TSTP Solution File: SCT122+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 : Thu Aug 31 14:11:15 EDT 2023
% Result : Theorem 150.33s 151.14s
% Output : CNFRefutation 150.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 184
% Syntax : Number of formulae : 246 ( 27 unt; 169 typ; 0 def)
% Number of atoms : 201 ( 23 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 205 ( 81 ~; 82 |; 23 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 537 ( 159 >; 378 *; 0 +; 0 <<)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-6 aty)
% Number of functors : 132 ( 132 usr; 10 con; 0-8 aty)
% Number of variables : 177 ( 24 sgn; 91 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
hAPP: ( $i * $i ) > $i ).
tff(decl_23,type,
tc_HOL_Obool: $i ).
tff(decl_24,type,
tc_fun: ( $i * $i ) > $i ).
tff(decl_25,type,
c_Orderings_Otop__class_Otop: $i > $i ).
tff(decl_26,type,
c_member: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
c_Relation_Oirrefl: ( $i * $i ) > $o ).
tff(decl_28,type,
tc_prod: ( $i * $i ) > $i ).
tff(decl_29,type,
c_Product__Type_OPair: ( $i * $i * $i * $i ) > $i ).
tff(decl_30,type,
c_Relation_Ototal__on: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(decl_32,type,
hBOOL: $i > $o ).
tff(decl_33,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
tff(decl_34,type,
c_Arrow__Order__Mirabelle_Omkbot: ( $i * $i ) > $i ).
tff(decl_35,type,
c_Arrow__Order__Mirabelle_Omktop: ( $i * $i ) > $i ).
tff(decl_36,type,
c_Order__Relation_Ostrict__linear__order__on: ( $i * $i * $i ) > $o ).
tff(decl_37,type,
class_Orderings_Otop: $i > $o ).
tff(decl_38,type,
c_fequal: $i > $i ).
tff(decl_39,type,
c_FunDef_Oin__rel: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_40,type,
c_Recdef_Osame__fst: ( $i * $i * $i * $i ) > $i ).
tff(decl_41,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
c_Relation_OId__on: ( $i * $i ) > $i ).
tff(decl_43,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
c_Nitpick_Orefl_H: ( $i * $i ) > $o ).
tff(decl_45,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
tff(decl_46,type,
c_Relation_Oinv__image: ( $i * $i * $i * $i ) > $i ).
tff(decl_47,type,
c_Arrow__Order__Mirabelle_Oabove: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
c_Arrow__Order__Mirabelle_Obelow: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
c_Wellfounded_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
c_Relation_Orefl__on: ( $i * $i * $i ) > $o ).
tff(decl_51,type,
c_Order__Relation_Opreorder__on: ( $i * $i * $i ) > $o ).
tff(decl_52,type,
c_Wellfounded_Oacc: ( $i * $i ) > $i ).
tff(decl_53,type,
c_Recdef_Owfrec__rel: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_54,type,
c_Relation_Osingle__valued: ( $i * $i * $i ) > $o ).
tff(decl_55,type,
c_Recdef_Ocut: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(decl_57,type,
c_Nitpick_Owf__wfrec_H: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
c_Nitpick_Owf__wfrec: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
c_Relation_OId: $i > $i ).
tff(decl_60,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(decl_61,type,
c_Lattices_Osemilattice__sup__class_Osup: ( $i * $i * $i ) > $i ).
tff(decl_62,type,
c_Relation_Oantisym: ( $i * $i ) > $o ).
tff(decl_63,type,
c_Product__Type_Oprod_Oprod__rec: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
class_Lattices_Olattice: $i > $o ).
tff(decl_65,type,
class_Lattices_Obounded__lattice__top: $i > $o ).
tff(decl_66,type,
c_Order__Relation_Opartial__order__on: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
class_Lattices_Osemilattice__sup: $i > $o ).
tff(decl_68,type,
c_Order__Relation_Olinear__order__on: ( $i * $i * $i ) > $o ).
tff(decl_69,type,
c_Wellfounded_Oacyclic: ( $i * $i ) > $o ).
tff(decl_70,type,
c_Product__Type_Ointernal__split: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_71,type,
c_Groups_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
c_Set_Oinsert: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
c_Relation_OField: ( $i * $i ) > $i ).
tff(decl_74,type,
class_Groups_Ominus: $i > $o ).
tff(decl_75,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(decl_76,type,
c_Wellfounded_Owf: ( $i * $i ) > $o ).
tff(decl_77,type,
c_Orderings_Oord__class_Oless__eq: ( $i * $i * $i ) > $o ).
tff(decl_78,type,
class_Orderings_Opreorder: $i > $o ).
tff(decl_79,type,
class_Orderings_Obot: $i > $o ).
tff(decl_80,type,
class_Orderings_Oord: $i > $o ).
tff(decl_81,type,
class_Orderings_Olinorder: $i > $o ).
tff(decl_82,type,
class_Orderings_Oorder: $i > $o ).
tff(decl_83,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
tff(decl_84,type,
c_Order__Relation_Owell__order__on: ( $i * $i * $i ) > $o ).
tff(decl_85,type,
c_Set_Othe__elem: ( $i * $i ) > $i ).
tff(decl_86,type,
c_Nitpick_Ofold__graph_H: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_87,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
c_Wellfounded_Omeasure: ( $i * $i ) > $i ).
tff(decl_89,type,
class_Groups_Oordered__ab__group__add: $i > $o ).
tff(decl_90,type,
class_Groups_Oab__group__add: $i > $o ).
tff(decl_91,type,
c_Equiv__Relations_Oequiv: ( $i * $i * $i ) > $o ).
tff(decl_92,type,
c_Recdef_Owfrec: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(decl_94,type,
c_Lattices_Osemilattice__inf__class_Oinf: ( $i * $i * $i ) > $i ).
tff(decl_95,type,
class_Lattices_Osemilattice__inf: $i > $o ).
tff(decl_96,type,
class_Lattices_Odistrib__lattice: $i > $o ).
tff(decl_97,type,
class_Lattices_Obounded__lattice: $i > $o ).
tff(decl_98,type,
v_P: $i ).
tff(decl_99,type,
v_a: $i ).
tff(decl_100,type,
v_b: $i ).
tff(decl_101,type,
v_F: $i > $i ).
tff(decl_102,type,
v_i: $i ).
tff(decl_103,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_104,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_105,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_106,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_107,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_110,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_111,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_114,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_115,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_116,type,
esk14_3: ( $i * $i * $i ) > $i ).
tff(decl_117,type,
esk15_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_118,type,
esk16_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_119,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_120,type,
esk18_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_121,type,
esk19_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_122,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_123,type,
esk21_3: ( $i * $i * $i ) > $i ).
tff(decl_124,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_125,type,
esk23_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_126,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_127,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_128,type,
esk26_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_129,type,
esk27_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_130,type,
esk28_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_131,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_132,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_133,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_134,type,
esk32_2: ( $i * $i ) > $i ).
tff(decl_135,type,
esk33_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_136,type,
esk34_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_137,type,
esk35_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_138,type,
esk36_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_139,type,
esk37_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_140,type,
esk38_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_141,type,
esk39_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_142,type,
esk40_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_143,type,
esk41_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_144,type,
esk42_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_145,type,
esk43_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_146,type,
esk44_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_147,type,
esk45_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_148,type,
esk46_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_149,type,
esk47_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_150,type,
esk48_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_151,type,
esk49_0: $i ).
tff(decl_152,type,
esk50_3: ( $i * $i * $i ) > $i ).
tff(decl_153,type,
esk51_3: ( $i * $i * $i ) > $i ).
tff(decl_154,type,
esk52_3: ( $i * $i * $i ) > $i ).
tff(decl_155,type,
esk53_2: ( $i * $i ) > $i ).
tff(decl_156,type,
esk54_2: ( $i * $i ) > $i ).
tff(decl_157,type,
esk55_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_158,type,
esk56_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_159,type,
esk57_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_160,type,
esk58_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_161,type,
esk59_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_162,type,
esk60_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_163,type,
esk61_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_164,type,
esk62_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_165,type,
esk63_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_166,type,
esk64_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_167,type,
esk65_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_168,type,
esk66_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_169,type,
esk67_2: ( $i * $i ) > $i ).
tff(decl_170,type,
esk68_2: ( $i * $i ) > $i ).
tff(decl_171,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_172,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_173,type,
esk71_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_174,type,
esk72_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_175,type,
esk73_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_176,type,
esk74_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_177,type,
esk75_2: ( $i * $i ) > $i ).
tff(decl_178,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_179,type,
esk77_2: ( $i * $i ) > $i ).
tff(decl_180,type,
esk78_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_181,type,
esk79_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_182,type,
esk80_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_183,type,
esk81_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_184,type,
esk82_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_185,type,
esk83_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_186,type,
esk84_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_187,type,
esk85_3: ( $i * $i * $i ) > $i ).
tff(decl_188,type,
esk86_3: ( $i * $i * $i ) > $i ).
tff(decl_189,type,
esk87_0: $i ).
tff(decl_190,type,
esk88_0: $i ).
fof(fact_insert__code,axiom,
! [X4,X7,X17,X5] :
( hBOOL(hAPP(c_Set_Oinsert(X5,X17,X7),X4))
<=> ( X17 = X4
| hBOOL(hAPP(X7,X4)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(fact_insert__absorb,axiom,
! [X7,X13,X5] :
( c_member(X5,X13,X7)
=> c_Set_Oinsert(X5,X13,X7) = X7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
fof(fact_irrefl__def,axiom,
! [X6,X5] :
( c_Relation_Oirrefl(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
fof(fact_mem__def,axiom,
! [X7,X4,X5] :
( c_member(X5,X4,X7)
<=> hBOOL(hAPP(X7,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(conj_2,hypothesis,
( ! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)) )
=> ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(conj_0,hypothesis,
! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(conj_1,hypothesis,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(fact_trancl__id,axiom,
! [X6,X5] :
( c_Relation_Otrans(X5,X6)
=> c_Transitive__Closure_Otrancl(X5,X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__id) ).
fof(fact_r__r__into__trancl,axiom,
! [X11,X19,X12,X13,X5] :
( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X12),X19)
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X12,X11),X19)
=> c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X13,X11),c_Transitive__Closure_Otrancl(X5,X19)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
fof(conj_3,hypothesis,
( ! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X3))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X3)) )
=> ! [X38,X39] :
( X38 != X39
=> ( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X38,X39),hAPP(v_P,v_i))
=> c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X38,X39),v_F(v_P)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(fact_top1I,axiom,
! [X4,X5] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X5,tc_HOL_Obool)),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(fact_acyclic__def,axiom,
! [X6,X5] :
( c_Wellfounded_Oacyclic(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(fact_total__on__def,axiom,
! [X6,X7,X5] :
( c_Relation_Ototal__on(X5,X7,X6)
<=> ! [X3] :
( c_member(X5,X3,X7)
=> ! [X8] :
( c_member(X5,X8,X7)
=> ( X3 != X8
=> ( c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X8),X6)
| c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X8,X3),X6) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(fact_in__rel__def,axiom,
! [X17,X4,X19,X18,X5] :
( c_FunDef_Oin__rel(X5,X18,X19,X4,X17)
<=> c_member(tc_prod(X5,X18),c_Product__Type_OPair(X5,X18,X4,X17),X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
fof(conj_4,conjecture,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(c_0_15,plain,
! [X955,X956,X957,X958] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X958,X957,X956),X955))
| X957 = X955
| hBOOL(hAPP(X956,X955)) )
& ( X957 != X955
| hBOOL(hAPP(c_Set_Oinsert(X958,X957,X956),X955)) )
& ( ~ hBOOL(hAPP(X956,X955))
| hBOOL(hAPP(c_Set_Oinsert(X958,X957,X956),X955)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__code])])]) ).
cnf(c_0_16,plain,
( hBOOL(hAPP(c_Set_Oinsert(X3,X1,X4),X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_17,plain,
! [X944,X945,X946] :
( ~ c_member(X946,X945,X944)
| c_Set_Oinsert(X946,X945,X944) = X944 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_insert__absorb])]) ).
fof(c_0_18,plain,
! [X6,X5] :
( c_Relation_Oirrefl(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),X6) ),
inference(fof_simplification,[status(thm)],[fact_irrefl__def]) ).
fof(c_0_19,plain,
! [X151,X152,X153] :
( ( ~ c_member(X153,X152,X151)
| hBOOL(hAPP(X151,X152)) )
& ( ~ hBOOL(hAPP(X151,X152))
| c_member(X153,X152,X151) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_mem__def])]) ).
cnf(c_0_20,plain,
hBOOL(hAPP(c_Set_Oinsert(X1,X2,X3),X2)),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( c_Set_Oinsert(X1,X2,X3) = X3
| ~ c_member(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,hypothesis,
( ( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk87_0)) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk87_0)) )
& ( c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk87_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_2])])])]) ).
fof(c_0_23,hypothesis,
! [X2030] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2030))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2030))
& c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X2030)) ),
inference(variable_rename,[status(thm)],[conj_0]) ).
fof(c_0_24,plain,
! [X83,X84,X85,X86,X87] :
( ( ~ c_Relation_Oirrefl(X84,X83)
| ~ c_member(tc_prod(X84,X84),c_Product__Type_OPair(X84,X84,X85,X85),X83) )
& ( c_member(tc_prod(X87,X87),c_Product__Type_OPair(X87,X87,esk2_2(X86,X87),esk2_2(X86,X87)),X86)
| c_Relation_Oirrefl(X87,X86) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])]) ).
cnf(c_0_25,plain,
( c_member(X3,X2,X1)
| ~ hBOOL(hAPP(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( hBOOL(hAPP(X1,X2))
| ~ c_member(X3,X2,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,hypothesis,
c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(split_conjunct,[status(thm)],[conj_1]) ).
fof(c_0_28,plain,
! [X700,X701] :
( ~ c_Relation_Otrans(X701,X700)
| c_Transitive__Closure_Otrancl(X701,X700) = X700 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_trancl__id])]) ).
cnf(c_0_29,hypothesis,
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk87_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,hypothesis,
c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,X1)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,plain,
c_member(X1,X2,c_Set_Oinsert(X3,X2,X4)),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
fof(c_0_35,plain,
! [X704,X705,X706,X707,X708] :
( ~ c_member(tc_prod(X708,X708),c_Product__Type_OPair(X708,X708,X707,X706),X705)
| ~ c_member(tc_prod(X708,X708),c_Product__Type_OPair(X708,X708,X706,X704),X705)
| c_member(tc_prod(X708,X708),c_Product__Type_OPair(X708,X708,X707,X704),c_Transitive__Closure_Otrancl(X708,X705)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_r__r__into__trancl])]) ).
cnf(c_0_36,hypothesis,
hBOOL(hAPP(v_F(v_P),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
( c_Transitive__Closure_Otrancl(X1,X2) = X2
| ~ c_Relation_Otrans(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,hypothesis,
c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_39,hypothesis,
! [X2033,X2034] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk88_0))
| X2033 = X2034
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2033,X2034),hAPP(v_P,v_i))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2033,X2034),v_F(v_P)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])]) ).
cnf(c_0_40,plain,
~ c_Relation_Oirrefl(X1,c_Set_Oinsert(X2,c_Product__Type_OPair(X1,X1,X3,X3),X4)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_41,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X5),c_Transitive__Closure_Otrancl(X1,X4))
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X2,X3),X4)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X5),X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_42,hypothesis,
c_member(X1,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),v_F(v_P)),
inference(spm,[status(thm)],[c_0_25,c_0_36]) ).
cnf(c_0_43,hypothesis,
c_Transitive__Closure_Otrancl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)) = v_F(v_P),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk87_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk87_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_45,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk88_0))
| ~ c_Relation_Ototal__on(tc_Arrow__Order__Mirabelle_Oalt,c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_HOL_Obool)),hAPP(v_P,esk88_0))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_46,plain,
! [X114,X115] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X115,tc_HOL_Obool)),X114)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(c_0_47,plain,
! [X6,X5] :
( c_Wellfounded_Oacyclic(X5,X6)
<=> ! [X3] : ~ c_member(tc_prod(X5,X5),c_Product__Type_OPair(X5,X5,X3,X3),c_Transitive__Closure_Otrancl(X5,X6)) ),
inference(fof_simplification,[status(thm)],[fact_acyclic__def]) ).
cnf(c_0_48,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_21]) ).
cnf(c_0_49,hypothesis,
( c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_b),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,v_a),v_F(v_P)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
cnf(c_0_50,hypothesis,
c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_51,plain,
( c_member(X1,X2,X3)
| ~ c_member(X4,X2,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_52,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_30]),c_0_31]),c_0_32])]) ).
fof(c_0_53,plain,
! [X89,X90,X91,X92,X93,X94,X95,X96] :
( ( ~ c_Relation_Ototal__on(X91,X90,X89)
| ~ c_member(X91,X92,X90)
| ~ c_member(X91,X93,X90)
| X92 = X93
| c_member(tc_prod(X91,X91),c_Product__Type_OPair(X91,X91,X92,X93),X89)
| c_member(tc_prod(X91,X91),c_Product__Type_OPair(X91,X91,X93,X92),X89) )
& ( c_member(X96,esk3_3(X94,X95,X96),X95)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( c_member(X96,esk4_3(X94,X95,X96),X95)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( esk3_3(X94,X95,X96) != esk4_3(X94,X95,X96)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( ~ c_member(tc_prod(X96,X96),c_Product__Type_OPair(X96,X96,esk3_3(X94,X95,X96),esk4_3(X94,X95,X96)),X94)
| c_Relation_Ototal__on(X96,X95,X94) )
& ( ~ c_member(tc_prod(X96,X96),c_Product__Type_OPair(X96,X96,esk4_3(X94,X95,X96),esk3_3(X94,X95,X96)),X94)
| c_Relation_Ototal__on(X96,X95,X94) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_total__on__def])])])])])]) ).
cnf(c_0_54,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_55,plain,
! [X856,X857,X858,X859,X860] :
( ( ~ c_Wellfounded_Oacyclic(X857,X856)
| ~ c_member(tc_prod(X857,X857),c_Product__Type_OPair(X857,X857,X858,X858),c_Transitive__Closure_Otrancl(X857,X856)) )
& ( c_member(tc_prod(X860,X860),c_Product__Type_OPair(X860,X860,esk67_2(X859,X860),esk67_2(X859,X860)),c_Transitive__Closure_Otrancl(X860,X859))
| c_Wellfounded_Oacyclic(X860,X859) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])])])]) ).
fof(c_0_56,plain,
! [X154,X155,X156,X157,X158] :
( ( ~ c_FunDef_Oin__rel(X158,X157,X156,X155,X154)
| c_member(tc_prod(X158,X157),c_Product__Type_OPair(X158,X157,X155,X154),X156) )
& ( ~ c_member(tc_prod(X158,X157),c_Product__Type_OPair(X158,X157,X155,X154),X156)
| c_FunDef_Oin__rel(X158,X157,X156,X155,X154) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(c_0_57,hypothesis,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_58,hypothesis,
( X1 = X2
| c_member(X3,c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,v_i)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
( X4 = X5
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X4,X5),X3)
| c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X5,X4),X3)
| ~ c_Relation_Ototal__on(X1,X2,X3)
| ~ c_member(X1,X4,X2)
| ~ c_member(X1,X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
c_member(X1,X2,c_Orderings_Otop__class_Otop(tc_fun(X3,tc_HOL_Obool))),
inference(spm,[status(thm)],[c_0_25,c_0_54]) ).
fof(c_0_61,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_4])]) ).
cnf(c_0_62,plain,
( c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,esk67_2(X2,X1),esk67_2(X2,X1)),c_Transitive__Closure_Otrancl(X1,X2))
| c_Wellfounded_Oacyclic(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_63,plain,
( c_FunDef_Oin__rel(X1,X2,X5,X3,X4)
| ~ c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,hypothesis,
( v_b = v_a
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_b,v_a),hAPP(v_P,v_i)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,hypothesis,
( X1 = X2
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X2),hAPP(v_P,X3))
| c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X2,X1),hAPP(v_P,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_32]),c_0_60]),c_0_60])]) ).
cnf(c_0_66,negated_conjecture,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_a,v_b),hAPP(v_P,v_i)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,plain,
( ~ c_Wellfounded_Oacyclic(X1,X2)
| ~ c_member(tc_prod(X1,X1),c_Product__Type_OPair(X1,X1,X3,X3),c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_68,plain,
( c_Wellfounded_Oacyclic(X1,X2)
| ~ c_Relation_Oirrefl(X1,c_Transitive__Closure_Otrancl(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_62]) ).
cnf(c_0_69,hypothesis,
c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_b),
inference(spm,[status(thm)],[c_0_63,c_0_42]) ).
cnf(c_0_70,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_71,hypothesis,
( ~ c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X1),v_F(v_P)) ),
inference(spm,[status(thm)],[c_0_67,c_0_43]) ).
cnf(c_0_72,hypothesis,
c_Wellfounded_Oacyclic(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_43]),c_0_50])]) ).
cnf(c_0_73,plain,
( c_member(tc_prod(X1,X2),c_Product__Type_OPair(X1,X2,X4,X5),X3)
| ~ c_FunDef_Oin__rel(X1,X2,X3,X4,X5) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_74,hypothesis,
c_FunDef_Oin__rel(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P),v_a,v_a),
inference(rw,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,hypothesis,
~ c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,X1,X1),v_F(v_P)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_72])]) ).
cnf(c_0_76,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SCT122+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Aug 24 16:36:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 150.33/151.14 % Version : CSE_E---1.5
% 150.33/151.14 % Problem : theBenchmark.p
% 150.33/151.14 % Proof found
% 150.33/151.14 % SZS status Theorem for theBenchmark.p
% 150.33/151.14 % SZS output start Proof
% See solution above
% 150.33/151.16 % Total time : 149.782000 s
% 150.33/151.16 % SZS output end Proof
% 150.33/151.16 % Total time : 149.811000 s
%------------------------------------------------------------------------------