%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 07:54:40 AM UTC 2026
% Result : Theorem 12.53s 7.69s
% Output : CNFRefutation 12.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 12 ~; 9 |; 1 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 5 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(implies_2,axiom,
( 'implies$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ) ).
fof(and_3,axiom,
( 'and$u3'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))) ) ).
fof(kn1,axiom,
( kn1
<=> ! [X0] : 'is$ua$utheorem'(implies(X0,and(X0,X0))) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_implies_2,axiom,
'implies$u2' ).
fof(hilbert_and_3,axiom,
'and$u3' ).
fof(rosser_kn1,conjecture,
kn1 ).
fof(negated_conjecture,negated_conjecture,
~ kn1,
inference(negate_conjecture,[status(cth)],[rosser_kn1]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c14,plain,
( 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ 'implies$u2' ),
inference(clausification,[status(esa)],[implies_2]) ).
cnf(c22,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1))))
| ~ 'and$u3' ),
inference(clausification,[status(esa)],[and_3]) ).
cnf(c37,plain,
( ~ 'is$ua$utheorem'(implies(sK65,and(sK65,sK65)))
| kn1 ),
inference(clausification,[status(esa)],[kn1]) ).
cnf(c66,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c69,plain,
'implies$u2',
inference(clausification,[status(esa)],[hilbert_implies_2]) ).
cnf(c73,plain,
'and$u3',
inference(clausification,[status(esa)],[hilbert_and_3]) ).
cnf(c81,plain,
~ kn1,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(sK65,and(sK65,sK65))),
inference(resolution,[status(thm)],[c81,c37]) ).
cnf(d1,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c73,c22]) ).
cnf(d2,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c69,c14]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d4,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL459+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/6.01 % Computer : n002.cluster.edu
% 0.10/6.01 % Model : x86_64 x86_64
% 0.10/6.01 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/6.01 % Memory : 8046.5625MB
% 0.10/6.01 % OS : Linux 6.8.0-71-generic
% 0.10/6.01 % CPULimit : 300
% 0.10/6.01 % WCLimit : 300
% 0.10/6.01 % DateTime : Fri Sep 25 22:39:13 UTC 2026
% 0.10/6.01 % CPUTime :
% 0.10/6.01 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.53/7.69 % SZS status Theorem for theBenchmark.p
% 12.53/7.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------