TSTP Solution File: SCT121+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SCT121+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 : n017.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 148.88s 148.89s
% Output : CNFRefutation 149.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 186
% Syntax : Number of formulae : 246 ( 27 unt; 171 typ; 0 def)
% Number of atoms : 196 ( 22 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 200 ( 79 ~; 79 |; 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 : 540 ( 162 >; 378 *; 0 +; 0 <<)
% Number of predicates : 39 ( 37 usr; 1 prp; 0-6 aty)
% Number of functors : 134 ( 134 usr; 9 con; 0-8 aty)
% Number of variables : 173 ( 21 sgn; 93 !; 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_i: $i ).
tff(decl_99,type,
v_F: $i > $i ).
tff(decl_100,type,
v_P: $i ).
tff(decl_101,type,
v_a: $i ).
tff(decl_102,type,
v_b: $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_1: $i > $i ).
tff(decl_190,type,
esk88_1: $i > $i ).
tff(decl_191,type,
esk89_1: $i > $i ).
tff(decl_192,type,
esk90_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_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)) )
=> ( 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_3) ).
fof(conj_1,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_1) ).
fof(conj_2,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_2) ).
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_0,hypothesis,
! [X78] :
( ! [X3] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X78,X3))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X78,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(X78,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(X78,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(X78)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
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,
! [X956,X957,X958,X959] :
( ( ~ hBOOL(hAPP(c_Set_Oinsert(X959,X958,X957),X956))
| X958 = X956
| hBOOL(hAPP(X957,X956)) )
& ( X958 != X956
| hBOOL(hAPP(c_Set_Oinsert(X959,X958,X957),X956)) )
& ( ~ hBOOL(hAPP(X957,X956))
| hBOOL(hAPP(c_Set_Oinsert(X959,X958,X957),X956)) ) ),
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,
! [X945,X946,X947] :
( ~ c_member(X947,X946,X945)
| c_Set_Oinsert(X947,X946,X945) = X945 ),
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,
! [X152,X153,X154] :
( ( ~ c_member(X154,X153,X152)
| hBOOL(hAPP(X152,X153)) )
& ( ~ hBOOL(hAPP(X152,X153))
| c_member(X154,X153,X152) ) ),
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,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_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,esk90_0)) )
& ( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_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,esk90_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,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_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,esk90_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_3])])])]) ).
fof(c_0_23,hypothesis,
! [X2037] :
( c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2037))
& c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,X2037))
& 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,X2037)) ),
inference(variable_rename,[status(thm)],[conj_1]) ).
fof(c_0_24,plain,
! [X84,X85,X86,X87,X88] :
( ( ~ c_Relation_Oirrefl(X85,X84)
| ~ c_member(tc_prod(X85,X85),c_Product__Type_OPair(X85,X85,X86,X86),X84) )
& ( c_member(tc_prod(X88,X88),c_Product__Type_OPair(X88,X88,esk2_2(X87,X88),esk2_2(X87,X88)),X87)
| c_Relation_Oirrefl(X88,X87) ) ),
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_2]) ).
fof(c_0_28,plain,
! [X701,X702] :
( ~ c_Relation_Otrans(X702,X701)
| c_Transitive__Closure_Otrancl(X702,X701) = X701 ),
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,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_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,esk90_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,
! [X705,X706,X707,X708,X709] :
( ~ c_member(tc_prod(X709,X709),c_Product__Type_OPair(X709,X709,X708,X707),X706)
| ~ c_member(tc_prod(X709,X709),c_Product__Type_OPair(X709,X709,X707,X705),X706)
| c_member(tc_prod(X709,X709),c_Product__Type_OPair(X709,X709,X708,X705),c_Transitive__Closure_Otrancl(X709,X706)) ),
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])]) ).
cnf(c_0_39,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_40,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_41,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_42,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_43,hypothesis,
( c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,v_F(v_P))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_0))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(v_P,esk90_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,esk90_0)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_44,hypothesis,
! [X2031,X2035,X2036] :
( ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X2031,esk87_1(X2031)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X2031,esk88_1(X2031)))
| ~ 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(X2031,esk89_1(X2031)))
| X2035 = X2036
| ~ 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,X2035,X2036),hAPP(X2031,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,X2035,X2036),v_F(X2031)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[conj_0])])])])]) ).
fof(c_0_45,plain,
! [X115,X116] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X116,tc_HOL_Obool)),X115)),
inference(variable_rename,[status(thm)],[fact_top1I]) ).
fof(c_0_46,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_47,plain,
( ~ c_Relation_Oirrefl(X1,X2)
| ~ c_member(X3,c_Product__Type_OPair(X1,X1,X4,X4),X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_21]) ).
cnf(c_0_48,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_40,c_0_41]),c_0_42]) ).
cnf(c_0_49,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_43,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_50,hypothesis,
( X2 = 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,X3),v_F(X1))
| ~ c_Relation_Otrans(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk87_1(X1)))
| ~ c_Relation_Oirrefl(tc_Arrow__Order__Mirabelle_Oalt,hAPP(X1,esk88_1(X1)))
| ~ 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(X1,esk89_1(X1)))
| ~ 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,X3),hAPP(X1,v_i)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_51,plain,
! [X90,X91,X92,X93,X94,X95,X96,X97] :
( ( ~ c_Relation_Ototal__on(X92,X91,X90)
| ~ c_member(X92,X93,X91)
| ~ c_member(X92,X94,X91)
| X93 = X94
| c_member(tc_prod(X92,X92),c_Product__Type_OPair(X92,X92,X93,X94),X90)
| c_member(tc_prod(X92,X92),c_Product__Type_OPair(X92,X92,X94,X93),X90) )
& ( c_member(X97,esk3_3(X95,X96,X97),X96)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( c_member(X97,esk4_3(X95,X96,X97),X96)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( esk3_3(X95,X96,X97) != esk4_3(X95,X96,X97)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( ~ c_member(tc_prod(X97,X97),c_Product__Type_OPair(X97,X97,esk3_3(X95,X96,X97),esk4_3(X95,X96,X97)),X95)
| c_Relation_Ototal__on(X97,X96,X95) )
& ( ~ c_member(tc_prod(X97,X97),c_Product__Type_OPair(X97,X97,esk4_3(X95,X96,X97),esk3_3(X95,X96,X97)),X95)
| c_Relation_Ototal__on(X97,X96,X95) ) ),
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_52,plain,
hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X2)),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
fof(c_0_53,plain,
! [X857,X858,X859,X860,X861] :
( ( ~ c_Wellfounded_Oacyclic(X858,X857)
| ~ c_member(tc_prod(X858,X858),c_Product__Type_OPair(X858,X858,X859,X859),c_Transitive__Closure_Otrancl(X858,X857)) )
& ( c_member(tc_prod(X861,X861),c_Product__Type_OPair(X861,X861,esk67_2(X860,X861),esk67_2(X860,X861)),c_Transitive__Closure_Otrancl(X861,X860))
| c_Wellfounded_Oacyclic(X861,X860) ) ),
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_46])])])])]) ).
fof(c_0_54,plain,
! [X155,X156,X157,X158,X159] :
( ( ~ c_FunDef_Oin__rel(X159,X158,X157,X156,X155)
| c_member(tc_prod(X159,X158),c_Product__Type_OPair(X159,X158,X156,X155),X157) )
& ( ~ c_member(tc_prod(X159,X158),c_Product__Type_OPair(X159,X158,X156,X155),X157)
| c_FunDef_Oin__rel(X159,X158,X157,X156,X155) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_in__rel__def])]) ).
cnf(c_0_55,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_47,c_0_48]),c_0_49])]) ).
cnf(c_0_56,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(spm,[status(thm)],[c_0_50,c_0_32]),c_0_31]),c_0_30])]) ).
cnf(c_0_57,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_51]) ).
cnf(c_0_58,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_52]) ).
fof(c_0_59,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_60,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_53]) ).
cnf(c_0_61,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_54]) ).
cnf(c_0_62,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_55,c_0_56]) ).
cnf(c_0_63,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_57,c_0_32]),c_0_58]),c_0_58])]) ).
cnf(c_0_64,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_59]) ).
cnf(c_0_65,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_53]) ).
cnf(c_0_66,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_60]) ).
cnf(c_0_67,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_61,c_0_41]) ).
cnf(c_0_68,hypothesis,
v_b = v_a,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]) ).
cnf(c_0_69,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_65,c_0_42]) ).
cnf(c_0_70,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_66,c_0_42]),c_0_49])]) ).
cnf(c_0_71,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_54]) ).
cnf(c_0_72,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_67,c_0_68]) ).
cnf(c_0_73,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_69,c_0_70])]) ).
cnf(c_0_74,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT121+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 14:44:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 148.88/148.89 % Version : CSE_E---1.5
% 148.88/148.89 % Problem : theBenchmark.p
% 148.88/148.89 % Proof found
% 148.88/148.89 % SZS status Theorem for theBenchmark.p
% 148.88/148.89 % SZS output start Proof
% See solution above
% 149.00/148.90 % Total time : 148.306000 s
% 149.00/148.90 % SZS output end Proof
% 149.00/148.90 % Total time : 148.334000 s
%------------------------------------------------------------------------------