TSTP Solution File: COM140+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COM140+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Wed Aug 30 18:36:39 EDT 2023
% Result : Theorem 2.13s 2.19s
% Output : CNFRefutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 118
% Syntax : Number of formulae : 191 ( 28 unt; 107 typ; 0 def)
% Number of atoms : 239 ( 109 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 260 ( 105 ~; 105 |; 27 &)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 276 ( 97 >; 179 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-4 aty)
% Number of functors : 97 ( 97 usr; 10 con; 0-5 aty)
% Number of variables : 298 ( 61 sgn; 116 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
vvar: $i > $i ).
tff(decl_23,type,
vabs: ( $i * $i * $i ) > $i ).
tff(decl_24,type,
vapp: ( $i * $i ) > $i ).
tff(decl_25,type,
visValue: $i > $o ).
tff(decl_26,type,
visFreeVar: ( $i * $i ) > $o ).
tff(decl_27,type,
vempty: $i ).
tff(decl_28,type,
vbind: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
vnoType: $i ).
tff(decl_30,type,
vsomeType: $i > $i ).
tff(decl_31,type,
visSomeType: $i > $o ).
tff(decl_32,type,
vgetSomeType: $i > $i ).
tff(decl_33,type,
vlookup: ( $i * $i ) > $i ).
tff(decl_34,type,
vtcheck: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
vgensym: $i > $i ).
tff(decl_36,type,
vsubst: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
vnoExp: $i ).
tff(decl_38,type,
vsomeExp: $i > $i ).
tff(decl_39,type,
visSomeExp: $i > $o ).
tff(decl_40,type,
vgetSomeExp: $i > $i ).
tff(decl_41,type,
vreduce: $i > $i ).
tff(decl_42,type,
varrow: ( $i * $i ) > $i ).
tff(decl_43,type,
valphaEquivalent: ( $i * $i ) > $o ).
tff(decl_44,type,
veabs: $i ).
tff(decl_45,type,
epred1_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_46,type,
epred2_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_47,type,
epred3_2: ( $i * $i ) > $o ).
tff(decl_48,type,
epred4_2: ( $i * $i ) > $o ).
tff(decl_49,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_60,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk15_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk16_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk17_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
esk18_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
esk19_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
esk20_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_69,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
esk32_0: $i ).
tff(decl_81,type,
esk33_0: $i ).
tff(decl_82,type,
esk34_0: $i ).
tff(decl_83,type,
esk35_0: $i ).
tff(decl_84,type,
esk36_0: $i ).
tff(decl_85,type,
esk37_0: $i ).
tff(decl_86,type,
esk38_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
esk39_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk40_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk41_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
esk42_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk43_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
esk44_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
esk45_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
esk46_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk47_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
esk48_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
esk49_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_98,type,
esk50_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
esk51_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
esk52_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
esk53_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
esk54_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_103,type,
esk55_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
esk56_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
esk57_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
esk58_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
esk59_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk60_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk61_2: ( $i * $i ) > $i ).
tff(decl_110,type,
esk62_2: ( $i * $i ) > $i ).
tff(decl_111,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk64_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk65_2: ( $i * $i ) > $i ).
tff(decl_114,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk67_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk68_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk71_2: ( $i * $i ) > $i ).
tff(decl_120,type,
esk72_2: ( $i * $i ) > $i ).
tff(decl_121,type,
esk73_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk74_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk75_2: ( $i * $i ) > $i ).
tff(decl_124,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk77_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk78_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk79_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk80_2: ( $i * $i ) > $i ).
fof('gensym-is-fresh',axiom,
! [X14,X11] :
( vgensym(X11) = X14
=> ~ visFreeVar(X14,X11) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','gensym-is-fresh') ).
fof(isFreeVar2,axiom,
! [X1,X4,X12,X14,X13] :
( ( X1 = X14
& X4 = vapp(X12,X13) )
=> ( ( ( visFreeVar(X14,X12)
| visFreeVar(X14,X13) )
=> visFreeVar(X1,X4) )
& ( visFreeVar(X1,X4)
=> ( visFreeVar(X14,X12)
| visFreeVar(X14,X13) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar2) ).
fof('T-Weak-abs-2',conjecture,
! [X9,X10,X20,X21,X36,X15] :
( ( X9 = X21
& vlookup(X9,X20) = vnoType
& vtcheck(X20,vabs(X21,X36,veabs),X15) )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-abs-2') ).
fof(subst2,axiom,
! [X1,X4,X6,X19,X12,X9,X11,X13] :
( ( X1 = X9
& X4 = X11
& X6 = vapp(X12,X13) )
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vapp(vsubst(X9,X11,X12),vsubst(X9,X11,X13)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',subst2) ).
fof(isFreeVar1,axiom,
! [X15,X1,X4,X9,X14,X11] :
( ( X1 = X14
& X4 = vabs(X9,X15,X11) )
=> ( ( ( X9 != X14
& visFreeVar(X14,X11) )
=> visFreeVar(X1,X4) )
& ( visFreeVar(X1,X4)
=> ( X9 != X14
& visFreeVar(X14,X11) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).
fof(subst0,axiom,
! [X9,X21,X1,X4,X6,X19,X11] :
( ( X1 = X9
& X4 = X11
& X6 = vvar(X21) )
=> ( X9 = X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = X11 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',subst0) ).
fof(isFreeVar0,axiom,
! [X1,X4,X9,X14] :
( ( X1 = X14
& X4 = vvar(X9) )
=> ( ( X9 = X14
=> visFreeVar(X1,X4) )
& ( visFreeVar(X1,X4)
=> X9 = X14 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',isFreeVar0) ).
fof('alpha-equiv-typing',axiom,
! [X11,X20,X12,X15] :
( ( vtcheck(X20,X11,X15)
& valphaEquivalent(X11,X12) )
=> vtcheck(X20,X12,X15) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-typing') ).
fof('alpha-equiv-subst-abs',axiom,
! [X10,X9,X21,X11] :
( ~ visFreeVar(X21,X11)
=> valphaEquivalent(vabs(X9,X10,X11),vabs(X21,X10,vsubst(X9,vvar(X21),X11))) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-subst-abs') ).
fof('T-Weak-abs-1-gen',axiom,
! [X9,X10,X20,X21,X36,X12,X15] :
( ( X9 != X21
& vlookup(X9,X20) = vnoType
& vtcheck(X20,vabs(X21,X36,X12),X15) )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,X12),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','T-Weak-abs-1-gen') ).
fof('alpha-equiv-sym',axiom,
! [X13,X12] :
( valphaEquivalent(X12,X13)
=> valphaEquivalent(X13,X12) ),
file('/export/starexec/sandbox/benchmark/Axioms/COM001+1.ax','alpha-equiv-sym') ).
fof(c_0_11,plain,
! [X14,X11] :
( vgensym(X11) = X14
=> ~ visFreeVar(X14,X11) ),
inference(fof_simplification,[status(thm)],['gensym-is-fresh']) ).
fof(c_0_12,plain,
! [X147,X148] :
( vgensym(X148) != X147
| ~ visFreeVar(X147,X148) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).
fof(c_0_13,plain,
! [X80,X81,X82,X83,X84] :
( ( ~ visFreeVar(X83,X82)
| visFreeVar(X80,X81)
| X80 != X83
| X81 != vapp(X82,X84) )
& ( ~ visFreeVar(X83,X84)
| visFreeVar(X80,X81)
| X80 != X83
| X81 != vapp(X82,X84) )
& ( ~ visFreeVar(X80,X81)
| visFreeVar(X83,X82)
| visFreeVar(X83,X84)
| X80 != X83
| X81 != vapp(X82,X84) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar2])])]) ).
fof(c_0_14,negated_conjecture,
~ ! [X9,X10,X20,X21,X36,X15] :
( ( X9 = X21
& vlookup(X9,X20) = vnoType
& vtcheck(X20,vabs(X21,X36,veabs),X15) )
=> vtcheck(vbind(X9,X10,X20),vabs(X21,X36,veabs),X15) ),
inference(assume_negation,[status(cth)],['T-Weak-abs-2']) ).
cnf(c_0_15,plain,
( vgensym(X1) != X2
| ~ visFreeVar(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( visFreeVar(X3,X4)
| ~ visFreeVar(X1,X2)
| X3 != X1
| X4 != vapp(X5,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X163,X164,X165,X166,X167,X168,X169,X170] :
( X163 != X168
| X164 != X169
| X165 != vapp(X167,X170)
| X166 != vsubst(X163,X164,X165)
| X166 = vapp(vsubst(X168,X169,X167),vsubst(X168,X169,X170)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst2])]) ).
fof(c_0_18,plain,
! [X74,X75,X76,X77,X78,X79] :
( ( X77 = X78
| ~ visFreeVar(X78,X79)
| visFreeVar(X75,X76)
| X75 != X78
| X76 != vabs(X77,X74,X79) )
& ( X77 != X78
| ~ visFreeVar(X75,X76)
| X75 != X78
| X76 != vabs(X77,X74,X79) )
& ( visFreeVar(X78,X79)
| ~ visFreeVar(X75,X76)
| X75 != X78
| X76 != vabs(X77,X74,X79) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar1])])]) ).
fof(c_0_19,negated_conjecture,
( esk32_0 = esk35_0
& vlookup(esk32_0,esk34_0) = vnoType
& vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0)
& ~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
cnf(c_0_20,plain,
~ visFreeVar(vgensym(X1),X1),
inference(er,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( visFreeVar(X1,vapp(X2,X3))
| ~ visFreeVar(X1,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_16])]) ).
cnf(c_0_22,plain,
( X8 = vapp(vsubst(X2,X4,X6),vsubst(X2,X4,X7))
| X1 != X2
| X3 != X4
| X5 != vapp(X6,X7)
| X8 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,plain,
! [X149,X150,X151,X152,X153,X154,X155] :
( X151 != X149
| X152 != X155
| X153 != vvar(X150)
| X149 != X150
| X154 != vsubst(X151,X152,X153)
| X154 = X155 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst0])]) ).
cnf(c_0_24,plain,
( X1 = X2
| visFreeVar(X4,X5)
| ~ visFreeVar(X2,X3)
| X4 != X2
| X5 != vabs(X1,X6,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,plain,
! [X70,X71,X72,X73] :
( ( X72 != X73
| visFreeVar(X70,X71)
| X70 != X73
| X71 != vvar(X72) )
& ( ~ visFreeVar(X70,X71)
| X72 = X73
| X70 != X73
| X71 != vvar(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar0])])]) ).
fof(c_0_26,plain,
! [X308,X309,X310,X311] :
( ~ vtcheck(X309,X308,X311)
| ~ valphaEquivalent(X308,X310)
| vtcheck(X309,X310,X311) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-typing'])]) ).
cnf(c_0_27,negated_conjecture,
vtcheck(esk34_0,vabs(esk35_0,esk36_0,veabs),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,negated_conjecture,
esk32_0 = esk35_0,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_29,plain,
! [X10,X9,X21,X11] :
( ~ visFreeVar(X21,X11)
=> valphaEquivalent(vabs(X9,X10,X11),vabs(X21,X10,vsubst(X9,vvar(X21),X11))) ),
inference(fof_simplification,[status(thm)],['alpha-equiv-subst-abs']) ).
cnf(c_0_30,plain,
~ visFreeVar(vgensym(vapp(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_31,plain,
vapp(vsubst(X1,X2,X3),vsubst(X1,X2,X4)) = vsubst(X1,X2,vapp(X3,X4)),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_32,plain,
( X7 = X4
| X1 != X2
| X3 != X4
| X5 != vvar(X6)
| X2 != X6
| X7 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( X1 = X2
| visFreeVar(X2,vabs(X1,X3,X4))
| ~ visFreeVar(X2,X4) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_24])]) ).
cnf(c_0_34,plain,
( visFreeVar(X3,X4)
| X1 != X2
| X3 != X2
| X4 != vvar(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
( vtcheck(X1,X4,X3)
| ~ vtcheck(X1,X2,X3)
| ~ valphaEquivalent(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,negated_conjecture,
vtcheck(esk34_0,vabs(esk32_0,esk36_0,veabs),esk37_0),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_37,plain,
! [X304,X305,X306,X307] :
( visFreeVar(X306,X307)
| valphaEquivalent(vabs(X305,X304,X307),vabs(X306,X304,vsubst(X305,vvar(X306),X307))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])]) ).
cnf(c_0_38,plain,
~ visFreeVar(vgensym(vsubst(X1,X2,vapp(X3,X4))),vsubst(X1,X2,X4)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_39,plain,
vsubst(X1,X2,vvar(X1)) = X2,
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_32])])])])]) ).
cnf(c_0_40,plain,
( visFreeVar(X1,X2)
| ~ visFreeVar(X3,X4)
| X3 != X1
| X4 != vabs(X5,X6,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,plain,
( X1 = X2
| visFreeVar(X2,vabs(X1,X3,vapp(X4,X5)))
| ~ visFreeVar(X2,X5) ),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_42,plain,
visFreeVar(X1,vvar(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_34])])]) ).
fof(c_0_43,plain,
! [X315,X316,X317,X318,X319,X320,X321] :
( X315 = X318
| vlookup(X315,X317) != vnoType
| ~ vtcheck(X317,vabs(X318,X319,X320),X321)
| vtcheck(vbind(X315,X316,X317),vabs(X318,X319,X320),X321) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-Weak-abs-1-gen'])]) ).
cnf(c_0_44,negated_conjecture,
( vtcheck(esk34_0,X1,esk37_0)
| ~ valphaEquivalent(vabs(esk32_0,esk36_0,veabs),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,plain,
( visFreeVar(X1,X2)
| valphaEquivalent(vabs(X3,X4,X2),vabs(X1,X4,vsubst(X3,vvar(X1),X2))) ),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_46,plain,
~ visFreeVar(vgensym(vsubst(X1,X2,vapp(X3,vvar(X1)))),X2),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
( visFreeVar(X1,X2)
| ~ visFreeVar(X1,vabs(X3,X4,X2)) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_40])]) ).
cnf(c_0_48,plain,
( X1 = X2
| visFreeVar(X2,vabs(X1,X3,vapp(X4,vvar(X2)))) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_49,plain,
( visFreeVar(X3,X4)
| ~ visFreeVar(X1,X2)
| X3 != X1
| X4 != vapp(X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_50,plain,
( X1 = X2
| vtcheck(vbind(X1,X7,X3),vabs(X2,X4,X5),X6)
| vlookup(X1,X3) != vnoType
| ~ vtcheck(X3,vabs(X2,X4,X5),X6) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_51,negated_conjecture,
( vtcheck(esk34_0,vabs(X1,esk36_0,vsubst(esk32_0,vvar(X1),veabs)),esk37_0)
| visFreeVar(X1,veabs) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,plain,
~ visFreeVar(vgensym(vsubst(X1,vapp(X2,X3),vapp(X4,vvar(X1)))),X3),
inference(spm,[status(thm)],[c_0_46,c_0_21]) ).
cnf(c_0_53,plain,
( X1 = X2
| visFreeVar(X2,vapp(X3,vvar(X2))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( visFreeVar(X1,vapp(X2,X3))
| ~ visFreeVar(X1,X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_49])]) ).
cnf(c_0_55,negated_conjecture,
( X1 = X2
| vtcheck(vbind(X1,X3,esk34_0),vabs(X2,esk36_0,vsubst(esk32_0,vvar(X2),veabs)),esk37_0)
| visFreeVar(X2,veabs)
| vlookup(X1,esk34_0) != vnoType ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
vlookup(esk32_0,esk34_0) = vnoType,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_57,plain,
! [X299,X300] :
( ~ valphaEquivalent(X300,X299)
| valphaEquivalent(X299,X300) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['alpha-equiv-sym'])]) ).
cnf(c_0_58,plain,
( visFreeVar(X1,vapp(X2,vvar(X1)))
| ~ visFreeVar(X1,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
~ visFreeVar(vgensym(vapp(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_20,c_0_54]) ).
cnf(c_0_60,negated_conjecture,
( esk32_0 = X1
| vtcheck(vbind(esk32_0,X2,esk34_0),vabs(X1,esk36_0,vsubst(esk32_0,vvar(X1),veabs)),esk37_0)
| visFreeVar(X1,veabs) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
( valphaEquivalent(X2,X1)
| ~ valphaEquivalent(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_62,plain,
visFreeVar(X1,vapp(X2,vvar(X1))),
inference(spm,[status(thm)],[c_0_58,c_0_42]) ).
cnf(c_0_63,plain,
~ visFreeVar(vgensym(vapp(vapp(X1,X2),X3)),X2),
inference(spm,[status(thm)],[c_0_59,c_0_21]) ).
cnf(c_0_64,negated_conjecture,
~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk35_0,esk36_0,veabs),esk37_0),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_65,negated_conjecture,
( esk32_0 = X1
| vtcheck(vbind(esk32_0,X2,esk34_0),X3,esk37_0)
| visFreeVar(X1,veabs)
| ~ valphaEquivalent(vabs(X1,esk36_0,vsubst(esk32_0,vvar(X1),veabs)),X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_60]) ).
cnf(c_0_66,plain,
( valphaEquivalent(vabs(X1,X2,vsubst(X3,vvar(X1),X4)),vabs(X3,X2,X4))
| visFreeVar(X1,X4) ),
inference(spm,[status(thm)],[c_0_61,c_0_45]) ).
cnf(c_0_67,plain,
vapp(vsubst(X1,X2,X3),X2) = vsubst(X1,X2,vapp(X3,vvar(X1))),
inference(spm,[status(thm)],[c_0_31,c_0_39]) ).
cnf(c_0_68,plain,
( X1 = X2
| visFreeVar(X2,vabs(X1,X3,vapp(X4,vapp(X5,vvar(X2))))) ),
inference(spm,[status(thm)],[c_0_41,c_0_62]) ).
cnf(c_0_69,plain,
~ visFreeVar(vgensym(vapp(vapp(X1,vapp(X2,X3)),X4)),X2),
inference(spm,[status(thm)],[c_0_63,c_0_54]) ).
cnf(c_0_70,negated_conjecture,
~ vtcheck(vbind(esk32_0,esk33_0,esk34_0),vabs(esk32_0,esk36_0,veabs),esk37_0),
inference(rw,[status(thm)],[c_0_64,c_0_28]) ).
cnf(c_0_71,negated_conjecture,
( esk32_0 = X1
| vtcheck(vbind(esk32_0,X2,esk34_0),vabs(esk32_0,esk36_0,veabs),esk37_0)
| visFreeVar(X1,veabs) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_72,plain,
~ visFreeVar(vgensym(vsubst(X1,vsubst(X2,X3,vapp(X4,vvar(X2))),vapp(X5,vvar(X1)))),X3),
inference(spm,[status(thm)],[c_0_52,c_0_67]) ).
cnf(c_0_73,plain,
( X1 = X2
| visFreeVar(X2,vapp(X3,vapp(X4,vvar(X2)))) ),
inference(spm,[status(thm)],[c_0_47,c_0_68]) ).
cnf(c_0_74,plain,
~ visFreeVar(vgensym(vapp(vapp(X1,vapp(vapp(X2,X3),X4)),X5)),X3),
inference(spm,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_75,negated_conjecture,
( esk32_0 = X1
| visFreeVar(X1,veabs) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_76,plain,
( visFreeVar(X1,vapp(X2,vapp(X3,vvar(X1))))
| ~ visFreeVar(X1,X4) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_77,plain,
visFreeVar(X1,vsubst(X2,vvar(X1),vapp(X3,vvar(X2)))),
inference(spm,[status(thm)],[c_0_62,c_0_67]) ).
cnf(c_0_78,plain,
~ visFreeVar(vgensym(vapp(vsubst(X1,vapp(vapp(X2,X3),X4),vapp(X5,vvar(X1))),X6)),X3),
inference(spm,[status(thm)],[c_0_74,c_0_67]) ).
cnf(c_0_79,negated_conjecture,
vgensym(vapp(X1,veabs)) = esk32_0,
inference(spm,[status(thm)],[c_0_30,c_0_75]) ).
cnf(c_0_80,plain,
visFreeVar(X1,vapp(X2,vapp(X3,vvar(X1)))),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,negated_conjecture,
~ visFreeVar(esk32_0,X1),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_82,plain,
visFreeVar(X1,vsubst(X2,vapp(X3,vvar(X1)),vapp(X4,vvar(X2)))),
inference(spm,[status(thm)],[c_0_80,c_0_67]) ).
cnf(c_0_83,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_81,c_0_82]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COM140+1 : TPTP v8.1.2. Released v6.4.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 13:27:20 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 2.13/2.19 % Version : CSE_E---1.5
% 2.13/2.19 % Problem : theBenchmark.p
% 2.13/2.19 % Proof found
% 2.13/2.19 % SZS status Theorem for theBenchmark.p
% 2.13/2.19 % SZS output start Proof
% See solution above
% 2.13/2.21 % Total time : 1.638000 s
% 2.13/2.21 % SZS output end Proof
% 2.13/2.21 % Total time : 1.644000 s
%------------------------------------------------------------------------------