%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:03:29 PM UTC 2026
% Result : Theorem 2.63s 0.78s
% Output : Proof 2.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 10 unt; 0 def)
% Number of atoms : 223 ( 47 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 235 ( 62 ~; 106 |; 63 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 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 : 33 ( 0 sgn 14 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W3)
& aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( ( sdtmndtplgtdt0(W2,W1,W3)
& sdtmndtplgtdt0(W0,W1,W2) )
=> sdtmndtplgtdt0(W0,W1,W3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCTrans) ).
fof(f6_nnf,plain,
! [W0,W1,W2,W3] :
( sdtmndtplgtdt0(W0,W1,W3)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [W0,W1,W2,W3] :
( sdtmndtplgtdt0(W0,W1,W3)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ aElement0(W3)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c10,plain,
( sdtmndtplgtdt0(X0,X1,X3)
| ~ sdtmndtplgtdt0(X2,X1,X3)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
fof(f8,hypothesis,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__349) ).
fof(f8_nnf,plain,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
( aElement0(xz)
& aElement0(xy)
& aRewritingSystem0(xR)
& aElement0(xx) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c16,plain,
aElement0(xy),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f9,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f9_neg,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) )
=> ( sdtmndtasgtdt0(xx,xR,xz)
| sdtmndtplgtdt0(xx,xR,xz)
| ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xx,xR)
| xx = xz ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ! [W0] :
( ~ sdtmndtplgtdt0(W0,xR,xz)
| ~ aReductOfIn0(W0,xx,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xz)
& aReductOfIn0(W0,xy,xR)
& aElement0(W0) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ? [W0] :
( sdtmndtplgtdt0(W0,xR,xy)
& aReductOfIn0(W0,xx,xR)
& aElement0(W0) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
! [W0] :
( ~ sdtmndtasgtdt0(xx,xR,xz)
& ~ sdtmndtplgtdt0(xx,xR,xz)
& ( ~ sdtmndtplgtdt0(W0,xR,xz)
| ~ aReductOfIn0(W0,xx,xR)
| ~ aElement0(W0) )
& ~ aReductOfIn0(xz,xx,xR)
& xx != xz
& sdtmndtasgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(xy,xR,xz)
& ( ( sdtmndtplgtdt0(sk2,xR,xz)
& aReductOfIn0(sk2,xy,xR)
& aElement0(sk2) )
| aReductOfIn0(xz,xy,xR) ) )
| xy = xz )
& sdtmndtasgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(xx,xR,xy)
& ( ( sdtmndtplgtdt0(sk1,xR,xy)
& aReductOfIn0(sk1,xx,xR)
& aElement0(sk1) )
| aReductOfIn0(xy,xx,xR) ) )
| xx = xy ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f9_nnf]) ).
cnf(c30,plain,
( ~ sdtmndtplgtdt0(X0,xR,xz)
| ~ aReductOfIn0(X0,xx,xR)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p37,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ aReductOfIn0(xy,xx,xR) ),
inference(resolution,[status(thm)],[c16,c30]) ).
cnf(c18,plain,
( aElement0(sk1)
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p40,plain,
( aElement0(sk1)
| xx = xy
| ~ sdtmndtplgtdt0(xy,xR,xz) ),
inference(resolution,[status(thm)],[p37,c18]) ).
cnf(c26,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p44,plain,
( xy = xz
| aElement0(sk1)
| xx = xy ),
inference(resolution,[status(thm)],[p40,c26]) ).
cnf(c31,plain,
~ sdtmndtplgtdt0(xx,xR,xz),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p47,plain,
( ~ sdtmndtplgtdt0(xx,xR,xy)
| aElement0(sk1)
| xx = xy ),
inference(superposition,[status(thm)],[p44,c31]) ).
cnf(c21,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p54,plain,
( xx = xy
| aElement0(sk1)
| xx = xy ),
inference(resolution,[status(thm)],[p47,c21]) ).
cnf(p55,plain,
( aElement0(sk1)
| xx = xy ),
inference(factoring,[status(thm)],[p54]) ).
cnf(c27,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p57,plain,
( sdtmndtasgtdt0(xx,xR,xz)
| aElement0(sk1) ),
inference(superposition,[status(thm)],[p55,c27]) ).
cnf(c32,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p65,plain,
aElement0(sk1),
inference(resolution,[status(thm)],[p57,c32]) ).
cnf(p85,plain,
( sdtmndtplgtdt0(sk1,X0,X2)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ sdtmndtplgtdt0(sk1,X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c10,p65]) ).
cnf(c15,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p200,plain,
( sdtmndtplgtdt0(sk1,xR,X1)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ sdtmndtplgtdt0(sk1,xR,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p85,c15]) ).
cnf(p202,plain,
( sdtmndtplgtdt0(sk1,xR,X0)
| ~ sdtmndtplgtdt0(xy,xR,X0)
| ~ sdtmndtplgtdt0(sk1,xR,xy)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p200,c16]) ).
cnf(c17,plain,
aElement0(xz),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p215,plain,
( sdtmndtplgtdt0(sk1,xR,xz)
| ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ sdtmndtplgtdt0(sk1,xR,xy) ),
inference(resolution,[status(thm)],[p202,c17]) ).
cnf(c20,plain,
( sdtmndtplgtdt0(sk1,xR,xy)
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p220,plain,
( aReductOfIn0(xy,xx,xR)
| xx = xy
| sdtmndtplgtdt0(sk1,xR,xz)
| ~ sdtmndtplgtdt0(xy,xR,xz) ),
inference(resolution,[status(thm)],[p215,c20]) ).
cnf(p230,plain,
( xy = xz
| aReductOfIn0(xy,xx,xR)
| xx = xy
| sdtmndtplgtdt0(sk1,xR,xz) ),
inference(resolution,[status(thm)],[p220,c26]) ).
cnf(p66,plain,
( ~ sdtmndtplgtdt0(sk1,xR,xz)
| ~ aReductOfIn0(sk1,xx,xR) ),
inference(resolution,[status(thm)],[p65,c30]) ).
cnf(c19,plain,
( aReductOfIn0(sk1,xx,xR)
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p72,plain,
( aReductOfIn0(xy,xx,xR)
| xx = xy
| ~ sdtmndtplgtdt0(sk1,xR,xz) ),
inference(resolution,[status(thm)],[p66,c19]) ).
cnf(p231,plain,
( aReductOfIn0(xy,xx,xR)
| xx = xy
| xy = xz
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(resolution,[status(thm)],[p230,p72]) ).
cnf(p240,plain,
( xx = xy
| xy = xz
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(factoring,[status(thm)],[p231]) ).
cnf(p241,plain,
( xy = xz
| aReductOfIn0(xy,xx,xR)
| xx = xy ),
inference(factoring,[status(thm)],[p240]) ).
cnf(p242,plain,
( ~ sdtmndtplgtdt0(xy,xR,xz)
| xy = xz
| xx = xy ),
inference(resolution,[status(thm)],[p241,p37]) ).
cnf(p244,plain,
( xy = xz
| xy = xz
| xx = xy ),
inference(resolution,[status(thm)],[p242,c26]) ).
cnf(p245,plain,
( xy = xz
| xx = xy ),
inference(factoring,[status(thm)],[p244]) ).
cnf(p248,plain,
( ~ sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(superposition,[status(thm)],[p245,c31]) ).
cnf(p268,plain,
( xx = xy
| xx = xy ),
inference(resolution,[status(thm)],[p248,c21]) ).
cnf(p269,plain,
xx = xy,
inference(factoring,[status(thm)],[p268]) ).
cnf(p271,plain,
sdtmndtasgtdt0(xx,xR,xz),
inference(superposition,[status(thm)],[p269,c27]) ).
cnf(p288,plain,
$false,
inference(resolution,[status(thm)],[p271,c32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n020.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Fri Sep 25 07:47:18 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.63/0.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.63/0.78 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------