%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM022+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 : n014.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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 0 def)
% Number of atoms : 202 ( 20 equ)
% Maximal formula atoms : 41 ( 5 avg)
% Number of connectives : 252 ( 88 ~; 98 |; 56 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-3 aty)
% Number of variables : 39 ( 0 sgn 15 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xb)
& ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& sdtmndtasgtdt0(X2,xR,xc)
& ? [X3] :
( aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X3)
& sdtmndtasgtdt0(X2,xR,X3)
& ? [X4] :
( aNormalFormOfIn0(X4,X3,xR)
& sdtmndtasgtdt0(xb,xR,X4)
& sdtmndtasgtdt0(xc,xR,X4) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xb,xR,X1)
& sdtmndtasgtdt0(xc,xR,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
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(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__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(c_0_5,negated_conjecture,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xa,xR)
& sdtmndtasgtdt0(X1,xR,xb)
& ? [X2] :
( aElement0(X2)
& aReductOfIn0(X2,xa,xR)
& sdtmndtasgtdt0(X2,xR,xc)
& ? [X3] :
( aElement0(X3)
& sdtmndtasgtdt0(X1,xR,X3)
& sdtmndtasgtdt0(X2,xR,X3)
& ? [X4] :
( aNormalFormOfIn0(X4,X3,xR)
& sdtmndtasgtdt0(xb,xR,X4)
& sdtmndtasgtdt0(xc,xR,X4) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [X1] :
( aElement0(X1)
& sdtmndtasgtdt0(xb,xR,X1)
& sdtmndtasgtdt0(xc,xR,X1) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_6,plain,
! [X72,X73,X74] :
( ( ~ sdtmndtasgtdt0(X72,X73,X74)
| X72 = X74
| sdtmndtplgtdt0(X72,X73,X74)
| ~ aElement0(X72)
| ~ aRewritingSystem0(X73)
| ~ aElement0(X74) )
& ( X72 != X74
| sdtmndtasgtdt0(X72,X73,X74)
| ~ aElement0(X72)
| ~ aRewritingSystem0(X73)
| ~ aElement0(X74) )
& ( ~ sdtmndtplgtdt0(X72,X73,X74)
| sdtmndtasgtdt0(X72,X73,X74)
| ~ aElement0(X72)
| ~ aRewritingSystem0(X73)
| ~ aElement0(X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCRDef])])]) ).
fof(c_0_7,negated_conjecture,
! [X119] :
( ( aElement0(esk15_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( aReductOfIn0(esk15_0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( sdtmndtasgtdt0(esk15_0,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( aElement0(esk16_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( aReductOfIn0(esk16_0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( sdtmndtasgtdt0(esk16_0,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( aElement0(esk17_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( sdtmndtasgtdt0(esk15_0,xR,esk17_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( sdtmndtasgtdt0(esk16_0,xR,esk17_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( aNormalFormOfIn0(esk18_0,esk17_0,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( sdtmndtasgtdt0(xb,xR,esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( sdtmndtasgtdt0(xc,xR,esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ~ aElement0(X119)
| ~ sdtmndtasgtdt0(xb,xR,X119)
| ~ sdtmndtasgtdt0(xc,xR,X119) ) ),
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])])])])]) ).
fof(c_0_8,plain,
! [X102,X103,X104,X105,X106] :
( ( aElement0(X104)
| ~ aNormalFormOfIn0(X104,X102,X103)
| ~ aElement0(X102)
| ~ aRewritingSystem0(X103) )
& ( sdtmndtasgtdt0(X102,X103,X104)
| ~ aNormalFormOfIn0(X104,X102,X103)
| ~ aElement0(X102)
| ~ aRewritingSystem0(X103) )
& ( ~ aReductOfIn0(X105,X104,X103)
| ~ aNormalFormOfIn0(X104,X102,X103)
| ~ aElement0(X102)
| ~ aRewritingSystem0(X103) )
& ( ~ aElement0(X106)
| ~ sdtmndtasgtdt0(X102,X103,X106)
| aReductOfIn0(esk12_3(X102,X103,X106),X106,X103)
| aNormalFormOfIn0(X106,X102,X103)
| ~ aElement0(X102)
| ~ aRewritingSystem0(X103) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( X1 = X3
| sdtmndtplgtdt0(X1,X2,X3)
| ~ sdtmndtasgtdt0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xc),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__656]) ).
cnf(c_0_12,hypothesis,
aElement0(xc),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_13,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_14,plain,
( aElement0(X1)
| ~ aNormalFormOfIn0(X1,X2,X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( aNormalFormOfIn0(esk18_0,esk17_0,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,negated_conjecture,
( aElement0(esk17_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( sdtmndtasgtdt0(xc,xR,esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_18,negated_conjecture,
( xc = xa
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_19,negated_conjecture,
sdtmndtasgtdt0(xa,xR,xb),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__731]) ).
cnf(c_0_21,negated_conjecture,
( aElement0(esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_11])]),c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( sdtmndtasgtdt0(xb,xR,esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
( xc = xa
| sdtmndtasgtdt0(xc,xR,esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( xb = xa
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_19]),c_0_11]),c_0_20]),c_0_13])]) ).
cnf(c_0_25,negated_conjecture,
( xc = xa
| aElement0(esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
( xc = xa
| sdtmndtasgtdt0(xb,xR,esk18_0)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( ~ aElement0(X1)
| ~ sdtmndtasgtdt0(xb,xR,X1)
| ~ sdtmndtasgtdt0(xc,xR,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_28,negated_conjecture,
( xb = xa
| xc = xa
| sdtmndtasgtdt0(xc,xR,esk18_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( xb = xa
| xc = xa
| aElement0(esk18_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( xb = xa
| xc = xa
| sdtmndtasgtdt0(xb,xR,esk18_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_31,plain,
( sdtmndtasgtdt0(X1,X3,X2)
| X1 != X2
| ~ aElement0(X1)
| ~ aRewritingSystem0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
( xc = xa
| xb = xa ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
( sdtmndtasgtdt0(X1,X2,X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_34,negated_conjecture,
( xb = xa
| ~ sdtmndtasgtdt0(xb,xR,X1)
| ~ sdtmndtasgtdt0(xa,xR,X1)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
~ sdtmndtasgtdt0(xb,xR,xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_33]),c_0_12]),c_0_11])]) ).
cnf(c_0_36,negated_conjecture,
xb = xa,
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_33]),c_0_19]),c_0_20]),c_0_11])]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36]),c_0_10])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM022+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 : n014.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 16:20:06 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.373s
%------------------------------------------------------------------------------