%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN073+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 : n003.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 02:29:30 PM UTC 2026
% Result : Theorem 5.20s 1.14s
% Output : Proof 5.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 22 unt; 0 def)
% Number of atoms : 109 ( 40 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 121 ( 57 ~; 42 |; 22 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 66 ( 3 sgn 40 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3a) ).
fof(f6_nnf,plain,
! [X3,X10] :
( X3 = X10
| ! [Y12] :
( ~ r2(X10,Y12)
| ! [Y13] :
( Y13 != Y12
| ~ r2(X3,Y13) ) ) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X3,Y13,Y12,X10] :
( X3 = X10
| ~ r2(X10,Y12)
| Y13 != Y12
| ~ r2(X3,Y13) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c26,plain,
( X0 = X1
| ~ r2(X1,X2)
| X3 != X2
| ~ r2(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p133,plain,
( X0 = X2
| ~ r2(X2,X1)
| ~ r2(X0,X1) ),
inference(equality_resolution,[status(thm)],[c26]) ).
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(f11,conjecture,
! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( Y2 != Y1
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',oneuneqtwo) ).
fof(f11_neg,negated_conjecture,
~ ! [Y1] :
( ! [Y3] :
( ~ r2(Y3,Y1)
| ! [Y5] :
( ~ r2(Y5,Y3)
| ~ r1(Y5) ) )
| ! [Y2] :
( Y2 != Y1
| ! [Y4] :
( ~ r2(Y4,Y2)
| ~ r1(Y4) ) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
? [Y1] :
( ? [Y3] :
( r2(Y3,Y1)
& ? [Y5] :
( r2(Y5,Y3)
& r1(Y5) ) )
& ? [Y2] :
( Y2 = Y1
& ? [Y4] :
( r2(Y4,Y2)
& r1(Y4) ) ) ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
( r2(sk23,sk20)
& r2(sk24,sk23)
& r1(sk24)
& sk21 = sk20
& r2(sk22,sk21)
& r1(sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24])],[f11_nnf]) ).
cnf(c39,plain,
r1(sk22),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p46,plain,
sk22 = sk0,
inference(resolution,[status(thm)],[c1,c39]) ).
cnf(c40,plain,
r2(sk22,sk21),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p48,plain,
r2(sk0,sk21),
inference(demodulation,[status(thm)],[p46,c40]) ).
cnf(p197,plain,
( sk0 = X0
| ~ r2(X0,sk20) ),
inference(resolution,[status(thm)],[p133,p48]) ).
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(p60,plain,
sk20 = sk1(sk0),
inference(resolution,[status(thm)],[c5,p48]) ).
cnf(c42,plain,
r1(sk24),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p50,plain,
sk24 = sk0,
inference(resolution,[status(thm)],[c1,c42]) ).
cnf(c43,plain,
r2(sk24,sk23),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p51,plain,
r2(sk0,sk23),
inference(demodulation,[status(thm)],[p50,c43]) ).
cnf(p61,plain,
sk23 = sk1(sk0),
inference(resolution,[status(thm)],[c5,p51]) ).
cnf(p68,plain,
sk23 = sk20,
inference(superposition,[status(thm)],[p60,p61]) ).
cnf(c44,plain,
r2(sk23,sk20),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p69,plain,
r2(sk20,sk20),
inference(demodulation,[status(thm)],[p68,c44]) ).
cnf(p204,plain,
sk0 = sk20,
inference(resolution,[status(thm)],[p197,p69]) ).
cnf(c41,plain,
sk21 = sk20,
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p205,plain,
sk20 = sk0,
inference(superposition,[status(thm)],[p204,c41]) ).
cnf(p45,plain,
r2(sk22,sk20),
inference(superposition,[status(thm)],[c41,c40]) ).
cnf(p49,plain,
r2(sk0,sk20),
inference(demodulation,[status(thm)],[p46,p45]) ).
cnf(p207,plain,
r2(sk0,sk0),
inference(demodulation,[status(thm)],[p205,p49]) ).
fof(f10,axiom,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7a) ).
fof(f10_nnf,plain,
! [X7,Y10] :
( ~ r2(X7,Y10)
| ! [Y20] :
( Y20 != Y10
| ~ r1(Y20) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [Y20,Y10,X7] :
( ~ r2(X7,Y10)
| Y20 != Y10
| ~ r1(Y20) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c38,plain,
( ~ r2(X0,X1)
| X2 != X1
| ~ r1(X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p159,plain,
( ~ r2(X1,X0)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c38]) ).
cnf(p47,plain,
r1(sk0),
inference(demodulation,[status(thm)],[p46,c39]) ).
cnf(p161,plain,
~ r2(X0,sk0),
inference(resolution,[status(thm)],[p159,p47]) ).
cnf(p226,plain,
$false,
inference(resolution,[status(thm)],[p207,p161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN073+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n003.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 : Thu Sep 24 05:57:51 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.20/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.20/1.14 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------