%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 5.30s 1.11s
% Output : Proof 5.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 4
% Syntax : Number of formulae : 46 ( 10 unt; 1 def)
% Number of atoms : 165 ( 23 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 195 ( 76 ~; 88 |; 25 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 46 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(c14,plain,
aElement0(xx),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f7,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mTCRDef) ).
fof(f7_nnf,plain,
! [W0,W1,W2] :
( ( ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
& W0 != W2 )
| sdtmndtasgtdt0(W0,W1,W2) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2
| ~ sdtmndtasgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0,W1,W2] :
( ( ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
& W0 != W2 )
| sdtmndtasgtdt0(W0,W1,W2) )
& ( sdtmndtplgtdt0(W0,W1,W2)
| W0 = W2
| ~ sdtmndtasgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c11,plain,
( sdtmndtplgtdt0(X0,X1,X2)
| X0 = X2
| ~ sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p38,plain,
( sdtmndtplgtdt0(xx,X0,X1)
| xx = X1
| ~ sdtmndtasgtdt0(xx,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c14,c11]) ).
cnf(c15,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p87,plain,
( sdtmndtplgtdt0(xx,xR,X0)
| xx = X0
| ~ sdtmndtasgtdt0(xx,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p38,c15]) ).
cnf(c16,plain,
aElement0(xy),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p143,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy
| ~ sdtmndtasgtdt0(xx,xR,xy) ),
inference(resolution,[status(thm)],[p87,c16]) ).
fof(f9,conjecture,
( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f9_neg,negated_conjecture,
~ ( ( sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f9_nnf,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) ),
inference(nnf_transformation,[status(thm)],[f9_neg]) ).
fof(f9_sk,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& sdtmndtasgtdt0(xy,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c18,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p208,plain,
( sdtmndtplgtdt0(xx,xR,xy)
| xx = xy ),
inference(resolution,[status(thm)],[p143,c18]) ).
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]) ).
cnf(p37,plain,
( sdtmndtplgtdt0(xx,X0,X2)
| ~ sdtmndtplgtdt0(X1,X0,X2)
| ~ sdtmndtplgtdt0(xx,X0,X1)
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(p86,plain,
( sdtmndtplgtdt0(xx,xR,X1)
| ~ sdtmndtplgtdt0(X0,xR,X1)
| ~ sdtmndtplgtdt0(xx,xR,X0)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p37,c15]) ).
cnf(p141,plain,
( sdtmndtplgtdt0(xx,xR,X0)
| ~ sdtmndtplgtdt0(xy,xR,X0)
| ~ sdtmndtplgtdt0(xx,xR,xy)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p86,c16]) ).
cnf(c17,plain,
aElement0(xz),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p206,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ sdtmndtplgtdt0(xy,xR,xz)
| ~ sdtmndtplgtdt0(xx,xR,xy) ),
inference(resolution,[status(thm)],[p141,c17]) ).
cnf(p222,plain,
( sdtmndtplgtdt0(xx,xR,xz)
| ~ sdtmndtplgtdt0(xy,xR,xz)
| xx = xy ),
inference(resolution,[status(thm)],[p208,p206]) ).
cnf(p48,plain,
( sdtmndtplgtdt0(xy,X0,X1)
| xy = X1
| ~ sdtmndtasgtdt0(xy,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c16,c11]) ).
cnf(p97,plain,
( sdtmndtplgtdt0(xy,xR,X0)
| xy = X0
| ~ sdtmndtasgtdt0(xy,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p48,c15]) ).
cnf(p162,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz
| ~ sdtmndtasgtdt0(xy,xR,xz) ),
inference(resolution,[status(thm)],[p97,c17]) ).
cnf(c19,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p213,plain,
( sdtmndtplgtdt0(xy,xR,xz)
| xy = xz ),
inference(resolution,[status(thm)],[p162,c19]) ).
cnf(p286,plain,
( xy = xz
| sdtmndtplgtdt0(xx,xR,xz)
| xx = xy ),
inference(resolution,[status(thm)],[p222,p213]) ).
cnf(c13,plain,
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p40,plain,
( ~ sdtmndtplgtdt0(xx,X0,X1)
| sdtmndtasgtdt0(xx,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c14,c13]) ).
cnf(p89,plain,
( ~ sdtmndtplgtdt0(xx,xR,X0)
| sdtmndtasgtdt0(xx,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p40,c15]) ).
cnf(p148,plain,
( ~ sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolution,[status(thm)],[p89,c17]) ).
cnf(p388,plain,
( sdtmndtasgtdt0(xx,xR,xz)
| xy = xz
| xx = xy ),
inference(resolution,[status(thm)],[p286,p148]) ).
cnf(c20,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p558,plain,
( xy = xz
| xx = xy ),
inference(resolution,[status(thm)],[p388,c20]) ).
cnf(p611,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| xx = xy ),
inference(superposition,[status(thm)],[p558,c20]) ).
cnf(p718,plain,
xx = xy,
inference(resolution,[status(thm)],[p611,c18]) ).
cnf(p732,plain,
sdtmndtasgtdt0(xx,xR,xz),
inference(superposition,[status(thm)],[p718,c19]) ).
cnf(p881,plain,
$false,
inference(resolution,[status(thm)],[p732,c20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM012+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 07:46:32 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.30/1.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.30/1.11 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------