%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : COM012+3 : 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 : n018.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 1.27s 1.72s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 10 unt; 0 def)
% Number of atoms : 120 ( 22 equ)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 123 ( 25 ~; 51 |; 43 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 20 ( 0 sgn 9 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( ( ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xx,xR)
& sdtmndtplgtdt0(X1,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xy,xR)
& sdtmndtplgtdt0(X1,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) )
=> ( xx = xz
| aReductOfIn0(xz,xx,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xx,xR)
& sdtmndtplgtdt0(X1,xR,xz) )
| sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mTCTrans,axiom,
! [X1,X2,X3,X4] :
( ( aElement0(X1)
& aRewritingSystem0(X2)
& aElement0(X3)
& aElement0(X4) )
=> ( ( sdtmndtplgtdt0(X1,X2,X3)
& sdtmndtplgtdt0(X3,X2,X4) )
=> sdtmndtplgtdt0(X1,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCTrans) ).
fof(m__349,hypothesis,
( aElement0(xx)
& aRewritingSystem0(xR)
& aElement0(xy)
& aElement0(xz) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__349) ).
fof(c_0_3,negated_conjecture,
~ ( ( ( xx = xy
| ( ( aReductOfIn0(xy,xx,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xx,xR)
& sdtmndtplgtdt0(X1,xR,xy) ) )
& sdtmndtplgtdt0(xx,xR,xy) ) )
& sdtmndtasgtdt0(xx,xR,xy)
& ( xy = xz
| ( ( aReductOfIn0(xz,xy,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xy,xR)
& sdtmndtplgtdt0(X1,xR,xz) ) )
& sdtmndtplgtdt0(xy,xR,xz) ) )
& sdtmndtasgtdt0(xy,xR,xz) )
=> ( xx = xz
| aReductOfIn0(xz,xx,xR)
| ? [X1] :
( aElement0(X1)
& aReductOfIn0(X1,xx,xR)
& sdtmndtplgtdt0(X1,xR,xz) )
| sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_4,plain,
! [X37,X38,X39,X40] :
( ~ aElement0(X37)
| ~ aRewritingSystem0(X38)
| ~ aElement0(X39)
| ~ aElement0(X40)
| ~ sdtmndtplgtdt0(X37,X38,X39)
| ~ sdtmndtplgtdt0(X39,X38,X40)
| sdtmndtplgtdt0(X37,X38,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mTCTrans])]) ).
fof(c_0_5,negated_conjecture,
! [X46] :
( ( aElement0(esk2_0)
| aReductOfIn0(xy,xx,xR)
| xx = xy )
& ( aReductOfIn0(esk2_0,xx,xR)
| aReductOfIn0(xy,xx,xR)
| xx = xy )
& ( sdtmndtplgtdt0(esk2_0,xR,xy)
| aReductOfIn0(xy,xx,xR)
| xx = xy )
& ( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy )
& sdtmndtasgtdt0(xx,xR,xy)
& ( aElement0(esk3_0)
| aReductOfIn0(xz,xy,xR)
| xy = xz )
& ( aReductOfIn0(esk3_0,xy,xR)
| aReductOfIn0(xz,xy,xR)
| xy = xz )
& ( sdtmndtplgtdt0(esk3_0,xR,xz)
| aReductOfIn0(xz,xy,xR)
| xy = xz )
& ( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz )
& sdtmndtasgtdt0(xy,xR,xz)
& xx != xz
& ~ aReductOfIn0(xz,xx,xR)
& ( ~ aElement0(X46)
| ~ aReductOfIn0(X46,xx,xR)
| ~ sdtmndtplgtdt0(X46,xR,xz) )
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ~ sdtmndtasgtdt0(xx,xR,xz) ),
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_3])])])])]) ).
cnf(c_0_6,plain,
( sdtmndtplgtdt0(X1,X2,X4)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X2)
| ~ aElement0(X3)
| ~ aElement0(X4)
| ~ sdtmndtplgtdt0(X1,X2,X3)
| ~ sdtmndtplgtdt0(X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
aRewritingSystem0(xR),
inference(split_conjunct,[status(thm)],[m__349]) ).
cnf(c_0_9,hypothesis,
aElement0(xz),
inference(split_conjunct,[status(thm)],[m__349]) ).
cnf(c_0_10,hypothesis,
aElement0(xy),
inference(split_conjunct,[status(thm)],[m__349]) ).
cnf(c_0_11,negated_conjecture,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
( xz = xy
| sdtmndtplgtdt0(X1,xR,xz)
| ~ sdtmndtplgtdt0(X1,xR,xy)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_13,hypothesis,
aElement0(xx),
inference(split_conjunct,[status(thm)],[m__349]) ).
cnf(c_0_14,negated_conjecture,
( xz = xy
| ~ sdtmndtplgtdt0(xx,xR,xy) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_15,negated_conjecture,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
( xx = xy
| xz = xy ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
sdtmndtasgtdt0(xy,xR,xz),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
xz = xy,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_20,negated_conjecture,
sdtmndtasgtdt0(xx,xR,xy),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_19]),c_0_20])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM012+3 : 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 : n018.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 16:20:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Theorem for theBenchmark.p
% 1.27/1.72 % SZS output start CNFRefutation
% See solution above
% 1.27/1.72 % Total time : 1.367s
%------------------------------------------------------------------------------