) != vAPP(X1,X0,X2,vAPP(sTfun(X1,X0),X1,vAPP(sTfun(X1,X0),sTfun(sTfun(X1,X0),X1),sK88(X0,X1),X3),X2))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1071,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : ((X2 = X3) | ? [X4 : X1] : (vAPP(X1,X0,X3,X4) != vAPP(X1,X0,X2,X4)))),
% 2.36/0.77 inference(ennf_transformation,[],[f845])).
% 2.36/0.77 thf(f845,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : X1 > X0] : (! [X4 : X1] : (vAPP(X1,X0,X3,X4) = vAPP(X1,X0,X2,X4)) => (X2 = X3))),
% 2.36/0.77 inference(rectify,[],[f49])).
% 2.36/0.77 thf(f49,axiom,(
% 2.36/0.77 ! [X1 : $tType,X0 : $tType,X41 : X0 > X1,X42 : X0 > X1] : (! [X38 : X0] : (vAPP(X0,X1,X41,X38) = vAPP(X0,X1,X42,X38)) => (X41 = X42))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_ext)).
% 2.36/0.77 thf(f3387,plain,(
% 2.36/0.77 spl108_133),
% 2.36/0.77 inference(avatar_split_clause,[],[f1561,f3385])).
% 2.36/0.77 thf(f3385,plain,(
% 2.36/0.77 spl108_133 <=> ! [X1 : $tType,X0 : $tType,X3 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1 > X1 > X1,X2 : X1] : (vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X1,sTfun(X1,X1))))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X1,sTfun(X1,X1))))),sTfun(binary1291135688e_Tree(X0),X1)),binary1929596613c_Tree(X1,X0),X2),X3),binary1746293266le_Tip(X0)) = X2)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_133])])).
% 2.36/0.77 thf(f1561,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1 > X1 > X1] : ((vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X1,sTfun(X1,X1))))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X1,sTfun(X1,X1))))),sTfun(binary1291135688e_Tree(X0),X1)),binary1929596613c_Tree(X1,X0),X2),X3),binary1746293266le_Tip(X0)) = X2)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f844])).
% 2.36/0.77 thf(f844,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1 > X1 > X1] : (vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X1,sTfun(X1,X1))))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X1,sTfun(X1,X1))))),sTfun(binary1291135688e_Tree(X0),X1)),binary1929596613c_Tree(X1,X0),X2),X3),binary1746293266le_Tip(X0)) = X2)),
% 2.36/0.77 inference(rectify,[],[f29])).
% 2.36/0.77 thf(f29,axiom,(
% 2.36/0.77 ! [X0 : $tType,X2 : $tType,X31 : X2,X32 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X2 > X2 > X2] : (vAPP(binary1291135688e_Tree(X0),X2,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X2,sTfun(X2,X2))))),sTfun(binary1291135688e_Tree(X0),X2),vAPP(X2,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),sTfun(X2,sTfun(X2,X2))))),sTfun(binary1291135688e_Tree(X0),X2)),binary1929596613c_Tree(X2,X0),X31),X32),binary1746293266le_Tip(X0)) = X31)),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_Tree_Osimps_I6_J)).
% 2.36/0.77 thf(f3365,plain,(
% 2.36/0.77 spl108_132),
% 2.36/0.77 inference(avatar_split_clause,[],[f1610,f3363])).
% 2.36/0.77 thf(f3363,plain,(
% 2.36/0.77 spl108_132 <=> ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : (vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_case_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_132])])).
% 2.36/0.77 thf(f1610,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : ((vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_case_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f851])).
% 2.36/0.77 thf(f851,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X0 > X2 > X1,X4 : X0,X5 : X2] : (vAPP(product_prod(X0,X2),X1,vAPP(sTfun(X0,sTfun(X2,X1)),sTfun(product_prod(X0,X2),X1),product_case_prod(X0,X2,X1),X3),vAPP(X2,product_prod(X0,X2),vAPP(X0,sTfun(X2,product_prod(X0,X2)),product_Pair(X0,X2),X4),X5)) = vAPP(X2,X1,vAPP(X0,sTfun(X2,X1),X3,X4),X5))),
% 2.36/0.77 inference(rectify,[],[f232])).
% 2.36/0.77 thf(f232,axiom,(
% 2.36/0.77 ! [X1 : $tType,X0 : $tType,X2 : $tType,X41 : X1 > X2 > X0,X18 : X1,X19 : X2] : (vAPP(product_prod(X1,X2),X0,vAPP(sTfun(X1,sTfun(X2,X0)),sTfun(product_prod(X1,X2),X0),product_case_prod(X1,X2,X0),X41),vAPP(X2,product_prod(X1,X2),vAPP(X1,sTfun(X2,product_prod(X1,X2)),product_Pair(X1,X2),X18),X19)) = vAPP(X2,X0,vAPP(X1,sTfun(X2,X0),X41,X18),X19))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_231_case__prod__conv)).
% 2.36/0.77 thf(f3361,plain,(
% 2.36/0.77 spl108_131),
% 2.36/0.77 inference(avatar_split_clause,[],[f1603,f3359])).
% 2.36/0.77 thf(f3359,plain,(
% 2.36/0.77 spl108_131 <=> ! [X0 : $tType,X2 : X0 > X0 > $o,X4 : X0,X3 : X0,X1 : X0 > X0 > $o] : ((X3 = X4) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_131])])).
% 2.36/0.77 thf(f1603,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : ((X3 = X4) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1109])).
% 2.36/0.77 thf(f1109,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : ((X3 = X4) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 inference(flattening,[],[f1108])).
% 2.36/0.77 thf(f1108,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (((X3 = X4) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X4))) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 inference(ennf_transformation,[],[f731])).
% 2.36/0.77 thf(f731,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X4)) => (X3 = X4)))),
% 2.36/0.77 inference(fool_elimination,[],[f730])).
% 2.36/0.77 thf(f730,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X3),X4) => (X3 = X4)))),
% 2.36/0.77 inference(rectify,[],[f181])).
% 2.36/0.77 thf(f181,axiom,(
% 2.36/0.77 ! [X0 : $tType,X70 : X0 > X0 > $o,X71 : X0 > X0 > $o,X72 : X0,X18 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X70),X71),X72) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X70,X72),X18) => (X18 = X72)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_180_ordering__top_Oextremum__uniqueI)).
% 2.36/0.77 thf(f3357,plain,(
% 2.36/0.77 spl108_130),
% 2.36/0.77 inference(avatar_split_clause,[],[f1580,f3355])).
% 2.36/0.77 thf(f3355,plain,(
% 2.36/0.77 spl108_130 <=> ! [X0 : $tType,X3 : X0,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_130])])).
% 2.36/0.77 thf(f1580,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X3 : X0,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1085])).
% 2.36/0.77 thf(f1085,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1084])).
% 2.36/0.77 thf(f1084,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : ((($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f701])).
% 2.36/0.77 thf(f701,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f700])).
% 2.36/0.77 thf(f700,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)))),
% 2.36/0.77 inference(rectify,[],[f113])).
% 2.36/0.77 thf(f113,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0),X5 : X0] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),X36) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X5),X37)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_112_in__mono)).
% 2.36/0.77 thf(f3353,plain,(
% 2.36/0.77 spl108_129 | ~spl108_18 | ~spl108_25),
% 2.36/0.77 inference(avatar_split_clause,[],[f2369,f2344,f2285,f3351])).
% 2.36/0.77 thf(f3351,plain,(
% 2.36/0.77 spl108_129 <=> ! [X1 : $tType,X0 : $tType] : ($true = order_bot(sTfun(X1,set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_129])])).
% 2.36/0.77 thf(f2285,plain,(
% 2.36/0.77 spl108_18 <=> ! [X0 : $tType] : ($true = order_bot(set(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_18])])).
% 2.36/0.77 thf(f2344,plain,(
% 2.36/0.77 spl108_25 <=> ! [X1 : $tType,X0 : $tType] : (($true = order_bot(sTfun(X0,X1))) | ($true != order_bot(X1)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_25])])).
% 2.36/0.77 thf(f2369,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true = order_bot(sTfun(X1,set(X0))))) ) | (~spl108_18 | ~spl108_25)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2366])).
% 2.36/0.77 thf(f2366,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = order_bot(sTfun(X1,set(X0))))) ) | (~spl108_18 | ~spl108_25)),
% 2.36/0.77 inference(superposition,[],[f2345,f2286])).
% 2.36/0.77 thf(f2286,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = order_bot(set(X0)))) ) | ~spl108_18),
% 2.36/0.77 inference(avatar_component_clause,[],[f2285])).
% 2.36/0.77 thf(f2345,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != order_bot(X1)) | ($true = order_bot(sTfun(X0,X1)))) ) | ~spl108_25),
% 2.36/0.77 inference(avatar_component_clause,[],[f2344])).
% 2.36/0.77 thf(f3349,plain,(
% 2.36/0.77 spl108_128),
% 2.36/0.77 inference(avatar_split_clause,[],[f1576,f3347])).
% 2.36/0.77 thf(f3347,plain,(
% 2.36/0.77 spl108_128 <=> ! [X0 : $tType,X3 : X0,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_128])])).
% 2.36/0.77 thf(f1576,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X3 : X0,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1078])).
% 2.36/0.77 thf(f1078,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1077])).
% 2.36/0.77 thf(f1077,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : ((($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f693])).
% 2.36/0.77 thf(f693,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f692])).
% 2.36/0.77 thf(f692,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0),X3 : X0] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)))),
% 2.36/0.77 inference(rectify,[],[f218])).
% 2.36/0.77 thf(f218,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0),X39 : X0] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X39),X36) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X39),X37)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_217_psubsetD)).
% 2.36/0.77 thf(f3327,plain,(
% 2.36/0.77 spl108_127),
% 2.36/0.77 inference(avatar_split_clause,[],[f1682,f3325])).
% 2.36/0.77 thf(f3325,plain,(
% 2.36/0.77 spl108_127 <=> ! [X0 : $tType,X4 : X0,X3 : binary1291135688e_Tree(X0),X2 : X0 > int] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),binary1746293266le_Tip(X0))) = X3)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_127])])).
% 2.36/0.77 thf(f1682,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X4 : X0] : ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),binary1746293266le_Tip(X0))) = X3)) )),
% 2.36/0.77 inference(equality_resolution,[],[f1593])).
% 2.36/0.77 thf(f1593,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0),X4 : X0] : ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = X3) | (binary1746293266le_Tip(X0) != X1)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1099])).
% 2.36/0.77 thf(f1099,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X4 : X0] : (((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),X1))) | (binary1746293266le_Tip(X0) = X1)) & ((vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = X3) | (binary1746293266le_Tip(X0) != X1)))),
% 2.36/0.77 inference(ennf_transformation,[],[f848])).
% 2.36/0.77 thf(f848,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X4 : X0] : (((binary1746293266le_Tip(X0) != X1) => (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),X1)))) & ((binary1746293266le_Tip(X0) = X1) => (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = X3)))),
% 2.36/0.77 inference(rectify,[],[f17])).
% 2.36/0.77 thf(f17,axiom,(
% 2.36/0.77 ! [X0 : $tType,X6 : binary1291135688e_Tree(X0),X3 : X0 > int,X4 : binary1291135688e_Tree(X0),X5 : X0] : (((binary1746293266le_Tip(X0) != X6) => (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X3),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),X6)) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X3),X6)))) & ((binary1746293266le_Tip(X0) = X6) => (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),binary213313527le_wrm(X0),X3),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),X6)) = X4)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_wrm_Osimps)).
% 2.36/0.77 thf(f3323,plain,(
% 2.36/0.77 spl108_126),
% 2.36/0.77 inference(avatar_split_clause,[],[f1547,f3321])).
% 2.36/0.77 thf(f3321,plain,(
% 2.36/0.77 spl108_126 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_126])])).
% 2.36/0.77 thf(f1547,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1267])).
% 2.36/0.77 thf(f1267,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X1))))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f1062,f1266])).
% 2.36/0.77 thf(f1266,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (? [X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))) => (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X1))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1062,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ? [X3 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) & ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1))))),
% 2.36/0.77 inference(ennf_transformation,[],[f655])).
% 2.36/0.77 thf(f655,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (! [X3 : X0] : (($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2))) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(fool_elimination,[],[f654])).
% 2.36/0.77 thf(f654,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (! [X3 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X1) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X3),X2)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))),
% 2.36/0.77 inference(rectify,[],[f35])).
% 2.36/0.77 thf(f35,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0)] : (! [X38 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X38),X36) => vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X38),X37)) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_subsetI)).
% 2.36/0.77 thf(f3319,plain,(
% 2.36/0.77 spl108_125),
% 2.36/0.77 inference(avatar_split_clause,[],[f1546,f3317])).
% 2.36/0.77 thf(f3317,plain,(
% 2.36/0.77 spl108_125 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X1)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_125])])).
% 2.36/0.77 thf(f1546,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,vAPP(set(X0),sTfun(set(X0),X0),sK84(X0),X2),X1)),X1))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1267])).
% 2.36/0.77 thf(f3315,plain,(
% 2.36/0.77 spl108_124),
% 2.36/0.77 inference(avatar_split_clause,[],[f1515,f3313])).
% 2.36/0.77 thf(f3313,plain,(
% 2.36/0.77 spl108_124 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_124])])).
% 2.36/0.77 thf(f1515,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1045])).
% 2.36/0.77 thf(f1045,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f611])).
% 2.36/0.77 thf(f611,plain,(
% 2.36/0.77 ! [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)))))),
% 2.36/0.77 inference(fool_elimination,[],[f610])).
% 2.36/0.77 thf(f610,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f44])).
% 2.36/0.77 thf(f44,axiom,(
% 2.36/0.77 ! [X1 : $tType,X0 : $tType] : (ord(X1) => ! [X41 : X0 > X1,X42 : X0 > X1,X5 : X0] : (vAPP(sTfun(X0,X1),$o,vAPP(sTfun(X0,X1),sTfun(sTfun(X0,X1),$o),ord_less_eq(sTfun(X0,X1)),X41),X42) => vAPP(X1,$o,vAPP(X1,sTfun(X1,$o),ord_less_eq(X1),vAPP(X0,X1,X41,X5)),vAPP(X0,X1,X42,X5))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_le__funE)).
% 2.36/0.77 thf(f3307,plain,(
% 2.36/0.77 spl108_123 | ~spl108_17 | ~spl108_23),
% 2.36/0.77 inference(avatar_split_clause,[],[f2363,f2335,f2281,f3305])).
% 2.36/0.77 thf(f3305,plain,(
% 2.36/0.77 spl108_123 <=> ! [X1 : $tType,X0 : $tType] : ($true = bot(sTfun(X1,set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_123])])).
% 2.36/0.77 thf(f2281,plain,(
% 2.36/0.77 spl108_17 <=> ! [X0 : $tType] : ($true = bot(set(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_17])])).
% 2.36/0.77 thf(f2335,plain,(
% 2.36/0.77 spl108_23 <=> ! [X1 : $tType,X0 : $tType] : (($true = bot(sTfun(X0,X1))) | (bot(X1) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_23])])).
% 2.36/0.77 thf(f2363,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true = bot(sTfun(X1,set(X0))))) ) | (~spl108_17 | ~spl108_23)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2360])).
% 2.36/0.77 thf(f2360,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : (($true != $true) | ($true = bot(sTfun(X1,set(X0))))) ) | (~spl108_17 | ~spl108_23)),
% 2.36/0.77 inference(superposition,[],[f2336,f2282])).
% 2.36/0.77 thf(f2282,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = bot(set(X0)))) ) | ~spl108_17),
% 2.36/0.77 inference(avatar_component_clause,[],[f2281])).
% 2.36/0.77 thf(f2336,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : ((bot(X1) != $true) | ($true = bot(sTfun(X0,X1)))) ) | ~spl108_23),
% 2.36/0.77 inference(avatar_component_clause,[],[f2335])).
% 2.36/0.77 thf(f3299,plain,(
% 2.36/0.77 spl108_122),
% 2.36/0.77 inference(avatar_split_clause,[],[f1605,f3297])).
% 2.36/0.77 thf(f3297,plain,(
% 2.36/0.77 spl108_122 <=> ! [X0 : $tType,X2 : X0 > X0 > $o,X4 : X0,X3 : X0,X1 : X0 > X0 > $o] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_122])])).
% 2.36/0.77 thf(f1605,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1111])).
% 2.36/0.77 thf(f1111,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 inference(ennf_transformation,[],[f735])).
% 2.36/0.77 thf(f735,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3)))),
% 2.36/0.77 inference(fool_elimination,[],[f734])).
% 2.36/0.77 thf(f734,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X1,X4),X3))),
% 2.36/0.77 inference(rectify,[],[f177])).
% 2.36/0.77 thf(f177,axiom,(
% 2.36/0.77 ! [X0 : $tType,X70 : X0 > X0 > $o,X71 : X0 > X0 > $o,X72 : X0,X18 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X70),X71),X72) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X70,X18),X72))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_176_ordering__top_Oextremum)).
% 2.36/0.77 thf(f3295,plain,(
% 2.36/0.77 spl108_121),
% 2.36/0.77 inference(avatar_split_clause,[],[f1604,f3293])).
% 2.36/0.77 thf(f3293,plain,(
% 2.36/0.77 spl108_121 <=> ! [X0 : $tType,X4 : X0,X3 : X0,X2 : X0 > X0 > $o,X1 : X0 > X0 > $o] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_121])])).
% 2.36/0.77 thf(f1604,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > X0 > $o,X3 : X0,X1 : X0 > X0 > $o,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1110])).
% 2.36/0.77 thf(f1110,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X3),X4)) | ($true != vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)))),
% 2.36/0.77 inference(ennf_transformation,[],[f850])).
% 2.36/0.77 thf(f850,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)) => ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X3),X4)))),
% 2.36/0.77 inference(flattening,[],[f733])).
% 2.36/0.77 thf(f733,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (($true = vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3)) => ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X3),X4)))),
% 2.36/0.77 inference(fool_elimination,[],[f732])).
% 2.36/0.77 thf(f732,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > X0 > $o,X2 : X0 > X0 > $o,X3 : X0,X4 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X1),X2),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X2,X3),X4))),
% 2.36/0.77 inference(rectify,[],[f178])).
% 2.36/0.77 thf(f178,axiom,(
% 2.36/0.77 ! [X0 : $tType,X70 : X0 > X0 > $o,X71 : X0 > X0 > $o,X72 : X0,X18 : X0] : (vAPP(X0,$o,vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(X0,$o)),sTfun(sTfun(X0,sTfun(X0,$o)),sTfun(X0,$o)),ordering_top(X0),X70),X71),X72) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),X71,X72),X18))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_177_ordering__top_Oextremum__strict)).
% 2.36/0.77 thf(f3070,plain,(
% 2.36/0.77 spl108_120),
% 2.36/0.77 inference(avatar_split_clause,[],[f1558,f3068])).
% 2.36/0.77 thf(f3068,plain,(
% 2.36/0.77 spl108_120 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ($true = vAPP(product_prod(X1,X0),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(product_prod(X1,X0),$o),product_case_prod(X1,X0,$o),vAPP(sTfun(X0,$o),sTfun(X1,sTfun(X0,$o)),kCOMB,vAPP($o,sTfun(X0,$o),kCOMB,$true))),X2))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_120])])).
% 2.36/0.77 thf(f1558,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : (($true = vAPP(product_prod(X1,X0),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(product_prod(X1,X0),$o),product_case_prod(X1,X0,$o),vAPP(sTfun(X0,$o),sTfun(X1,sTfun(X0,$o)),kCOMB,vAPP($o,sTfun(X0,$o),kCOMB,$true))),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f671])).
% 2.36/0.77 thf(f671,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0)] : ($true = vAPP(product_prod(X1,X0),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(product_prod(X1,X0),$o),product_case_prod(X1,X0,$o),vAPP(sTfun(X0,$o),sTfun(X1,sTfun(X0,$o)),kCOMB,vAPP($o,sTfun(X0,$o),kCOMB,$true))),X2))),
% 2.36/0.77 inference(fool_elimination,[],[f670])).
% 2.36/0.77 thf(f670,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0)] : vAPP(product_prod(X1,X0),$o,vAPP(sTfun(X1,sTfun(X0,$o)),sTfun(product_prod(X1,X0),$o),product_case_prod(X1,X0,$o),(^[X3 : X1, X4 : X0] : ($true))),X2)),
% 2.36/0.77 inference(rectify,[],[f255])).
% 2.36/0.77 thf(f255,axiom,(
% 2.36/0.77 ! [X1 : $tType,X0 : $tType,X88 : product_prod(X0,X1)] : vAPP(product_prod(X0,X1),$o,vAPP(sTfun(X0,sTfun(X1,$o)),sTfun(product_prod(X0,X1),$o),product_case_prod(X0,X1,$o),(^[X93 : X0, X94 : X1] : ($true))),X88)),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_254_prod_Odisc__eq__case)).
% 2.36/0.77 thf(f3066,plain,(
% 2.36/0.77 spl108_119),
% 2.36/0.77 inference(avatar_split_clause,[],[f1543,f3064])).
% 2.36/0.77 thf(f3064,plain,(
% 2.36/0.77 spl108_119 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_119])])).
% 2.36/0.77 thf(f1543,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1263])).
% 2.36/0.77 thf(f1263,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | (($true != vAPP(X0,$o,X2,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1)))))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f1060,f1262])).
% 2.36/0.77 thf(f1262,plain,(
% 2.36/0.77 ! [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),sK82(X0),X2),X1))) & ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1060,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ? [X3 : X0] : (($true != vAPP(X0,$o,X2,X3)) & ($true = vAPP(X0,$o,X1,X3))))),
% 2.36/0.77 inference(ennf_transformation,[],[f651])).
% 2.36/0.77 thf(f651,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true = vAPP(X0,$o,X1,X3)) => ($true = vAPP(X0,$o,X2,X3))) => ($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)))),
% 2.36/0.77 inference(fool_elimination,[],[f650])).
% 2.36/0.77 thf(f650,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (vAPP(X0,$o,X1,X3) => vAPP(X0,$o,X2,X3)) => vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2))),
% 2.36/0.77 inference(rectify,[],[f213])).
% 2.36/0.77 thf(f213,axiom,(
% 2.36/0.77 ! [X0 : $tType,X21 : X0 > $o,X43 : X0 > $o] : (! [X38 : X0] : (vAPP(X0,$o,X21,X38) => vAPP(X0,$o,X43,X38)) => vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X21),X43))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_212_predicate1I)).
% 2.36/0.77 thf(f3062,plain,(
% 2.36/0.77 spl108_118),
% 2.36/0.77 inference(avatar_split_clause,[],[f1542,f3060])).
% 2.36/0.77 thf(f3060,plain,(
% 2.36/0.77 spl108_118 <=> ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_118])])).
% 2.36/0.77 thf(f1542,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X2)) | ($true = vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),X0),sK82(X0),X2),X1)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1263])).
% 2.36/0.77 thf(f3058,plain,(
% 2.36/0.77 spl108_117),
% 2.36/0.77 inference(avatar_split_clause,[],[f1461,f3056])).
% 2.36/0.77 thf(f3056,plain,(
% 2.36/0.77 spl108_117 <=> ! [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)) | (order(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_117])])).
% 2.36/0.77 thf(f1461,plain,(
% 2.36/0.77 ( ! [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)) | (order(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1004])).
% 2.36/0.77 thf(f1004,plain,(
% 2.36/0.77 ! [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))) | (order(X0) != $true))),
% 2.36/0.77 inference(flattening,[],[f1003])).
% 2.36/0.77 thf(f1003,plain,(
% 2.36/0.77 ! [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))) | (order(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f529])).
% 2.36/0.77 thf(f529,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))))),
% 2.36/0.77 inference(fool_elimination,[],[f528])).
% 2.36/0.77 thf(f528,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3))))),
% 2.36/0.77 inference(rectify,[],[f60])).
% 2.36/0.77 thf(f60,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X18 : X0,X19 : X0,X39 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),X19) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X19),X39) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),X39))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_order_Otrans)).
% 2.36/0.77 thf(f3054,plain,(
% 2.36/0.77 spl108_116),
% 2.36/0.77 inference(avatar_split_clause,[],[f1458,f3052])).
% 2.36/0.77 thf(f3052,plain,(
% 2.36/0.77 spl108_116 <=> ! [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,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_116])])).
% 2.36/0.77 thf(f1458,plain,(
% 2.36/0.77 ( ! [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,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f998])).
% 2.36/0.77 thf(f998,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 2.36/0.77 inference(flattening,[],[f997])).
% 2.36/0.77 thf(f997,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f523])).
% 2.36/0.77 thf(f523,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))))),
% 2.36/0.77 inference(fool_elimination,[],[f522])).
% 2.36/0.77 thf(f522,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 2.36/0.77 inference(rectify,[],[f150])).
% 2.36/0.77 thf(f150,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X18 : X0,X19 : X0,X39 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X19) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X19),X39) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X39))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_149_order_Ostrict__trans2)).
% 2.36/0.77 thf(f3050,plain,(
% 2.36/0.77 spl108_115),
% 2.36/0.77 inference(avatar_split_clause,[],[f1457,f3048])).
% 2.36/0.77 thf(f3048,plain,(
% 2.36/0.77 spl108_115 <=> ! [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,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_115])])).
% 2.36/0.77 thf(f1457,plain,(
% 2.36/0.77 ( ! [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,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (order(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f996])).
% 2.36/0.77 thf(f996,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 2.36/0.77 inference(flattening,[],[f995])).
% 2.36/0.77 thf(f995,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X3),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (order(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f521])).
% 2.36/0.77 thf(f521,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X3),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)))))),
% 2.36/0.77 inference(fool_elimination,[],[f520])).
% 2.36/0.77 thf(f520,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X3),X1) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))))),
% 2.36/0.77 inference(rectify,[],[f154])).
% 2.36/0.77 thf(f154,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X19 : X0,X18 : X0,X39 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X19),X18) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X39),X19) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X39),X18))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_153_dual__order_Ostrict__trans2)).
% 2.36/0.77 thf(f3042,plain,(
% 2.36/0.77 spl108_114),
% 2.36/0.77 inference(avatar_split_clause,[],[f1455,f3040])).
% 2.36/0.77 thf(f3040,plain,(
% 2.36/0.77 spl108_114 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_114])])).
% 2.36/0.77 thf(f1455,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f992])).
% 2.36/0.77 thf(f992,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(flattening,[],[f991])).
% 2.36/0.77 thf(f991,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f517])).
% 2.36/0.77 thf(f517,plain,(
% 2.36/0.77 ! [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)))))),
% 2.36/0.77 inference(fool_elimination,[],[f516])).
% 2.36/0.77 thf(f516,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f104])).
% 2.36/0.77 thf(f104,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X19 : X0,X18 : X0,X39 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X19),X18) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X39),X19) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X39),X18))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_103_dual__order_Ostrict__trans)).
% 2.36/0.77 thf(f3038,plain,(
% 2.36/0.77 spl108_113),
% 2.36/0.77 inference(avatar_split_clause,[],[f1356,f3036])).
% 2.36/0.77 thf(f3036,plain,(
% 2.36/0.77 spl108_113 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_113])])).
% 2.36/0.77 thf(f1356,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f902])).
% 2.36/0.77 thf(f902,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(flattening,[],[f901])).
% 2.36/0.77 thf(f901,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f377])).
% 2.36/0.77 thf(f377,plain,(
% 2.36/0.77 ! [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)))))),
% 2.36/0.77 inference(fool_elimination,[],[f376])).
% 2.36/0.77 thf(f376,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f67])).
% 2.36/0.77 thf(f67,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0,X26 : X0,X50 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X26) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X50) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X50))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_order__trans)).
% 2.36/0.77 thf(f3034,plain,(
% 2.36/0.77 spl108_112),
% 2.36/0.77 inference(avatar_split_clause,[],[f1355,f3032])).
% 2.36/0.77 thf(f3032,plain,(
% 2.36/0.77 spl108_112 <=> ! [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_eq(X0),X1),X2)) | (preorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_112])])).
% 2.36/0.77 thf(f1355,plain,(
% 2.36/0.77 ( ! [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_eq(X0),X1),X2)) | (preorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f900])).
% 2.36/0.77 thf(f900,plain,(
% 2.36/0.77 ! [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_eq(X0),X1),X2))) | (preorder(X0) != $true))),
% 2.36/0.77 inference(flattening,[],[f899])).
% 2.36/0.77 thf(f899,plain,(
% 2.36/0.77 ! [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_eq(X0),X1),X2))) | (preorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f375])).
% 2.36/0.77 thf(f375,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))))),
% 2.36/0.77 inference(fool_elimination,[],[f374])).
% 2.36/0.77 thf(f374,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 2.36/0.77 inference(rectify,[],[f141])).
% 2.36/0.77 thf(f141,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0,X26 : X0,X50 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X26) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X26),X50) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X50))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_140_le__less__trans)).
% 2.36/0.77 thf(f3030,plain,(
% 2.36/0.77 spl108_111),
% 2.36/0.77 inference(avatar_split_clause,[],[f1354,f3028])).
% 2.36/0.77 thf(f3028,plain,(
% 2.36/0.77 spl108_111 <=> ! [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,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_111])])).
% 2.36/0.77 thf(f1354,plain,(
% 2.36/0.77 ( ! [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,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (preorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f898])).
% 2.36/0.77 thf(f898,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (preorder(X0) != $true))),
% 2.36/0.77 inference(flattening,[],[f897])).
% 2.36/0.77 thf(f897,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (preorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f373])).
% 2.36/0.77 thf(f373,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))))),
% 2.36/0.77 inference(fool_elimination,[],[f372])).
% 2.36/0.77 thf(f372,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3))))),
% 2.36/0.77 inference(rectify,[],[f142])).
% 2.36/0.77 thf(f142,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0,X26 : X0,X50 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X26) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X50) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X50))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_141_less__le__trans)).
% 2.36/0.77 thf(f3026,plain,(
% 2.36/0.77 spl108_110),
% 2.36/0.77 inference(avatar_split_clause,[],[f1353,f3024])).
% 2.36/0.77 thf(f3024,plain,(
% 2.36/0.77 spl108_110 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_110])])).
% 2.36/0.77 thf(f1353,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f896])).
% 2.36/0.77 thf(f896,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(flattening,[],[f895])).
% 2.36/0.77 thf(f895,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f371])).
% 2.36/0.77 thf(f371,plain,(
% 2.36/0.77 ! [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)))))),
% 2.36/0.77 inference(fool_elimination,[],[f370])).
% 2.36/0.77 thf(f370,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f86])).
% 2.36/0.77 thf(f86,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0,X26 : X0,X50 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X26) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X26),X50) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X50))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_less__trans)).
% 2.36/0.77 thf(f3021,plain,(
% 2.36/0.77 spl108_109),
% 2.36/0.77 inference(avatar_split_clause,[],[f1681,f3019])).
% 2.36/0.77 thf(f3019,plain,(
% 2.36/0.77 spl108_109 <=> ! [X0 : $tType,X4 : X0,X3 : binary1291135688e_Tree(X0),X2 : X0 > int] : (vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),binary1746293266le_Tip(X0))) = X4)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_109])])).
% 2.36/0.77 thf(f1681,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X4 : X0] : ((vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),binary1746293266le_Tip(X0))) = X4)) )),
% 2.36/0.77 inference(equality_resolution,[],[f1591])).
% 2.36/0.77 thf(f1591,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0),X4 : X0] : ((vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = X4) | (binary1746293266le_Tip(X0) != X1)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1098])).
% 2.36/0.77 thf(f1098,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X4 : X0] : (((vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1) = vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1))) | (binary1746293266le_Tip(X0) = X1)) & ((vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = X4) | (binary1746293266le_Tip(X0) != X1)))),
% 2.36/0.77 inference(ennf_transformation,[],[f847])).
% 2.36/0.77 thf(f847,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0 > int,X3 : binary1291135688e_Tree(X0),X4 : X0] : (((binary1746293266le_Tip(X0) != X1) => (vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),X1) = vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)))) & ((binary1746293266le_Tip(X0) = X1) => (vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X2),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X1)) = X4)))),
% 2.36/0.77 inference(rectify,[],[f21])).
% 2.36/0.77 thf(f21,axiom,(
% 2.36/0.77 ! [X0 : $tType,X6 : binary1291135688e_Tree(X0),X3 : X0 > int,X4 : binary1291135688e_Tree(X0),X5 : X0] : (((binary1746293266le_Tip(X0) != X6) => (vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X3),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),X6)) = vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X3),X6))) & ((binary1746293266le_Tip(X0) = X6) => (vAPP(binary1291135688e_Tree(X0),X0,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),X0),binary576689334lle_rm(X0),X3),vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X4),X5),X6)) = X5)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_rm_Osimps)).
% 2.36/0.77 thf(f3017,plain,(
% 2.36/0.77 spl108_108),
% 2.36/0.77 inference(avatar_split_clause,[],[f1651,f3014])).
% 2.36/0.77 thf(f1651,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),vAPP(binary1291135688e_Tree(a),sTfun(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a))),binary210054475elle_T(a),t1),x),t2)) = $true)),
% 2.36/0.77 inference(cnf_transformation,[],[f801])).
% 2.36/0.77 thf(f801,plain,(
% 2.36/0.77 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),vAPP(binary1291135688e_Tree(a),sTfun(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a))),binary210054475elle_T(a),t1),x),t2)) = $true)),
% 2.36/0.77 inference(fool_elimination,[],[f800])).
% 2.36/0.77 thf(f800,plain,(
% 2.36/0.77 vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),vAPP(binary1291135688e_Tree(a),sTfun(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a))),binary210054475elle_T(a),t1),x),t2))),
% 2.36/0.77 inference(rectify,[],[f2])).
% 2.36/0.77 thf(f2,axiom,(
% 2.36/0.77 vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),vAPP(binary1291135688e_Tree(a),binary1291135688e_Tree(a),vAPP(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a)),vAPP(binary1291135688e_Tree(a),sTfun(a,sTfun(binary1291135688e_Tree(a),binary1291135688e_Tree(a))),binary210054475elle_T(a),t1),x),t2))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_s)).
% 2.36/0.77 thf(f2991,plain,(
% 2.36/0.77 spl108_107),
% 2.36/0.77 inference(avatar_split_clause,[],[f1560,f2989])).
% 2.36/0.77 thf(f2989,plain,(
% 2.36/0.77 spl108_107 <=> ! [X1 : $tType,X0 : $tType,X3 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1,X2 : X1] : (vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1)),binary536355927e_Tree(X1,X0),X2),X3),binary1746293266le_Tip(X0)) = X2)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_107])])).
% 2.36/0.77 thf(f1560,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : X1,X3 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1] : ((vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1)),binary536355927e_Tree(X1,X0),X2),X3),binary1746293266le_Tip(X0)) = X2)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f843])).
% 2.36/0.77 thf(f843,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : X1,X3 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1] : (vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1)),binary536355927e_Tree(X1,X0),X2),X3),binary1746293266le_Tip(X0)) = X2)),
% 2.36/0.77 inference(rectify,[],[f25])).
% 2.36/0.77 thf(f25,axiom,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X31 : X1,X32 : binary1291135688e_Tree(X0) > X0 > binary1291135688e_Tree(X0) > X1] : (vAPP(binary1291135688e_Tree(X0),X1,vAPP(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1),vAPP(X1,sTfun(sTfun(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),X1))),sTfun(binary1291135688e_Tree(X0),X1)),binary536355927e_Tree(X1,X0),X31),X32),binary1746293266le_Tip(X0)) = X31)),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_Tree_Osimps_I4_J)).
% 2.36/0.77 thf(f2987,plain,(
% 2.36/0.77 spl108_106),
% 2.36/0.77 inference(avatar_split_clause,[],[f1330,f2985])).
% 2.36/0.77 thf(f2985,plain,(
% 2.36/0.77 spl108_106 <=> ! [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),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))) | (dense_linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_106])])).
% 2.36/0.77 thf(f1330,plain,(
% 2.36/0.77 ( ! [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),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))) | (dense_linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1158])).
% 2.36/0.77 thf(f1158,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))))) | (dense_linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f873,f1157])).
% 2.36/0.77 thf(f1157,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X1),X3))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f873,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)) | ? [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(X0),X1),X3)))) | (dense_linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f333])).
% 2.36/0.77 thf(f333,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((dense_linorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f332])).
% 2.36/0.77 thf(f332,plain,(
% 2.36/0.77 ! [X0 : $tType] : (dense_linorder(X0) => ! [X1 : X0,X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X3)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X2),X1)))),
% 2.36/0.77 inference(rectify,[],[f143])).
% 2.36/0.77 thf(f143,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (dense_linorder(X0) => ! [X50 : X0,X26 : X0] : (! [X38 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X50),X38) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X38)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X50)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_142_dense__ge)).
% 2.36/0.77 thf(f2983,plain,(
% 2.36/0.77 spl108_105),
% 2.36/0.77 inference(avatar_split_clause,[],[f1329,f2981])).
% 2.36/0.77 thf(f2981,plain,(
% 2.36/0.77 spl108_105 <=> ! [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(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))) | (dense_linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_105])])).
% 2.36/0.77 thf(f1329,plain,(
% 2.36/0.77 ( ! [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(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK13(X0),X2),X1))) | (dense_linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1158])).
% 2.36/0.77 thf(f2979,plain,(
% 2.36/0.77 spl108_104),
% 2.36/0.77 inference(avatar_split_clause,[],[f1328,f2977])).
% 2.36/0.77 thf(f2977,plain,(
% 2.36/0.77 spl108_104 <=> ! [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),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X2)) | (dense_linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_104])])).
% 2.36/0.77 thf(f1328,plain,(
% 2.36/0.77 ( ! [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),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X2)) | (dense_linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1156])).
% 2.36/0.77 thf(f1156,plain,(
% 2.36/0.77 ! [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,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X1)))) | (dense_linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f872,f1155])).
% 2.36/0.77 thf(f1155,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X3),X1))) => (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X1))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f872,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)) | ? [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(X0),X3),X1)))) | (dense_linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f331])).
% 2.36/0.77 thf(f331,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((dense_linorder(X0) = $true) => ! [X1 : X0,X2 : X0] : (! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2))) => ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f330])).
% 2.36/0.77 thf(f330,plain,(
% 2.36/0.77 ! [X0 : $tType] : (dense_linorder(X0) => ! [X1 : X0,X2 : X0] : (! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X2)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X2)))),
% 2.36/0.77 inference(rectify,[],[f144])).
% 2.36/0.77 thf(f144,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (dense_linorder(X0) => ! [X26 : X0,X50 : X0] : (! [X38 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X38),X26) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X38),X50)) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X50)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_143_dense__le)).
% 2.36/0.77 thf(f2973,plain,(
% 2.36/0.77 spl108_103),
% 2.36/0.77 inference(avatar_split_clause,[],[f1327,f2971])).
% 2.36/0.77 thf(f2971,plain,(
% 2.36/0.77 spl108_103 <=> ! [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),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X1)) | (dense_linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_103])])).
% 2.36/0.77 thf(f1327,plain,(
% 2.36/0.77 ( ! [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),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK12(X0),X2),X1)),X1)) | (dense_linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1156])).
% 2.36/0.77 thf(f2969,plain,(
% 2.36/0.77 spl108_102),
% 2.36/0.77 inference(avatar_split_clause,[],[f1314,f2967])).
% 2.36/0.77 thf(f2967,plain,(
% 2.36/0.77 spl108_102 <=> ! [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),sK6(X0),X2),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_102])])).
% 2.36/0.77 thf(f1314,plain,(
% 2.36/0.77 ( ! [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),sK6(X0),X2),X1)),X2)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1141])).
% 2.36/0.77 thf(f1141,plain,(
% 2.36/0.77 ! [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),sK6(X0),X2),X1)),X2)) & ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,vAPP(X0,sTfun(X0,X0),sK6(X0),X2),X1)))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))) | (dense_order(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f865,f1140])).
% 2.36/0.77 thf(f1140,plain,(
% 2.36/0.77 ! [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),sK6(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),sK6(X0),X2),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f865,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f319])).
% 2.36/0.77 thf(f319,plain,(
% 2.36/0.77 ! [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)))))),
% 2.36/0.77 inference(fool_elimination,[],[f318])).
% 2.36/0.77 thf(f318,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f82])).
% 2.36/0.77 thf(f82,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (dense_order(X0) => ! [X5 : X0,X26 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X26) => ? [X54 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X26) & vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X54))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_dense)).
% 2.36/0.77 thf(f2965,plain,(
% 2.36/0.77 spl108_101),
% 2.36/0.77 inference(avatar_split_clause,[],[f1313,f2963])).
% 2.36/0.77 thf(f2963,plain,(
% 2.36/0.77 spl108_101 <=> ! [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),sK6(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_101])])).
% 2.36/0.77 thf(f1313,plain,(
% 2.36/0.77 ( ! [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),sK6(X0),X2),X1))) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (dense_order(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1141])).
% 2.36/0.77 thf(f2956,plain,(
% 2.36/0.77 spl108_100),
% 2.36/0.77 inference(avatar_split_clause,[],[f1503,f2954])).
% 2.36/0.77 thf(f2954,plain,(
% 2.36/0.77 spl108_100 <=> ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK77(X0),X1)),X1)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_100])])).
% 2.36/0.77 thf(f1503,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK77(X0),X1)),X1))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1253])).
% 2.36/0.77 thf(f1253,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0)))) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK77(X0),X1)),X1)))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK77])],[f1033,f1252])).
% 2.36/0.77 thf(f1252,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK77(X0),X1)),X1)))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1033,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0)))) | ? [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))),
% 2.36/0.77 inference(ennf_transformation,[],[f830])).
% 2.36/0.77 thf(f830,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0)))))),
% 2.36/0.77 inference(flattening,[],[f587])).
% 2.36/0.77 thf(f587,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0)))))),
% 2.36/0.77 inference(fool_elimination,[],[f586])).
% 2.36/0.77 thf(f586,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),bot_bot(set(X0))))),
% 2.36/0.77 inference(rectify,[],[f167])).
% 2.36/0.77 thf(f167,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0)] : (! [X38 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X38),X36) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),bot_bot(set(X0))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_166_subset__emptyI)).
% 2.36/0.77 thf(f2952,plain,(
% 2.36/0.77 spl108_99),
% 2.36/0.77 inference(avatar_split_clause,[],[f1312,f2950])).
% 2.36/0.77 thf(f2950,plain,(
% 2.36/0.77 spl108_99 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK5(X0),X1)),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK5(X0),X1))) | (condit1656338222tinuum(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_99])])).
% 2.36/0.77 thf(f1312,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK5(X0),X1)),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK5(X0),X1))) | (condit1656338222tinuum(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1139])).
% 2.36/0.77 thf(f1139,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK5(X0),X1)),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK5(X0),X1)))) | (condit1656338222tinuum(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f864,f1138])).
% 2.36/0.77 thf(f1138,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X1),X2))) => (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK5(X0),X1)),X1)) | ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK5(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f864,plain,(
% 2.36/0.77 ! [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))) | (condit1656338222tinuum(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f317])).
% 2.36/0.77 thf(f317,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((condit1656338222tinuum(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : (($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))))),
% 2.36/0.77 inference(fool_elimination,[],[f316])).
% 2.36/0.77 thf(f316,plain,(
% 2.36/0.77 ! [X0 : $tType] : (condit1656338222tinuum(X0) => ! [X1 : X0] : ? [X2 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 2.36/0.77 inference(rectify,[],[f192])).
% 2.36/0.77 thf(f192,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (condit1656338222tinuum(X0) => ! [X18 : X0] : ? [X52 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X52),X18) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X52)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_191_ex__gt__or__lt)).
% 2.36/0.77 thf(f2938,plain,(
% 2.36/0.77 spl108_98),
% 2.36/0.77 inference(avatar_split_clause,[],[f1555,f2936])).
% 2.36/0.77 thf(f2936,plain,(
% 2.36/0.77 spl108_98 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_98])])).
% 2.36/0.77 thf(f1555,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1070])).
% 2.36/0.77 thf(f1070,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : ((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1069])).
% 2.36/0.77 thf(f1069,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (((X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f665])).
% 2.36/0.77 thf(f665,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) => (X1 = X2)))),
% 2.36/0.77 inference(fool_elimination,[],[f664])).
% 2.36/0.77 thf(f664,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1) => (X1 = X2)))),
% 2.36/0.77 inference(rectify,[],[f34])).
% 2.36/0.77 thf(f34,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37) => (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X37),X36) => (X36 = X37)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_subset__antisym)).
% 2.36/0.77 thf(f2930,plain,(
% 2.36/0.77 spl108_97),
% 2.36/0.77 inference(avatar_split_clause,[],[f1554,f2928])).
% 2.36/0.77 thf(f2928,plain,(
% 2.36/0.77 spl108_97 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) | (X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_97])])).
% 2.36/0.77 thf(f1554,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) | (X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1068])).
% 2.36/0.77 thf(f1068,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) | (X1 = X2) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(flattening,[],[f1067])).
% 2.36/0.77 thf(f1067,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : ((($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) | (X1 = X2)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f663])).
% 2.36/0.77 thf(f663,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => ((X1 != X2) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f662])).
% 2.36/0.77 thf(f662,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => ((X1 != X2) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(rectify,[],[f175])).
% 2.36/0.77 thf(f175,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37) => ((X36 != X37) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X37)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_174_psubsetI)).
% 2.36/0.77 thf(f2923,plain,(
% 2.36/0.77 spl108_96),
% 2.36/0.77 inference(avatar_split_clause,[],[f1318,f2921])).
% 2.36/0.77 thf(f2921,plain,(
% 2.36/0.77 spl108_96 <=> ! [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,sK9(X0),X1))) | (wellorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_96])])).
% 2.36/0.77 thf(f1318,plain,(
% 2.36/0.77 ( ! [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,sK9(X0),X1))) | (wellorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1147])).
% 2.36/0.77 thf(f1147,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0 > $o,X2 : X0] : (($true = vAPP(X0,$o,X1,X2)) | (($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK9(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,sK9(X0),X1)))))) | (wellorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f869,f1146])).
% 2.36/0.77 thf(f1146,plain,(
% 2.36/0.77 ! [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,$o),X0,sK9(X0),X1))) & ! [X4 : X0] : (($true = vAPP(X0,$o,X1,X4)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X4),vAPP(sTfun(X0,$o),X0,sK9(X0),X1))))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f869,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f327])).
% 2.36/0.77 thf(f327,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(fool_elimination,[],[f326])).
% 2.36/0.77 thf(f326,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f94])).
% 2.36/0.77 thf(f94,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (wellorder(X0) => ! [X21 : X0 > $o,X18 : X0] : (! [X38 : X0] : (! [X55 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X55),X38) => vAPP(X0,$o,X21,X55)) => vAPP(X0,$o,X21,X38)) => vAPP(X0,$o,X21,X18)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_less__induct)).
% 2.36/0.77 thf(f2912,plain,(
% 2.36/0.77 spl108_95),
% 2.36/0.77 inference(avatar_split_clause,[],[f1476,f2910])).
% 2.36/0.77 thf(f2910,plain,(
% 2.36/0.77 spl108_95 <=> ! [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)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_95])])).
% 2.36/0.77 thf(f1476,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f559])).
% 2.36/0.77 thf(f559,plain,(
% 2.36/0.77 ! [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)),
% 2.36/0.77 inference(fool_elimination,[],[f558])).
% 2.36/0.77 thf(f558,plain,(
% 2.36/0.77 ! [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)),
% 2.36/0.77 inference(rectify,[],[f47])).
% 2.36/0.77 thf(f47,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0)] : (vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X30 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X30),X36)))) = X36)),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Collect__mem__eq)).
% 2.36/0.77 thf(f2864,plain,(
% 2.36/0.77 spl108_94),
% 2.36/0.77 inference(avatar_split_clause,[],[f1372,f2862])).
% 2.36/0.77 thf(f2862,plain,(
% 2.36/0.77 spl108_94 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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(X0),X3),vAPP(X0,X0,sK27(X0),X1))) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_94])])).
% 2.36/0.77 thf(f1372,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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(X0),X3),vAPP(X0,X0,sK27(X0),X1))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1186])).
% 2.36/0.77 thf(f1186,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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(X0),X3),vAPP(X0,X0,sK27(X0),X1)))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f922,f1185])).
% 2.36/0.77 thf(f1185,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))) => ! [X3 : X0] : (($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(X0),X3),vAPP(X0,X0,sK27(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f922,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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(X0),X3),X2))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f409])).
% 2.36/0.77 thf(f409,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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_eq(X0),X3),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f408])).
% 2.36/0.77 thf(f408,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)))),
% 2.36/0.77 inference(rectify,[],[f169])).
% 2.36/0.77 thf(f169,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X54) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X65),X13)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_168_minf_I6_J)).
% 2.36/0.77 thf(f2860,plain,(
% 2.36/0.77 spl108_93),
% 2.36/0.77 inference(avatar_split_clause,[],[f1371,f2858])).
% 2.36/0.77 thf(f2858,plain,(
% 2.36/0.77 spl108_93 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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(X0),vAPP(X0,X0,sK26(X0),X1)),X3)) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_93])])).
% 2.36/0.77 thf(f1371,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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(X0),vAPP(X0,X0,sK26(X0),X1)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1184])).
% 2.36/0.77 thf(f1184,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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(X0),vAPP(X0,X0,sK26(X0),X1)),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f921,f1183])).
% 2.36/0.77 thf(f1183,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X2),X3))) => ! [X3 : X0] : (($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(X0),vAPP(X0,X0,sK26(X0),X1)),X3))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f921,plain,(
% 2.36/0.77 ! [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(X0),X2),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f407])).
% 2.36/0.77 thf(f407,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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_eq(X0),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f406])).
% 2.36/0.77 thf(f406,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f170])).
% 2.36/0.77 thf(f170,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X65) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X13),X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_169_pinf_I8_J)).
% 2.36/0.77 thf(f2856,plain,(
% 2.36/0.77 spl108_92),
% 2.36/0.77 inference(avatar_split_clause,[],[f1370,f2854])).
% 2.36/0.77 thf(f2854,plain,(
% 2.36/0.77 spl108_92 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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),vAPP(X0,X0,sK25(X0),X1))) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_92])])).
% 2.36/0.77 thf(f1370,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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),vAPP(X0,X0,sK25(X0),X1))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1182])).
% 2.36/0.77 thf(f1182,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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),vAPP(X0,X0,sK25(X0),X1)))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f920,f1181])).
% 2.36/0.77 thf(f1181,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))) => ! [X3 : X0] : (($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),vAPP(X0,X0,sK25(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f920,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f405])).
% 2.36/0.77 thf(f405,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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))))),
% 2.36/0.77 inference(fool_elimination,[],[f404])).
% 2.36/0.77 thf(f404,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)))),
% 2.36/0.77 inference(rectify,[],[f205])).
% 2.36/0.77 thf(f205,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X54) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X13)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_204_minf_I5_J)).
% 2.36/0.77 thf(f2852,plain,(
% 2.36/0.77 spl108_91),
% 2.36/0.77 inference(avatar_split_clause,[],[f1369,f2850])).
% 2.36/0.77 thf(f2850,plain,(
% 2.36/0.77 spl108_91 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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,sK24(X0),X1)),X3)) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_91])])).
% 2.36/0.77 thf(f1369,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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,sK24(X0),X1)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1180])).
% 2.36/0.77 thf(f1180,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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,sK24(X0),X1)),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK24])],[f919,f1179])).
% 2.36/0.77 thf(f1179,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X2),X3))) => ! [X3 : X0] : (($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,sK24(X0),X1)),X3))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f919,plain,(
% 2.36/0.77 ! [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))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f403])).
% 2.36/0.77 thf(f403,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f402])).
% 2.36/0.77 thf(f402,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f199])).
% 2.36/0.77 thf(f199,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X65) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X13),X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_198_pinf_I7_J)).
% 2.36/0.77 thf(f2848,plain,(
% 2.36/0.77 spl108_90),
% 2.36/0.77 inference(avatar_split_clause,[],[f1368,f2846])).
% 2.36/0.77 thf(f2846,plain,(
% 2.36/0.77 spl108_90 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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(X0),X3),vAPP(X0,X0,sK23(X0),X1))) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_90])])).
% 2.36/0.77 thf(f1368,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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(X0),X3),vAPP(X0,X0,sK23(X0),X1))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1178])).
% 2.36/0.77 thf(f1178,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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(X0),X3),vAPP(X0,X0,sK23(X0),X1)))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK23])],[f918,f1177])).
% 2.36/0.77 thf(f1177,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X3),X2))) => ! [X3 : X0] : (($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(X0),X3),vAPP(X0,X0,sK23(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f918,plain,(
% 2.36/0.77 ! [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(X0),X3),X2))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f813])).
% 2.36/0.77 thf(f813,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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_eq(X0),X1),X3))))),
% 2.36/0.77 inference(flattening,[],[f401])).
% 2.36/0.77 thf(f401,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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_eq(X0),X1),X3))))),
% 2.36/0.77 inference(fool_elimination,[],[f400])).
% 2.36/0.77 thf(f400,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f168])).
% 2.36/0.77 thf(f168,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X54) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X13),X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_167_minf_I8_J)).
% 2.36/0.77 thf(f2844,plain,(
% 2.36/0.77 spl108_89),
% 2.36/0.77 inference(avatar_split_clause,[],[f1367,f2842])).
% 2.36/0.77 thf(f2842,plain,(
% 2.36/0.77 spl108_89 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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(X0),vAPP(X0,X0,sK22(X0),X1)),X3)) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_89])])).
% 2.36/0.77 thf(f1367,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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(X0),vAPP(X0,X0,sK22(X0),X1)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1176])).
% 2.36/0.77 thf(f1176,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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(X0),vAPP(X0,X0,sK22(X0),X1)),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f917,f1175])).
% 2.36/0.77 thf(f1175,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) => ! [X3 : X0] : (($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(X0),vAPP(X0,X0,sK22(X0),X1)),X3))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f917,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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(X0),X2),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f812])).
% 2.36/0.77 thf(f812,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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_eq(X0),X3),X1))))),
% 2.36/0.77 inference(flattening,[],[f399])).
% 2.36/0.77 thf(f399,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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_eq(X0),X3),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f398])).
% 2.36/0.77 thf(f398,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X3),X1)))),
% 2.36/0.77 inference(rectify,[],[f171])).
% 2.36/0.77 thf(f171,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X65) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X65),X13)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_170_pinf_I6_J)).
% 2.36/0.77 thf(f2840,plain,(
% 2.36/0.77 spl108_88),
% 2.36/0.77 inference(avatar_split_clause,[],[f1366,f2838])).
% 2.36/0.77 thf(f2838,plain,(
% 2.36/0.77 spl108_88 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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),vAPP(X0,X0,sK21(X0),X1)),X3)) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_88])])).
% 2.36/0.77 thf(f1366,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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),vAPP(X0,X0,sK21(X0),X1)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1174])).
% 2.36/0.77 thf(f1174,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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),vAPP(X0,X0,sK21(X0),X1)),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK21])],[f916,f1173])).
% 2.36/0.77 thf(f1173,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) => ! [X3 : X0] : (($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),vAPP(X0,X0,sK21(X0),X1)),X3))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f916,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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),X2),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f811])).
% 2.36/0.77 thf(f811,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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),X3),X1))))),
% 2.36/0.77 inference(flattening,[],[f397])).
% 2.36/0.77 thf(f397,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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),X3),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f396])).
% 2.36/0.77 thf(f396,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X1)))),
% 2.36/0.77 inference(rectify,[],[f198])).
% 2.36/0.77 thf(f198,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X65) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X13)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_197_pinf_I5_J)).
% 2.36/0.77 thf(f2832,plain,(
% 2.36/0.77 spl108_87),
% 2.36/0.77 inference(avatar_split_clause,[],[f1365,f2830])).
% 2.36/0.77 thf(f2830,plain,(
% 2.36/0.77 spl108_87 <=> ! [X0 : $tType,X1 : X0,X3 : X0] : (($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),X3),vAPP(X0,X0,sK20(X0),X1))) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_87])])).
% 2.36/0.77 thf(f1365,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : (($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),X3),vAPP(X0,X0,sK20(X0),X1))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1172])).
% 2.36/0.77 thf(f1172,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : (($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),X3),vAPP(X0,X0,sK20(X0),X1)))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK20])],[f915,f1171])).
% 2.36/0.77 thf(f1171,plain,(
% 2.36/0.77 ! [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,$o),ord_less(X0),X3),X2))) => ! [X3 : X0] : (($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),X3),vAPP(X0,X0,sK20(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f915,plain,(
% 2.36/0.77 ! [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),X3),X2))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f810])).
% 2.36/0.77 thf(f810,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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))))),
% 2.36/0.77 inference(flattening,[],[f395])).
% 2.36/0.77 thf(f395,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($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))))),
% 2.36/0.77 inference(fool_elimination,[],[f394])).
% 2.36/0.77 thf(f394,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X3)))),
% 2.36/0.77 inference(rectify,[],[f206])).
% 2.36/0.77 thf(f206,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X54) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X13),X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_205_minf_I7_J)).
% 2.36/0.77 thf(f2798,plain,(
% 2.36/0.77 spl108_86),
% 2.36/0.77 inference(avatar_split_clause,[],[f1575,f2796])).
% 2.36/0.77 thf(f2796,plain,(
% 2.36/0.77 spl108_86 <=> ! [X0 : $tType,X3 : X0 > $o,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) | ($true != vAPP(X0,$o,X1,X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_86])])).
% 2.36/0.77 thf(f1575,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) | ($true != vAPP(X0,$o,X1,X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1076])).
% 2.36/0.77 thf(f1076,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) | ($true != vAPP(X0,$o,X1,X2)))),
% 2.36/0.77 inference(flattening,[],[f1075])).
% 2.36/0.77 thf(f1075,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : ((($true = vAPP(X0,$o,X3,X2)) | ($true != vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3))) | ($true != vAPP(X0,$o,X1,X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f691])).
% 2.36/0.77 thf(f691,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) => (($true = vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3)) => ($true = vAPP(X0,$o,X3,X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f690])).
% 2.36/0.77 thf(f690,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0 > $o] : (vAPP(X0,$o,X1,X2) => (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X1),X3) => vAPP(X0,$o,X3,X2)))),
% 2.36/0.77 inference(rectify,[],[f215])).
% 2.36/0.77 thf(f215,axiom,(
% 2.36/0.77 ! [X0 : $tType,X21 : X0 > $o,X5 : X0,X43 : X0 > $o] : (vAPP(X0,$o,X21,X5) => (vAPP(sTfun(X0,$o),$o,vAPP(sTfun(X0,$o),sTfun(sTfun(X0,$o),$o),ord_less_eq(sTfun(X0,$o)),X21),X43) => vAPP(X0,$o,X43,X5)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_214_rev__predicate1D)).
% 2.36/0.77 thf(f2794,plain,(
% 2.36/0.77 spl108_85),
% 2.36/0.77 inference(avatar_split_clause,[],[f1552,f2792])).
% 2.36/0.77 thf(f2792,plain,(
% 2.36/0.77 spl108_85 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_85])])).
% 2.36/0.77 thf(f1552,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1065])).
% 2.36/0.77 thf(f1065,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : ((($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)) & ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2))) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 inference(ennf_transformation,[],[f659])).
% 2.36/0.77 thf(f659,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)) => ~(($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) => ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f658])).
% 2.36/0.77 thf(f658,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0),X2 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2) => ~(vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X2),X1)))),
% 2.36/0.77 inference(rectify,[],[f189])).
% 2.36/0.77 thf(f189,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0),X37 : set(X0)] : (vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),X37) => ~(vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X37) => vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X37),X36)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_188_psubsetE)).
% 2.36/0.77 thf(f2790,plain,(
% 2.36/0.77 spl108_84),
% 2.36/0.77 inference(avatar_split_clause,[],[f1551,f2788])).
% 2.36/0.77 thf(f2788,plain,(
% 2.36/0.77 spl108_84 <=> ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_84])])).
% 2.36/0.77 thf(f1551,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : set(X0),X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X2)) | ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),X2))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1065])).
% 2.36/0.77 thf(f2786,plain,(
% 2.36/0.77 spl108_83),
% 2.36/0.77 inference(avatar_split_clause,[],[f1528,f2784])).
% 2.36/0.77 thf(f2784,plain,(
% 2.36/0.77 spl108_83 <=> ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : (vAPP(product_prod(X1,X0),product_prod(X1,X0),vAPP(sTfun(X1,sTfun(X0,product_prod(X1,X0))),sTfun(product_prod(X1,X0),product_prod(X1,X0)),product_case_prod(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X2) = X2)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_83])])).
% 2.36/0.77 thf(f1528,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType,X2 : product_prod(X1,X0)] : ((vAPP(product_prod(X1,X0),product_prod(X1,X0),vAPP(sTfun(X1,sTfun(X0,product_prod(X1,X0))),sTfun(product_prod(X1,X0),product_prod(X1,X0)),product_case_prod(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X2) = X2)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f836])).
% 2.36/0.77 thf(f836,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType,X2 : product_prod(X1,X0)] : (vAPP(product_prod(X1,X0),product_prod(X1,X0),vAPP(sTfun(X1,sTfun(X0,product_prod(X1,X0))),sTfun(product_prod(X1,X0),product_prod(X1,X0)),product_case_prod(X1,X0,product_prod(X1,X0)),product_Pair(X1,X0)),X2) = X2)),
% 2.36/0.77 inference(rectify,[],[f226])).
% 2.36/0.77 thf(f226,axiom,(
% 2.36/0.77 ! [X1 : $tType,X0 : $tType,X84 : product_prod(X0,X1)] : (vAPP(product_prod(X0,X1),product_prod(X0,X1),vAPP(sTfun(X0,sTfun(X1,product_prod(X0,X1))),sTfun(product_prod(X0,X1),product_prod(X0,X1)),product_case_prod(X0,X1,product_prod(X0,X1)),product_Pair(X0,X1)),X84) = X84)),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_225_case__prod__Pair__iden)).
% 2.36/0.77 thf(f2782,plain,(
% 2.36/0.77 spl108_82),
% 2.36/0.77 inference(avatar_split_clause,[],[f1395,f2780])).
% 2.36/0.77 thf(f2780,plain,(
% 2.36/0.77 spl108_82 <=> ! [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)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_82])])).
% 2.36/0.77 thf(f1395,plain,(
% 2.36/0.77 ( ! [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))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1194])).
% 2.36/0.77 thf(f1194,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f1193])).
% 2.36/0.77 thf(f1193,plain,(
% 2.36/0.77 ! [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)),sP1(X0),X1),X2),X3)))),
% 2.36/0.77 inference(nnf_transformation,[],[f1133])).
% 2.36/0.77 thf(f1133,plain,(
% 2.36/0.77 ! [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)),sP1(X0),X1),X2),X3)))),
% 2.36/0.77 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 2.36/0.77 thf(f2778,plain,(
% 2.36/0.77 spl108_81),
% 2.36/0.77 inference(avatar_split_clause,[],[f1394,f2776])).
% 2.36/0.77 thf(f2776,plain,(
% 2.36/0.77 spl108_81 <=> ! [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)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_81])])).
% 2.36/0.77 thf(f1394,plain,(
% 2.36/0.77 ( ! [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))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1194])).
% 2.36/0.77 thf(f2774,plain,(
% 2.36/0.77 spl108_80 | ~spl108_13 | ~spl108_28),
% 2.36/0.77 inference(avatar_split_clause,[],[f2394,f2356,f2261,f2772])).
% 2.36/0.77 thf(f2772,plain,(
% 2.36/0.77 spl108_80 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,int)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_80])])).
% 2.36/0.77 thf(f2261,plain,(
% 2.36/0.77 spl108_13 <=> (order(int) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_13])])).
% 2.36/0.77 thf(f2394,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,int)))) ) | (~spl108_13 | ~spl108_28)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2387])).
% 2.36/0.77 thf(f2387,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,int)))) ) | (~spl108_13 | ~spl108_28)),
% 2.36/0.77 inference(superposition,[],[f2357,f2263])).
% 2.36/0.77 thf(f2263,plain,(
% 2.36/0.77 (order(int) = $true) | ~spl108_13),
% 2.36/0.77 inference(avatar_component_clause,[],[f2261])).
% 2.36/0.77 thf(f2770,plain,(
% 2.36/0.77 spl108_79),
% 2.36/0.77 inference(avatar_split_clause,[],[f1393,f2768])).
% 2.36/0.77 thf(f2768,plain,(
% 2.36/0.77 spl108_79 <=> ! [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)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_79])])).
% 2.36/0.77 thf(f1393,plain,(
% 2.36/0.77 ( ! [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))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1192])).
% 2.36/0.77 thf(f1192,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f1191])).
% 2.36/0.77 thf(f1191,plain,(
% 2.36/0.77 ! [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)),sP2(X0),X2),X1),X3)))),
% 2.36/0.77 inference(nnf_transformation,[],[f1134])).
% 2.36/0.77 thf(f1134,plain,(
% 2.36/0.77 ! [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)),sP2(X0),X2),X1),X3)))),
% 2.36/0.77 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 2.36/0.77 thf(f2766,plain,(
% 2.36/0.77 spl108_78),
% 2.36/0.77 inference(avatar_split_clause,[],[f1392,f2764])).
% 2.36/0.77 thf(f2764,plain,(
% 2.36/0.77 spl108_78 <=> ! [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)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_78])])).
% 2.36/0.77 thf(f1392,plain,(
% 2.36/0.77 ( ! [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))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1192])).
% 2.36/0.77 thf(f2762,plain,(
% 2.36/0.77 spl108_77),
% 2.36/0.77 inference(avatar_split_clause,[],[f1391,f2760])).
% 2.36/0.77 thf(f2760,plain,(
% 2.36/0.77 spl108_77 <=> ! [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)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_77])])).
% 2.36/0.77 thf(f1391,plain,(
% 2.36/0.77 ( ! [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))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1190])).
% 2.36/0.77 thf(f1190,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f1189])).
% 2.36/0.77 thf(f1189,plain,(
% 2.36/0.77 ! [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)),sP3(X0),X1),X3),X2)))),
% 2.36/0.77 inference(nnf_transformation,[],[f1135])).
% 2.36/0.77 thf(f1135,plain,(
% 2.36/0.77 ! [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)),sP3(X0),X1),X3),X2)))),
% 2.36/0.77 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 2.36/0.77 thf(f2758,plain,(
% 2.36/0.77 spl108_76),
% 2.36/0.77 inference(avatar_split_clause,[],[f1390,f2756])).
% 2.36/0.77 thf(f2756,plain,(
% 2.36/0.77 spl108_76 <=> ! [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)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_76])])).
% 2.36/0.77 thf(f1390,plain,(
% 2.36/0.77 ( ! [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))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1190])).
% 2.36/0.77 thf(f2754,plain,(
% 2.36/0.77 spl108_75),
% 2.36/0.77 inference(avatar_split_clause,[],[f1389,f2752])).
% 2.36/0.77 thf(f2752,plain,(
% 2.36/0.77 spl108_75 <=> ! [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)),sP4(X2),X3),X1),X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_75])])).
% 2.36/0.77 thf(f1389,plain,(
% 2.36/0.77 ( ! [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)),sP4(X2),X3),X1),X0))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1188])).
% 2.36/0.77 thf(f1188,plain,(
% 2.36/0.77 ! [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)),sP4(X2),X3),X1),X0)))),
% 2.36/0.77 inference(rectify,[],[f1187])).
% 2.36/0.77 thf(f1187,plain,(
% 2.36/0.77 ! [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)),sP4(X0),X3),X2),X1)))),
% 2.36/0.77 inference(nnf_transformation,[],[f1136])).
% 2.36/0.77 thf(f1136,plain,(
% 2.36/0.77 ! [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)),sP4(X0),X3),X2),X1)))),
% 2.36/0.77 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 2.36/0.77 thf(f2750,plain,(
% 2.36/0.77 spl108_74),
% 2.36/0.77 inference(avatar_split_clause,[],[f1388,f2748])).
% 2.36/0.77 thf(f2748,plain,(
% 2.36/0.77 spl108_74 <=> ! [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)),sP4(X2),X3),X1),X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_74])])).
% 2.36/0.77 thf(f1388,plain,(
% 2.36/0.77 ( ! [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)),sP4(X2),X3),X1),X0))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1188])).
% 2.36/0.77 thf(f2746,plain,(
% 2.36/0.77 spl108_73),
% 2.36/0.77 inference(avatar_split_clause,[],[f1311,f2744])).
% 2.36/0.77 thf(f2744,plain,(
% 2.36/0.77 spl108_73 <=> ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),bot_bot(set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_73])])).
% 2.36/0.77 thf(f1311,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : ((bot_bot(sTfun(X0,$o)) = vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),bot_bot(set(X0))))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f315])).
% 2.36/0.77 thf(f315,plain,(
% 2.36/0.77 ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = vAPP(set(X0),sTfun(X0,$o),vAPP(sTfun(X0,sTfun(set(X0),$o)),sTfun(set(X0),sTfun(X0,$o)),cCOMB,member(X0)),bot_bot(set(X0))))),
% 2.36/0.77 inference(fool_elimination,[],[f314])).
% 2.36/0.77 thf(f314,plain,(
% 2.36/0.77 ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = (^[X1 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))))),
% 2.36/0.77 inference(rectify,[],[f210])).
% 2.36/0.77 thf(f210,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (bot_bot(sTfun(X0,$o)) = (^[X30 : X0] : (vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X30),bot_bot(set(X0))))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_209_bot__empty__eq)).
% 2.36/0.77 thf(f2723,plain,(
% 2.36/0.77 spl108_72 | ~spl108_14 | ~spl108_28),
% 2.36/0.77 inference(avatar_split_clause,[],[f2393,f2356,f2266,f2721])).
% 2.36/0.77 thf(f2721,plain,(
% 2.36/0.77 spl108_72 <=> ! [X0 : $tType] : ($true = order(sTfun(X0,$o)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_72])])).
% 2.36/0.77 thf(f2266,plain,(
% 2.36/0.77 spl108_14 <=> (order($o) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_14])])).
% 2.36/0.77 thf(f2393,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = order(sTfun(X0,$o)))) ) | (~spl108_14 | ~spl108_28)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2388])).
% 2.36/0.77 thf(f2388,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order(sTfun(X0,$o)))) ) | (~spl108_14 | ~spl108_28)),
% 2.36/0.77 inference(superposition,[],[f2357,f2268])).
% 2.36/0.77 thf(f2268,plain,(
% 2.36/0.77 (order($o) = $true) | ~spl108_14),
% 2.36/0.77 inference(avatar_component_clause,[],[f2266])).
% 2.36/0.77 thf(f2719,plain,(
% 2.36/0.77 spl108_71),
% 2.36/0.77 inference(avatar_split_clause,[],[f1451,f2717])).
% 2.36/0.77 thf(f2717,plain,(
% 2.36/0.77 spl108_71 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_71])])).
% 2.36/0.77 thf(f1451,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f985])).
% 2.36/0.77 thf(f985,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(flattening,[],[f984])).
% 2.36/0.77 thf(f984,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f509])).
% 2.36/0.77 thf(f509,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(fool_elimination,[],[f508])).
% 2.36/0.77 thf(f508,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f56])).
% 2.36/0.77 thf(f56,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X5 : X0,X26 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X26) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X5) => (X5 = X26))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_antisym)).
% 2.36/0.77 thf(f2715,plain,(
% 2.36/0.77 spl108_70),
% 2.36/0.77 inference(avatar_split_clause,[],[f1436,f2713])).
% 2.36/0.77 thf(f2713,plain,(
% 2.36/0.77 spl108_70 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_70])])).
% 2.36/0.77 thf(f1436,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f967])).
% 2.36/0.77 thf(f967,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(flattening,[],[f966])).
% 2.36/0.77 thf(f966,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f479])).
% 2.36/0.77 thf(f479,plain,(
% 2.36/0.77 ! [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)))))),
% 2.36/0.77 inference(fool_elimination,[],[f478])).
% 2.36/0.77 thf(f478,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(rectify,[],[f161])).
% 2.36/0.77 thf(f161,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X18 : X0,X19 : X0] : ((X18 != X19) => (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),X19) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X19))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_160_order_Onot__eq__order__implies__strict)).
% 2.36/0.77 thf(f2711,plain,(
% 2.36/0.77 spl108_69),
% 2.36/0.77 inference(avatar_split_clause,[],[f1378,f2709])).
% 2.36/0.77 thf(f2709,plain,(
% 2.36/0.77 spl108_69 <=> ! [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)) | (X1 = X2) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_69])])).
% 2.36/0.77 thf(f1378,plain,(
% 2.36/0.77 ( ! [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)) | (X1 = X2) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f928])).
% 2.36/0.77 thf(f928,plain,(
% 2.36/0.77 ! [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)) | (X1 = X2)) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f814])).
% 2.36/0.77 thf(f814,plain,(
% 2.36/0.77 ! [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)) | (X1 = X2)))),
% 2.36/0.77 inference(flattening,[],[f421])).
% 2.36/0.77 thf(f421,plain,(
% 2.36/0.77 ! [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)) | (X1 = X2)))),
% 2.36/0.77 inference(fool_elimination,[],[f420])).
% 2.36/0.77 thf(f420,plain,(
% 2.36/0.77 ! [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) | (X1 = X2)))),
% 2.36/0.77 inference(rectify,[],[f191])).
% 2.36/0.77 thf(f191,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X18 : X0,X19 : X0] : (~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X19),X18) | ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),X19) | (X18 = X19)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_190_verit__la__disequality)).
% 2.36/0.77 thf(f2683,plain,(
% 2.36/0.77 spl108_68),
% 2.36/0.77 inference(avatar_split_clause,[],[f1549,f2681])).
% 2.36/0.77 thf(f2681,plain,(
% 2.36/0.77 spl108_68 <=> ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0) > $o] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK87(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_68])])).
% 2.36/0.77 thf(f1549,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0) > $o] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK87(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1269])).
% 2.36/0.77 thf(f1269,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0) > $o,X2 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | (($true != vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK85(X0),X1)),vAPP(sTfun(binary1291135688e_Tree(X0),$o),X0,sK86(X0),X1)),vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK87(X0),X1)))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK87(X0),X1))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK85(X0),X1)))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0))))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK85,sK86,sK87])],[f1064,f1268])).
% 2.36/0.77 thf(f1268,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0) > $o] : (? [X3 : binary1291135688e_Tree(X0),X4 : X0,X5 : binary1291135688e_Tree(X0)] : (($true != vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X5))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X5)) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X3))) => (($true != vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK85(X0),X1)),vAPP(sTfun(binary1291135688e_Tree(X0),$o),X0,sK86(X0),X1)),vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK87(X0),X1)))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK87(X0),X1))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK85(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1064,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0) > $o,X2 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | ? [X3 : binary1291135688e_Tree(X0),X4 : X0,X5 : binary1291135688e_Tree(X0)] : (($true != vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X5))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X5)) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X3))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0))))),
% 2.36/0.77 inference(flattening,[],[f1063])).
% 2.36/0.77 thf(f1063,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0) > $o,X2 : binary1291135688e_Tree(X0)] : ((($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | ? [X3 : binary1291135688e_Tree(X0),X4 : X0,X5 : binary1291135688e_Tree(X0)] : ((($true != vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X5))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X5))) & ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X3)))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0))))),
% 2.36/0.77 inference(ennf_transformation,[],[f657])).
% 2.36/0.77 thf(f657,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0) > $o,X2 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0))) => (! [X3 : binary1291135688e_Tree(X0),X4 : X0,X5 : binary1291135688e_Tree(X0)] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X3)) => (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X5)) => ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X5))))) => ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f656])).
% 2.36/0.77 thf(f656,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0) > $o,X2 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0)) => (! [X3 : binary1291135688e_Tree(X0),X4 : X0,X5 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,X1,X3) => (vAPP(binary1291135688e_Tree(X0),$o,X1,X5) => vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X3),X4),X5)))) => vAPP(binary1291135688e_Tree(X0),$o,X1,X2)))),
% 2.36/0.77 inference(rectify,[],[f18])).
% 2.36/0.77 thf(f18,axiom,(
% 2.36/0.77 ! [X0 : $tType,X21 : binary1291135688e_Tree(X0) > $o,X22 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,X21,binary1746293266le_Tip(X0)) => (! [X23 : binary1291135688e_Tree(X0),X24 : X0,X25 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),$o,X21,X23) => (vAPP(binary1291135688e_Tree(X0),$o,X21,X25) => vAPP(binary1291135688e_Tree(X0),$o,X21,vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X23),X24),X25)))) => vAPP(binary1291135688e_Tree(X0),$o,X21,X22)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Tree_Oinduct)).
% 2.36/0.77 thf(f2679,plain,(
% 2.36/0.77 spl108_67),
% 2.36/0.77 inference(avatar_split_clause,[],[f1548,f2677])).
% 2.36/0.77 thf(f2677,plain,(
% 2.36/0.77 spl108_67 <=> ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0) > $o] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK85(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_67])])).
% 2.36/0.77 thf(f1548,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0) > $o] : (($true = vAPP(binary1291135688e_Tree(X0),$o,X1,X2)) | ($true = vAPP(binary1291135688e_Tree(X0),$o,X1,vAPP(sTfun(binary1291135688e_Tree(X0),$o),binary1291135688e_Tree(X0),sK85(X0),X1))) | ($true != vAPP(binary1291135688e_Tree(X0),$o,X1,binary1746293266le_Tip(X0)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1269])).
% 2.36/0.77 thf(f2675,plain,(
% 2.36/0.77 spl108_66),
% 2.36/0.77 inference(avatar_split_clause,[],[f1527,f2673])).
% 2.36/0.77 thf(f2673,plain,(
% 2.36/0.77 spl108_66 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > int] : (binary1746293266le_Tip(X0) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary997842527remove(X0),X1),X2),binary1746293266le_Tip(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_66])])).
% 2.36/0.77 thf(f1527,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > int] : ((binary1746293266le_Tip(X0) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary997842527remove(X0),X1),X2),binary1746293266le_Tip(X0)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f835])).
% 2.36/0.77 thf(f835,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int,X2 : X0] : (binary1746293266le_Tip(X0) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary997842527remove(X0),X1),X2),binary1746293266le_Tip(X0)))),
% 2.36/0.77 inference(rectify,[],[f24])).
% 2.36/0.77 thf(f24,axiom,(
% 2.36/0.77 ! [X0 : $tType,X3 : X0 > int,X20 : X0] : (binary1746293266le_Tip(X0) = vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(sTfun(X0,int),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary997842527remove(X0),X3),X20),binary1746293266le_Tip(X0)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_remove_Osimps_I1_J)).
% 2.36/0.77 thf(f2665,plain,(
% 2.36/0.77 spl108_65 | ~spl108_9 | ~spl108_27),
% 2.36/0.77 inference(avatar_split_clause,[],[f2386,f2352,f2241,f2663])).
% 2.36/0.77 thf(f2663,plain,(
% 2.36/0.77 spl108_65 <=> ! [X0 : $tType] : ($true = ord(sTfun(X0,int)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_65])])).
% 2.36/0.77 thf(f2241,plain,(
% 2.36/0.77 spl108_9 <=> (ord(int) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_9])])).
% 2.36/0.77 thf(f2386,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,int)))) ) | (~spl108_9 | ~spl108_27)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2379])).
% 2.36/0.77 thf(f2379,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X0,int)))) ) | (~spl108_9 | ~spl108_27)),
% 2.36/0.77 inference(superposition,[],[f2353,f2243])).
% 2.36/0.77 thf(f2243,plain,(
% 2.36/0.77 (ord(int) = $true) | ~spl108_9),
% 2.36/0.77 inference(avatar_component_clause,[],[f2241])).
% 2.36/0.77 thf(f2647,plain,(
% 2.36/0.77 spl108_64),
% 2.36/0.77 inference(avatar_split_clause,[],[f1454,f2645])).
% 2.36/0.77 thf(f2645,plain,(
% 2.36/0.77 spl108_64 <=> ! [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_eq(X0),X1),X2)) | (order(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_64])])).
% 2.36/0.77 thf(f1454,plain,(
% 2.36/0.77 ( ! [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_eq(X0),X1),X2)) | (order(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f990])).
% 2.36/0.77 thf(f990,plain,(
% 2.36/0.77 ! [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_eq(X0),X1),X2))) | (order(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f827])).
% 2.36/0.77 thf(f827,plain,(
% 2.36/0.77 ! [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(X0),X2),X1))))),
% 2.36/0.77 inference(flattening,[],[f515])).
% 2.36/0.77 thf(f515,plain,(
% 2.36/0.77 ! [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(X0),X2),X1))))),
% 2.36/0.77 inference(fool_elimination,[],[f514])).
% 2.36/0.77 thf(f514,plain,(
% 2.36/0.77 ! [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(X0),X2),X1)))),
% 2.36/0.77 inference(rectify,[],[f127])).
% 2.36/0.77 thf(f127,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X26 : X0,X5 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X5) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X26)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_126_leD)).
% 2.36/0.77 thf(f2643,plain,(
% 2.36/0.77 spl108_63),
% 2.36/0.77 inference(avatar_split_clause,[],[f1445,f2641])).
% 2.36/0.77 thf(f2641,plain,(
% 2.36/0.77 spl108_63 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_63])])).
% 2.36/0.77 thf(f1445,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f976])).
% 2.36/0.77 thf(f976,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f497])).
% 2.36/0.77 thf(f497,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(fool_elimination,[],[f496])).
% 2.36/0.77 thf(f496,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f157])).
% 2.36/0.77 thf(f157,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X18 : X0,X19 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X19) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),X19)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_156_order_Ostrict__implies__order)).
% 2.36/0.77 thf(f2639,plain,(
% 2.36/0.77 spl108_62),
% 2.36/0.77 inference(avatar_split_clause,[],[f1443,f2637])).
% 2.36/0.77 thf(f2637,plain,(
% 2.36/0.77 spl108_62 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_62])])).
% 2.36/0.77 thf(f1443,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f974])).
% 2.36/0.77 thf(f974,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f825])).
% 2.36/0.77 thf(f825,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(flattening,[],[f493])).
% 2.36/0.77 thf(f493,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(fool_elimination,[],[f492])).
% 2.36/0.77 thf(f492,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f81])).
% 2.36/0.77 thf(f81,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order(X0) => ! [X18 : X0,X19 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X19) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X19),X18)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_order_Oasym)).
% 2.36/0.77 thf(f2635,plain,(
% 2.36/0.77 spl108_61),
% 2.36/0.77 inference(avatar_split_clause,[],[f1381,f2633])).
% 2.36/0.77 thf(f2633,plain,(
% 2.36/0.77 spl108_61 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_61])])).
% 2.36/0.77 thf(f1381,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f931])).
% 2.36/0.77 thf(f931,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f427])).
% 2.36/0.77 thf(f427,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(fool_elimination,[],[f426])).
% 2.36/0.77 thf(f426,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f57])).
% 2.36/0.77 thf(f57,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X5 : X0,X26 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X26),X5) | vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X26)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_linear)).
% 2.36/0.77 thf(f2631,plain,(
% 2.36/0.77 spl108_60),
% 2.36/0.77 inference(avatar_split_clause,[],[f1351,f2629])).
% 2.36/0.77 thf(f2629,plain,(
% 2.36/0.77 spl108_60 <=> ! [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)) | (preorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_60])])).
% 2.36/0.77 thf(f1351,plain,(
% 2.36/0.77 ( ! [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)) | (preorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f892])).
% 2.36/0.77 thf(f892,plain,(
% 2.36/0.77 ! [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))) | (preorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f367])).
% 2.36/0.77 thf(f367,plain,(
% 2.36/0.77 ! [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_eq(X0),X1),X2))))),
% 2.36/0.77 inference(fool_elimination,[],[f366])).
% 2.36/0.77 thf(f366,plain,(
% 2.36/0.77 ! [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_eq(X0),X1),X2)))),
% 2.36/0.77 inference(rectify,[],[f140])).
% 2.36/0.77 thf(f140,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0,X26 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X26) => vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X26)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_139_less__imp__le)).
% 2.36/0.77 thf(f2627,plain,(
% 2.36/0.77 spl108_59 | ~spl108_10 | ~spl108_27),
% 2.36/0.77 inference(avatar_split_clause,[],[f2385,f2352,f2246,f2625])).
% 2.36/0.77 thf(f2625,plain,(
% 2.36/0.77 spl108_59 <=> ! [X0 : $tType] : ($true = ord(sTfun(X0,$o)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_59])])).
% 2.36/0.77 thf(f2246,plain,(
% 2.36/0.77 spl108_10 <=> (ord($o) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_10])])).
% 2.36/0.77 thf(f2385,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = ord(sTfun(X0,$o)))) ) | (~spl108_10 | ~spl108_27)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2380])).
% 2.36/0.77 thf(f2380,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = ord(sTfun(X0,$o)))) ) | (~spl108_10 | ~spl108_27)),
% 2.36/0.77 inference(superposition,[],[f2353,f2248])).
% 2.36/0.77 thf(f2248,plain,(
% 2.36/0.77 (ord($o) = $true) | ~spl108_10),
% 2.36/0.77 inference(avatar_component_clause,[],[f2246])).
% 2.36/0.77 thf(f2623,plain,(
% 2.36/0.77 spl108_58),
% 2.36/0.77 inference(avatar_split_clause,[],[f1347,f2621])).
% 2.36/0.77 thf(f2621,plain,(
% 2.36/0.77 spl108_58 <=> ! [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))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_58])])).
% 2.36/0.77 thf(f1347,plain,(
% 2.36/0.77 ( ! [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)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f888])).
% 2.36/0.77 thf(f888,plain,(
% 2.36/0.77 ! [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))),
% 2.36/0.77 inference(ennf_transformation,[],[f806])).
% 2.36/0.77 thf(f806,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(flattening,[],[f359])).
% 2.36/0.77 thf(f359,plain,(
% 2.36/0.77 ! [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))))),
% 2.36/0.77 inference(fool_elimination,[],[f358])).
% 2.36/0.77 thf(f358,plain,(
% 2.36/0.77 ! [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)))),
% 2.36/0.77 inference(rectify,[],[f93])).
% 2.36/0.77 thf(f93,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0,X26 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X26) => ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X26),X5)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_less__not__sym)).
% 2.36/0.77 thf(f2619,plain,(
% 2.36/0.77 spl108_57),
% 2.36/0.77 inference(avatar_split_clause,[],[f1559,f2617])).
% 2.36/0.77 thf(f2617,plain,(
% 2.36/0.77 spl108_57 <=> ! [X0 : $tType,X3 : binary1291135688e_Tree(X0),X2 : X0,X1 : binary1291135688e_Tree(X0)] : (binary1746293266le_Tip(X0) != vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X1),X2),X3))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_57])])).
% 2.36/0.77 thf(f1559,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0,X3 : binary1291135688e_Tree(X0),X1 : binary1291135688e_Tree(X0)] : ((binary1746293266le_Tip(X0) != vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X1),X2),X3))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f842])).
% 2.36/0.77 thf(f842,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : binary1291135688e_Tree(X0),X2 : X0,X3 : binary1291135688e_Tree(X0)] : (binary1746293266le_Tip(X0) != vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X1),X2),X3))),
% 2.36/0.77 inference(rectify,[],[f15])).
% 2.36/0.77 thf(f15,axiom,(
% 2.36/0.77 ! [X0 : $tType,X7 : binary1291135688e_Tree(X0),X8 : X0,X9 : binary1291135688e_Tree(X0)] : (vAPP(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0),vAPP(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0)),vAPP(binary1291135688e_Tree(X0),sTfun(X0,sTfun(binary1291135688e_Tree(X0),binary1291135688e_Tree(X0))),binary210054475elle_T(X0),X7),X8),X9) != binary1746293266le_Tip(X0))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Tree_Odistinct_I1_J)).
% 2.36/0.77 thf(f2613,plain,(
% 2.36/0.77 spl108_56),
% 2.36/0.77 inference(avatar_split_clause,[],[f1502,f2611])).
% 2.36/0.77 thf(f2611,plain,(
% 2.36/0.77 spl108_56 <=> ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK76(X0),X1)),X1)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_56])])).
% 2.36/0.77 thf(f1502,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK76(X0),X1)),X1))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1251])).
% 2.36/0.77 thf(f1251,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK76(X0),X1)),X1)))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK76])],[f1032,f1250])).
% 2.36/0.77 thf(f1250,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (? [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),vAPP(set(X0),X0,sK76(X0),X1)),X1)))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f1032,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ((bot_bot(set(X0)) = X1) | ? [X2 : X0] : ($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)))),
% 2.36/0.77 inference(ennf_transformation,[],[f829])).
% 2.36/0.77 thf(f829,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => (bot_bot(set(X0)) = X1))),
% 2.36/0.77 inference(flattening,[],[f585])).
% 2.36/0.77 thf(f585,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1)) => (bot_bot(set(X0)) = X1))),
% 2.36/0.77 inference(fool_elimination,[],[f584])).
% 2.36/0.77 thf(f584,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : (! [X2 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X2),X1) => (bot_bot(set(X0)) = X1))),
% 2.36/0.77 inference(rectify,[],[f111])).
% 2.36/0.77 thf(f111,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0)] : (! [X46 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X46),X36) => (bot_bot(set(X0)) = X36))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_110_equals0I)).
% 2.36/0.77 thf(f2581,plain,(
% 2.36/0.77 spl108_55),
% 2.36/0.77 inference(avatar_split_clause,[],[f1319,f2579])).
% 2.36/0.77 thf(f2579,plain,(
% 2.36/0.77 spl108_55 <=> ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK9(X0),X1))) | (wellorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_55])])).
% 2.36/0.77 thf(f1319,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : (($true = vAPP(X0,$o,X1,X2)) | ($true != vAPP(X0,$o,X1,vAPP(sTfun(X0,$o),X0,sK9(X0),X1))) | (wellorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1147])).
% 2.36/0.77 thf(f2562,plain,(
% 2.36/0.77 spl108_54 | ~spl108_7 | ~spl108_26),
% 2.36/0.77 inference(avatar_split_clause,[],[f2378,f2348,f2231,f2560])).
% 2.36/0.77 thf(f2560,plain,(
% 2.36/0.77 spl108_54 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,int)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_54])])).
% 2.36/0.77 thf(f2231,plain,(
% 2.36/0.77 spl108_7 <=> (preorder(int) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_7])])).
% 2.36/0.77 thf(f2378,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,int)))) ) | (~spl108_7 | ~spl108_26)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2371])).
% 2.36/0.77 thf(f2371,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,int)))) ) | (~spl108_7 | ~spl108_26)),
% 2.36/0.77 inference(superposition,[],[f2349,f2233])).
% 2.36/0.77 thf(f2233,plain,(
% 2.36/0.77 (preorder(int) = $true) | ~spl108_7),
% 2.36/0.77 inference(avatar_component_clause,[],[f2231])).
% 2.36/0.77 thf(f2538,plain,(
% 2.36/0.77 spl108_53),
% 2.36/0.77 inference(avatar_split_clause,[],[f1661,f2536])).
% 2.36/0.77 thf(f2536,plain,(
% 2.36/0.77 spl108_53 <=> ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK19(X0),X3)),X3)) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_53])])).
% 2.36/0.77 thf(f1661,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK19(X0),X3)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(equality_resolution,[],[f1364])).
% 2.36/0.77 thf(f1364,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK19(X0),X1)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1170])).
% 2.36/0.77 thf(f1170,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK19(X0),X1)),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f914,f1169])).
% 2.36/0.77 thf(f1169,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) => ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK19(X0),X1)),X3))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f914,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f393])).
% 2.36/0.77 thf(f393,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) => (X1 != X3)))),
% 2.36/0.77 inference(fool_elimination,[],[f392])).
% 2.36/0.77 thf(f392,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => (X1 != X3)))),
% 2.36/0.77 inference(rectify,[],[f196])).
% 2.36/0.77 thf(f196,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X65) => (X13 != X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_195_pinf_I3_J)).
% 2.36/0.77 thf(f2534,plain,(
% 2.36/0.77 spl108_52),
% 2.36/0.77 inference(avatar_split_clause,[],[f1660,f2532])).
% 2.36/0.77 thf(f2532,plain,(
% 2.36/0.77 spl108_52 <=> ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK18(X0),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_52])])).
% 2.36/0.77 thf(f1660,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK18(X0),X3))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(equality_resolution,[],[f1363])).
% 2.36/0.77 thf(f1363,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK18(X0),X1))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1168])).
% 2.36/0.77 thf(f1168,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK18(X0),X1)))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK18])],[f913,f1167])).
% 2.36/0.77 thf(f1167,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))) => ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK18(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f913,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f391])).
% 2.36/0.77 thf(f391,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) => (X1 != X3)))),
% 2.36/0.77 inference(fool_elimination,[],[f390])).
% 2.36/0.77 thf(f390,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) => (X1 != X3)))),
% 2.36/0.77 inference(rectify,[],[f204])).
% 2.36/0.77 thf(f204,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X54) => (X13 != X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_203_minf_I4_J)).
% 2.36/0.77 thf(f2530,plain,(
% 2.36/0.77 spl108_51),
% 2.36/0.77 inference(avatar_split_clause,[],[f1659,f2528])).
% 2.36/0.77 thf(f2528,plain,(
% 2.36/0.77 spl108_51 <=> ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK17(X0),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_51])])).
% 2.36/0.77 thf(f1659,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK17(X0),X3))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(equality_resolution,[],[f1362])).
% 2.36/0.77 thf(f1362,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK17(X0),X1))) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1166])).
% 2.36/0.77 thf(f1166,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK17(X0),X1)))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f912,f1165])).
% 2.36/0.77 thf(f1165,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))) => ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),vAPP(X0,X0,sK17(X0),X1)))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f912,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f389])).
% 2.36/0.77 thf(f389,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2)) => (X1 != X3)))),
% 2.36/0.77 inference(fool_elimination,[],[f388])).
% 2.36/0.77 thf(f388,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X3),X2) => (X1 != X3)))),
% 2.36/0.77 inference(rectify,[],[f203])).
% 2.36/0.77 thf(f203,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X65),X54) => (X13 != X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_202_minf_I3_J)).
% 2.36/0.77 thf(f2526,plain,(
% 2.36/0.77 spl108_50),
% 2.36/0.77 inference(avatar_split_clause,[],[f1658,f2524])).
% 2.36/0.77 thf(f2524,plain,(
% 2.36/0.77 spl108_50 <=> ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK16(X0),X3)),X3)) | (linorder(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_50])])).
% 2.36/0.77 thf(f1658,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK16(X0),X3)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(equality_resolution,[],[f1361])).
% 2.36/0.77 thf(f1361,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X3 : X0,X1 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK16(X0),X1)),X3)) | (linorder(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1164])).
% 2.36/0.77 thf(f1164,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK16(X0),X1)),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f911,f1163])).
% 2.36/0.77 thf(f1163,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0] : (? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) => ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK16(X0),X1)),X3))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f911,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : ((X1 != X3) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3))) | (linorder(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f387])).
% 2.36/0.77 thf(f387,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((linorder(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3)) => (X1 != X3)))),
% 2.36/0.77 inference(fool_elimination,[],[f386])).
% 2.36/0.77 thf(f386,plain,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X1 : X0] : ? [X2 : X0] : ! [X3 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X3) => (X1 != X3)))),
% 2.36/0.77 inference(rectify,[],[f197])).
% 2.36/0.77 thf(f197,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (linorder(X0) => ! [X13 : X0] : ? [X54 : X0] : ! [X65 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X54),X65) => (X13 != X65)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_196_pinf_I4_J)).
% 2.36/0.77 thf(f2522,plain,(
% 2.36/0.77 spl108_49),
% 2.36/0.77 inference(avatar_split_clause,[],[f1339,f2520])).
% 2.36/0.77 thf(f2520,plain,(
% 2.36/0.77 spl108_49 <=> ! [X0 : $tType,X1 : X0] : ((bot_bot(X0) = X1) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),bot_bot(X0))) | (order_bot(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_49])])).
% 2.36/0.77 thf(f1339,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0] : ((bot_bot(X0) = X1) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),bot_bot(X0))) | (order_bot(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f880])).
% 2.36/0.77 thf(f880,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ((bot_bot(X0) = X1) | ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),bot_bot(X0)))) | (order_bot(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f343])).
% 2.36/0.77 thf(f343,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((order_bot(X0) = $true) => ! [X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),bot_bot(X0))) => (bot_bot(X0) = X1)))),
% 2.36/0.77 inference(fool_elimination,[],[f342])).
% 2.36/0.77 thf(f342,plain,(
% 2.36/0.77 ! [X0 : $tType] : (order_bot(X0) => ! [X1 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),bot_bot(X0)) => (bot_bot(X0) = X1)))),
% 2.36/0.77 inference(rectify,[],[f164])).
% 2.36/0.77 thf(f164,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order_bot(X0) => ! [X18 : X0] : (vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),bot_bot(X0)) => (bot_bot(X0) = X18)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_163_bot_Oextremum__uniqueI)).
% 2.36/0.77 thf(f2518,plain,(
% 2.36/0.77 spl108_48),
% 2.36/0.77 inference(avatar_split_clause,[],[f1317,f2516])).
% 2.36/0.77 thf(f2516,plain,(
% 2.36/0.77 spl108_48 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK8(X0),X1))) | (no_top(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_48])])).
% 2.36/0.77 thf(f1317,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK8(X0),X1))) | (no_top(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1145])).
% 2.36/0.77 thf(f1145,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),vAPP(X0,X0,sK8(X0),X1))) | (no_top(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f868,f1144])).
% 2.36/0.77 thf(f1144,plain,(
% 2.36/0.77 ! [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,sK8(X0),X1))))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f868,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)) | (no_top(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f325])).
% 2.36/0.77 thf(f325,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((no_top(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2)))),
% 2.36/0.77 inference(fool_elimination,[],[f324])).
% 2.36/0.77 thf(f324,plain,(
% 2.36/0.77 ! [X0 : $tType] : (no_top(X0) => ! [X1 : X0] : ? [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X2))),
% 2.36/0.77 inference(rectify,[],[f78])).
% 2.36/0.77 thf(f78,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (no_top(X0) => ! [X5 : X0] : ? [X53 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X53))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_gt__ex)).
% 2.36/0.77 thf(f2514,plain,(
% 2.36/0.77 spl108_47 | ~spl108_8 | ~spl108_26),
% 2.36/0.77 inference(avatar_split_clause,[],[f2377,f2348,f2236,f2512])).
% 2.36/0.77 thf(f2512,plain,(
% 2.36/0.77 spl108_47 <=> ! [X0 : $tType] : ($true = preorder(sTfun(X0,$o)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_47])])).
% 2.36/0.77 thf(f2236,plain,(
% 2.36/0.77 spl108_8 <=> (preorder($o) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_8])])).
% 2.36/0.77 thf(f2377,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = preorder(sTfun(X0,$o)))) ) | (~spl108_8 | ~spl108_26)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2372])).
% 2.36/0.77 thf(f2372,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = preorder(sTfun(X0,$o)))) ) | (~spl108_8 | ~spl108_26)),
% 2.36/0.77 inference(superposition,[],[f2349,f2238])).
% 2.36/0.77 thf(f2238,plain,(
% 2.36/0.77 (preorder($o) = $true) | ~spl108_8),
% 2.36/0.77 inference(avatar_component_clause,[],[f2236])).
% 2.36/0.77 thf(f2510,plain,(
% 2.36/0.77 spl108_46),
% 2.36/0.77 inference(avatar_split_clause,[],[f1316,f2508])).
% 2.36/0.77 thf(f2508,plain,(
% 2.36/0.77 spl108_46 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK7(X0),X1)),X1)) | (no_bot(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_46])])).
% 2.36/0.77 thf(f1316,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK7(X0),X1)),X1)) | (no_bot(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1143])).
% 2.36/0.77 thf(f1143,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),vAPP(X0,X0,sK7(X0),X1)),X1)) | (no_bot(X0) != $true))),
% 2.36/0.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f867,f1142])).
% 2.36/0.77 thf(f1142,plain,(
% 2.36/0.77 ! [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,sK7(X0),X1)),X1)))),
% 2.36/0.77 introduced(choice_axiom,[])).
% 2.36/0.77 thf(f867,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)) | (no_bot(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f323])).
% 2.36/0.77 thf(f323,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((no_bot(X0) = $true) => ! [X1 : X0] : ? [X2 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1)))),
% 2.36/0.77 inference(fool_elimination,[],[f322])).
% 2.36/0.77 thf(f322,plain,(
% 2.36/0.77 ! [X0 : $tType] : (no_bot(X0) => ! [X1 : X0] : ? [X2 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X2),X1))),
% 2.36/0.77 inference(rectify,[],[f77])).
% 2.36/0.77 thf(f77,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (no_bot(X0) => ! [X5 : X0] : ? [X46 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X46),X5))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_lt__ex)).
% 2.36/0.77 thf(f2506,plain,(
% 2.36/0.77 spl108_45),
% 2.36/0.77 inference(avatar_split_clause,[],[f1303,f2504])).
% 2.36/0.77 thf(f2504,plain,(
% 2.36/0.77 spl108_45 <=> ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP($o,sTfun(X0,$o),kCOMB,$false)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_45])])).
% 2.36/0.77 thf(f1303,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : ((bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP($o,sTfun(X0,$o),kCOMB,$false)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f299])).
% 2.36/0.77 thf(f299,plain,(
% 2.36/0.77 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),vAPP($o,sTfun(X0,$o),kCOMB,$false)))),
% 2.36/0.77 inference(fool_elimination,[],[f298])).
% 2.36/0.77 thf(f298,plain,(
% 2.36/0.77 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X1 : X0] : ($false))))),
% 2.36/0.77 inference(rectify,[],[f125])).
% 2.36/0.77 thf(f125,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),(^[X30 : X0] : ($false))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_124_empty__def)).
% 2.36/0.77 thf(f2496,plain,(
% 2.36/0.77 spl108_44),
% 2.36/0.77 inference(avatar_split_clause,[],[f1504,f2494])).
% 2.36/0.77 thf(f2494,plain,(
% 2.36/0.77 spl108_44 <=> ! [X1 : $tType,X0 : $tType] : ((bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))) | ($true != bot(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_44])])).
% 2.36/0.77 thf(f1504,plain,(
% 2.36/0.77 ( ! [X1 : $tType,X0 : $tType] : ((bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))) | ($true != bot(X0))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f1034])).
% 2.36/0.77 thf(f1034,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType] : ((bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))) | ($true != bot(X0)))),
% 2.36/0.77 inference(ennf_transformation,[],[f589])).
% 2.36/0.77 thf(f589,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType] : (($true = bot(X0)) => (bot_bot(sTfun(X1,X0)) = vAPP(X0,sTfun(X1,X0),kCOMB,bot_bot(X0))))),
% 2.36/0.77 inference(fool_elimination,[],[f588])).
% 2.36/0.77 thf(f588,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : $tType] : (bot(X0) => (bot_bot(sTfun(X1,X0)) = (^[X2 : X1] : (bot_bot(X0)))))),
% 2.36/0.77 inference(rectify,[],[f108])).
% 2.36/0.77 thf(f108,axiom,(
% 2.36/0.77 ! [X1 : $tType,X0 : $tType] : (bot(X1) => (bot_bot(sTfun(X0,X1)) = (^[X30 : X0] : (bot_bot(X1)))))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_107_bot__fun__def)).
% 2.36/0.77 thf(f2490,plain,(
% 2.36/0.77 spl108_43),
% 2.36/0.77 inference(avatar_split_clause,[],[f1524,f2488])).
% 2.36/0.77 thf(f2488,plain,(
% 2.36/0.77 spl108_43 <=> ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_43])])).
% 2.36/0.77 thf(f1524,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f629])).
% 2.36/0.77 thf(f629,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1))),
% 2.36/0.77 inference(fool_elimination,[],[f628])).
% 2.36/0.77 thf(f628,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X1)),
% 2.36/0.77 inference(rectify,[],[f32])).
% 2.36/0.77 thf(f32,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),bot_bot(set(X0))),X36)),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_empty__subsetI)).
% 2.36/0.77 thf(f2486,plain,(
% 2.36/0.77 spl108_42),
% 2.36/0.77 inference(avatar_split_clause,[],[f1521,f2484])).
% 2.36/0.77 thf(f2484,plain,(
% 2.36/0.77 spl108_42 <=> ! [X0 : $tType,X1 : set(X0)] : ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),bot_bot(set(X0))))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_42])])).
% 2.36/0.77 thf(f1521,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : set(X0)] : (($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),bot_bot(set(X0))))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f833])).
% 2.36/0.77 thf(f833,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ($true != vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),bot_bot(set(X0))))),
% 2.36/0.77 inference(flattening,[],[f623])).
% 2.36/0.77 thf(f623,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ~($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),bot_bot(set(X0))))),
% 2.36/0.77 inference(fool_elimination,[],[f622])).
% 2.36/0.77 thf(f622,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ~vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X1),bot_bot(set(X0)))),
% 2.36/0.77 inference(rectify,[],[f182])).
% 2.36/0.77 thf(f182,axiom,(
% 2.36/0.77 ! [X0 : $tType,X36 : set(X0)] : ~vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less(set(X0)),X36),bot_bot(set(X0)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_181_not__psubset__empty)).
% 2.36/0.77 thf(f2482,plain,(
% 2.36/0.77 spl108_41 | ~spl108_6 | ~spl108_25),
% 2.36/0.77 inference(avatar_split_clause,[],[f2370,f2344,f2226,f2480])).
% 2.36/0.77 thf(f2480,plain,(
% 2.36/0.77 spl108_41 <=> ! [X0 : $tType] : ($true = order_bot(sTfun(X0,$o)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_41])])).
% 2.36/0.77 thf(f2226,plain,(
% 2.36/0.77 spl108_6 <=> (order_bot($o) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_6])])).
% 2.36/0.77 thf(f2370,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = order_bot(sTfun(X0,$o)))) ) | (~spl108_6 | ~spl108_25)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2365])).
% 2.36/0.77 thf(f2365,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = order_bot(sTfun(X0,$o)))) ) | (~spl108_6 | ~spl108_25)),
% 2.36/0.77 inference(superposition,[],[f2345,f2228])).
% 2.36/0.77 thf(f2228,plain,(
% 2.36/0.77 (order_bot($o) = $true) | ~spl108_6),
% 2.36/0.77 inference(avatar_component_clause,[],[f2226])).
% 2.36/0.77 thf(f2467,plain,(
% 2.36/0.77 spl108_40),
% 2.36/0.77 inference(avatar_split_clause,[],[f1523,f2465])).
% 2.36/0.77 thf(f2465,plain,(
% 2.36/0.77 spl108_40 <=> ! [X0 : $tType,X1 : X0 > int] : ($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),binary1746293266le_Tip(X0)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_40])])).
% 2.36/0.77 thf(f1523,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0 > int] : (($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),binary1746293266le_Tip(X0)))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f627])).
% 2.36/0.77 thf(f627,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int] : ($true = vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),binary1746293266le_Tip(X0)))),
% 2.36/0.77 inference(fool_elimination,[],[f626])).
% 2.36/0.77 thf(f626,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : X0 > int] : vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X1),binary1746293266le_Tip(X0))),
% 2.36/0.77 inference(rectify,[],[f9])).
% 2.36/0.77 thf(f9,axiom,(
% 2.36/0.77 ! [X0 : $tType,X3 : X0 > int] : vAPP(binary1291135688e_Tree(X0),$o,vAPP(sTfun(X0,int),sTfun(binary1291135688e_Tree(X0),$o),binary1610619414edTree(X0),X3),binary1746293266le_Tip(X0))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_sortedTree_Osimps_I1_J)).
% 2.36/0.77 thf(f2463,plain,(
% 2.36/0.77 spl108_39),
% 2.36/0.77 inference(avatar_split_clause,[],[f1341,f2461])).
% 2.36/0.77 thf(f2461,plain,(
% 2.36/0.77 spl108_39 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),bot_bot(X0)),X1)) | (order_bot(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_39])])).
% 2.36/0.77 thf(f1341,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),bot_bot(X0)),X1)) | (order_bot(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f882])).
% 2.36/0.77 thf(f882,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),bot_bot(X0)),X1)) | (order_bot(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f347])).
% 2.36/0.77 thf(f347,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((order_bot(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),bot_bot(X0)),X1)))),
% 2.36/0.77 inference(fool_elimination,[],[f346])).
% 2.36/0.77 thf(f346,plain,(
% 2.36/0.77 ! [X0 : $tType] : (order_bot(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),bot_bot(X0)),X1))),
% 2.36/0.77 inference(rectify,[],[f162])).
% 2.36/0.77 thf(f162,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order_bot(X0) => ! [X18 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),bot_bot(X0)),X18))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_161_bot_Oextremum)).
% 2.36/0.77 thf(f2459,plain,(
% 2.36/0.77 spl108_38),
% 2.36/0.77 inference(avatar_split_clause,[],[f1340,f2457])).
% 2.36/0.77 thf(f2457,plain,(
% 2.36/0.77 spl108_38 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),bot_bot(X0))) | (order_bot(X0) != $true))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_38])])).
% 2.36/0.77 thf(f1340,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),bot_bot(X0))) | (order_bot(X0) != $true)) )),
% 2.36/0.77 inference(cnf_transformation,[],[f881])).
% 2.36/0.77 thf(f881,plain,(
% 2.36/0.77 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),bot_bot(X0))) | (order_bot(X0) != $true))),
% 2.36/0.77 inference(ennf_transformation,[],[f804])).
% 2.36/0.77 thf(f804,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((order_bot(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),bot_bot(X0))))),
% 2.36/0.77 inference(flattening,[],[f345])).
% 2.36/0.77 thf(f345,plain,(
% 2.36/0.77 ! [X0 : $tType] : ((order_bot(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),bot_bot(X0))))),
% 2.36/0.77 inference(fool_elimination,[],[f344])).
% 2.36/0.77 thf(f344,plain,(
% 2.36/0.77 ! [X0 : $tType] : (order_bot(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),bot_bot(X0)))),
% 2.36/0.77 inference(rectify,[],[f165])).
% 2.36/0.77 thf(f165,axiom,(
% 2.36/0.77 ! [X0 : $tType] : (order_bot(X0) => ! [X18 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),bot_bot(X0)))),
% 2.36/0.77 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_164_bot_Oextremum__strict)).
% 2.36/0.77 thf(f2435,plain,(
% 2.36/0.77 spl108_37 | ~spl108_5 | ~spl108_23),
% 2.36/0.77 inference(avatar_split_clause,[],[f2364,f2335,f2221,f2433])).
% 2.36/0.77 thf(f2433,plain,(
% 2.36/0.77 spl108_37 <=> ! [X0 : $tType] : ($true = bot(sTfun(X0,$o)))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_37])])).
% 2.36/0.77 thf(f2221,plain,(
% 2.36/0.77 spl108_5 <=> (bot($o) = $true)),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_5])])).
% 2.36/0.77 thf(f2364,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true = bot(sTfun(X0,$o)))) ) | (~spl108_5 | ~spl108_23)),
% 2.36/0.77 inference(trivial_inequality_removal,[],[f2359])).
% 2.36/0.77 thf(f2359,plain,(
% 2.36/0.77 ( ! [X0 : $tType] : (($true != $true) | ($true = bot(sTfun(X0,$o)))) ) | (~spl108_5 | ~spl108_23)),
% 2.36/0.77 inference(superposition,[],[f2336,f2223])).
% 2.36/0.77 thf(f2223,plain,(
% 2.36/0.77 (bot($o) = $true) | ~spl108_5),
% 2.36/0.77 inference(avatar_component_clause,[],[f2221])).
% 2.36/0.77 thf(f2429,plain,(
% 2.36/0.77 spl108_36),
% 2.36/0.77 inference(avatar_split_clause,[],[f1522,f2427])).
% 2.36/0.77 thf(f2427,plain,(
% 2.36/0.77 spl108_36 <=> ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))),
% 2.36/0.77 introduced(avatar_definition,[new_symbols(naming,[spl108_36])])).
% 2.36/0.77 thf(f1522,plain,(
% 2.36/0.77 ( ! [X0 : $tType,X1 : set(X0)] : (($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))) )),
% 2.36/0.77 inference(cnf_transformation,[],[f625])).
% 2.36/0.77 thf(f625,plain,(
% 2.36/0.77 ! [X0 : $tType,X1 : set(X0)] : ($true = vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1))),
% 2.36/0.77 inference(fool_elimination,[],[f624])).
% 2.36/0.78 thf(f624,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X1),X1)),
% 2.36/0.78 inference(rectify,[],[f120])).
% 2.36/0.78 thf(f120,axiom,(
% 2.36/0.78 ! [X0 : $tType,X36 : set(X0)] : vAPP(set(X0),$o,vAPP(set(X0),sTfun(set(X0),$o),ord_less_eq(set(X0)),X36),X36)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_119_subset__refl)).
% 2.36/0.78 thf(f2425,plain,(
% 2.36/0.78 spl108_35),
% 2.36/0.78 inference(avatar_split_clause,[],[f1519,f2423])).
% 2.36/0.78 thf(f2423,plain,(
% 2.36/0.78 spl108_35 <=> ! [X0 : $tType,X1 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_35])])).
% 2.36/0.78 thf(f1519,plain,(
% 2.36/0.78 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f831])).
% 2.36/0.78 thf(f831,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : X0] : ($true != vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))),
% 2.36/0.78 inference(flattening,[],[f619])).
% 2.36/0.78 thf(f619,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : X0] : ~($true = vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0))))),
% 2.36/0.78 inference(fool_elimination,[],[f618])).
% 2.36/0.78 thf(f618,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X1),bot_bot(set(X0)))),
% 2.36/0.78 inference(rectify,[],[f39])).
% 2.36/0.78 thf(f39,axiom,(
% 2.36/0.78 ! [X0 : $tType,X39 : X0] : ~vAPP(set(X0),$o,vAPP(X0,sTfun(set(X0),$o),member(X0),X39),bot_bot(set(X0)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_empty__iff)).
% 2.36/0.78 thf(f2421,plain,(
% 2.36/0.78 spl108_34),
% 2.36/0.78 inference(avatar_split_clause,[],[f1435,f2419])).
% 2.36/0.78 thf(f2419,plain,(
% 2.36/0.78 spl108_34 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_34])])).
% 2.36/0.78 thf(f1435,plain,(
% 2.36/0.78 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f965])).
% 2.36/0.78 thf(f965,plain,(
% 2.36/0.78 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (order(X0) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f477])).
% 2.36/0.78 thf(f477,plain,(
% 2.36/0.78 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 2.36/0.78 inference(fool_elimination,[],[f476])).
% 2.36/0.78 thf(f476,plain,(
% 2.36/0.78 ! [X0 : $tType] : (order(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 2.36/0.78 inference(rectify,[],[f68])).
% 2.36/0.78 thf(f68,axiom,(
% 2.36/0.78 ! [X0 : $tType] : (order(X0) => ! [X18 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X18),X18))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_dual__order_Orefl)).
% 2.36/0.78 thf(f2417,plain,(
% 2.36/0.78 spl108_33),
% 2.36/0.78 inference(avatar_split_clause,[],[f1433,f2415])).
% 2.36/0.78 thf(f2415,plain,(
% 2.36/0.78 spl108_33 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_33])])).
% 2.36/0.78 thf(f1433,plain,(
% 2.36/0.78 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f963])).
% 2.36/0.78 thf(f963,plain,(
% 2.36/0.78 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (order(X0) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f822])).
% 2.36/0.78 thf(f822,plain,(
% 2.36/0.78 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 2.36/0.78 inference(flattening,[],[f473])).
% 2.36/0.78 thf(f473,plain,(
% 2.36/0.78 ! [X0 : $tType] : ((order(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 2.36/0.78 inference(fool_elimination,[],[f472])).
% 2.36/0.78 thf(f472,plain,(
% 2.36/0.78 ! [X0 : $tType] : (order(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))),
% 2.36/0.78 inference(rectify,[],[f193])).
% 2.36/0.78 thf(f193,axiom,(
% 2.36/0.78 ! [X0 : $tType] : (order(X0) => ! [X18 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X18),X18))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_192_verit__comp__simplify1_I1_J)).
% 2.36/0.78 thf(f2413,plain,(
% 2.36/0.78 spl108_32),
% 2.36/0.78 inference(avatar_split_clause,[],[f1345,f2411])).
% 2.36/0.78 thf(f2411,plain,(
% 2.36/0.78 spl108_32 <=> ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_32])])).
% 2.36/0.78 thf(f1345,plain,(
% 2.36/0.78 ( ! [X0 : $tType,X1 : X0] : (($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f886])).
% 2.36/0.78 thf(f886,plain,(
% 2.36/0.78 ! [X0 : $tType] : (! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)) | (preorder(X0) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f355])).
% 2.36/0.78 thf(f355,plain,(
% 2.36/0.78 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1)))),
% 2.36/0.78 inference(fool_elimination,[],[f354])).
% 2.36/0.78 thf(f354,plain,(
% 2.36/0.78 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X1),X1))),
% 2.36/0.78 inference(rectify,[],[f41])).
% 2.36/0.78 thf(f41,axiom,(
% 2.36/0.78 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0] : vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less_eq(X0),X5),X5))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_order__refl)).
% 2.36/0.78 thf(f2409,plain,(
% 2.36/0.78 spl108_31),
% 2.36/0.78 inference(avatar_split_clause,[],[f1344,f2407])).
% 2.36/0.78 thf(f2407,plain,(
% 2.36/0.78 spl108_31 <=> ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_31])])).
% 2.36/0.78 thf(f1344,plain,(
% 2.36/0.78 ( ! [X0 : $tType,X1 : X0] : (($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f885])).
% 2.36/0.78 thf(f885,plain,(
% 2.36/0.78 ! [X0 : $tType] : (! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)) | (preorder(X0) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f805])).
% 2.36/0.78 thf(f805,plain,(
% 2.36/0.78 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ($true != vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 2.36/0.78 inference(flattening,[],[f353])).
% 2.36/0.78 thf(f353,plain,(
% 2.36/0.78 ! [X0 : $tType] : ((preorder(X0) = $true) => ! [X1 : X0] : ~($true = vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1)))),
% 2.36/0.78 inference(fool_elimination,[],[f352])).
% 2.36/0.78 thf(f352,plain,(
% 2.36/0.78 ! [X0 : $tType] : (preorder(X0) => ! [X1 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X1),X1))),
% 2.36/0.78 inference(rectify,[],[f88])).
% 2.36/0.78 thf(f88,axiom,(
% 2.36/0.78 ! [X0 : $tType] : (preorder(X0) => ! [X5 : X0] : ~vAPP(X0,$o,vAPP(X0,sTfun(X0,$o),ord_less(X0),X5),X5))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_less__irrefl)).
% 2.36/0.78 thf(f2405,plain,(
% 2.36/0.78 spl108_30),
% 2.36/0.78 inference(avatar_split_clause,[],[f1299,f2403])).
% 2.36/0.78 thf(f2403,plain,(
% 2.36/0.78 spl108_30 <=> ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),bot_bot(sTfun(X0,$o))))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_30])])).
% 2.36/0.78 thf(f1299,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : ((bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),bot_bot(sTfun(X0,$o))))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f42])).
% 2.36/0.78 thf(f42,axiom,(
% 2.36/0.78 ! [X0 : $tType] : (bot_bot(set(X0)) = vAPP(sTfun(X0,$o),set(X0),collect(X0),bot_bot(sTfun(X0,$o))))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_bot__set__def)).
% 2.36/0.78 thf(f2398,plain,(
% 2.36/0.78 spl108_29),
% 2.36/0.78 inference(avatar_split_clause,[],[f1298,f2396])).
% 2.36/0.78 thf(f2396,plain,(
% 2.36/0.78 spl108_29 <=> ! [X0 : $tType] : (vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),binary1746293266le_Tip(X0)) = bot_bot(set(X0)))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_29])])).
% 2.36/0.78 thf(f1298,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : ((vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),binary1746293266le_Tip(X0)) = bot_bot(set(X0)))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f28])).
% 2.36/0.78 thf(f28,axiom,(
% 2.36/0.78 ! [X0 : $tType] : (vAPP(binary1291135688e_Tree(X0),set(X0),binary1653327646_setOf(X0),binary1746293266le_Tip(X0)) = bot_bot(set(X0)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_setOf_Osimps_I1_J)).
% 2.36/0.78 thf(f2358,plain,(
% 2.36/0.78 spl108_28),
% 2.36/0.78 inference(avatar_split_clause,[],[f1518,f2356])).
% 2.36/0.78 thf(f1518,plain,(
% 2.36/0.78 ( ! [X1 : $tType,X0 : $tType] : (($true = order(sTfun(X0,X1))) | (order(X1) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f1048])).
% 2.36/0.78 thf(f1048,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = order(sTfun(X0,X1))) | (order(X1) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f617])).
% 2.36/0.78 thf(f617,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : ((order(X1) = $true) => ($true = order(sTfun(X0,X1))))),
% 2.36/0.78 inference(fool_elimination,[],[f616])).
% 2.36/0.78 thf(f616,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (order(X1) => order(sTfun(X0,X1)))),
% 2.36/0.78 inference(rectify,[],[f259])).
% 2.36/0.78 thf(f259,axiom,(
% 2.36/0.78 ! [X95 : $tType,X96 : $tType] : (order(X96) => order(sTfun(X95,X96)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder)).
% 2.36/0.78 thf(f2354,plain,(
% 2.36/0.78 spl108_27),
% 2.36/0.78 inference(avatar_split_clause,[],[f1517,f2352])).
% 2.36/0.78 thf(f1517,plain,(
% 2.36/0.78 ( ! [X1 : $tType,X0 : $tType] : (($true = ord(sTfun(X0,X1))) | (ord(X1) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f1047])).
% 2.36/0.78 thf(f1047,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = ord(sTfun(X0,X1))) | (ord(X1) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f615])).
% 2.36/0.78 thf(f615,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : ((ord(X1) = $true) => ($true = ord(sTfun(X0,X1))))),
% 2.36/0.78 inference(fool_elimination,[],[f614])).
% 2.36/0.78 thf(f614,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (ord(X1) => ord(sTfun(X0,X1)))),
% 2.36/0.78 inference(rectify,[],[f260])).
% 2.36/0.78 thf(f260,axiom,(
% 2.36/0.78 ! [X95 : $tType,X96 : $tType] : (ord(X96) => ord(sTfun(X95,X96)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oord)).
% 2.36/0.78 thf(f2350,plain,(
% 2.36/0.78 spl108_26),
% 2.36/0.78 inference(avatar_split_clause,[],[f1508,f2348])).
% 2.36/0.78 thf(f1508,plain,(
% 2.36/0.78 ( ! [X1 : $tType,X0 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f1038])).
% 2.36/0.78 thf(f1038,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = preorder(sTfun(X0,X1))) | ($true != preorder(X1)))),
% 2.36/0.78 inference(ennf_transformation,[],[f597])).
% 2.36/0.78 thf(f597,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = preorder(X1)) => ($true = preorder(sTfun(X0,X1))))),
% 2.36/0.78 inference(fool_elimination,[],[f596])).
% 2.36/0.78 thf(f596,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (preorder(X1) => preorder(sTfun(X0,X1)))),
% 2.36/0.78 inference(rectify,[],[f258])).
% 2.36/0.78 thf(f258,axiom,(
% 2.36/0.78 ! [X95 : $tType,X96 : $tType] : (preorder(X96) => preorder(sTfun(X95,X96)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Opreorder)).
% 2.36/0.78 thf(f2346,plain,(
% 2.36/0.78 spl108_25),
% 2.36/0.78 inference(avatar_split_clause,[],[f1507,f2344])).
% 2.36/0.78 thf(f1507,plain,(
% 2.36/0.78 ( ! [X1 : $tType,X0 : $tType] : (($true = order_bot(sTfun(X0,X1))) | ($true != order_bot(X1))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f1037])).
% 2.36/0.78 thf(f1037,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = order_bot(sTfun(X0,X1))) | ($true != order_bot(X1)))),
% 2.36/0.78 inference(ennf_transformation,[],[f595])).
% 2.36/0.78 thf(f595,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = order_bot(X1)) => ($true = order_bot(sTfun(X0,X1))))),
% 2.36/0.78 inference(fool_elimination,[],[f594])).
% 2.36/0.78 thf(f594,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (order_bot(X1) => order_bot(sTfun(X0,X1)))),
% 2.36/0.78 inference(rectify,[],[f257])).
% 2.36/0.78 thf(f257,axiom,(
% 2.36/0.78 ! [X95 : $tType,X96 : $tType] : (order_bot(X96) => order_bot(sTfun(X95,X96)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Oorder__bot)).
% 2.36/0.78 thf(f2342,plain,(
% 2.36/0.78 spl108_24 | spl108_15 | ~spl108_22),
% 2.36/0.78 inference(avatar_split_clause,[],[f2315,f2301,f2271,f2339])).
% 2.36/0.78 thf(f2271,plain,(
% 2.36/0.78 spl108_15 <=> (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $true)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_15])])).
% 2.36/0.78 thf(f2301,plain,(
% 2.36/0.78 spl108_22 <=> ! [X0 : $o] : (($true = X0) | ($false = X0))),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_22])])).
% 2.36/0.78 thf(f2315,plain,(
% 2.36/0.78 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $false) | (spl108_15 | ~spl108_22)),
% 2.36/0.78 inference(trivial_inequality_removal,[],[f2313])).
% 2.36/0.78 thf(f2313,plain,(
% 2.36/0.78 ($true != $true) | (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $false) | (spl108_15 | ~spl108_22)),
% 2.36/0.78 inference(superposition,[],[f2273,f2302])).
% 2.36/0.78 thf(f2302,plain,(
% 2.36/0.78 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) ) | ~spl108_22),
% 2.36/0.78 inference(avatar_component_clause,[],[f2301])).
% 2.36/0.78 thf(f2273,plain,(
% 2.36/0.78 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) != $true) | spl108_15),
% 2.36/0.78 inference(avatar_component_clause,[],[f2271])).
% 2.36/0.78 thf(f2337,plain,(
% 2.36/0.78 spl108_23),
% 2.36/0.78 inference(avatar_split_clause,[],[f1506,f2335])).
% 2.36/0.78 thf(f1506,plain,(
% 2.36/0.78 ( ! [X1 : $tType,X0 : $tType] : (($true = bot(sTfun(X0,X1))) | (bot(X1) != $true)) )),
% 2.36/0.78 inference(cnf_transformation,[],[f1036])).
% 2.36/0.78 thf(f1036,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (($true = bot(sTfun(X0,X1))) | (bot(X1) != $true))),
% 2.36/0.78 inference(ennf_transformation,[],[f593])).
% 2.36/0.78 thf(f593,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : ((bot(X1) = $true) => ($true = bot(sTfun(X0,X1))))),
% 2.36/0.78 inference(fool_elimination,[],[f592])).
% 2.36/0.78 thf(f592,plain,(
% 2.36/0.78 ! [X0 : $tType,X1 : $tType] : (bot(X1) => bot(sTfun(X0,X1)))),
% 2.36/0.78 inference(rectify,[],[f261])).
% 2.36/0.78 thf(f261,axiom,(
% 2.36/0.78 ! [X95 : $tType,X96 : $tType] : (bot(X96) => bot(sTfun(X95,X96)))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_fun___Orderings_Obot)).
% 2.36/0.78 thf(f2303,plain,(
% 2.36/0.78 spl108_22),
% 2.36/0.78 inference(avatar_split_clause,[],[f283,f2301])).
% 2.36/0.78 thf(f283,plain,(
% 2.36/0.78 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 2.36/0.78 introduced(fool_axiom,[])).
% 2.36/0.78 thf(f2299,plain,(
% 2.36/0.78 spl108_21),
% 2.36/0.78 inference(avatar_split_clause,[],[f1467,f2297])).
% 2.36/0.78 thf(f1467,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : (($true = order(set(X0)))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f541])).
% 2.36/0.78 thf(f541,plain,(
% 2.36/0.78 ! [X0 : $tType] : ($true = order(set(X0)))),
% 2.36/0.78 inference(fool_elimination,[],[f540])).
% 2.36/0.78 thf(f540,plain,(
% 2.36/0.78 ! [X0 : $tType] : order(set(X0))),
% 2.36/0.78 inference(rectify,[],[f271])).
% 2.36/0.78 thf(f271,axiom,(
% 2.36/0.78 ! [X95 : $tType] : order(set(X95))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder_6)).
% 2.36/0.78 thf(f2295,plain,(
% 2.36/0.78 spl108_20),
% 2.36/0.78 inference(avatar_split_clause,[],[f1466,f2293])).
% 2.36/0.78 thf(f1466,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : (($true = ord(set(X0)))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f539])).
% 2.36/0.78 thf(f539,plain,(
% 2.36/0.78 ! [X0 : $tType] : ($true = ord(set(X0)))),
% 2.36/0.78 inference(fool_elimination,[],[f538])).
% 2.36/0.78 thf(f538,plain,(
% 2.36/0.78 ! [X0 : $tType] : ord(set(X0))),
% 2.36/0.78 inference(rectify,[],[f272])).
% 2.36/0.78 thf(f272,axiom,(
% 2.36/0.78 ! [X95 : $tType] : ord(set(X95))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oord_7)).
% 2.36/0.78 thf(f2291,plain,(
% 2.36/0.78 spl108_19),
% 2.36/0.78 inference(avatar_split_clause,[],[f1465,f2289])).
% 2.36/0.78 thf(f1465,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : (($true = preorder(set(X0)))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f537])).
% 2.36/0.78 thf(f537,plain,(
% 2.36/0.78 ! [X0 : $tType] : ($true = preorder(set(X0)))),
% 2.36/0.78 inference(fool_elimination,[],[f536])).
% 2.36/0.78 thf(f536,plain,(
% 2.36/0.78 ! [X0 : $tType] : preorder(set(X0))),
% 2.36/0.78 inference(rectify,[],[f270])).
% 2.36/0.78 thf(f270,axiom,(
% 2.36/0.78 ! [X95 : $tType] : preorder(set(X95))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Opreorder_5)).
% 2.36/0.78 thf(f2287,plain,(
% 2.36/0.78 spl108_18),
% 2.36/0.78 inference(avatar_split_clause,[],[f1464,f2285])).
% 2.36/0.78 thf(f1464,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : (($true = order_bot(set(X0)))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f535])).
% 2.36/0.78 thf(f535,plain,(
% 2.36/0.78 ! [X0 : $tType] : ($true = order_bot(set(X0)))),
% 2.36/0.78 inference(fool_elimination,[],[f534])).
% 2.36/0.78 thf(f534,plain,(
% 2.36/0.78 ! [X0 : $tType] : order_bot(set(X0))),
% 2.36/0.78 inference(rectify,[],[f269])).
% 2.36/0.78 thf(f269,axiom,(
% 2.36/0.78 ! [X95 : $tType] : order_bot(set(X95))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Oorder__bot_4)).
% 2.36/0.78 thf(f2283,plain,(
% 2.36/0.78 spl108_17),
% 2.36/0.78 inference(avatar_split_clause,[],[f1463,f2281])).
% 2.36/0.78 thf(f1463,plain,(
% 2.36/0.78 ( ! [X0 : $tType] : (($true = bot(set(X0)))) )),
% 2.36/0.78 inference(cnf_transformation,[],[f533])).
% 2.36/0.78 thf(f533,plain,(
% 2.36/0.78 ! [X0 : $tType] : ($true = bot(set(X0)))),
% 2.36/0.78 inference(fool_elimination,[],[f532])).
% 2.36/0.78 thf(f532,plain,(
% 2.36/0.78 ! [X0 : $tType] : bot(set(X0))),
% 2.36/0.78 inference(rectify,[],[f273])).
% 2.36/0.78 thf(f273,axiom,(
% 2.36/0.78 ! [X95 : $tType] : bot(set(X95))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Set_Oset___Orderings_Obot_8)).
% 2.36/0.78 thf(f2279,plain,(
% 2.36/0.78 ~spl108_16),
% 2.36/0.78 inference(avatar_split_clause,[],[f1293,f2276])).
% 2.36/0.78 thf(f1293,plain,(
% 2.36/0.78 (t2 != binary1746293266le_Tip(a))),
% 2.36/0.78 inference(cnf_transformation,[],[f1])).
% 2.36/0.78 thf(f1,axiom,(
% 2.36/0.78 (t2 != binary1746293266le_Tip(a))),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_t2nTip)).
% 2.36/0.78 thf(f2274,plain,(
% 2.36/0.78 ~spl108_15),
% 2.36/0.78 inference(avatar_split_clause,[],[f1292,f2271])).
% 2.36/0.78 thf(f1292,plain,(
% 2.36/0.78 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) != $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f802])).
% 2.36/0.78 thf(f802,plain,(
% 2.36/0.78 (vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) != $true)),
% 2.36/0.78 inference(flattening,[],[f285])).
% 2.36/0.78 thf(f285,plain,(
% 2.36/0.78 ~(vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f284])).
% 2.36/0.78 thf(f284,plain,(
% 2.36/0.78 ~vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1)),
% 2.36/0.78 inference(rectify,[],[f281])).
% 2.36/0.78 thf(f281,negated_conjecture,(
% 2.36/0.78 ~vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1)),
% 2.36/0.78 inference(negated_conjecture,[],[f280])).
% 2.36/0.78 thf(f280,conjecture,(
% 2.36/0.78 vAPP(binary1291135688e_Tree(a),$o,vAPP(sTfun(a,int),sTfun(binary1291135688e_Tree(a),$o),binary1610619414edTree(a),h),t1)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0)).
% 2.36/0.78 thf(f2269,plain,(
% 2.36/0.78 spl108_14),
% 2.36/0.78 inference(avatar_split_clause,[],[f1650,f2266])).
% 2.36/0.78 thf(f1650,plain,(
% 2.36/0.78 (order($o) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f799])).
% 2.36/0.78 thf(f799,plain,(
% 2.36/0.78 (order($o) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f798])).
% 2.36/0.78 thf(f798,plain,(
% 2.36/0.78 order($o)),
% 2.36/0.78 inference(rectify,[],[f277])).
% 2.36/0.78 thf(f277,axiom,(
% 2.36/0.78 order($o)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder_12)).
% 2.36/0.78 thf(f2264,plain,(
% 2.36/0.78 spl108_13),
% 2.36/0.78 inference(avatar_split_clause,[],[f1649,f2261])).
% 2.36/0.78 thf(f1649,plain,(
% 2.36/0.78 (order(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f797])).
% 2.36/0.78 thf(f797,plain,(
% 2.36/0.78 (order(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f796])).
% 2.36/0.78 thf(f796,plain,(
% 2.36/0.78 order(int)),
% 2.36/0.78 inference(rectify,[],[f267])).
% 2.36/0.78 thf(f267,axiom,(
% 2.36/0.78 order(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oorder_2)).
% 2.36/0.78 thf(f2259,plain,(
% 2.36/0.78 spl108_12),
% 2.36/0.78 inference(avatar_split_clause,[],[f1648,f2256])).
% 2.36/0.78 thf(f2256,plain,(
% 2.36/0.78 spl108_12 <=> (linorder($o) = $true)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_12])])).
% 2.36/0.78 thf(f1648,plain,(
% 2.36/0.78 (linorder($o) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f795])).
% 2.36/0.78 thf(f795,plain,(
% 2.36/0.78 (linorder($o) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f794])).
% 2.36/0.78 thf(f794,plain,(
% 2.36/0.78 linorder($o)),
% 2.36/0.78 inference(rectify,[],[f276])).
% 2.36/0.78 thf(f276,axiom,(
% 2.36/0.78 linorder($o)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Olinorder_11)).
% 2.36/0.78 thf(f2254,plain,(
% 2.36/0.78 spl108_11),
% 2.36/0.78 inference(avatar_split_clause,[],[f1647,f2251])).
% 2.36/0.78 thf(f2251,plain,(
% 2.36/0.78 spl108_11 <=> (linorder(int) = $true)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_11])])).
% 2.36/0.78 thf(f1647,plain,(
% 2.36/0.78 (linorder(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f793])).
% 2.36/0.78 thf(f793,plain,(
% 2.36/0.78 (linorder(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f792])).
% 2.36/0.78 thf(f792,plain,(
% 2.36/0.78 linorder(int)),
% 2.36/0.78 inference(rectify,[],[f264])).
% 2.36/0.78 thf(f264,axiom,(
% 2.36/0.78 linorder(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Olinorder)).
% 2.36/0.78 thf(f2249,plain,(
% 2.36/0.78 spl108_10),
% 2.36/0.78 inference(avatar_split_clause,[],[f1646,f2246])).
% 2.36/0.78 thf(f1646,plain,(
% 2.36/0.78 (ord($o) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f791])).
% 2.36/0.78 thf(f791,plain,(
% 2.36/0.78 (ord($o) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f790])).
% 2.36/0.78 thf(f790,plain,(
% 2.36/0.78 ord($o)),
% 2.36/0.78 inference(rectify,[],[f278])).
% 2.36/0.78 thf(f278,axiom,(
% 2.36/0.78 ord($o)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oord_13)).
% 2.36/0.78 thf(f2244,plain,(
% 2.36/0.78 spl108_9),
% 2.36/0.78 inference(avatar_split_clause,[],[f1645,f2241])).
% 2.36/0.78 thf(f1645,plain,(
% 2.36/0.78 (ord(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f789])).
% 2.36/0.78 thf(f789,plain,(
% 2.36/0.78 (ord(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f788])).
% 2.36/0.78 thf(f788,plain,(
% 2.36/0.78 ord(int)),
% 2.36/0.78 inference(rectify,[],[f268])).
% 2.36/0.78 thf(f268,axiom,(
% 2.36/0.78 ord(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Oord_3)).
% 2.36/0.78 thf(f2239,plain,(
% 2.36/0.78 spl108_8),
% 2.36/0.78 inference(avatar_split_clause,[],[f1644,f2236])).
% 2.36/0.78 thf(f1644,plain,(
% 2.36/0.78 (preorder($o) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f787])).
% 2.36/0.78 thf(f787,plain,(
% 2.36/0.78 (preorder($o) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f786])).
% 2.36/0.78 thf(f786,plain,(
% 2.36/0.78 preorder($o)),
% 2.36/0.78 inference(rectify,[],[f275])).
% 2.36/0.78 thf(f275,axiom,(
% 2.36/0.78 preorder($o)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Opreorder_10)).
% 2.36/0.78 thf(f2234,plain,(
% 2.36/0.78 spl108_7),
% 2.36/0.78 inference(avatar_split_clause,[],[f1643,f2231])).
% 2.36/0.78 thf(f1643,plain,(
% 2.36/0.78 (preorder(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f785])).
% 2.36/0.78 thf(f785,plain,(
% 2.36/0.78 (preorder(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f784])).
% 2.36/0.78 thf(f784,plain,(
% 2.36/0.78 preorder(int)),
% 2.36/0.78 inference(rectify,[],[f263])).
% 2.36/0.78 thf(f263,axiom,(
% 2.36/0.78 preorder(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Opreorder_1)).
% 2.36/0.78 thf(f2229,plain,(
% 2.36/0.78 spl108_6),
% 2.36/0.78 inference(avatar_split_clause,[],[f1642,f2226])).
% 2.36/0.78 thf(f1642,plain,(
% 2.36/0.78 (order_bot($o) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f783])).
% 2.36/0.78 thf(f783,plain,(
% 2.36/0.78 (order_bot($o) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f782])).
% 2.36/0.78 thf(f782,plain,(
% 2.36/0.78 order_bot($o)),
% 2.36/0.78 inference(rectify,[],[f274])).
% 2.36/0.78 thf(f274,axiom,(
% 2.36/0.78 order_bot($o)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Oorder__bot_9)).
% 2.36/0.78 thf(f2224,plain,(
% 2.36/0.78 spl108_5),
% 2.36/0.78 inference(avatar_split_clause,[],[f1641,f2221])).
% 2.36/0.78 thf(f1641,plain,(
% 2.36/0.78 (bot($o) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f781])).
% 2.36/0.78 thf(f781,plain,(
% 2.36/0.78 (bot($o) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f780])).
% 2.36/0.78 thf(f780,plain,(
% 2.36/0.78 bot($o)),
% 2.36/0.78 inference(rectify,[],[f279])).
% 2.36/0.78 thf(f279,axiom,(
% 2.36/0.78 bot($o)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_HOL_Obool___Orderings_Obot_14)).
% 2.36/0.78 thf(f2219,plain,(
% 2.36/0.78 spl108_4),
% 2.36/0.78 inference(avatar_split_clause,[],[f1640,f2216])).
% 2.36/0.78 thf(f2216,plain,(
% 2.36/0.78 spl108_4 <=> (no_bot(int) = $true)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_4])])).
% 2.36/0.78 thf(f1640,plain,(
% 2.36/0.78 (no_bot(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f779])).
% 2.36/0.78 thf(f779,plain,(
% 2.36/0.78 (no_bot(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f778])).
% 2.36/0.78 thf(f778,plain,(
% 2.36/0.78 no_bot(int)),
% 2.36/0.78 inference(rectify,[],[f266])).
% 2.36/0.78 thf(f266,axiom,(
% 2.36/0.78 no_bot(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__bot)).
% 2.36/0.78 thf(f2214,plain,(
% 2.36/0.78 spl108_3),
% 2.36/0.78 inference(avatar_split_clause,[],[f1639,f2211])).
% 2.36/0.78 thf(f2211,plain,(
% 2.36/0.78 spl108_3 <=> (no_top(int) = $true)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_3])])).
% 2.36/0.78 thf(f1639,plain,(
% 2.36/0.78 (no_top(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f777])).
% 2.36/0.78 thf(f777,plain,(
% 2.36/0.78 (no_top(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f776])).
% 2.36/0.78 thf(f776,plain,(
% 2.36/0.78 no_top(int)),
% 2.36/0.78 inference(rectify,[],[f265])).
% 2.36/0.78 thf(f265,axiom,(
% 2.36/0.78 no_top(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Orderings_Ono__top)).
% 2.36/0.78 thf(f2209,plain,(
% 2.36/0.78 spl108_2),
% 2.36/0.78 inference(avatar_split_clause,[],[f1638,f2206])).
% 2.36/0.78 thf(f2206,plain,(
% 2.36/0.78 spl108_2 <=> (condit1037483654norder(int) = $true)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_2])])).
% 2.36/0.78 thf(f1638,plain,(
% 2.36/0.78 (condit1037483654norder(int) = $true)),
% 2.36/0.78 inference(cnf_transformation,[],[f775])).
% 2.36/0.78 thf(f775,plain,(
% 2.36/0.78 (condit1037483654norder(int) = $true)),
% 2.36/0.78 inference(fool_elimination,[],[f774])).
% 2.36/0.78 thf(f774,plain,(
% 2.36/0.78 condit1037483654norder(int)),
% 2.36/0.78 inference(rectify,[],[f262])).
% 2.36/0.78 thf(f262,axiom,(
% 2.36/0.78 condit1037483654norder(int)),
% 2.36/0.78 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tcon_Int_Oint___Conditionally__Complete__Lattices_Oconditionally__complete__linorder)).
% 2.36/0.78 thf(f2204,plain,(
% 2.36/0.78 ~spl108_1),
% 2.36/0.78 inference(avatar_split_clause,[],[f282,f2201])).
% 2.36/0.78 thf(f2201,plain,(
% 2.36/0.78 spl108_1 <=> ($true = $false)),
% 2.36/0.78 introduced(avatar_definition,[new_symbols(naming,[spl108_1])])).
% 2.36/0.78 thf(f282,plain,(
% 2.36/0.78 ($true != $false)),
% 2.36/0.78 introduced(fool_axiom,[])).
% 2.36/0.78 % SZS output end Proof for theBenchmark
% 2.36/0.78 % (4176)------------------------------
% 2.36/0.78 % (4176)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.36/0.78 % (4176)Termination reason: Refutation
% 2.36/0.78
% 2.36/0.78 % (4176)Memory used [KB]: 3747
% 2.36/0.78 % (4176)Time elapsed: 0.338 s
% 2.36/0.78 % (4176)Instructions burned: 607 (million)
% 2.36/0.78 % (4171)Success in time 0.372 s
%------------------------------------------------------------------------------