%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN057+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 : n004.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 02:29:25 PM UTC 2026
% Result : Theorem 14.01s 2.43s
% Output : Proof 14.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 21 unt; 0 def)
% Number of atoms : 196 ( 44 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 248 ( 109 ~; 85 |; 54 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 175 ( 4 sgn 45 !; 36 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4a) ).
fof(f7_nnf,plain,
! [X4] :
? [Y9] :
( Y9 = X4
& ? [Y16] :
( r3(X4,Y16,Y9)
& r1(Y16) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X4] :
( sk12(X4) = X4
& r3(X4,sk13(X4),sk12(X4))
& r1(sk13(X4)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk12,sk13])],[f7_nnf]) ).
cnf(c27,plain,
r1(sk13(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
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]) ).
cnf(p206,plain,
sk13(X0) = sk0,
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(c28,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p207,plain,
r3(X0,sk0,sk12(X0)),
inference(demodulation,[status(thm)],[p206,c28]) ).
fof(f2,axiom,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
fof(f2_nnf,plain,
! [X13,X14] :
? [Y22] :
! [X15] :
( ( X15 = Y22
& r3(X13,X14,X15) )
| ( X15 != Y22
& ~ r3(X13,X14,X15) ) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X13,X14,X15] :
( ( X15 = sk2(X13,X14)
& r3(X13,X14,X15) )
| ( X15 != sk2(X13,X14)
& ~ r3(X13,X14,X15) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f2_nnf]) ).
cnf(c9,plain,
( X3 = sk2(X0,X1)
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p644,plain,
X0 = sk2(X0,sk0),
inference(resolution,[status(thm)],[p207,c9]) ).
fof(f4,axiom,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1a) ).
fof(f4_nnf,plain,
! [X1,X8] :
? [Y4] :
( ? [Y7] :
( r3(X1,X8,Y7)
& r2(Y7,Y4) )
& ? [Y5] :
( Y5 = Y4
& ? [Y15] :
( r3(X1,Y15,Y5)
& r2(X8,Y15) ) ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X8,X1] :
( r3(X1,X8,sk7(X1,X8))
& r2(sk7(X1,X8),sk4(X1,X8))
& sk5(X1,X8) = sk4(X1,X8)
& r3(X1,sk6(X1,X8),sk5(X1,X8))
& r2(X8,sk6(X1,X8)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4,sk5,sk6,sk7])],[f4_nnf]) ).
cnf(c20,plain,
r3(X0,X1,sk7(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p172,plain,
sk7(X0,X1) = sk2(X0,X1),
inference(resolution,[status(thm)],[c20,c9]) ).
cnf(p1517,plain,
sk2(X0,sk0) = X0,
inference(superposition,[status(thm)],[p644,p172]) ).
cnf(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
fof(f1_nnf,plain,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X11,X12] :
( ( X12 = sk1(X11)
& r2(X11,X12) )
| ( X12 != sk1(X11)
& ~ r2(X11,X12) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c5,plain,
( X2 = sk1(X0)
| ~ r2(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p147,plain,
sk6(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c16,c5]) ).
cnf(c17,plain,
r3(X0,sk6(X0,X1),sk5(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p148,plain,
r3(X0,sk1(X1),sk5(X0,X1)),
inference(demodulation,[status(thm)],[p147,c17]) ).
cnf(p498,plain,
sk4(X0,X1) = sk2(X0,sk1(X1)),
inference(resolution,[status(thm)],[p148,c9]) ).
cnf(p1176,plain,
sk2(X0,sk1(X1)) = sk4(X0,X1),
inference(superposition,[status(thm)],[p498,p172]) ).
fof(f11,conjecture,
? [Y1] :
( ? [Y5] :
( ? [Y7] :
( ? [Y9] :
( r2(Y9,Y7)
& r1(Y9) )
& r2(Y7,Y5) )
& r3(Y5,Y5,Y1) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y6] :
( ? [Y8] :
( r2(Y8,Y6)
& r1(Y8) )
& r2(Y6,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',twoplustwoeqfour) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y5] :
( ? [Y7] :
( ? [Y9] :
( r2(Y9,Y7)
& r1(Y9) )
& r2(Y7,Y5) )
& r3(Y5,Y5,Y1) )
& ? [Y2] :
( ? [Y3] :
( ? [Y4] :
( ? [Y6] :
( ? [Y8] :
( r2(Y8,Y6)
& r1(Y8) )
& r2(Y6,Y4) )
& r2(Y4,Y3) )
& r2(Y3,Y2) )
& Y1 = Y2 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1] :
( ! [Y5] :
( ! [Y7] :
( ! [Y9] :
( ~ r2(Y9,Y7)
| ~ r1(Y9) )
| ~ r2(Y7,Y5) )
| ~ r3(Y5,Y5,Y1) )
| ! [Y2] :
( ! [Y3] :
( ! [Y4] :
( ! [Y6] :
( ! [Y8] :
( ~ r2(Y8,Y6)
| ~ r1(Y8) )
| ~ r2(Y6,Y4) )
| ~ r2(Y4,Y3) )
| ~ r2(Y3,Y2) )
| Y1 != Y2 ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y1,Y2,Y3,Y4,Y6,Y8,Y5,Y7,Y9] :
( ~ r2(Y9,Y7)
| ~ r1(Y9)
| ~ r2(Y7,Y5)
| ~ r3(Y5,Y5,Y1)
| ~ r2(Y8,Y6)
| ~ r1(Y8)
| ~ r2(Y6,Y4)
| ~ r2(Y4,Y3)
| ~ r2(Y3,Y2)
| Y1 != Y2 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X8,X7)
| ~ r1(X8)
| ~ r2(X7,X6)
| ~ r3(X6,X6,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p50,plain,
( ~ r2(X6,X4)
| ~ r1(X6)
| ~ r3(X3,X3,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[c39]) ).
cnf(p443,plain,
( ~ r1(X5)
| ~ r3(X3,X3,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[p50]) ).
cnf(p949,plain,
( ~ r3(X3,X3,X0)
| ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r2(X3,X2)
| ~ r2(X2,X1)
| X0 != X1 ),
inference(factoring,[status(thm)],[p443]) ).
cnf(p950,plain,
( ~ r3(X2,X2,X1)
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(equality_resolution,[status(thm)],[p949]) ).
cnf(c19,plain,
r2(sk7(X0,X1),sk4(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p173,plain,
r2(sk2(X0,X1),sk4(X0,X1)),
inference(demodulation,[status(thm)],[p172,c19]) ).
cnf(p958,plain,
( ~ r3(X0,X0,sk4(X1,X2))
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X0)
| ~ r2(X0,sk2(X1,X2)) ),
inference(resolution,[status(thm)],[p950,p173]) ).
cnf(p2999,plain,
( ~ r3(X0,X0,sk4(X1,sk1(X2)))
| ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X0)
| ~ r2(X0,sk4(X1,X2)) ),
inference(superposition,[status(thm)],[p1176,p958]) ).
cnf(p3049,plain,
( ~ r3(sk2(X1,X2),sk2(X1,X2),sk4(X1,sk1(X2)))
| ~ r2(X3,X0)
| ~ r1(X3)
| ~ r2(X0,sk2(X1,X2)) ),
inference(resolution,[status(thm)],[p2999,p173]) ).
cnf(p3607,plain,
( ~ r3(X1,X1,sk4(X1,sk1(sk0)))
| ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(superposition,[status(thm)],[p1517,p3049]) ).
cnf(c6,plain,
( r2(X0,X2)
| X2 != sk1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p99,plain,
r2(X0,sk1(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(p3666,plain,
( ~ r3(sk1(X1),sk1(X1),sk4(sk1(X1),sk1(sk0)))
| ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p3607,p99]) ).
cnf(c2,plain,
( r1(X1)
| X1 != sk0 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p86,plain,
r1(sk0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p3670,plain,
( ~ r3(sk1(X0),sk1(X0),sk4(sk1(X0),sk1(sk0)))
| ~ r2(sk0,X0) ),
inference(resolution,[status(thm)],[p3666,p86]) ).
cnf(p3671,plain,
~ r3(sk1(sk1(sk0)),sk1(sk1(sk0)),sk4(sk1(sk1(sk0)),sk1(sk0))),
inference(resolution,[status(thm)],[p3670,p99]) ).
cnf(c8,plain,
( r3(X0,X1,X3)
| ~ r3(X0,X1,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p497,plain,
r3(X0,sk1(X1),sk4(X0,X1)),
inference(resolution,[status(thm)],[p148,c8]) ).
cnf(p3675,plain,
$false,
inference(resolution,[status(thm)],[p3671,p497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN057+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 05:50:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.01/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.01/2.43 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------