%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM432+3 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 : Tue May 5 04:57:19 PM UTC 2026
% Result : Theorem 0.29s 1.66s
% Output : CNFRefutation 0.29s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 58)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xc)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mEquModSym,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
=> sdteqdtlpzmzozddtrp0(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
fof(m__853,hypothesis,
( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xb,smndt0(xc)) )
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__853) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mMulMinOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
& smndt0(X1) = sdtasdt0(X1,smndt0(sz10)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulMinOne) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(m__924,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__924) ).
fof(m__899,hypothesis,
( aInteger0(xm)
& sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__899) ).
fof(m__876,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__876) ).
fof(m__818,hypothesis,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& xq != sz00
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(i_0_26,negated_conjecture,
~ ( ? [X1] :
( aInteger0(X1)
& sdtasdt0(xq,X1) = sdtpldt0(xa,smndt0(xc)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
| sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_27,plain,
! [X79,X80,X81] :
( ~ aInteger0(X79)
| ~ aInteger0(X80)
| ~ aInteger0(X81)
| X81 = sz00
| ~ sdteqdtlpzmzozddtrp0(X79,X80,X81)
| sdteqdtlpzmzozddtrp0(X80,X79,X81) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModSym])]) ).
fof(i_0_28,plain,
! [X74,X75,X76] :
( ( ~ sdteqdtlpzmzozddtrp0(X74,X75,X76)
| aDivisorOf0(X76,sdtpldt0(X74,smndt0(X75)))
| ~ aInteger0(X74)
| ~ aInteger0(X75)
| ~ aInteger0(X76)
| X76 = sz00 )
& ( ~ aDivisorOf0(X76,sdtpldt0(X74,smndt0(X75)))
| sdteqdtlpzmzozddtrp0(X74,X75,X76)
| ~ aInteger0(X74)
| ~ aInteger0(X75)
| ~ aInteger0(X76)
| X76 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
fof(i_0_29,plain,
! [X62,X63,X64] :
( ( sdtasdt0(X62,sdtpldt0(X63,X64)) = sdtpldt0(sdtasdt0(X62,X63),sdtasdt0(X62,X64))
| ~ aInteger0(X62)
| ~ aInteger0(X63)
| ~ aInteger0(X64) )
& ( sdtasdt0(sdtpldt0(X62,X63),X64) = sdtpldt0(sdtasdt0(X62,X64),sdtasdt0(X63,X64))
| ~ aInteger0(X62)
| ~ aInteger0(X63)
| ~ aInteger0(X64) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
fof(i_0_30,plain,
! [X56,X57,X58] :
( ~ aInteger0(X56)
| ~ aInteger0(X57)
| ~ aInteger0(X58)
| sdtasdt0(X56,sdtasdt0(X57,X58)) = sdtasdt0(sdtasdt0(X56,X57),X58) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(i_0_31,plain,
! [X49,X50,X51] :
( ~ aInteger0(X49)
| ~ aInteger0(X50)
| ~ aInteger0(X51)
| sdtpldt0(X49,sdtpldt0(X50,X51)) = sdtpldt0(sdtpldt0(X49,X50),X51) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
fof(i_0_32,negated_conjecture,
! [X84] :
( ( ~ aInteger0(X84)
| sdtasdt0(xq,X84) != sdtpldt0(xa,smndt0(xc)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc)))
& ~ sdteqdtlpzmzozddtrp0(xa,xc,xq) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_26])])]) ).
fof(i_0_33,plain,
! [X69,X70,X72,X73] :
( ( aInteger0(X70)
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( X70 != sz00
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( aInteger0(esk1_2(X69,X70))
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( sdtasdt0(X70,esk1_2(X69,X70)) = X69
| ~ aDivisorOf0(X70,X69)
| ~ aInteger0(X69) )
& ( ~ aInteger0(X72)
| X72 = sz00
| ~ aInteger0(X73)
| sdtasdt0(X72,X73) != X69
| aDivisorOf0(X72,X69)
| ~ aInteger0(X69) ) ),
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)],[mDivisor])])])])])]) ).
fof(i_0_34,plain,
! [X77,X78] :
( ~ aInteger0(X77)
| ~ aInteger0(X78)
| X78 = sz00
| sdteqdtlpzmzozddtrp0(X77,X77,X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
fof(i_0_35,hypothesis,
( aInteger0(esk2_0)
& sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb))
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aInteger0(esk3_0)
& sdtasdt0(xq,esk3_0) = sdtpldt0(xb,smndt0(xc))
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__853])]) ).
fof(i_0_36,plain,
! [X47,X48] :
( ~ aInteger0(X47)
| ~ aInteger0(X48)
| aInteger0(sdtasdt0(X47,X48)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])]) ).
fof(i_0_37,plain,
! [X45,X46] :
( ~ aInteger0(X45)
| ~ aInteger0(X46)
| aInteger0(sdtpldt0(X45,X46)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])]) ).
fof(i_0_38,plain,
! [X59,X60] :
( ~ aInteger0(X59)
| ~ aInteger0(X60)
| sdtasdt0(X59,X60) = sdtasdt0(X60,X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(i_0_39,plain,
! [X52,X53] :
( ~ aInteger0(X52)
| ~ aInteger0(X53)
| sdtpldt0(X52,X53) = sdtpldt0(X53,X52) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
fof(i_0_40,plain,
! [X67,X68] :
( ~ aInteger0(X67)
| ~ aInteger0(X68)
| sdtasdt0(X67,X68) != sz00
| X67 = sz00
| X68 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
fof(i_0_41,plain,
! [X66] :
( ( sdtasdt0(smndt0(sz10),X66) = smndt0(X66)
| ~ aInteger0(X66) )
& ( smndt0(X66) = sdtasdt0(X66,smndt0(sz10))
| ~ aInteger0(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulMinOne])])]) ).
fof(i_0_42,plain,
! [X55] :
( ( sdtpldt0(X55,smndt0(X55)) = sz00
| ~ aInteger0(X55) )
& ( sz00 = sdtpldt0(smndt0(X55),X55)
| ~ aInteger0(X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
fof(i_0_43,plain,
! [X61] :
( ( sdtasdt0(X61,sz10) = X61
| ~ aInteger0(X61) )
& ( X61 = sdtasdt0(sz10,X61)
| ~ aInteger0(X61) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
fof(i_0_44,plain,
! [X54] :
( ( sdtpldt0(X54,sz00) = X54
| ~ aInteger0(X54) )
& ( X54 = sdtpldt0(sz00,X54)
| ~ aInteger0(X54) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(i_0_45,plain,
! [X65] :
( ( sdtasdt0(X65,sz00) = sz00
| ~ aInteger0(X65) )
& ( sz00 = sdtasdt0(sz00,X65)
| ~ aInteger0(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(i_0_46,plain,
! [X44] :
( ~ aInteger0(X44)
| aInteger0(smndt0(X44)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
cnf(i_0_47,plain,
( X3 = sz00
| sdteqdtlpzmzozddtrp0(X2,X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_48,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_49,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_50,plain,
( sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_51,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_52,plain,
( sdtasdt0(X1,sdtasdt0(X2,X3)) = sdtasdt0(sdtasdt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_53,plain,
( sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_54,negated_conjecture,
~ sdteqdtlpzmzozddtrp0(xa,xc,xq),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_55,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_56,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_57,negated_conjecture,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xc))),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_58,plain,
( X1 = sz00
| aDivisorOf0(X1,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X3
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_59,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_60,negated_conjecture,
( ~ aInteger0(X1)
| sdtasdt0(xq,X1) != sdtpldt0(xa,smndt0(xc)) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_61,hypothesis,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_62,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,xq),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_63,hypothesis,
sdtasdt0(xq,sdtpldt0(xn,xm)) = sdtpldt0(xa,smndt0(xc)),
inference(split_conjunct,[status(thm)],[m__924]),
[final] ).
cnf(i_0_64,plain,
( aInteger0(sdtasdt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_65,plain,
( aInteger0(sdtpldt0(X1,X2))
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_66,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_67,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_68,hypothesis,
aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc))),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_69,hypothesis,
aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_70,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_71,plain,
( aInteger0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_72,plain,
( X1 != sz00
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_73,plain,
( sdtasdt0(smndt0(sz10),X1) = smndt0(X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_74,plain,
( smndt0(X1) = sdtasdt0(X1,smndt0(sz10))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_75,plain,
( sdtpldt0(X1,smndt0(X1)) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_76,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_77,hypothesis,
sdtasdt0(xq,esk3_0) = sdtpldt0(xb,smndt0(xc)),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_78,hypothesis,
sdtasdt0(xq,esk2_0) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_79,hypothesis,
sdtasdt0(xq,xm) = sdtpldt0(xb,smndt0(xc)),
inference(split_conjunct,[status(thm)],[m__899]),
[final] ).
cnf(i_0_80,hypothesis,
sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)),
inference(split_conjunct,[status(thm)],[m__876]),
[final] ).
cnf(i_0_81,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_82,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_83,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_84,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_85,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_86,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_87,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_88,hypothesis,
aInteger0(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_89,hypothesis,
aInteger0(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_90,hypothesis,
aInteger0(xm),
inference(split_conjunct,[status(thm)],[m__899]),
[final] ).
cnf(i_0_91,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__876]),
[final] ).
cnf(i_0_92,hypothesis,
aInteger0(xc),
inference(split_conjunct,[status(thm)],[m__818]),
[final] ).
cnf(i_0_93,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[m__818]),
[final] ).
cnf(i_0_94,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[m__818]),
[final] ).
cnf(i_0_95,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[m__818]),
[final] ).
cnf(i_0_96,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]),
[final] ).
cnf(i_0_97,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]),
[final] ).
cnf(i_0_98,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[m__818]),
[final] ).
cnf(i_0_99,axiom,
X1 = X1 ).
cnf(i_0_100,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_101,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_102,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_103,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_104,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_105,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_106,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_107,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_108,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_109,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_110,axiom,
( X1 != X2
| ~ aInteger0(X1)
| aInteger0(X2) ) ).
cnf(i_0_111,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_112,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_99_001,axiom,
X1 = X1 ).
cnf(i_0_100_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_101_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_102_004,axiom,
( X1 != X2
| sdtpldt0(X1,X3) = sdtpldt0(X2,X3) ) ).
cnf(i_0_103_005,axiom,
( X1 != X2
| sdtpldt0(X3,X1) = sdtpldt0(X3,X2) ) ).
cnf(i_0_104_006,axiom,
( X1 != X2
| smndt0(X1) = smndt0(X2) ) ).
cnf(i_0_105_007,axiom,
( X1 != X2
| sdtasdt0(X1,X3) = sdtasdt0(X2,X3) ) ).
cnf(i_0_106_008,axiom,
( X1 != X2
| sdtasdt0(X3,X1) = sdtasdt0(X3,X2) ) ).
cnf(i_0_107_009,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X1,X3,X4)
| sdteqdtlpzmzozddtrp0(X2,X3,X4) ) ).
cnf(i_0_108_010,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X1,X4)
| sdteqdtlpzmzozddtrp0(X3,X2,X4) ) ).
cnf(i_0_109_011,axiom,
( X1 != X2
| ~ sdteqdtlpzmzozddtrp0(X3,X4,X1)
| sdteqdtlpzmzozddtrp0(X3,X4,X2) ) ).
cnf(i_0_110_012,axiom,
( X1 != X2
| ~ aInteger0(X1)
| aInteger0(X2) ) ).
cnf(i_0_111_013,axiom,
( X1 != X2
| ~ aDivisorOf0(X1,X3)
| aDivisorOf0(X2,X3) ) ).
cnf(i_0_112_014,axiom,
( X1 != X2
| ~ aDivisorOf0(X3,X1)
| aDivisorOf0(X3,X2) ) ).
cnf(i_0_113,plain,
( ~ aInteger0(X1)
| ~ aInteger0(sdtasdt0(X1,X2))
| aDivisorOf0(X1,sdtasdt0(X1,X2))
| ~ aInteger0(X2)
| X1 = sz00 ),
inference(equality_inference,[],[58]) ).
cnf(i_0_114,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(sz00,X1) ),
inference(equality_inference,[],[72]) ).
cnf(i_0_115,plain,
~ aInteger0(sdtpldt0(xn,xm)),
inference(scs_inference,[],[i_0_63,i_0_60]) ).
cnf(i_0_116,plain,
( sdtasdt0(xq,X1) != sdtpldt0(xa,smndt0(xc))
| ~ aInteger0(X1) ),
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_117,plain,
sdtpldt0(xa,smndt0(xc)) = sdtasdt0(xq,sdtpldt0(xn,xm)),
inference(scs_inference,[],[i_0_63,i_0_60,i_0_100]) ).
cnf(i_0_118,plain,
xb != xa,
inference(scs_inference,[],[i_0_54,i_0_61,i_0_63,i_0_60,i_0_100,i_0_107]) ).
cnf(i_0_119,plain,
$false,
inference(scs_inference,[],[i_0_54,i_0_61,i_0_90,i_0_91,i_0_63,i_0_60,i_0_100,i_0_107,i_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.15 % Problem : NUM432+3 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.15 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.37 % Computer : n003.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Tue May 5 00:34:41 EDT 2026
% 0.16/0.37 % CPUTime :
% 0.16/0.38 % start to proof: theBenchmark
% 0.29/1.66 % Version : CSE_E---1.7
% 0.29/1.66 % Problem : theBenchmark.p
% 0.29/1.66 % SZS status Theorem for theBenchmark.p
% 0.29/1.66 % SZS output start CNFRefutation
% See solution above
% 0.29/1.68 % Total time : 1.272s
%------------------------------------------------------------------------------