%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 08:18:56 AM UTC 2026
% Result : Theorem 11.53s 1.87s
% Output : CNFRefutation 11.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 19 unt; 0 def)
% Number of atoms : 81 ( 22 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 83 ( 36 ~; 26 |; 21 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 79 ( 16 sgn 5 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_1,axiom,
? [X0] :
! [X1] :
( ( X1 = X0
& r1(X1) )
| ( X1 != X0
& ~ r1(X1) ) ) ).
fof(axiom_2,axiom,
! [X0] :
? [X1] :
! [X2] :
( ( X2 = X1
& r2(X0,X2) )
| ( X2 != X1
& ~ r2(X0,X2) ) ) ).
fof(axiom_4a,axiom,
! [X0] :
? [X1] :
( X1 = X0
& ? [X2] :
( r3(X0,X2,X1)
& r1(X2) ) ) ).
fof(axiom_5a,axiom,
! [X0] :
? [X1] :
( ? [X3] :
( X1 = X3
& r1(X3) )
& ? [X2] :
( r4(X0,X2,X1)
& r1(X2) ) ) ).
fof(thereexistsanevennumber,conjecture,
? [X0,X1,X2] :
( ? [X7] :
( X7 = X0
& r3(X1,X2,X7) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& X3 = X0 ) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X7] :
( X7 = X0
& r3(X1,X2,X7) )
& ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r4(X4,X1,X3) )
& X3 = X0 ) ),
inference(negate_conjecture,[status(cth)],[thereexistsanevennumber]) ).
cnf(c1,plain,
( X0 = sK0
| ~ r1(X0) ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c2,plain,
( r1(X0)
| X0 != sK0 ),
inference(clausification,[status(esa)],[axiom_1]) ).
cnf(c6,plain,
( r2(X1,X0)
| X0 != sK3(X1) ),
inference(clausification,[status(esa)],[axiom_2]) ).
cnf(c27,plain,
r1(sK31(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c28,plain,
r3(X0,sK31(X0),sK30(X0)),
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c29,plain,
sK30(X0) = X0,
inference(clausification,[status(esa)],[axiom_4a]) ).
cnf(c30,plain,
r1(sK34(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c31,plain,
r4(X0,sK34(X0),sK33(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c32,plain,
r1(sK35(X0)),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c33,plain,
sK33(X0) = sK35(X0),
inference(clausification,[status(esa)],[axiom_5a]) ).
cnf(c39,plain,
( X7 != X6
| ~ r4(X5,X1,X7)
| X3 != X6
| ~ r2(X0,X4)
| ~ r2(X4,X5)
| ~ r3(X1,X2,X3)
| ~ r1(X0) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
r1(sK0),
inference(equality_resolution,[status(thm)],[c2]) ).
cnf(d1,plain,
r2(X0,sK3(X0)),
inference(equality_resolution,[status(thm)],[c6]) ).
cnf(d2,plain,
sK31(X0) = sK0,
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(d3,plain,
r3(X0,sK0,sK30(X0)),
inference(demodulation,[status(thm)],[c28,d2]) ).
cnf(d4,plain,
r3(X0,sK0,X0),
inference(demodulation,[status(thm)],[d3,c29]) ).
cnf(d5,plain,
( ~ r4(X4,X5,X0)
| ~ r3(X5,X6,X1)
| ~ r2(X3,X4)
| ~ r2(X2,X3)
| ~ r1(X2)
| X0 != X1 ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(d6,plain,
( ~ r4(X2,X3,X5)
| ~ r3(X3,X4,X5)
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[d5]) ).
cnf(d7,plain,
sK35(X0) = sK0,
inference(resolution,[status(thm)],[c32,c1]) ).
cnf(d8,plain,
sK33(X0) = sK0,
inference(demodulation,[status(thm)],[c33,d7]) ).
cnf(d9,plain,
sK34(X0) = sK0,
inference(resolution,[status(thm)],[c30,c1]) ).
cnf(d10,plain,
r4(X0,sK0,sK33(X0)),
inference(demodulation,[status(thm)],[c31,d9]) ).
cnf(d11,plain,
r4(X0,sK0,sK0),
inference(demodulation,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
( ~ r3(sK0,X3,sK0)
| ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d11,d6]) ).
cnf(d13,plain,
( ~ r2(X0,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d12,d4]) ).
cnf(d14,plain,
( ~ r2(sK3(X0),X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
~ r1(X0),
inference(resolution,[status(thm)],[d14,d1]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN076+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 04:33:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.53/1.87 % SZS status Theorem for theBenchmark.p
% 11.53/1.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------