%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM023+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 : n002.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 04:13:10 PM UTC 2026
% Result : Theorem 1.22s 1.67s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 7 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 44 ( 5 avg)
% Number of connectives : 212 ( 92 ~; 94 |; 22 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 15 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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) )
=> ? [X4] :
( aElement0(X4)
& sdtmndtasgtdt0(X2,xR,X4)
& sdtmndtasgtdt0(X3,xR,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__715) ).
fof(m__,conjecture,
isConfluent0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__656) ).
fof(c_0_4,plain,
! [X74,X75,X76,X77,X82] :
( ( aElement0(esk2_4(X74,X75,X76,X77))
| ~ aElement0(X75)
| ~ aElement0(X76)
| ~ aElement0(X77)
| ~ sdtmndtasgtdt0(X75,X74,X76)
| ~ sdtmndtasgtdt0(X75,X74,X77)
| ~ isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( sdtmndtasgtdt0(X76,X74,esk2_4(X74,X75,X76,X77))
| ~ aElement0(X75)
| ~ aElement0(X76)
| ~ aElement0(X77)
| ~ sdtmndtasgtdt0(X75,X74,X76)
| ~ sdtmndtasgtdt0(X75,X74,X77)
| ~ isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( sdtmndtasgtdt0(X77,X74,esk2_4(X74,X75,X76,X77))
| ~ aElement0(X75)
| ~ aElement0(X76)
| ~ aElement0(X77)
| ~ sdtmndtasgtdt0(X75,X74,X76)
| ~ sdtmndtasgtdt0(X75,X74,X77)
| ~ isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( aElement0(esk3_1(X74))
| isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( aElement0(esk4_1(X74))
| isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( aElement0(esk5_1(X74))
| isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( sdtmndtasgtdt0(esk3_1(X74),X74,esk4_1(X74))
| isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( sdtmndtasgtdt0(esk3_1(X74),X74,esk5_1(X74))
| isConfluent0(X74)
| ~ aRewritingSystem0(X74) )
& ( ~ aElement0(X82)
| ~ sdtmndtasgtdt0(esk4_1(X74),X74,X82)
| ~ sdtmndtasgtdt0(esk5_1(X74),X74,X82)
| isConfluent0(X74)
| ~ aRewritingSystem0(X74) ) ),
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(c_0_5,hypothesis,
! [X106,X107,X108] :
( ( aElement0(esk14_3(X106,X107,X108))
| ~ aElement0(X106)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ sdtmndtasgtdt0(X106,xR,X107)
| ~ sdtmndtasgtdt0(X106,xR,X108) )
& ( sdtmndtasgtdt0(X107,xR,esk14_3(X106,X107,X108))
| ~ aElement0(X106)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ sdtmndtasgtdt0(X106,xR,X107)
| ~ sdtmndtasgtdt0(X106,xR,X108) )
& ( sdtmndtasgtdt0(X108,xR,esk14_3(X106,X107,X108))
| ~ aElement0(X106)
| ~ aElement0(X107)
| ~ aElement0(X108)
| ~ sdtmndtasgtdt0(X106,xR,X107)
| ~ sdtmndtasgtdt0(X106,xR,X108) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__715])])])]) ).
fof(c_0_6,negated_conjecture,
~ isConfluent0(xR),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
cnf(c_0_7,plain,
( isConfluent0(X2)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(esk4_1(X2),X2,X1)
| ~ sdtmndtasgtdt0(esk5_1(X2),X2,X1)
| ~ aRewritingSystem0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,hypothesis,
( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X3,X1))
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ aElement0(X1)
| ~ sdtmndtasgtdt0(X2,xR,X3)
| ~ sdtmndtasgtdt0(X2,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_10,negated_conjecture,
~ isConfluent0(xR),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( aElement0(esk14_3(X1,X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ sdtmndtasgtdt0(X1,xR,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,hypothesis,
( ~ sdtmndtasgtdt0(esk4_1(xR),xR,esk14_3(X1,X2,esk5_1(xR)))
| ~ sdtmndtasgtdt0(X1,xR,esk5_1(xR))
| ~ sdtmndtasgtdt0(X1,xR,X2)
| ~ aElement0(esk5_1(xR))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),c_0_10]),c_0_11]) ).
cnf(c_0_13,hypothesis,
( sdtmndtasgtdt0(X1,xR,esk14_3(X2,X1,X3))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X3)
| ~ sdtmndtasgtdt0(X2,xR,X1)
| ~ sdtmndtasgtdt0(X2,xR,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,hypothesis,
( ~ sdtmndtasgtdt0(X1,xR,esk5_1(xR))
| ~ sdtmndtasgtdt0(X1,xR,esk4_1(xR))
| ~ aElement0(esk5_1(xR))
| ~ aElement0(esk4_1(xR))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
( sdtmndtasgtdt0(esk3_1(X1),X1,esk5_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_16,hypothesis,
( ~ sdtmndtasgtdt0(esk3_1(xR),xR,esk4_1(xR))
| ~ aElement0(esk5_1(xR))
| ~ aElement0(esk4_1(xR))
| ~ aElement0(esk3_1(xR)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_9])]),c_0_10]) ).
cnf(c_0_17,plain,
( sdtmndtasgtdt0(esk3_1(X1),X1,esk4_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_18,hypothesis,
( ~ aElement0(esk5_1(xR))
| ~ aElement0(esk4_1(xR))
| ~ aElement0(esk3_1(xR)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_9])]),c_0_10]) ).
cnf(c_0_19,plain,
( aElement0(esk5_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_20,hypothesis,
( ~ aElement0(esk4_1(xR))
| ~ aElement0(esk3_1(xR)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_9])]),c_0_10]) ).
cnf(c_0_21,plain,
( aElement0(esk4_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_22,hypothesis,
~ aElement0(esk3_1(xR)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_9])]),c_0_10]) ).
cnf(c_0_23,plain,
( aElement0(esk3_1(X1))
| isConfluent0(X1)
| ~ aRewritingSystem0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_24,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_9])]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COM023+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.09 % 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
% 0.10/0.28 % Computer : n002.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Mon May 4 16:19:46 EDT 2026
% 0.10/0.28 % CPUTime :
% 0.10/0.29 % start to proof: theBenchmark
% 1.22/1.67 % Version : CSE_E---1.7
% 1.22/1.67 % Problem : theBenchmark.p
% 1.22/1.67 % SZS status Theorem for theBenchmark.p
% 1.22/1.67 % SZS output start CNFRefutation
% See solution above
% 1.22/1.67 % Total time : 1.369s
%------------------------------------------------------------------------------