%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM013+4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n019.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 1.30s 1.74s
% Output : CNFRefutation 1.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 9 unt; 0 def)
% Number of atoms : 266 ( 14 equ)
% Maximal formula atoms : 50 ( 7 avg)
% Number of connectives : 359 ( 130 ~; 152 |; 59 &)
% ( 2 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 76 ( 1 sgn 32 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
! [X1] :
( aElement0(X1)
=> ( ! [X2] :
( aElement0(X2)
=> ( iLess0(X2,X1)
=> ? [X3] :
( aElement0(X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3)
& ~ ? [X4] : aReductOfIn0(X4,X3,xR)
& aNormalFormOfIn0(X3,X2,xR) ) ) )
=> ? [X2] :
( ( aElement0(X2)
& ( X1 = X2
| aReductOfIn0(X2,X1,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X1,xR)
& sdtmndtplgtdt0(X3,xR,X2) )
| sdtmndtplgtdt0(X1,xR,X2)
| sdtmndtasgtdt0(X1,xR,X2) )
& ~ ? [X3] : aReductOfIn0(X3,X2,xR) )
| aNormalFormOfIn0(X2,X1,xR) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(mReduct,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aRewritingSystem0(X2) )
=> ! [X3] :
( aReductOfIn0(X3,X1,X2)
=> aElement0(X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mReduct) ).
fof(m__587,hypothesis,
( aRewritingSystem0(xR)
& ! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( ( aReductOfIn0(X2,X1,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X1,xR)
& sdtmndtplgtdt0(X3,xR,X2) )
| sdtmndtplgtdt0(X1,xR,X2) )
=> iLess0(X2,X1) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__587) ).
fof(mTermin,axiom,
! [X1] :
( aRewritingSystem0(X1)
=> ( isTerminating0(X1)
<=> ! [X2,X3] :
( ( aElement0(X2)
& aElement0(X3) )
=> ( sdtmndtplgtdt0(X2,X1,X3)
=> iLess0(X3,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermin) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( aElement0(X1)
=> ( ! [X2] :
( aElement0(X2)
=> ( iLess0(X2,X1)
=> ? [X3] :
( aElement0(X3)
& ( X2 = X3
| ( ( aReductOfIn0(X3,X2,xR)
| ? [X4] :
( aElement0(X4)
& aReductOfIn0(X4,X2,xR)
& sdtmndtplgtdt0(X4,xR,X3) ) )
& sdtmndtplgtdt0(X2,xR,X3) ) )
& sdtmndtasgtdt0(X2,xR,X3)
& ~ ? [X4] : aReductOfIn0(X4,X3,xR)
& aNormalFormOfIn0(X3,X2,xR) ) ) )
=> ? [X2] :
( ( aElement0(X2)
& ( X1 = X2
| aReductOfIn0(X2,X1,xR)
| ? [X3] :
( aElement0(X3)
& aReductOfIn0(X3,X1,xR)
& sdtmndtplgtdt0(X3,xR,X2) )
| sdtmndtplgtdt0(X1,xR,X2)
| sdtmndtasgtdt0(X1,xR,X2) )
& ~ ? [X3] : aReductOfIn0(X3,X2,xR) )
| aNormalFormOfIn0(X2,X1,xR) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,plain,
! [X62,X63,X64,X66] :
( ( aElement0(esk1_3(X62,X63,X64))
| aReductOfIn0(X64,X62,X63)
| ~ sdtmndtplgtdt0(X62,X63,X64)
| ~ aElement0(X62)
| ~ aRewritingSystem0(X63)
| ~ aElement0(X64) )
& ( aReductOfIn0(esk1_3(X62,X63,X64),X62,X63)
| aReductOfIn0(X64,X62,X63)
| ~ sdtmndtplgtdt0(X62,X63,X64)
| ~ aElement0(X62)
| ~ aRewritingSystem0(X63)
| ~ aElement0(X64) )
& ( sdtmndtplgtdt0(esk1_3(X62,X63,X64),X63,X64)
| aReductOfIn0(X64,X62,X63)
| ~ sdtmndtplgtdt0(X62,X63,X64)
| ~ aElement0(X62)
| ~ aRewritingSystem0(X63)
| ~ aElement0(X64) )
& ( ~ aReductOfIn0(X64,X62,X63)
| sdtmndtplgtdt0(X62,X63,X64)
| ~ aElement0(X62)
| ~ aRewritingSystem0(X63)
| ~ aElement0(X64) )
& ( ~ aElement0(X66)
| ~ aReductOfIn0(X66,X62,X63)
| ~ sdtmndtplgtdt0(X66,X63,X64)
| sdtmndtplgtdt0(X62,X63,X64)
| ~ aElement0(X62)
| ~ aRewritingSystem0(X63)
| ~ aElement0(X64) ) ),
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_7,plain,
! [X59,X60,X61] :
( ~ aElement0(X59)
| ~ aRewritingSystem0(X60)
| ~ aReductOfIn0(X61,X59,X60)
| aElement0(X61) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mReduct])])]) ).
fof(c_0_8,negated_conjecture,
! [X111,X114,X115,X116] :
( aElement0(esk13_0)
& ( aElement0(esk14_1(X111))
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( aElement0(esk15_1(X111))
| aReductOfIn0(esk14_1(X111),X111,xR)
| X111 = esk14_1(X111)
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( aReductOfIn0(esk15_1(X111),X111,xR)
| aReductOfIn0(esk14_1(X111),X111,xR)
| X111 = esk14_1(X111)
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( sdtmndtplgtdt0(esk15_1(X111),xR,esk14_1(X111))
| aReductOfIn0(esk14_1(X111),X111,xR)
| X111 = esk14_1(X111)
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( sdtmndtplgtdt0(X111,xR,esk14_1(X111))
| X111 = esk14_1(X111)
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( sdtmndtasgtdt0(X111,xR,esk14_1(X111))
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( ~ aReductOfIn0(X114,esk14_1(X111),xR)
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( aNormalFormOfIn0(esk14_1(X111),X111,xR)
| ~ iLess0(X111,esk13_0)
| ~ aElement0(X111) )
& ( esk13_0 != X115
| ~ aElement0(X115)
| aReductOfIn0(esk16_1(X115),X115,xR) )
& ( ~ aReductOfIn0(X115,esk13_0,xR)
| ~ aElement0(X115)
| aReductOfIn0(esk16_1(X115),X115,xR) )
& ( ~ aElement0(X116)
| ~ aReductOfIn0(X116,esk13_0,xR)
| ~ sdtmndtplgtdt0(X116,xR,X115)
| ~ aElement0(X115)
| aReductOfIn0(esk16_1(X115),X115,xR) )
& ( ~ sdtmndtplgtdt0(esk13_0,xR,X115)
| ~ aElement0(X115)
| aReductOfIn0(esk16_1(X115),X115,xR) )
& ( ~ sdtmndtasgtdt0(esk13_0,xR,X115)
| ~ aElement0(X115)
| aReductOfIn0(esk16_1(X115),X115,xR) )
& ~ aNormalFormOfIn0(X115,esk13_0,xR) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
cnf(c_0_9,plain,
( sdtmndtplgtdt0(X2,X3,X1)
| ~ aReductOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( aElement0(X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aReductOfIn0(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
( aReductOfIn0(esk16_1(X1),X1,xR)
| esk13_0 != X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
aElement0(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,hypothesis,
! [X107,X108,X109] :
( aRewritingSystem0(xR)
& ( ~ aReductOfIn0(X108,X107,xR)
| iLess0(X108,X107)
| ~ aElement0(X107)
| ~ aElement0(X108) )
& ( ~ aElement0(X109)
| ~ aReductOfIn0(X109,X107,xR)
| ~ sdtmndtplgtdt0(X109,xR,X108)
| iLess0(X108,X107)
| ~ aElement0(X107)
| ~ aElement0(X108) )
& ( ~ sdtmndtplgtdt0(X107,xR,X108)
| iLess0(X108,X107)
| ~ aElement0(X107)
| ~ aElement0(X108) )
& isTerminating0(xR) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__587])])])]) ).
cnf(c_0_14,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)],[c_0_6]) ).
fof(c_0_15,plain,
! [X96,X97,X98] :
( ( ~ isTerminating0(X96)
| ~ aElement0(X97)
| ~ aElement0(X98)
| ~ sdtmndtplgtdt0(X97,X96,X98)
| iLess0(X98,X97)
| ~ aRewritingSystem0(X96) )
& ( aElement0(esk10_1(X96))
| isTerminating0(X96)
| ~ aRewritingSystem0(X96) )
& ( aElement0(esk11_1(X96))
| isTerminating0(X96)
| ~ aRewritingSystem0(X96) )
& ( sdtmndtplgtdt0(esk10_1(X96),X96,esk11_1(X96))
| isTerminating0(X96)
| ~ aRewritingSystem0(X96) )
& ( ~ iLess0(esk11_1(X96),esk10_1(X96))
| isTerminating0(X96)
| ~ aRewritingSystem0(X96) ) ),
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_16,plain,
( sdtmndtplgtdt0(X1,X2,X3)
| ~ aReductOfIn0(X3,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_17,negated_conjecture,
aReductOfIn0(esk16_1(esk13_0),esk13_0,xR),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12])]) ).
cnf(c_0_18,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( sdtmndtplgtdt0(X1,X2,X3)
| ~ sdtmndtplgtdt0(X4,X2,X3)
| ~ aReductOfIn0(X4,X1,X2)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[c_0_14,c_0_10]) ).
cnf(c_0_20,plain,
( iLess0(X3,X2)
| ~ isTerminating0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
sdtmndtplgtdt0(esk13_0,xR,esk16_1(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_12])]) ).
cnf(c_0_22,hypothesis,
isTerminating0(xR),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_23,negated_conjecture,
aElement0(esk16_1(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_18]),c_0_12])]) ).
cnf(c_0_24,negated_conjecture,
( ~ aReductOfIn0(X1,esk14_1(X2),xR)
| ~ iLess0(X2,esk13_0)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
( aReductOfIn0(esk16_1(X1),X1,xR)
| ~ sdtmndtplgtdt0(esk13_0,xR,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
( aElement0(esk14_1(X1))
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( sdtmndtplgtdt0(esk13_0,xR,X1)
| ~ sdtmndtplgtdt0(esk16_1(esk13_0),xR,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_18]),c_0_12])]) ).
cnf(c_0_28,negated_conjecture,
( sdtmndtplgtdt0(X1,xR,esk14_1(X1))
| X1 = esk14_1(X1)
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_29,negated_conjecture,
iLess0(esk16_1(esk13_0),esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_18]),c_0_23]),c_0_12])]) ).
cnf(c_0_30,negated_conjecture,
( ~ sdtmndtplgtdt0(esk13_0,xR,esk14_1(X1))
| ~ iLess0(X1,esk13_0)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( esk14_1(esk16_1(esk13_0)) = esk16_1(esk13_0)
| sdtmndtplgtdt0(esk13_0,xR,esk14_1(esk16_1(esk13_0)))
| ~ aElement0(esk14_1(esk16_1(esk13_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_23])]) ).
cnf(c_0_32,negated_conjecture,
( aReductOfIn0(esk16_1(X1),X1,xR)
| ~ aReductOfIn0(X1,esk13_0,xR)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_33,negated_conjecture,
( esk14_1(esk16_1(esk13_0)) = esk16_1(esk13_0)
| ~ aElement0(esk14_1(esk16_1(esk13_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_29]),c_0_23])]) ).
cnf(c_0_34,negated_conjecture,
( ~ iLess0(X1,esk13_0)
| ~ aReductOfIn0(esk14_1(X1),esk13_0,xR)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_32]),c_0_26]) ).
cnf(c_0_35,negated_conjecture,
esk14_1(esk16_1(esk13_0)) = esk16_1(esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_26]),c_0_29]),c_0_23])]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_29]),c_0_17]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : COM013+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 16:20:14 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.19/0.36 % start to proof: theBenchmark
% 1.30/1.74 % Version : CSE_E---1.7
% 1.30/1.74 % Problem : theBenchmark.p
% 1.30/1.74 % SZS status Theorem for theBenchmark.p
% 1.30/1.74 % SZS output start CNFRefutation
% See solution above
% 1.30/1.74 % Total time : 1.368s
%------------------------------------------------------------------------------