%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUN080+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 : n013.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 02:29:31 PM UTC 2026
% Result : Theorem 4.52s 1.16s
% Output : Proof 4.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 11 unt; 0 def)
% Number of atoms : 100 ( 28 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 107 ( 40 ~; 26 |; 41 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 102 ( 11 sgn 36 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,conjecture,
? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& Y3 = Y2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xplustwoeqy) ).
fof(f11_neg,negated_conjecture,
~ ? [Y1,Y2,Y3] :
( ? [Y4] :
( ? [Y5] :
( ? [Y6] :
( r2(Y6,Y5)
& r1(Y6) )
& r2(Y5,Y4) )
& r3(Y1,Y4,Y3) )
& Y3 = Y2 ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f11_nnf,plain,
! [Y1,Y2,Y3] :
( ! [Y4] :
( ! [Y5] :
( ! [Y6] :
( ~ r2(Y6,Y5)
| ~ r1(Y6) )
| ~ r2(Y5,Y4) )
| ~ r3(Y1,Y4,Y3) )
| Y3 != Y2 ),
inference(nnf_transformation,[status(thm)],[f11_neg]) ).
fof(f11_sk,plain,
! [Y3,Y2,Y1,Y4,Y5,Y6] :
( ~ r2(Y6,Y5)
| ~ r1(Y6)
| ~ r2(Y5,Y4)
| ~ r3(Y1,Y4,Y3)
| Y3 != Y2 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c39,plain,
( ~ r2(X5,X4)
| ~ r1(X5)
| ~ r2(X4,X3)
| ~ r3(X0,X3,X2)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p134,plain,
( ~ r2(X4,X3)
| ~ r1(X4)
| ~ r2(X3,X1)
| ~ r3(X0,X1,X2) ),
inference(equality_resolution,[status(thm)],[c39]) ).
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]) ).
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(p65,plain,
sk7(X0,X1) = sk2(X0,X1),
inference(resolution,[status(thm)],[c9,c20]) ).
cnf(p67,plain,
r3(X0,X1,sk2(X0,X1)),
inference(demodulation,[status(thm)],[p65,c20]) ).
cnf(p340,plain,
( ~ r2(X2,X0)
| ~ r1(X2)
| ~ r2(X0,X1) ),
inference(resolution,[status(thm)],[p134,p67]) ).
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(c16,plain,
r2(X1,sk6(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p50,plain,
sk6(X0,X1) = sk1(X1),
inference(resolution,[status(thm)],[c5,c16]) ).
cnf(p51,plain,
r2(X0,sk1(X0)),
inference(demodulation,[status(thm)],[p50,c16]) ).
cnf(p423,plain,
( ~ r2(X0,X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[p340,p51]) ).
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(c33,plain,
sk14(X0) = sk16(X0),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(c32,plain,
r1(sk16(X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p40,plain,
r1(sk14(X0)),
inference(superposition,[status(thm)],[c33,c32]) ).
cnf(p425,plain,
~ r2(sk0,X0),
inference(resolution,[status(thm)],[p423,p40]) ).
cnf(p426,plain,
$false,
inference(resolution,[status(thm)],[p425,p51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUN080+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.32 % Computer : n013.cluster.edu
% 0.08/0.32 % Model : x86_64 x86_64
% 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.32 % Memory : 8046.5625MB
% 0.08/0.32 % OS : Linux 6.8.0-71-generic
% 0.08/0.32 % CPULimit : 300
% 0.08/0.32 % WCLimit : 300
% 0.08/0.32 % DateTime : Thu Sep 24 05:57:27 UTC 2026
% 0.08/0.32 % CPUTime :
% 0.08/0.32 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.52/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.52/1.16 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------