%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:29:26 PM UTC 2026
% Result : Theorem 4.42s 1.08s
% Output : Proof 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 5 unt; 0 def)
% Number of atoms : 103 ( 22 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 134 ( 57 ~; 41 |; 36 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 95 ( 9 sgn 31 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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]) ).
fof(f11,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& r3(Y2,Y4,Y3) )
& Y3 = Y1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greq4) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( ? [Y7] :
( ? [Y8] :
( r2(Y8,Y7)
& r1(Y8) )
& r2(Y7,Y6) )
& r2(Y6,Y5) )
& r2(Y5,Y4) )
& r3(Y2,Y4,Y3) )
& Y3 = Y1 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ! [Y7] :
( ! [Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8) )
| ~ r2(Y7,Y6) )
| ~ r2(Y6,Y5) )
| ~ r2(Y5,Y4) )
| ~ r3(Y2,Y4,Y3) )
| Y3 != Y1 ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y3,Y1,Y2,Y4,Y5,Y6,Y7,Y8] :
( ~ r2(Y8,Y7)
| ~ r1(Y8)
| ~ r2(Y7,Y6)
| ~ r2(Y6,Y5)
| ~ r2(Y5,Y4)
| ~ r3(Y2,Y4,Y3)
| Y3 != Y1 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X7,X6)
| ~ r1(X7)
| ~ r2(X6,X5)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r3(X1,X3,X2)
| X2 != X0 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p46,plain,
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ r2(X5,X4)
| ~ r2(X4,X3)
| ~ r2(X3,X1)
| ~ r3(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(p96,plain,
( ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X2)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[c20,p46]) ).
fof(f1,axiom,
! [X11] :
? [Y21] :
! [X12] :
( ( X12 = Y21
& r2(X11,X12) )
| ( X12 != Y21
& ~ r2(X11,X12) ) ),
file('/export/starexec/sandbox2/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(c6,plain,
( r2(X0,X2)
| X2 != sk1(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p68,plain,
r2(X0,sk1(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(p105,plain,
( ~ r2(X3,X2)
| ~ r1(X3)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[p96,p68]) ).
cnf(p106,plain,
( ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[p105,p68]) ).
cnf(p107,plain,
( ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p106,p68]) ).
fof(f0,axiom,
? [Y24] :
! [X19] :
( ( X19 = Y24
& r1(X19) )
| ( X19 != Y24
& ~ r1(X19) ) ),
file('/export/starexec/sandbox2/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(c2,plain,
( r1(X1)
| X1 != sk0 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p56,plain,
r1(sk0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(p108,plain,
~ r2(sk0,X0),
inference(resolution,[status(thm)],[p107,p56]) ).
cnf(p109,plain,
$false,
inference(resolution,[status(thm)],[p108,p68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n020.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 05:52:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.42/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.42/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------