TSTP Solution File: COM133+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COM133+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n031.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 18:36:37 EDT 2023
% Result : Theorem 0.21s 0.72s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 113
% Syntax : Number of formulae : 141 ( 8 unt; 107 typ; 0 def)
% Number of atoms : 123 ( 50 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 147 ( 58 ~; 53 |; 23 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 274 ( 96 >; 178 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 98 ( 98 usr; 11 con; 0-5 aty)
% Number of variables : 161 ( 11 sgn; 94 !; 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,
veabs: $i ).
tff(decl_44,type,
epred1_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_45,type,
epred2_4: ( $i * $i * $i * $i ) > $o ).
tff(decl_46,type,
epred3_2: ( $i * $i ) > $o ).
tff(decl_47,type,
epred4_2: ( $i * $i ) > $o ).
tff(decl_48,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
esk11_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_60,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk15_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk16_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk17_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk18_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
esk19_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
esk20_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk24_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
esk26_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
esk28_3: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
esk29_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk30_3: ( $i * $i * $i ) > $i ).
tff(decl_78,type,
esk31_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk32_0: $i ).
tff(decl_80,type,
esk33_0: $i ).
tff(decl_81,type,
esk34_0: $i ).
tff(decl_82,type,
esk35_0: $i ).
tff(decl_83,type,
esk36_0: $i ).
tff(decl_84,type,
esk37_0: $i ).
tff(decl_85,type,
esk38_0: $i ).
tff(decl_86,type,
esk39_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
esk40_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk41_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk42_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
esk43_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk44_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
esk45_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
esk46_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
esk47_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_95,type,
esk48_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
esk49_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_97,type,
esk50_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_98,type,
esk51_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_99,type,
esk52_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_100,type,
esk53_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_101,type,
esk54_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
esk55_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_103,type,
esk56_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_104,type,
esk57_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_105,type,
esk58_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_106,type,
esk59_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_107,type,
esk60_2: ( $i * $i ) > $i ).
tff(decl_108,type,
esk61_2: ( $i * $i ) > $i ).
tff(decl_109,type,
esk62_2: ( $i * $i ) > $i ).
tff(decl_110,type,
esk63_2: ( $i * $i ) > $i ).
tff(decl_111,type,
esk64_2: ( $i * $i ) > $i ).
tff(decl_112,type,
esk65_2: ( $i * $i ) > $i ).
tff(decl_113,type,
esk66_2: ( $i * $i ) > $i ).
tff(decl_114,type,
esk67_2: ( $i * $i ) > $i ).
tff(decl_115,type,
esk68_2: ( $i * $i ) > $i ).
tff(decl_116,type,
esk69_2: ( $i * $i ) > $i ).
tff(decl_117,type,
esk70_2: ( $i * $i ) > $i ).
tff(decl_118,type,
esk71_2: ( $i * $i ) > $i ).
tff(decl_119,type,
esk72_2: ( $i * $i ) > $i ).
tff(decl_120,type,
esk73_2: ( $i * $i ) > $i ).
tff(decl_121,type,
esk74_2: ( $i * $i ) > $i ).
tff(decl_122,type,
esk75_2: ( $i * $i ) > $i ).
tff(decl_123,type,
esk76_2: ( $i * $i ) > $i ).
tff(decl_124,type,
esk77_2: ( $i * $i ) > $i ).
tff(decl_125,type,
esk78_2: ( $i * $i ) > $i ).
tff(decl_126,type,
esk79_2: ( $i * $i ) > $i ).
tff(decl_127,type,
esk80_2: ( $i * $i ) > $i ).
tff(decl_128,type,
esk81_2: ( $i * $i ) > $i ).
fof('T-subst-abs-2',axiom,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( X9 != X21
& ~ visFreeVar(X21,X11)
& vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-2') ).
fof('T-subst-abs-3',axiom,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( X9 != X21
& visFreeVar(X21,X11)
& vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs-3') ).
fof('T-subst-abs',conjecture,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-subst-abs') ).
fof(subst3,axiom,
! [X11,X9,X1,X4,X6,X19,X21,X15,X12] :
( ( X1 = X9
& X4 = X11
& X6 = vabs(X21,X15,X12) )
=> ( X9 = X21
=> ( X19 = vsubst(X1,X4,X6)
=> X19 = vabs(X21,X15,X12) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/COM001+0.ax',subst3) ).
fof('T-Strong',axiom,
! [X9,X10,X20,X11,X15] :
( ( ~ visFreeVar(X9,X11)
& vtcheck(vbind(X9,X10,X20),X11,X15) )
=> vtcheck(X20,X11,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','T-Strong') ).
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/sandbox2/benchmark/Axioms/COM001+0.ax',isFreeVar1) ).
fof(c_0_6,plain,
! [X15,X20,X9,X11,X21,X10,X34] :
( ( X9 != X21
& ~ visFreeVar(X21,X11)
& vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(fof_simplification,[status(thm)],['T-subst-abs-2']) ).
fof(c_0_7,plain,
! [X331,X332,X333,X334,X335,X336,X337] :
( X333 = X335
| ~ visFreeVar(X335,X334)
| ~ vtcheck(X332,X334,X331)
| ~ vtcheck(vbind(X333,X331,X332),vabs(X335,X336,veabs),X337)
| vtcheck(X332,vsubst(X333,X334,vabs(X335,X336,veabs)),X337) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['T-subst-abs-3'])]) ).
fof(c_0_8,plain,
! [X324,X325,X326,X327,X328,X329,X330] :
( X326 = X328
| visFreeVar(X328,X327)
| ~ vtcheck(X325,X327,X324)
| ~ vtcheck(vbind(X326,X324,X325),vabs(X328,X329,veabs),X330)
| vtcheck(X325,vsubst(X326,X327,vabs(X328,X329,veabs)),X330) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])]) ).
fof(c_0_9,negated_conjecture,
~ ! [X15,X20,X9,X11,X21,X10,X34] :
( ( vtcheck(X20,X11,X15)
& vtcheck(vbind(X9,X15,X20),vabs(X21,X10,veabs),X34) )
=> vtcheck(X20,vsubst(X9,X11,vabs(X21,X10,veabs)),X34) ),
inference(assume_negation,[status(cth)],['T-subst-abs']) ).
fof(c_0_10,plain,
! [X169,X170,X171,X172,X173,X174,X175,X176,X177] :
( X171 != X170
| X172 != X169
| X173 != vabs(X175,X176,X177)
| X170 != X175
| X174 != vsubst(X171,X172,X173)
| X174 = vabs(X175,X176,X177) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[subst3])]) ).
cnf(c_0_11,plain,
( X1 = X2
| vtcheck(X4,vsubst(X1,X3,vabs(X2,X6,veabs)),X7)
| ~ visFreeVar(X2,X3)
| ~ vtcheck(X4,X3,X5)
| ~ vtcheck(vbind(X1,X5,X4),vabs(X2,X6,veabs),X7) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X2
| visFreeVar(X2,X3)
| vtcheck(X4,vsubst(X1,X3,vabs(X2,X6,veabs)),X7)
| ~ vtcheck(X4,X3,X5)
| ~ vtcheck(vbind(X1,X5,X4),vabs(X2,X6,veabs),X7) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,negated_conjecture,
( vtcheck(esk33_0,esk35_0,esk32_0)
& vtcheck(vbind(esk34_0,esk32_0,esk33_0),vabs(esk36_0,esk37_0,veabs),esk38_0)
& ~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vabs(esk36_0,esk37_0,veabs)),esk38_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_14,plain,
( X9 = vabs(X6,X7,X8)
| X1 != X2
| X3 != X4
| X5 != vabs(X6,X7,X8)
| X2 != X6
| X9 != vsubst(X1,X3,X5) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,plain,
! [X9,X10,X20,X11,X15] :
( ( ~ visFreeVar(X9,X11)
& vtcheck(vbind(X9,X10,X20),X11,X15) )
=> vtcheck(X20,X11,X15) ),
inference(fof_simplification,[status(thm)],['T-Strong']) ).
fof(c_0_16,plain,
! [X72,X73,X74,X75,X76,X77] :
( ( X75 = X76
| ~ visFreeVar(X76,X77)
| visFreeVar(X73,X74)
| X73 != X76
| X74 != vabs(X75,X72,X77) )
& ( X75 != X76
| ~ visFreeVar(X73,X74)
| X73 != X76
| X74 != vabs(X75,X72,X77) )
& ( visFreeVar(X76,X77)
| ~ visFreeVar(X73,X74)
| X73 != X76
| X74 != vabs(X75,X72,X77) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isFreeVar1])])]) ).
cnf(c_0_17,plain,
( X1 = X2
| vtcheck(X3,vsubst(X1,X4,vabs(X2,X5,veabs)),X6)
| ~ vtcheck(vbind(X1,X7,X3),vabs(X2,X5,veabs),X6)
| ~ vtcheck(X3,X4,X7) ),
inference(csr,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,negated_conjecture,
vtcheck(esk33_0,esk35_0,esk32_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( X1 = vabs(X2,X3,X4)
| X1 != vsubst(X2,X5,X6)
| X6 != vabs(X2,X3,X4) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_14])])]) ).
fof(c_0_20,plain,
! [X301,X302,X303,X304,X305] :
( visFreeVar(X301,X304)
| ~ vtcheck(vbind(X301,X302,X303),X304,X305)
| vtcheck(X303,X304,X305) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])]) ).
cnf(c_0_21,plain,
( X1 != X2
| ~ visFreeVar(X3,X4)
| X3 != X2
| X4 != vabs(X1,X5,X6) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( X1 = X2
| vtcheck(esk33_0,vsubst(X1,esk35_0,vabs(X2,X3,veabs)),X4)
| ~ vtcheck(vbind(X1,esk32_0,esk33_0),vabs(X2,X3,veabs),X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
vtcheck(vbind(esk34_0,esk32_0,esk33_0),vabs(esk36_0,esk37_0,veabs),esk38_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,negated_conjecture,
~ vtcheck(esk33_0,vsubst(esk34_0,esk35_0,vabs(esk36_0,esk37_0,veabs)),esk38_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_25,plain,
( vsubst(X1,X2,X3) = vabs(X1,X4,X5)
| X3 != vabs(X1,X4,X5) ),
inference(er,[status(thm)],[c_0_19]) ).
cnf(c_0_26,plain,
( visFreeVar(X1,X2)
| vtcheck(X4,X2,X5)
| ~ vtcheck(vbind(X1,X3,X4),X2,X5) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( X1 != vabs(X2,X3,X4)
| ~ visFreeVar(X2,X1) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_21])]) ).
cnf(c_0_28,negated_conjecture,
esk36_0 = esk34_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,plain,
vsubst(X1,X2,vabs(X1,X3,X4)) = vabs(X1,X3,X4),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
( vtcheck(esk33_0,vabs(esk36_0,esk37_0,veabs),esk38_0)
| visFreeVar(esk34_0,vabs(esk36_0,esk37_0,veabs)) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_31,plain,
~ visFreeVar(X1,vabs(X1,X2,X3)),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,negated_conjecture,
~ vtcheck(esk33_0,vabs(esk34_0,esk37_0,veabs),esk38_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_28]),c_0_29]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_31]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM133+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.18/0.35 % Computer : n031.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue Aug 29 13:47:26 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.72 % Version : CSE_E---1.5
% 0.21/0.72 % Problem : theBenchmark.p
% 0.21/0.72 % Proof found
% 0.21/0.72 % SZS status Theorem for theBenchmark.p
% 0.21/0.72 % SZS output start Proof
% See solution above
% 0.21/0.73 % Total time : 0.151000 s
% 0.21/0.73 % SZS output end Proof
% 0.21/0.73 % Total time : 0.157000 s
%------------------------------------------------------------------------------