%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM018+1 : 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 : n013.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 04:13:09 PM UTC 2026
% Result : Theorem 0.27s 1.61s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 60)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] : aNormalFormOfIn0(X1,xw,xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mWCRDef,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isLocallyConfluent0(X1)
<=> ! [X2,X3,X4] :
( ( aElement0(X2)
& aElement0(X3)
& aElement0(X4)
& aReductOfIn0(X3,X2,X1)
& aReductOfIn0(X4,X2,X1) )
=> ? [X5] :
( aElement0(X5)
& sdtmndtasgtdt0(X3,X1,X5)
& sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mWCRDef) ).
fof(mCRDef,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isConfluent0(X1)
<=> ! [X2,X3,X4] :
( ( aElement0(X2)
& aElement0(X3)
& aElement0(X4)
& sdtmndtasgtdt0(X2,X1,X3)
& sdtmndtasgtdt0(X2,X1,X4) )
=> ? [X5] :
( aElement0(X5)
& sdtmndtasgtdt0(X3,X1,X5)
& sdtmndtasgtdt0(X4,X1,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mCRDef) ).
fof(m__715,hypothesis,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X2)
& sdtmndtasgtdt0(X1,xR,X3) )
=> ( iLess0(X1,xa)
=> ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,xR,X4)
& sdtmndtasgtdt0(X3,xR,X4) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).
fof(mNFRDef,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aNormalFormOfIn0(X3,X1,X2)
<=> ( aElement0(X3)
& sdtmndtasgtdt0(X1,X2,X3)
& ~ ? [X4] : aReductOfIn0(X4,X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNFRDef) ).
fof(mTCDef,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(X1,X2,X3)
<=> ( aReductOfIn0(X3,X1,X2)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X1,X2)
& sdtmndtplgtdt0(X4,X2,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCDef) ).
fof(mTCRTrans,axiom,
! [X1,X2,X3,X4] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3)
& aElement0(X4) )
=> ( ( sdtmndtasgtdt0(X1,X2,X3)
& sdtmndtasgtdt0(X3,X2,X4) )
=> sdtmndtasgtdt0(X1,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRTrans) ).
fof(mTCTrans,axiom,
! [X1,X2,X3,X4] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3)
& aElement0(X4) )
=> ( ( sdtmndtplgtdt0(X1,X2,X3)
& sdtmndtplgtdt0(X3,X2,X4) )
=> sdtmndtplgtdt0(X1,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).
fof(mTCRDef,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3) )
=> ( sdtmndtasgtdt0(X1,X2,X3)
<=> ( X1 = X3
| sdtmndtplgtdt0(X1,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(mTermin,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isTerminating0(X1)
<=> ! [X2,X3] :
( ( aElement0(X2)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(X2,X1,X3)
=> iLess0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermin) ).
fof(mReduct,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aReductOfIn0(X3,X1,X2)
=> aElement0(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
fof(mTermNF,axiom,
! [X1] :
( ( aRewritingSystem0(X1)
& isTerminating0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ? [X3] : aNormalFormOfIn0(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTermNF) ).
fof(m__799,hypothesis,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__799) ).
fof(m__779,hypothesis,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__779) ).
fof(m__755,hypothesis,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__755) ).
fof(m__731_02,hypothesis,
( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731_02) ).
fof(m__656_01,hypothesis,
( isLocallyConfluent0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656_01) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(m__731,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__731) ).
fof(i_0_19,negated_conjecture,
~ ? [X1] : aNormalFormOfIn0(X1,xw,xR),
inference(assume_negation,[status(cth)],[m__]) ).
fof(i_0_20,plain,
! [X84,X85,X86,X87,X92] :
( ( aElement0(esk6_4(X84,X85,X86,X87))
| ~ aElement0(X85)
| ~ aElement0(X86)
| ~ aElement0(X87)
| ~ aReductOfIn0(X86,X85,X84)
| ~ aReductOfIn0(X87,X85,X84)
| ~ isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( sdtmndtasgtdt0(X86,X84,esk6_4(X84,X85,X86,X87))
| ~ aElement0(X85)
| ~ aElement0(X86)
| ~ aElement0(X87)
| ~ aReductOfIn0(X86,X85,X84)
| ~ aReductOfIn0(X87,X85,X84)
| ~ isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( sdtmndtasgtdt0(X87,X84,esk6_4(X84,X85,X86,X87))
| ~ aElement0(X85)
| ~ aElement0(X86)
| ~ aElement0(X87)
| ~ aReductOfIn0(X86,X85,X84)
| ~ aReductOfIn0(X87,X85,X84)
| ~ isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aElement0(esk7_1(X84))
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aElement0(esk8_1(X84))
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aElement0(esk9_1(X84))
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aReductOfIn0(esk8_1(X84),esk7_1(X84),X84)
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( aReductOfIn0(esk9_1(X84),esk7_1(X84),X84)
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) )
& ( ~ aElement0(X92)
| ~ sdtmndtasgtdt0(esk8_1(X84),X84,X92)
| ~ sdtmndtasgtdt0(esk9_1(X84),X84,X92)
| isLocallyConfluent0(X84)
| ~ aRewritingSystem0(X84) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mWCRDef])])])])]) ).
fof(i_0_21,plain,
! [X75,X76,X77,X78,X83] :
( ( aElement0(esk2_4(X75,X76,X77,X78))
| ~ aElement0(X76)
| ~ aElement0(X77)
| ~ aElement0(X78)
| ~ sdtmndtasgtdt0(X76,X75,X77)
| ~ sdtmndtasgtdt0(X76,X75,X78)
| ~ isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( sdtmndtasgtdt0(X77,X75,esk2_4(X75,X76,X77,X78))
| ~ aElement0(X76)
| ~ aElement0(X77)
| ~ aElement0(X78)
| ~ sdtmndtasgtdt0(X76,X75,X77)
| ~ sdtmndtasgtdt0(X76,X75,X78)
| ~ isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( sdtmndtasgtdt0(X78,X75,esk2_4(X75,X76,X77,X78))
| ~ aElement0(X76)
| ~ aElement0(X77)
| ~ aElement0(X78)
| ~ sdtmndtasgtdt0(X76,X75,X77)
| ~ sdtmndtasgtdt0(X76,X75,X78)
| ~ isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( aElement0(esk3_1(X75))
| isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( aElement0(esk4_1(X75))
| isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( aElement0(esk5_1(X75))
| isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( sdtmndtasgtdt0(esk3_1(X75),X75,esk4_1(X75))
| isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( sdtmndtasgtdt0(esk3_1(X75),X75,esk5_1(X75))
| isConfluent0(X75)
| ~ aRewritingSystem0(X75) )
& ( ~ aElement0(X83)
| ~ sdtmndtasgtdt0(esk4_1(X75),X75,X83)
| ~ sdtmndtasgtdt0(esk5_1(X75),X75,X83)
| isConfluent0(X75)
| ~ aRewritingSystem0(X75) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mCRDef])])])])]) ).
fof(i_0_22,hypothesis,
! [X107,X108,X109] :
( ( aElement0(esk14_3(X107,X108,X109))
| ~ iLess0(X107,xa)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| ~ sdtmndtasgtdt0(X107,xR,X108)
| ~ sdtmndtasgtdt0(X107,xR,X109) )
& ( sdtmndtasgtdt0(X108,xR,esk14_3(X107,X108,X109))
| ~ iLess0(X107,xa)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| ~ sdtmndtasgtdt0(X107,xR,X108)
| ~ sdtmndtasgtdt0(X107,xR,X109) )
& ( sdtmndtasgtdt0(X109,xR,esk14_3(X107,X108,X109))
| ~ iLess0(X107,xa)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ aElement0(X109)
| ~ sdtmndtasgtdt0(X107,xR,X108)
| ~ sdtmndtasgtdt0(X107,xR,X109) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__715])])])]) ).
fof(i_0_23,plain,
! [X98,X99,X100,X101,X102] :
( ( aElement0(X100)
| ~ aNormalFormOfIn0(X100,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) )
& ( sdtmndtasgtdt0(X98,X99,X100)
| ~ aNormalFormOfIn0(X100,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) )
& ( ~ aReductOfIn0(X101,X100,X99)
| ~ aNormalFormOfIn0(X100,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) )
& ( ~ aElement0(X102)
| ~ sdtmndtasgtdt0(X98,X99,X102)
| aReductOfIn0(esk12_3(X98,X99,X102),X102,X99)
| aNormalFormOfIn0(X102,X98,X99)
| ~ aElement0(X98)
| ~ aRewritingSystem0(X99) ) ),
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)],[mNFRDef])])])])])]) ).
fof(i_0_24,plain,
! [X59,X60,X61,X63] :
( ( aElement0(esk1_3(X59,X60,X61))
| aReductOfIn0(X61,X59,X60)
| ~ sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( aReductOfIn0(esk1_3(X59,X60,X61),X59,X60)
| aReductOfIn0(X61,X59,X60)
| ~ sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( sdtmndtplgtdt0(esk1_3(X59,X60,X61),X60,X61)
| aReductOfIn0(X61,X59,X60)
| ~ sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( ~ aReductOfIn0(X61,X59,X60)
| sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) )
& ( ~ aElement0(X63)
| ~ aReductOfIn0(X63,X59,X60)
| ~ sdtmndtplgtdt0(X63,X60,X61)
| sdtmndtplgtdt0(X59,X60,X61)
| ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aElement0(X61) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCDef])])])])]) ).
fof(i_0_25,plain,
! [X71,X72,X73,X74] :
( ~ aElement0(X71)
| ~ aRewritingSystem0(X72)
| ~ aElement0(X73)
| ~ aElement0(X74)
| ~ sdtmndtasgtdt0(X71,X72,X73)
| ~ sdtmndtasgtdt0(X73,X72,X74)
| sdtmndtasgtdt0(X71,X72,X74) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRTrans])]) ).
fof(i_0_26,plain,
! [X64,X65,X66,X67] :
( ~ aElement0(X64)
| ~ aRewritingSystem0(X65)
| ~ aElement0(X66)
| ~ aElement0(X67)
| ~ sdtmndtplgtdt0(X64,X65,X66)
| ~ sdtmndtplgtdt0(X66,X65,X67)
| sdtmndtplgtdt0(X64,X65,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCTrans])]) ).
fof(i_0_27,plain,
! [X68,X69,X70] :
( ( ~ sdtmndtasgtdt0(X68,X69,X70)
| X68 = X70
| sdtmndtplgtdt0(X68,X69,X70)
| ~ aElement0(X68)
| ~ aRewritingSystem0(X69)
| ~ aElement0(X70) )
& ( X68 != X70
| sdtmndtasgtdt0(X68,X69,X70)
| ~ aElement0(X68)
| ~ aRewritingSystem0(X69)
| ~ aElement0(X70) )
& ( ~ sdtmndtplgtdt0(X68,X69,X70)
| sdtmndtasgtdt0(X68,X69,X70)
| ~ aElement0(X68)
| ~ aRewritingSystem0(X69)
| ~ aElement0(X70) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRDef])])]) ).
fof(i_0_28,plain,
! [X93,X94,X95] :
( ( ~ isTerminating0(X93)
| ~ aElement0(X94)
| ~ aElement0(X95)
| ~ sdtmndtplgtdt0(X94,X93,X95)
| iLess0(X95,X94)
| ~ aRewritingSystem0(X93) )
& ( aElement0(esk10_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) )
& ( aElement0(esk11_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) )
& ( sdtmndtplgtdt0(esk10_1(X93),X93,esk11_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) )
& ( ~ iLess0(esk11_1(X93),esk10_1(X93))
| isTerminating0(X93)
| ~ aRewritingSystem0(X93) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermin])])])])]) ).
fof(i_0_29,plain,
! [X56,X57,X58] :
( ~ aElement0(X56)
| ~ aRewritingSystem0(X57)
| ~ aReductOfIn0(X58,X56,X57)
| aElement0(X58) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mReduct])])]) ).
fof(i_0_30,plain,
! [X104,X105] :
( ~ aRewritingSystem0(X104)
| ~ isTerminating0(X104)
| ~ aElement0(X105)
| aNormalFormOfIn0(esk13_2(X104,X105),X105,X104) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermNF])])])]) ).
fof(i_0_31,negated_conjecture,
! [X111] : ~ aNormalFormOfIn0(X111,xw,xR),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_19])]) ).
cnf(i_0_32,plain,
( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X1,X4))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X4)
| ~ aReductOfIn0(X1,X3,X2)
| ~ aReductOfIn0(X4,X3,X2)
| ~ isLocallyConfluent0(X2)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_33,plain,
( sdtmndtasgtdt0(X1,X2,esk6_4(X2,X3,X4,X1))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElement0(X1)
| ~ aReductOfIn0(X4,X3,X2)
| ~ aReductOfIn0(X1,X3,X2)
| ~ isLocallyConfluent0(X2)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_34,plain,
( sdtmndtasgtdt0(X1,X2,esk2_4(X2,X3,X1,X4))
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ aElement0(X4)
| ~ sdtmndtasgtdt0(X3,X2,X1)
| ~ sdtmndtasgtdt0(X3,X2,X4)
| ~ isConfluent0(X2)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_35,plain,
( sdtmndtasgtdt0(X1,X2,esk2_4(X2,X3,X4,X1))
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X3,X2,X4)
| ~ sdtmndtasgtdt0(X3,X2,X1)
| ~ isConfluent0(X2)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_36,plain,
( aElement0(esk6_4(X1,X2,X3,X4))
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ aReductOfIn0(X3,X2,X1)
| ~ aReductOfIn0(X4,X2,X1)
| ~ isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_37,plain,
( aElement0(esk2_4(X1,X2,X3,X4))
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtmndtasgtdt0(X2,X1,X3)
| ~ sdtmndtasgtdt0(X2,X1,X4)
| ~ isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_38,hypothesis,
( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X1,X3))
| ~ iLess0(X2,xa)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X2,xR,X1)
| ~ sdtmndtasgtdt0(X2,xR,X3) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_39,hypothesis,
( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X3,X1))
| ~ iLess0(X2,xa)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X2,xR,X3)
| ~ sdtmndtasgtdt0(X2,xR,X1) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_40,plain,
( aReductOfIn0(esk12_3(X2,X3,X1),X1,X3)
| aNormalFormOfIn0(X1,X2,X3)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X2,X3,X1)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_41,plain,
( sdtmndtplgtdt0(esk1_3(X1,X2,X3),X2,X3)
| aReductOfIn0(X3,X1,X2)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_42,plain,
( aReductOfIn0(esk1_3(X1,X2,X3),X1,X2)
| aReductOfIn0(X3,X1,X2)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_43,hypothesis,
( aElement0(esk14_3(X1,X2,X3))
| ~ iLess0(X1,xa)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ sdtmndtasgtdt0(X1,xR,X3) ),
inference(split_conjunct,[status(thm)],[i_0_22]),
[final] ).
cnf(i_0_44,plain,
( aElement0(esk1_3(X1,X2,X3))
| aReductOfIn0(X3,X1,X2)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_45,plain,
( sdtmndtasgtdt0(X1,X2,X4)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtmndtasgtdt0(X1,X2,X3)
| ~ sdtmndtasgtdt0(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_25]),
[final] ).
cnf(i_0_46,plain,
( sdtmndtplgtdt0(X1,X2,X4)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ sdtmndtplgtdt0(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[i_0_26]),
[final] ).
cnf(i_0_47,plain,
( sdtmndtplgtdt0(X2,X3,X4)
| ~ aElement0(X1)
| ~ aReductOfIn0(X1,X2,X3)
| ~ sdtmndtplgtdt0(X1,X3,X4)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X4) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_48,plain,
( isLocallyConfluent0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(esk8_1(X2),X2,X1)
| ~ sdtmndtasgtdt0(esk9_1(X2),X2,X1)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_49,plain,
( isConfluent0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(esk4_1(X2),X2,X1)
| ~ sdtmndtasgtdt0(esk5_1(X2),X2,X1)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_50,plain,
( ~ aReductOfIn0(X1,X2,X3)
| ~ aNormalFormOfIn0(X2,X4,X3)
| ~ aElement0(X4)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_51,plain,
( X1 = X3
| sdtmndtplgtdt0(X1,X2,X3)
| ~ sdtmndtasgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_52,plain,
( sdtmndtasgtdt0(X1,X2,X3)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_53,plain,
( sdtmndtplgtdt0(X2,X3,X1)
| ~ aReductOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_24]),
[final] ).
cnf(i_0_54,plain,
( sdtmndtasgtdt0(X1,X2,X3)
| ~ aNormalFormOfIn0(X3,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_55,plain,
( iLess0(X3,X2)
| ~ isTerminating0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_56,plain,
( aElement0(X1)
| ~ aNormalFormOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[i_0_23]),
[final] ).
cnf(i_0_57,plain,
( aElement0(X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aReductOfIn0(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_29]),
[final] ).
cnf(i_0_58,plain,
( aNormalFormOfIn0(esk13_2(X1,X2),X2,X1)
| ~ aRewritingSystem0(X1)
| ~ isTerminating0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_30]),
[final] ).
cnf(i_0_59,negated_conjecture,
~ aNormalFormOfIn0(X1,xw,xR),
inference(split_conjunct,[status(thm)],[i_0_31]),
[final] ).
cnf(i_0_60,plain,
( sdtmndtasgtdt0(X1,X3,X2)
| X1 != X2
| ~ aElement0(X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[i_0_27]),
[final] ).
cnf(i_0_61,plain,
( aReductOfIn0(esk9_1(X1),esk7_1(X1),X1)
| isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_62,plain,
( aReductOfIn0(esk8_1(X1),esk7_1(X1),X1)
| isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_63,plain,
( sdtmndtplgtdt0(esk10_1(X1),X1,esk11_1(X1))
| isTerminating0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_64,plain,
( sdtmndtasgtdt0(esk3_1(X1),X1,esk5_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_65,plain,
( sdtmndtasgtdt0(esk3_1(X1),X1,esk4_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_66,plain,
( isTerminating0(X1)
| ~ iLess0(esk11_1(X1),esk10_1(X1))
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_67,hypothesis,
sdtmndtasgtdt0(xv,xR,xw),
inference(split_conjunct,[status(thm)],[m__799]),
[final] ).
cnf(i_0_68,hypothesis,
sdtmndtasgtdt0(xv,xR,xc),
inference(split_conjunct,[status(thm)],[m__779]),
[final] ).
cnf(i_0_69,hypothesis,
sdtmndtasgtdt0(xu,xR,xw),
inference(split_conjunct,[status(thm)],[m__799]),
[final] ).
cnf(i_0_70,hypothesis,
sdtmndtasgtdt0(xu,xR,xb),
inference(split_conjunct,[status(thm)],[m__755]),
[final] ).
cnf(i_0_71,hypothesis,
sdtmndtplgtdt0(xa,xR,xc),
inference(split_conjunct,[status(thm)],[m__731_02]),
[final] ).
cnf(i_0_72,hypothesis,
sdtmndtplgtdt0(xa,xR,xb),
inference(split_conjunct,[status(thm)],[m__731_02]),
[final] ).
cnf(i_0_73,hypothesis,
aReductOfIn0(xv,xa,xR),
inference(split_conjunct,[status(thm)],[m__779]),
[final] ).
cnf(i_0_74,hypothesis,
aReductOfIn0(xu,xa,xR),
inference(split_conjunct,[status(thm)],[m__755]),
[final] ).
cnf(i_0_75,plain,
( aElement0(esk11_1(X1))
| isTerminating0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_76,plain,
( aElement0(esk10_1(X1))
| isTerminating0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_28]),
[final] ).
cnf(i_0_77,plain,
( aElement0(esk9_1(X1))
| isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_78,plain,
( aElement0(esk8_1(X1))
| isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_79,plain,
( aElement0(esk7_1(X1))
| isLocallyConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_20]),
[final] ).
cnf(i_0_80,plain,
( aElement0(esk5_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_81,plain,
( aElement0(esk4_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_82,plain,
( aElement0(esk3_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[i_0_21]),
[final] ).
cnf(i_0_83,hypothesis,
isTerminating0(xR),
inference(split_conjunct,[status(thm)],[m__656_01]),
[final] ).
cnf(i_0_84,hypothesis,
isLocallyConfluent0(xR),
inference(split_conjunct,[status(thm)],[m__656_01]),
[final] ).
cnf(i_0_85,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]),
[final] ).
cnf(i_0_86,hypothesis,
aElement0(xw),
inference(split_conjunct,[status(thm)],[m__799]),
[final] ).
cnf(i_0_87,hypothesis,
aElement0(xv),
inference(split_conjunct,[status(thm)],[m__779]),
[final] ).
cnf(i_0_88,hypothesis,
aElement0(xu),
inference(split_conjunct,[status(thm)],[m__755]),
[final] ).
cnf(i_0_89,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__731]),
[final] ).
cnf(i_0_90,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__731]),
[final] ).
cnf(i_0_91,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__731]),
[final] ).
cnf(i_0_92,axiom,
X1 = X1 ).
cnf(i_0_93,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_94,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_95,axiom,
( X1 != X2
| ~ sdtmndtasgtdt0(X1,X3,X4)
| sdtmndtasgtdt0(X2,X3,X4) ) ).
cnf(i_0_96,axiom,
( X1 != X2
| ~ sdtmndtasgtdt0(X3,X1,X4)
| sdtmndtasgtdt0(X3,X2,X4) ) ).
cnf(i_0_97,axiom,
( X1 != X2
| ~ sdtmndtasgtdt0(X3,X4,X1)
| sdtmndtasgtdt0(X3,X4,X2) ) ).
cnf(i_0_98,axiom,
( X1 != X2
| ~ isTerminating0(X1)
| isTerminating0(X2) ) ).
cnf(i_0_99,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_100,axiom,
( X1 != X2
| ~ aReductOfIn0(X1,X3,X4)
| aReductOfIn0(X2,X3,X4) ) ).
cnf(i_0_101,axiom,
( X1 != X2
| ~ aReductOfIn0(X3,X1,X4)
| aReductOfIn0(X3,X2,X4) ) ).
cnf(i_0_102,axiom,
( X1 != X2
| ~ aReductOfIn0(X3,X4,X1)
| aReductOfIn0(X3,X4,X2) ) ).
cnf(i_0_103,axiom,
( X1 != X2
| ~ isLocallyConfluent0(X1)
| isLocallyConfluent0(X2) ) ).
cnf(i_0_104,axiom,
( X1 != X2
| ~ aRewritingSystem0(X1)
| aRewritingSystem0(X2) ) ).
cnf(i_0_105,axiom,
( X1 != X2
| ~ isConfluent0(X1)
| isConfluent0(X2) ) ).
cnf(i_0_106,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_107,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_108,axiom,
( X1 != X2
| ~ aNormalFormOfIn0(X1,X3,X4)
| aNormalFormOfIn0(X2,X3,X4) ) ).
cnf(i_0_109,axiom,
( X1 != X2
| ~ aNormalFormOfIn0(X3,X1,X4)
| aNormalFormOfIn0(X3,X2,X4) ) ).
cnf(i_0_110,axiom,
( X1 != X2
| ~ aNormalFormOfIn0(X3,X4,X1)
| aNormalFormOfIn0(X3,X4,X2) ) ).
cnf(i_0_111,axiom,
( X1 != X2
| ~ sdtmndtplgtdt0(X1,X3,X4)
| sdtmndtplgtdt0(X2,X3,X4) ) ).
cnf(i_0_112,axiom,
( X1 != X2
| ~ sdtmndtplgtdt0(X3,X1,X4)
| sdtmndtplgtdt0(X3,X2,X4) ) ).
cnf(i_0_113,axiom,
( X1 != X2
| ~ sdtmndtplgtdt0(X3,X4,X1)
| sdtmndtplgtdt0(X3,X4,X2) ) ).
cnf(i_0_92_001,axiom,
X1 = X1 ).
cnf(i_0_93_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_94_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_95_004,axiom,
( X1 != X2
| ~ sdtmndtasgtdt0(X1,X3,X4)
| sdtmndtasgtdt0(X2,X3,X4) ) ).
cnf(i_0_96_005,axiom,
( X1 != X2
| ~ sdtmndtasgtdt0(X3,X1,X4)
| sdtmndtasgtdt0(X3,X2,X4) ) ).
cnf(i_0_97_006,axiom,
( X1 != X2
| ~ sdtmndtasgtdt0(X3,X4,X1)
| sdtmndtasgtdt0(X3,X4,X2) ) ).
cnf(i_0_98_007,axiom,
( X1 != X2
| ~ isTerminating0(X1)
| isTerminating0(X2) ) ).
cnf(i_0_99_008,axiom,
( X1 != X2
| ~ aElement0(X1)
| aElement0(X2) ) ).
cnf(i_0_100_009,axiom,
( X1 != X2
| ~ aReductOfIn0(X1,X3,X4)
| aReductOfIn0(X2,X3,X4) ) ).
cnf(i_0_101_010,axiom,
( X1 != X2
| ~ aReductOfIn0(X3,X1,X4)
| aReductOfIn0(X3,X2,X4) ) ).
cnf(i_0_102_011,axiom,
( X1 != X2
| ~ aReductOfIn0(X3,X4,X1)
| aReductOfIn0(X3,X4,X2) ) ).
cnf(i_0_103_012,axiom,
( X1 != X2
| ~ isLocallyConfluent0(X1)
| isLocallyConfluent0(X2) ) ).
cnf(i_0_104_013,axiom,
( X1 != X2
| ~ aRewritingSystem0(X1)
| aRewritingSystem0(X2) ) ).
cnf(i_0_105_014,axiom,
( X1 != X2
| ~ isConfluent0(X1)
| isConfluent0(X2) ) ).
cnf(i_0_106_015,axiom,
( X1 != X2
| ~ iLess0(X1,X3)
| iLess0(X2,X3) ) ).
cnf(i_0_107_016,axiom,
( X1 != X2
| ~ iLess0(X3,X1)
| iLess0(X3,X2) ) ).
cnf(i_0_108_017,axiom,
( X1 != X2
| ~ aNormalFormOfIn0(X1,X3,X4)
| aNormalFormOfIn0(X2,X3,X4) ) ).
cnf(i_0_109_018,axiom,
( X1 != X2
| ~ aNormalFormOfIn0(X3,X1,X4)
| aNormalFormOfIn0(X3,X2,X4) ) ).
cnf(i_0_110_019,axiom,
( X1 != X2
| ~ aNormalFormOfIn0(X3,X4,X1)
| aNormalFormOfIn0(X3,X4,X2) ) ).
cnf(i_0_111_020,axiom,
( X1 != X2
| ~ sdtmndtplgtdt0(X1,X3,X4)
| sdtmndtplgtdt0(X2,X3,X4) ) ).
cnf(i_0_112_021,axiom,
( X1 != X2
| ~ sdtmndtplgtdt0(X3,X1,X4)
| sdtmndtplgtdt0(X3,X2,X4) ) ).
cnf(i_0_113_022,axiom,
( X1 != X2
| ~ sdtmndtplgtdt0(X3,X4,X1)
| sdtmndtplgtdt0(X3,X4,X2) ) ).
cnf(i_0_114,plain,
( ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1)
| sdtmndtasgtdt0(X1,X2,X1) ),
inference(equality_inference,[],[60]) ).
cnf(i_0_115,plain,
$false,
inference(scs_inference,[],[i_0_59,i_0_85,i_0_83,i_0_86,i_0_58]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM018+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 16:19:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.27/1.61 % Version : CSE_E---1.7
% 0.27/1.61 % Problem : theBenchmark.p
% 0.27/1.61 % SZS status Theorem for theBenchmark.p
% 0.27/1.61 % SZS output start CNFRefutation
% See solution above
% 0.27/1.63 % Total time : 1.272s
%------------------------------------------------------------------------------