%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN070+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 : n007.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 02:29:29 PM UTC 2026
% Result : Theorem 4.47s 1.18s
% Output : Proof 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 7 unt; 0 def)
% Number of atoms : 103 ( 25 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 128 ( 53 ~; 39 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 81 ( 4 sgn 24 !; 26 ?)
% 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(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]) ).
cnf(p120,plain,
sk13(X0) = sk0,
inference(resolution,[status(thm)],[c1,c27]) ).
cnf(c28,plain,
r3(X0,sk13(X0),sk12(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p122,plain,
r3(X0,sk0,sk12(X0)),
inference(demodulation,[status(thm)],[p120,c28]) ).
fof(f11,conjecture,
? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',onepluszeroeqone) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1] :
( ? [Y3] :
( ? [Y6] :
( r2(Y6,Y3)
& r1(Y6) )
& Y1 = Y3 )
& ? [Y2] :
( ? [Y5] :
( r2(Y5,Y2)
& r1(Y5) )
& ? [Y4] :
( r3(Y2,Y4,Y1)
& r1(Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1] :
( ! [Y3] :
( ! [Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6) )
| Y1 != Y3 )
| ! [Y2] :
( ! [Y5] :
( ~ r2(Y5,Y2)
| ~ r1(Y5) )
| ! [Y4] :
( ~ r3(Y2,Y4,Y1)
| ~ r1(Y4) ) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y4,Y2,Y1,Y5,Y3,Y6] :
( ~ r2(Y6,Y3)
| ~ r1(Y6)
| Y1 != Y3
| ~ r2(Y5,Y2)
| ~ r1(Y5)
| ~ r3(Y2,Y4,Y1)
| ~ r1(Y4) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X5,X4)
| ~ r1(X5)
| X0 != X4
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X1,X2,X0)
| ~ r1(X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p43,plain,
( ~ r1(X3)
| X2 != X1
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X1,X0,X2)
| ~ r1(X0) ),
inference(factoring,[status(thm)],[c39]) ).
cnf(p46,plain,
( X2 != X1
| ~ r2(X3,X1)
| ~ r1(X3)
| ~ r3(X1,X0,X2)
| ~ r1(X0) ),
inference(factoring,[status(thm)],[p43]) ).
cnf(p47,plain,
( X2 != X1
| ~ r2(X0,X1)
| ~ r3(X1,X0,X2)
| ~ r1(X0) ),
inference(factoring,[status(thm)],[p46]) ).
cnf(p59,plain,
( X2 != X0
| ~ r2(sk13(X1),X0)
| ~ r3(X0,sk13(X1),X2) ),
inference(resolution,[status(thm)],[c27,p47]) ).
cnf(p127,plain,
( X1 != X0
| ~ r2(sk0,X0)
| ~ r3(X0,sk0,X1) ),
inference(demodulation,[status(thm)],[p120,p59]) ).
cnf(p150,plain,
( X0 != X0
| ~ r2(sk0,X0) ),
inference(resolution,[status(thm)],[p122,p127]) ).
cnf(p161,plain,
~ r2(sk0,X0),
inference(equality_resolution,[status(thm)],[p150]) ).
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(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p162,plain,
$false,
inference(resolution,[status(thm)],[p161,c16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN070+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 : n007.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 05:51:23 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.47/1.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.47/1.18 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------