%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM018+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 : 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 : Tue May 5 04:13:09 PM UTC 2026
% Result : Theorem 1.43s 1.79s
% Output : CNFRefutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 222 ( 23 equ)
% Maximal formula atoms : 96 ( 13 avg)
% Number of connectives : 295 ( 89 ~; 132 |; 69 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 1 sgn 18 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
? [X1] :
( ( aElement0(X1)
& ( xw = X1
| aReductOfIn0(X1,xw,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xw,xR)
& sdtmndtplgtdt0(X2,xR,X1) )
| sdtmndtplgtdt0(xw,xR,X1)
| sdtmndtasgtdt0(xw,xR,X1) )
& ~ ? [X2] : aReductOfIn0(X2,X1,xR) )
| aNormalFormOfIn0(X1,xw,xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mTermNF,axiom,
! [X1] :
( ( aRewritingSystem0(X1)
& isTerminating0(X1) )
=> ! [X2] :
( aElement0(X2)
=> ? [X3] : aNormalFormOfIn0(X3,X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTermNF) ).
fof(m__656_01,hypothesis,
( ! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3)
& aReductOfIn0(X2,X1,xR)
& aReductOfIn0(X3,X1,xR) )
=> ? [X4] :
( aElement0(X4)
& ( X2 = X4
| ( ( aReductOfIn0(X4,X2,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X2,xR)
& sdtmndtplgtdt0(X5,xR,X4) ) )
& sdtmndtplgtdt0(X2,xR,X4) ) )
& sdtmndtasgtdt0(X2,xR,X4)
& ( X3 = X4
| ( ( aReductOfIn0(X4,X3,xR)
| ? [X5] :
( aElement0(X5)
& aReductOfIn0(X5,X3,xR)
& sdtmndtplgtdt0(X5,xR,X4) ) )
& sdtmndtplgtdt0(X3,xR,X4) ) )
& sdtmndtasgtdt0(X3,xR,X4) ) )
& isLocallyConfluent0(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__656_01) ).
fof(m__799,hypothesis,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xu,xR)
& sdtmndtplgtdt0(X1,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xv,xR)
& sdtmndtplgtdt0(X1,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__799) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(c_0_5,negated_conjecture,
~ ? [X1] :
( ( aElement0(X1)
& ( xw = X1
| aReductOfIn0(X1,xw,xR)
| ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xw,xR)
& sdtmndtplgtdt0(X2,xR,X1) )
| sdtmndtplgtdt0(xw,xR,X1)
| sdtmndtasgtdt0(xw,xR,X1) )
& ~ ? [X2] : aReductOfIn0(X2,X1,xR) )
| aNormalFormOfIn0(X1,xw,xR) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,negated_conjecture,
! [X151,X152,X154] :
( ( xw != X151
| ~ aElement0(X151)
| aReductOfIn0(esk26_1(X151),X151,xR) )
& ( ~ aReductOfIn0(X151,xw,xR)
| ~ aElement0(X151)
| aReductOfIn0(esk26_1(X151),X151,xR) )
& ( ~ aElement0(X152)
| ~ aReductOfIn0(X152,xw,xR)
| ~ sdtmndtplgtdt0(X152,xR,X151)
| ~ aElement0(X151)
| aReductOfIn0(esk26_1(X151),X151,xR) )
& ( ~ sdtmndtplgtdt0(xw,xR,X151)
| ~ aElement0(X151)
| aReductOfIn0(esk26_1(X151),X151,xR) )
& ( ~ sdtmndtasgtdt0(xw,xR,X151)
| ~ aElement0(X151)
| aReductOfIn0(esk26_1(X151),X151,xR) )
& ~ aNormalFormOfIn0(X154,xw,xR) ),
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)],[c_0_5])])])])])]) ).
fof(c_0_7,plain,
! [X125,X126] :
( ~ aRewritingSystem0(X125)
| ~ isTerminating0(X125)
| ~ aElement0(X126)
| aNormalFormOfIn0(esk13_2(X125,X126),X126,X125) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTermNF])])])]) ).
fof(c_0_8,hypothesis,
! [X128,X129,X130,X134,X135,X136] :
( ( aElement0(esk14_3(X128,X129,X130))
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( aElement0(esk15_3(X128,X129,X130))
| aReductOfIn0(esk14_3(X128,X129,X130),X129,xR)
| X129 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( aReductOfIn0(esk15_3(X128,X129,X130),X129,xR)
| aReductOfIn0(esk14_3(X128,X129,X130),X129,xR)
| X129 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( sdtmndtplgtdt0(esk15_3(X128,X129,X130),xR,esk14_3(X128,X129,X130))
| aReductOfIn0(esk14_3(X128,X129,X130),X129,xR)
| X129 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( sdtmndtplgtdt0(X129,xR,esk14_3(X128,X129,X130))
| X129 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( sdtmndtasgtdt0(X129,xR,esk14_3(X128,X129,X130))
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( aElement0(esk16_3(X128,X129,X130))
| aReductOfIn0(esk14_3(X128,X129,X130),X130,xR)
| X130 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( aReductOfIn0(esk16_3(X128,X129,X130),X130,xR)
| aReductOfIn0(esk14_3(X128,X129,X130),X130,xR)
| X130 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( sdtmndtplgtdt0(esk16_3(X128,X129,X130),xR,esk14_3(X128,X129,X130))
| aReductOfIn0(esk14_3(X128,X129,X130),X130,xR)
| X130 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( sdtmndtplgtdt0(X130,xR,esk14_3(X128,X129,X130))
| X130 = esk14_3(X128,X129,X130)
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& ( sdtmndtasgtdt0(X130,xR,esk14_3(X128,X129,X130))
| ~ aElement0(X128)
| ~ aElement0(X129)
| ~ aElement0(X130)
| ~ aReductOfIn0(X129,X128,xR)
| ~ aReductOfIn0(X130,X128,xR) )
& isLocallyConfluent0(xR)
& ( ~ aReductOfIn0(X135,X134,xR)
| iLess0(X135,X134)
| ~ aElement0(X134)
| ~ aElement0(X135) )
& ( ~ aElement0(X136)
| ~ aReductOfIn0(X136,X134,xR)
| ~ sdtmndtplgtdt0(X136,xR,X135)
| iLess0(X135,X134)
| ~ aElement0(X134)
| ~ aElement0(X135) )
& ( ~ sdtmndtplgtdt0(X134,xR,X135)
| iLess0(X135,X134)
| ~ aElement0(X134)
| ~ aElement0(X135) )
& isTerminating0(xR) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__656_01])])])])]) ).
fof(c_0_9,hypothesis,
( aElement0(xw)
& ( aElement0(esk24_0)
| aReductOfIn0(xw,xu,xR)
| xu = xw )
& ( aReductOfIn0(esk24_0,xu,xR)
| aReductOfIn0(xw,xu,xR)
| xu = xw )
& ( sdtmndtplgtdt0(esk24_0,xR,xw)
| aReductOfIn0(xw,xu,xR)
| xu = xw )
& ( sdtmndtplgtdt0(xu,xR,xw)
| xu = xw )
& sdtmndtasgtdt0(xu,xR,xw)
& ( aElement0(esk25_0)
| aReductOfIn0(xw,xv,xR)
| xv = xw )
& ( aReductOfIn0(esk25_0,xv,xR)
| aReductOfIn0(xw,xv,xR)
| xv = xw )
& ( sdtmndtplgtdt0(esk25_0,xR,xw)
| aReductOfIn0(xw,xv,xR)
| xv = xw )
& ( sdtmndtplgtdt0(xv,xR,xw)
| xv = xw )
& sdtmndtasgtdt0(xv,xR,xw) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__799])])]) ).
cnf(c_0_10,negated_conjecture,
~ aNormalFormOfIn0(X1,xw,xR),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( aNormalFormOfIn0(esk13_2(X1,X2),X2,X1)
| ~ aRewritingSystem0(X1)
| ~ isTerminating0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,hypothesis,
isTerminating0(xR),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_14,hypothesis,
aElement0(xw),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,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_10,c_0_11]),c_0_12]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM018+4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n031.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 16:22:08 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.43/1.79 % Version : CSE_E---1.7
% 1.43/1.79 % Problem : theBenchmark.p
% 1.43/1.79 % SZS status Theorem for theBenchmark.p
% 1.43/1.79 % SZS output start CNFRefutation
% See solution above
% 1.43/1.79 % Total time : 1.423s
%------------------------------------------------------------------------------