%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 02:29:33 PM UTC 2026
% Result : Theorem 3.59s 0.92s
% Output : Proof 3.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 11 unt; 0 def)
% Number of atoms : 62 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 65 ( 28 ~; 16 |; 21 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 43 ( 5 sgn 12 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
fof(f0_nnf,plain,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X19] :
( ( X19 = sk0
& r1(X19) )
| ( X19 != sk0
& ~ r1(X19) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( X1 = sk0
| ~ r1(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f8,axiom,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5a) ).
fof(f8_nnf,plain,
! [X5] :
? [Y8] :
( ? [Y18] :
( Y8 = Y18
& r1(Y18) )
& ? [Y17] :
( r4(X5,Y17,Y8)
& r1(Y17) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X5] :
( sk14(X5) = sk16(X5)
& r1(sk16(X5))
& r4(X5,sk15(X5),sk14(X5))
& r1(sk15(X5)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk14,sk15,sk16])],[f8_nnf]) ).
cnf(c30,plain,
r1(sk15(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p80,plain,
sk15(X0) = sk0,
inference(resolution,[status(thm)],[c1,c30]) ).
cnf(c31,plain,
r4(X0,sk15(X0),sk14(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p81,plain,
r4(X0,sk0,sk14(X0)),
inference(demodulation,[status(thm)],[p80,c31]) ).
cnf(c32,plain,
r1(sk16(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p82,plain,
sk16(X0) = sk0,
inference(resolution,[status(thm)],[c1,c32]) ).
cnf(c33,plain,
sk14(X0) = sk16(X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
fof(f11,conjecture,
? [Y1] :
( ? [Y3] :
( Y1 = Y3
& r1(Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zerotimeszeroeqzero) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( Y1 = Y3
& r1(Y3) )
& ? [Y2] :
( r4(Y2,Y2,Y1)
& r1(Y2) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1] :
( ! [Y3] :
( Y1 != Y3
| ~ r1(Y3) )
| ! [Y2] :
( ~ r4(Y2,Y2,Y1)
| ~ r1(Y2) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y2,Y1,Y3] :
( Y1 != Y3
| ~ r1(Y3)
| ~ r4(Y2,Y2,Y1)
| ~ r1(Y2) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( X0 != X2
| ~ r1(X2)
| ~ r4(X1,X1,X0)
| ~ r1(X1) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p41,plain,
( ~ r1(X1)
| ~ r4(X0,X0,X1)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(p42,plain,
( ~ r4(X0,X0,X0)
| ~ r1(X0) ),
inference(factoring,[status(thm)],[p41]) ).
cnf(p53,plain,
~ r4(sk16(X0),sk16(X0),sk16(X0)),
inference(resolution,[status(thm)],[c32,p42]) ).
cnf(p58,plain,
~ r4(sk16(X0),sk16(X0),sk14(X0)),
inference(superposition,[status(thm)],[c33,p53]) ).
cnf(p86,plain,
~ r4(sk0,sk0,sk14(X0)),
inference(demodulation,[status(thm)],[p82,p58]) ).
cnf(p98,plain,
$false,
inference(resolution,[status(thm)],[p81,p86]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN087+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n009.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 : Thu Sep 24 06:00:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.59/0.92 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/0.92 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------