%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM022+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 01:03:31 PM UTC 2026
% Result : Theorem 23.97s 3.70s
% Output : Proof 23.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 16 unt; 2 def)
% Number of atoms : 285 ( 44 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 309 ( 99 ~; 121 |; 79 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 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 : 60 ( 0 sgn 22 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/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]) ).
fof(f16,hypothesis,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
fof(f16_nnf,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
( aElement0(xc)
& aElement0(xb)
& aElement0(xa) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c46,plain,
aElement0(xa),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p1682,plain,
( sdtmndtplgtdt0(xa,X0,X1)
| xa = X1
| ~ sdtmndtasgtdt0(xa,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c11,c46]) ).
fof(f14,hypothesis,
aRewritingSystem0(xR),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656) ).
fof(f14_nnf,plain,
aRewritingSystem0(xR),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c43,plain,
aRewritingSystem0(xR),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p1709,plain,
( sdtmndtplgtdt0(xa,xR,X0)
| xa = X0
| ~ sdtmndtasgtdt0(xa,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p1682,c43]) ).
cnf(c48,plain,
aElement0(xc),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p1711,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| xa = xc
| ~ sdtmndtasgtdt0(xa,xR,xc) ),
inference(resolution,[status(thm)],[p1709,c48]) ).
fof(f18,conjecture,
( ( ( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) )
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( ? [W3] :
( sdtmndtasgtdt0(xc,xR,W3)
& sdtmndtasgtdt0(xb,xR,W3)
& aNormalFormOfIn0(W3,W2,xR) )
& sdtmndtasgtdt0(W1,xR,W2)
& sdtmndtasgtdt0(W0,xR,W2)
& aElement0(W2) )
& sdtmndtasgtdt0(W1,xR,xc)
& aReductOfIn0(W1,xa,xR)
& aElement0(W1) )
& sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb) )
=> ? [W0] :
( sdtmndtasgtdt0(xc,xR,W0)
& sdtmndtasgtdt0(xb,xR,W0)
& aElement0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f18_neg,negated_conjecture,
~ ( ( ( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) )
=> ? [W0] :
( ? [W1] :
( ? [W2] :
( ? [W3] :
( sdtmndtasgtdt0(xc,xR,W3)
& sdtmndtasgtdt0(xb,xR,W3)
& aNormalFormOfIn0(W3,W2,xR) )
& sdtmndtasgtdt0(W1,xR,W2)
& sdtmndtasgtdt0(W0,xR,W2)
& aElement0(W2) )
& sdtmndtasgtdt0(W1,xR,xc)
& aReductOfIn0(W1,xa,xR)
& aElement0(W1) )
& sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb) )
=> ? [W0] :
( sdtmndtasgtdt0(xc,xR,W0)
& sdtmndtasgtdt0(xb,xR,W0)
& aElement0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f18_nnf,plain,
( ! [W0] :
( ~ sdtmndtasgtdt0(xc,xR,W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ aElement0(W0) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ( ? [W0] :
( ? [W1] :
( ? [W2] :
( ? [W3] :
( sdtmndtasgtdt0(xc,xR,W3)
& sdtmndtasgtdt0(xb,xR,W3)
& aNormalFormOfIn0(W3,W2,xR) )
& sdtmndtasgtdt0(W1,xR,W2)
& sdtmndtasgtdt0(W0,xR,W2)
& aElement0(W2) )
& sdtmndtasgtdt0(W1,xR,xc)
& aReductOfIn0(W1,xa,xR)
& aElement0(W1) )
& sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) )
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
inference(nnf_transformation,[status(thm)],[f18_neg]) ).
fof(f18_sk,plain,
! [W0] :
( ( ~ sdtmndtasgtdt0(xc,xR,W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ aElement0(W0) )
& sdtmndtasgtdt0(xa,xR,xc)
& sdtmndtasgtdt0(xa,xR,xb)
& ( ( sdtmndtasgtdt0(xc,xR,sk17)
& sdtmndtasgtdt0(xb,xR,sk17)
& aNormalFormOfIn0(sk17,sk16,xR)
& sdtmndtasgtdt0(sk15,xR,sk16)
& sdtmndtasgtdt0(sk14,xR,sk16)
& aElement0(sk16)
& sdtmndtasgtdt0(sk15,xR,xc)
& aReductOfIn0(sk15,xa,xR)
& aElement0(sk15)
& sdtmndtasgtdt0(sk14,xR,xb)
& aReductOfIn0(sk14,xa,xR)
& aElement0(sk14) )
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16,sk17])],[f18_nnf]) ).
cnf(c65,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1750,plain,
( sdtmndtplgtdt0(xa,xR,xc)
| xa = xc ),
inference(resolution,[status(thm)],[p1711,c65]) ).
cnf(c47,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p1710,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb
| ~ sdtmndtasgtdt0(xa,xR,xb) ),
inference(resolution,[status(thm)],[p1709,c47]) ).
cnf(c64,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1736,plain,
( sdtmndtplgtdt0(xa,xR,xb)
| xa = xb ),
inference(resolution,[status(thm)],[p1710,c64]) ).
cnf(c58,plain,
( aElement0(sk16)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1738,plain,
( aElement0(sk16)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| xa = xb ),
inference(resolution,[status(thm)],[p1736,c58]) ).
cnf(p1753,plain,
( aElement0(sk16)
| xa = xb
| xa = xc ),
inference(resolution,[status(thm)],[p1750,p1738]) ).
cnf(c12,plain,
( X0 != X2
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p287,plain,
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(p309,plain,
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(factoring,[status(thm)],[p287]) ).
cnf(p311,plain,
( sdtmndtasgtdt0(xb,X0,xb)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[p309,c47]) ).
cnf(p332,plain,
sdtmndtasgtdt0(xb,xR,xb),
inference(resolution,[status(thm)],[p311,c43]) ).
cnf(c66,plain,
( ~ sdtmndtasgtdt0(xc,xR,X0)
| ~ sdtmndtasgtdt0(xb,xR,X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p68,plain,
( ~ sdtmndtasgtdt0(xc,xR,xb)
| ~ sdtmndtasgtdt0(xb,xR,xb) ),
inference(resolution,[status(thm)],[c47,c66]) ).
cnf(p333,plain,
~ sdtmndtasgtdt0(xc,xR,xb),
inference(resolution,[status(thm)],[p332,p68]) ).
cnf(p2042,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| aElement0(sk16)
| xa = xb ),
inference(superposition,[status(thm)],[p1753,p333]) ).
cnf(p2830,plain,
( aElement0(sk16)
| xa = xb ),
inference(resolution,[status(thm)],[p2042,c64]) ).
cnf(p69,plain,
( ~ sdtmndtasgtdt0(xc,xR,xc)
| ~ sdtmndtasgtdt0(xb,xR,xc) ),
inference(resolution,[status(thm)],[c48,c66]) ).
cnf(p2843,plain,
( ~ sdtmndtasgtdt0(xc,xR,xc)
| ~ sdtmndtasgtdt0(xa,xR,xc)
| aElement0(sk16) ),
inference(superposition,[status(thm)],[p2830,p69]) ).
cnf(p3581,plain,
( ~ sdtmndtasgtdt0(xc,xR,xc)
| aElement0(sk16) ),
inference(resolution,[status(thm)],[p2843,c65]) ).
cnf(p312,plain,
( sdtmndtasgtdt0(xc,X0,xc)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[p309,c48]) ).
cnf(p334,plain,
sdtmndtasgtdt0(xc,xR,xc),
inference(resolution,[status(thm)],[p312,c43]) ).
cnf(p3582,plain,
aElement0(sk16),
inference(resolution,[status(thm)],[p3581,p334]) ).
fof(f12,definition,
! [W0,W1] :
( ( aRewritingSystem0(W1)
& aElement0(W0) )
=> ! [W2] :
( aNormalFormOfIn0(W2,W0,W1)
<=> ( ~ ? [W3] : aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNFRDef) ).
fof(f12_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( ? [W3] : aReductOfIn0(W3,W2,W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W2)
| aNormalFormOfIn0(W2,W0,W1) )
& ( ( ! [W3] : ~ aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) )
| ~ aNormalFormOfIn0(W2,W0,W1) ) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [W0,W1,W2,W3] :
( ( ( aReductOfIn0(sk11(W0,W1,W2),W2,W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ aElement0(W2)
| aNormalFormOfIn0(W2,W0,W1) )
& ( ( ~ aReductOfIn0(W3,W2,W1)
& sdtmndtasgtdt0(W0,W1,W2)
& aElement0(W2) )
| ~ aNormalFormOfIn0(W2,W0,W1) ) )
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f12_nnf]) ).
cnf(c38,plain,
( aElement0(X2)
| ~ aNormalFormOfIn0(X2,X0,X1)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p3585,plain,
( aElement0(X1)
| ~ aNormalFormOfIn0(X1,sk16,X0)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[p3582,c38]) ).
cnf(p3646,plain,
( aElement0(X0)
| ~ aNormalFormOfIn0(X0,sk16,xR) ),
inference(resolution,[status(thm)],[p3585,c43]) ).
cnf(c61,plain,
( aNormalFormOfIn0(sk17,sk16,xR)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1745,plain,
( aNormalFormOfIn0(sk17,sk16,xR)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| xa = xb ),
inference(resolution,[status(thm)],[p1736,c61]) ).
cnf(p1761,plain,
( aNormalFormOfIn0(sk17,sk16,xR)
| xa = xb
| xa = xc ),
inference(resolution,[status(thm)],[p1750,p1745]) ).
cnf(p3647,plain,
( xa = xb
| xa = xc
| aElement0(sk17) ),
inference(resolution,[status(thm)],[p3646,p1761]) ).
cnf(p3724,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| xa = xb
| aElement0(sk17) ),
inference(superposition,[status(thm)],[p3647,p333]) ).
cnf(p4006,plain,
( xa = xb
| aElement0(sk17) ),
inference(resolution,[status(thm)],[p3724,c64]) ).
cnf(p4018,plain,
( ~ sdtmndtasgtdt0(xc,xR,xc)
| ~ sdtmndtasgtdt0(xa,xR,xc)
| aElement0(sk17) ),
inference(superposition,[status(thm)],[p4006,p69]) ).
cnf(p4621,plain,
( ~ sdtmndtasgtdt0(xc,xR,xc)
| aElement0(sk17) ),
inference(resolution,[status(thm)],[p4018,c65]) ).
cnf(p4622,plain,
aElement0(sk17),
inference(resolution,[status(thm)],[p4621,p334]) ).
cnf(p4623,plain,
( ~ sdtmndtasgtdt0(xc,xR,sk17)
| ~ sdtmndtasgtdt0(xb,xR,sk17) ),
inference(resolution,[status(thm)],[p4622,c66]) ).
cnf(c62,plain,
( sdtmndtasgtdt0(xb,xR,sk17)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1746,plain,
( sdtmndtasgtdt0(xb,xR,sk17)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| xa = xb ),
inference(resolution,[status(thm)],[p1736,c62]) ).
cnf(p1762,plain,
( sdtmndtasgtdt0(xb,xR,sk17)
| xa = xb
| xa = xc ),
inference(resolution,[status(thm)],[p1750,p1746]) ).
cnf(p4682,plain,
( xa = xb
| xa = xc
| ~ sdtmndtasgtdt0(xc,xR,sk17) ),
inference(resolution,[status(thm)],[p4623,p1762]) ).
cnf(c63,plain,
( sdtmndtasgtdt0(xc,xR,sk17)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p1747,plain,
( sdtmndtasgtdt0(xc,xR,sk17)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| xa = xb ),
inference(resolution,[status(thm)],[p1736,c63]) ).
cnf(p1763,plain,
( sdtmndtasgtdt0(xc,xR,sk17)
| xa = xb
| xa = xc ),
inference(resolution,[status(thm)],[p1750,p1747]) ).
cnf(p4866,plain,
( xa = xb
| xa = xc
| xa = xb
| xa = xc ),
inference(resolution,[status(thm)],[p4682,p1763]) ).
cnf(p5863,plain,
( xa = xb
| xa = xb
| xa = xc ),
inference(factoring,[status(thm)],[p4866]) ).
cnf(p5865,plain,
( xa = xb
| xa = xc ),
inference(factoring,[status(thm)],[p5863]) ).
cnf(p5885,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| xa = xb ),
inference(superposition,[status(thm)],[p5865,p333]) ).
cnf(p6204,plain,
xa = xb,
inference(resolution,[status(thm)],[p5885,c64]) ).
cnf(p6215,plain,
( ~ sdtmndtasgtdt0(xc,xR,xc)
| ~ sdtmndtasgtdt0(xa,xR,xc) ),
inference(superposition,[status(thm)],[p6204,p69]) ).
cnf(p6575,plain,
~ sdtmndtasgtdt0(xc,xR,xc),
inference(resolution,[status(thm)],[p6215,c65]) ).
cnf(p6576,plain,
$false,
inference(resolution,[status(thm)],[p6575,p334]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM022+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.55 % Computer : n019.cluster.edu
% 0.08/0.55 % Model : x86_64 x86_64
% 0.08/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.55 % Memory : 8046.5625MB
% 0.08/0.55 % OS : Linux 6.8.0-71-generic
% 0.08/0.55 % CPULimit : 300
% 0.08/0.55 % WCLimit : 300
% 0.08/0.55 % DateTime : Fri Sep 25 07:49:35 UTC 2026
% 0.12/0.56 % CPUTime :
% 0.12/0.56 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 23.97/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.97/3.70 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------