%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM013+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 : n007.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 04:13:08 PM UTC 2026
% Result : Theorem 2.02s 1.91s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 6 unt; 0 def)
% Number of atoms : 275 ( 4 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 394 ( 168 ~; 173 |; 31 &)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 117 ( 3 sgn 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( aElement0(X1)
=> ( ! [X2] :
( aElement0(X2)
=> ( iLess0(X2,X1)
=> ? [X3] : aNormalFormOfIn0(X3,X2,xR) ) )
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(m__587,hypothesis,
( aRewritingSystem0(xR)
& isTerminating0(xR) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__587) ).
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(mReduct,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aReductOfIn0(X3,X1,X2)
=> aElement0(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mReduct) ).
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(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(c_0_8,negated_conjecture,
~ ! [X1] :
( aElement0(X1)
=> ( ! [X2] :
( aElement0(X2)
=> ( iLess0(X2,X1)
=> ? [X3] : aNormalFormOfIn0(X3,X2,xR) ) )
=> ? [X2] : aNormalFormOfIn0(X2,X1,xR) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_9,plain,
! [X94,X95,X96,X97,X98] :
( ( aElement0(X96)
| ~ aNormalFormOfIn0(X96,X94,X95)
| ~ aElement0(X94)
| ~ aRewritingSystem0(X95) )
& ( sdtmndtasgtdt0(X94,X95,X96)
| ~ aNormalFormOfIn0(X96,X94,X95)
| ~ aElement0(X94)
| ~ aRewritingSystem0(X95) )
& ( ~ aReductOfIn0(X97,X96,X95)
| ~ aNormalFormOfIn0(X96,X94,X95)
| ~ aElement0(X94)
| ~ aRewritingSystem0(X95) )
& ( ~ aElement0(X98)
| ~ sdtmndtasgtdt0(X94,X95,X98)
| aReductOfIn0(esk12_3(X94,X95,X98),X98,X95)
| aNormalFormOfIn0(X98,X94,X95)
| ~ aElement0(X94)
| ~ aRewritingSystem0(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)],[mNFRDef])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X101,X103] :
( aElement0(esk13_0)
& ( ~ aElement0(X101)
| ~ iLess0(X101,esk13_0)
| aNormalFormOfIn0(esk14_1(X101),X101,xR) )
& ~ aNormalFormOfIn0(X103,esk13_0,xR) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_11,plain,
( ~ aReductOfIn0(X1,X2,X3)
| ~ aNormalFormOfIn0(X2,X4,X3)
| ~ aElement0(X4)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
( aNormalFormOfIn0(esk14_1(X1),X1,xR)
| ~ aElement0(X1)
| ~ iLess0(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__587]) ).
cnf(c_0_14,plain,
( aElement0(X1)
| ~ aNormalFormOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X55,X56,X57,X59] :
( ( aElement0(esk1_3(X55,X56,X57))
| aReductOfIn0(X57,X55,X56)
| ~ sdtmndtplgtdt0(X55,X56,X57)
| ~ aElement0(X55)
| ~ aRewritingSystem0(X56)
| ~ aElement0(X57) )
& ( aReductOfIn0(esk1_3(X55,X56,X57),X55,X56)
| aReductOfIn0(X57,X55,X56)
| ~ sdtmndtplgtdt0(X55,X56,X57)
| ~ aElement0(X55)
| ~ aRewritingSystem0(X56)
| ~ aElement0(X57) )
& ( sdtmndtplgtdt0(esk1_3(X55,X56,X57),X56,X57)
| aReductOfIn0(X57,X55,X56)
| ~ sdtmndtplgtdt0(X55,X56,X57)
| ~ aElement0(X55)
| ~ aRewritingSystem0(X56)
| ~ aElement0(X57) )
& ( ~ aReductOfIn0(X57,X55,X56)
| sdtmndtplgtdt0(X55,X56,X57)
| ~ aElement0(X55)
| ~ aRewritingSystem0(X56)
| ~ aElement0(X57) )
& ( ~ aElement0(X59)
| ~ aReductOfIn0(X59,X55,X56)
| ~ sdtmndtplgtdt0(X59,X56,X57)
| sdtmndtplgtdt0(X55,X56,X57)
| ~ aElement0(X55)
| ~ aRewritingSystem0(X56)
| ~ aElement0(X57) ) ),
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(c_0_16,plain,
! [X52,X53,X54] :
( ~ aElement0(X52)
| ~ aRewritingSystem0(X53)
| ~ aReductOfIn0(X54,X52,X53)
| aElement0(X54) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mReduct])])]) ).
cnf(c_0_17,negated_conjecture,
( ~ iLess0(X1,esk13_0)
| ~ aReductOfIn0(X2,esk14_1(X1),xR)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_18,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)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( aElement0(esk14_1(X1))
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_13])]) ).
fof(c_0_20,plain,
! [X67,X68,X69,X70] :
( ~ aElement0(X67)
| ~ aRewritingSystem0(X68)
| ~ aElement0(X69)
| ~ aElement0(X70)
| ~ sdtmndtasgtdt0(X67,X68,X69)
| ~ sdtmndtasgtdt0(X69,X68,X70)
| sdtmndtasgtdt0(X67,X68,X70) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRTrans])]) ).
cnf(c_0_21,plain,
( sdtmndtasgtdt0(X1,X2,X3)
| ~ aNormalFormOfIn0(X3,X1,X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_22,plain,
( sdtmndtplgtdt0(X2,X3,X1)
| ~ aReductOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( aElement0(X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aReductOfIn0(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
~ aNormalFormOfIn0(X1,esk13_0,xR),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( aNormalFormOfIn0(esk14_1(X1),X2,xR)
| ~ sdtmndtasgtdt0(X2,xR,esk14_1(X1))
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_13])]),c_0_19]) ).
cnf(c_0_26,negated_conjecture,
aElement0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_27,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)],[c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( sdtmndtasgtdt0(X1,xR,esk14_1(X1))
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_12]),c_0_13])]) ).
fof(c_0_29,plain,
! [X64,X65,X66] :
( ( ~ sdtmndtasgtdt0(X64,X65,X66)
| X64 = X66
| sdtmndtplgtdt0(X64,X65,X66)
| ~ aElement0(X64)
| ~ aRewritingSystem0(X65)
| ~ aElement0(X66) )
& ( X64 != X66
| sdtmndtasgtdt0(X64,X65,X66)
| ~ aElement0(X64)
| ~ aRewritingSystem0(X65)
| ~ aElement0(X66) )
& ( ~ sdtmndtplgtdt0(X64,X65,X66)
| sdtmndtasgtdt0(X64,X65,X66)
| ~ aElement0(X64)
| ~ aRewritingSystem0(X65)
| ~ aElement0(X66) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRDef])])]) ).
cnf(c_0_30,plain,
( sdtmndtplgtdt0(X1,X2,X3)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
( ~ sdtmndtasgtdt0(esk13_0,xR,esk14_1(X1))
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_32,negated_conjecture,
( sdtmndtasgtdt0(X1,xR,esk14_1(X2))
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ iLess0(X2,esk13_0)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_13])]),c_0_19]) ).
cnf(c_0_33,plain,
( sdtmndtasgtdt0(X1,X2,X3)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,plain,
( aNormalFormOfIn0(X1,X2,X3)
| sdtmndtplgtdt0(X1,X3,esk12_3(X2,X3,X1))
| ~ sdtmndtasgtdt0(X2,X3,X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_35,plain,
( aNormalFormOfIn0(X1,X2,X3)
| aElement0(esk12_3(X2,X3,X1))
| ~ sdtmndtasgtdt0(X2,X3,X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
fof(c_0_36,plain,
! [X89,X90,X91] :
( ( ~ isTerminating0(X89)
| ~ aElement0(X90)
| ~ aElement0(X91)
| ~ sdtmndtplgtdt0(X90,X89,X91)
| iLess0(X91,X90)
| ~ aRewritingSystem0(X89) )
& ( aElement0(esk10_1(X89))
| isTerminating0(X89)
| ~ aRewritingSystem0(X89) )
& ( aElement0(esk11_1(X89))
| isTerminating0(X89)
| ~ aRewritingSystem0(X89) )
& ( sdtmndtplgtdt0(esk10_1(X89),X89,esk11_1(X89))
| isTerminating0(X89)
| ~ aRewritingSystem0(X89) )
& ( ~ iLess0(esk11_1(X89),esk10_1(X89))
| isTerminating0(X89)
| ~ aRewritingSystem0(X89) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermin])])])])]) ).
cnf(c_0_37,negated_conjecture,
( ~ sdtmndtasgtdt0(esk13_0,xR,X1)
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26])]) ).
cnf(c_0_38,plain,
( aNormalFormOfIn0(X1,X2,X3)
| sdtmndtasgtdt0(X1,X3,esk12_3(X2,X3,X1))
| ~ sdtmndtasgtdt0(X2,X3,X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_39,plain,
( iLess0(X3,X2)
| ~ isTerminating0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( aNormalFormOfIn0(esk13_0,X1,xR)
| ~ sdtmndtasgtdt0(X1,xR,esk13_0)
| ~ iLess0(esk12_3(X1,xR,esk13_0),esk13_0)
| ~ aElement0(esk12_3(X1,xR,esk13_0))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_13]),c_0_26])]) ).
cnf(c_0_41,plain,
( aNormalFormOfIn0(X1,X2,X3)
| iLess0(esk12_3(X2,X3,X1),X1)
| ~ isTerminating0(X3)
| ~ sdtmndtasgtdt0(X2,X3,X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_34]),c_0_35]) ).
cnf(c_0_42,hypothesis,
isTerminating0(xR),
inference(split_conjunct,[status(thm)],[m__587]) ).
cnf(c_0_43,negated_conjecture,
( aNormalFormOfIn0(esk13_0,X1,xR)
| ~ sdtmndtasgtdt0(X1,xR,esk13_0)
| ~ aElement0(esk12_3(X1,xR,esk13_0))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_13]),c_0_26])]) ).
cnf(c_0_44,negated_conjecture,
( aNormalFormOfIn0(esk13_0,X1,xR)
| ~ sdtmndtasgtdt0(X1,xR,esk13_0)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_13]),c_0_26])]) ).
cnf(c_0_45,plain,
( sdtmndtasgtdt0(X1,X3,X2)
| X1 != X2
| ~ aElement0(X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_46,negated_conjecture,
~ sdtmndtasgtdt0(esk13_0,xR,esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_44]),c_0_26])]) ).
cnf(c_0_47,plain,
( sdtmndtasgtdt0(X1,X2,X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_45]) ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_13]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM013+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 : n007.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 16:19:24 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 2.02/1.91 % Version : CSE_E---1.7
% 2.02/1.91 % Problem : theBenchmark.p
% 2.02/1.91 % SZS status Theorem for theBenchmark.p
% 2.02/1.91 % SZS output start CNFRefutation
% See solution above
% 2.02/1.91 % Total time : 1.372s
%------------------------------------------------------------------------------