%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COM016+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 : n013.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 01:03:30 PM UTC 2026
% Result : Theorem 20.09s 3.43s
% Output : Proof 20.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 10 unt; 2 def)
% Number of atoms : 206 ( 6 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 244 ( 95 ~; 114 |; 31 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn 22 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,definition,
! [W0,W1,W2] :
( ( aElement0(W2)
& aRewritingSystem0(W1)
& aElement0(W0) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mTCDef) ).
fof(f5_nnf,plain,
! [W0,W1,W2] :
( ( ( ( ! [W3] :
( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ? [W3] :
( sdtmndtplgtdt0(W3,W1,W2)
& aReductOfIn0(W3,W0,W1)
& aElement0(W3) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( ( ~ sdtmndtplgtdt0(W3,W1,W2)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aElement0(W3) )
& ~ aReductOfIn0(W2,W0,W1) )
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ( sdtmndtplgtdt0(sk0(W0,W1,W2),W1,W2)
& aReductOfIn0(sk0(W0,W1,W2),W0,W1)
& aElement0(sk0(W0,W1,W2)) )
| aReductOfIn0(W2,W0,W1)
| ~ sdtmndtplgtdt0(W0,W1,W2) ) )
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f5_nnf]) ).
cnf(c5,plain,
( aElement0(sk0(X0,X1,X2))
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_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(p2599,plain,
( aElement0(sk0(xa,X0,X1))
| aReductOfIn0(X1,xa,X0)
| ~ sdtmndtplgtdt0(xa,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c5,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(p2668,plain,
( aElement0(sk0(xa,xR,X0))
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p2599,c43]) ).
cnf(c47,plain,
aElement0(xb),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p2669,plain,
( aElement0(sk0(xa,xR,xb))
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolution,[status(thm)],[p2668,c47]) ).
fof(f18,hypothesis,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731_02) ).
fof(f18_nnf,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
( sdtmndtplgtdt0(xa,xR,xc)
& sdtmndtplgtdt0(xa,xR,xb) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c52,plain,
sdtmndtplgtdt0(xa,xR,xb),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p2701,plain,
( aElement0(sk0(xa,xR,xb))
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p2669,c52]) ).
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(c13,plain,
( ~ sdtmndtplgtdt0(X0,X1,X2)
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p2718,plain,
( ~ sdtmndtplgtdt0(sk0(xa,xR,xb),X0,X1)
| sdtmndtasgtdt0(sk0(xa,xR,xb),X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p2701,c13]) ).
cnf(p17310,plain,
( ~ sdtmndtplgtdt0(sk0(xa,xR,xb),xR,X0)
| sdtmndtasgtdt0(sk0(xa,xR,xb),xR,X0)
| ~ aElement0(X0)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p2718,c43]) ).
cnf(p17312,plain,
( ~ sdtmndtplgtdt0(sk0(xa,xR,xb),xR,xb)
| sdtmndtasgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p17310,c47]) ).
cnf(c7,plain,
( sdtmndtplgtdt0(sk0(X0,X1,X2),X1,X2)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p4621,plain,
( sdtmndtplgtdt0(sk0(xa,X0,X1),X0,X1)
| aReductOfIn0(X1,xa,X0)
| ~ sdtmndtplgtdt0(xa,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c7,c46]) ).
cnf(p4712,plain,
( sdtmndtplgtdt0(sk0(xa,xR,X0),xR,X0)
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p4621,c43]) ).
cnf(p4713,plain,
( sdtmndtplgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolution,[status(thm)],[p4712,c47]) ).
cnf(p4753,plain,
( sdtmndtplgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p4713,c52]) ).
cnf(p17380,plain,
( aReductOfIn0(xb,xa,xR)
| sdtmndtasgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p17312,p4753]) ).
cnf(p17381,plain,
( sdtmndtasgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR) ),
inference(factoring,[status(thm)],[p17380]) ).
cnf(c6,plain,
( aReductOfIn0(sk0(X0,X1,X2),X0,X1)
| aReductOfIn0(X2,X0,X1)
| ~ sdtmndtplgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p4372,plain,
( aReductOfIn0(sk0(xa,X0,X1),xa,X0)
| aReductOfIn0(X1,xa,X0)
| ~ sdtmndtplgtdt0(xa,X0,X1)
| ~ aElement0(X1)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[c6,c46]) ).
cnf(p4463,plain,
( aReductOfIn0(sk0(xa,xR,X0),xa,xR)
| aReductOfIn0(X0,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p4372,c43]) ).
cnf(p4464,plain,
( aReductOfIn0(sk0(xa,xR,xb),xa,xR)
| aReductOfIn0(xb,xa,xR)
| ~ sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolution,[status(thm)],[p4463,c47]) ).
cnf(p4507,plain,
( aReductOfIn0(sk0(xa,xR,xb),xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p4464,c52]) ).
fof(f19,conjecture,
? [W0] :
( sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f19_neg,negated_conjecture,
~ ? [W0] :
( sdtmndtasgtdt0(W0,xR,xb)
& aReductOfIn0(W0,xa,xR)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f19_nnf,plain,
! [W0] :
( ~ sdtmndtasgtdt0(W0,xR,xb)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f19_neg]) ).
fof(f19_sk,plain,
! [W0] :
( ~ sdtmndtasgtdt0(W0,xR,xb)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c54,plain,
( ~ sdtmndtasgtdt0(X0,xR,xb)
| ~ aReductOfIn0(X0,xa,xR)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p2702,plain,
( ~ sdtmndtasgtdt0(sk0(xa,xR,xb),xR,xb)
| ~ aReductOfIn0(sk0(xa,xR,xb),xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p2701,c54]) ).
cnf(p4508,plain,
( ~ sdtmndtasgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p4507,p2702]) ).
cnf(p4510,plain,
( ~ sdtmndtasgtdt0(sk0(xa,xR,xb),xR,xb)
| aReductOfIn0(xb,xa,xR) ),
inference(factoring,[status(thm)],[p4508]) ).
cnf(p17382,plain,
( aReductOfIn0(xb,xa,xR)
| aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[p17381,p4510]) ).
cnf(p17383,plain,
aReductOfIn0(xb,xa,xR),
inference(factoring,[status(thm)],[p17382]) ).
cnf(p56,plain,
( ~ sdtmndtasgtdt0(xb,xR,xb)
| ~ aReductOfIn0(xb,xa,xR) ),
inference(resolution,[status(thm)],[c47,c54]) ).
cnf(p17384,plain,
~ sdtmndtasgtdt0(xb,xR,xb),
inference(resolution,[status(thm)],[p17383,p56]) ).
cnf(c12,plain,
( X0 != X2
| sdtmndtasgtdt0(X0,X1,X2)
| ~ aElement0(X2)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p274,plain,
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aElement0(X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(equality_resolution,[status(thm)],[c12]) ).
cnf(p296,plain,
( sdtmndtasgtdt0(X0,X1,X0)
| ~ aRewritingSystem0(X1)
| ~ aElement0(X0) ),
inference(factoring,[status(thm)],[p274]) ).
cnf(p298,plain,
( sdtmndtasgtdt0(xb,X0,xb)
| ~ aRewritingSystem0(X0) ),
inference(resolution,[status(thm)],[p296,c47]) ).
cnf(p319,plain,
sdtmndtasgtdt0(xb,xR,xb),
inference(resolution,[status(thm)],[p298,c43]) ).
cnf(p17385,plain,
$false,
inference(resolution,[status(thm)],[p17384,p319]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM016+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 07:47:29 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 20.09/3.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.09/3.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------