%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : NUN060+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 : n001.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 08:18:53 AM UTC 2026
% Result : Theorem 11.71s 3.09s
% Output : CNFRefutation 11.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 64 ( 10 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 80 ( 35 ~; 25 |; 20 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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; 0-2 aty)
% Number of variables : 66 ( 11 sgn 5 !; 22 ?)
% 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_1a,axiom,
! [X0,X1] :
? [X2] :
( ? [X5] :
( r3(X0,X1,X5)
& r2(X5,X2) )
& ? [X3] :
( X3 = X2
& ? [X4] :
( r3(X0,X4,X3)
& r2(X1,X4) ) ) ) ).
fof(greq4,conjecture,
? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& r2(X5,X4) )
& r2(X4,X3) )
& r3(X1,X3,X2) )
& X2 = X0 ) ).
fof(negated_conjecture,negated_conjecture,
~ ? [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( r2(X7,X6)
& r1(X7) )
& r2(X6,X5) )
& r2(X5,X4) )
& r2(X4,X3) )
& r3(X1,X3,X2) )
& X2 = X0 ),
inference(negate_conjecture,[status(cth)],[greq4]) ).
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(c16,plain,
r2(X0,sK17(X1,X0)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c17,plain,
r3(X0,sK17(X0,X1),sK16(X0,X1)),
inference(clausification,[status(esa)],[axiom_1a]) ).
cnf(c39,plain,
( ~ r2(X4,X2)
| X6 != X7
| ~ r1(X3)
| ~ r3(X5,X1,X6)
| ~ r2(X3,X4)
| ~ r2(X2,X0)
| ~ r2(X0,X1) ),
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(X5,X2,X6)
| ~ r2(X3,X4)
| ~ r2(X4,X1)
| ~ r2(X0,X3)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(equality_resolution,[status(thm)],[c39]) ).
cnf(d3,plain,
( ~ r2(X0,X3)
| ~ r2(X2,sK17(X4,X5))
| ~ r2(X3,X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[c17,d2]) ).
cnf(d4,plain,
( ~ r2(X0,X1)
| ~ r2(X2,X3)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d3,c16]) ).
cnf(d5,plain,
( ~ r2(sK3(X0),X1)
| ~ r2(X1,X2)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ r2(sK3(sK3(X0)),X1)
| ~ r1(X0) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
~ r1(X0),
inference(resolution,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
$false,
inference(resolution,[status(thm)],[d7,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUN060+2 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n001.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Sat Sep 26 04:34:13 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.47 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.71/3.09 % SZS status Theorem for theBenchmark.p
% 11.71/3.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------