%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN081+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 : n017.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 08:18:57 AM UTC 2026
% Result : Theorem 8.04s 3.17s
% Output : CNFRefutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 59 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 65 ( 29 ~; 20 |; 16 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 56 ( 10 sgn 4 !; 18 ?)
% 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(xplusyeqthree,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r2(X4,X3) )
& X2 = X3 )
& r3(X0,X1,X2) ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( r2(X6,X5)
& r1(X6) )
& r2(X5,X4) )
& r2(X4,X3) )
& X2 = X3 )
& r3(X0,X1,X2) ),
inference(negate_conjecture,[status(cth)],[xplusyeqthree]) ).
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(c39,plain,
( X6 != X2
| ~ r3(X4,X5,X6)
| ~ r2(X0,X3)
| ~ r2(X3,X1)
| ~ r2(X1,X2)
| ~ 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,
( ~ r3(X4,X5,X3)
| ~ r2(X2,X3)
| ~ r2(X1,X2)
| ~ r2(X0,X1)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(d3,plain,
sK31(X0) = sK0,
inference(resolution,[status(thm)],[c27,c1]) ).
cnf(d4,plain,
r3(X0,sK0,sK30(X0)),
inference(demodulation,[status(thm)],[c28,d3]) ).
cnf(d5,plain,
r3(X0,sK0,X0),
inference(demodulation,[status(thm)],[d4,c29]) ).
cnf(d6,plain,
( ~ r2(X0,X3)
| ~ r2(X3,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
( ~ r2(X1,X2)
| ~ r2(sK3(X0),X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ~ r2(sK3(sK3(X0)),X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
~ r1(X0),
inference(resolution,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUN081+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.40 % Computer : n017.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.40 % CPULimit : 300
% 0.15/0.40 % WCLimit : 300
% 0.15/0.40 % DateTime : Sat Sep 26 04:27:18 UTC 2026
% 0.18/0.40 % CPUTime :
% 0.18/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.04/3.17 % SZS status Theorem for theBenchmark.p
% 8.04/3.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------