%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL456+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 : 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 07:54:40 AM UTC 2026
% Result : Theorem 10.09s 2.44s
% Output : CNFRefutation 10.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 31 ( 17 unt; 0 def)
% Number of atoms : 51 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 18 ~; 13 |; 1 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 4 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(or_1,axiom,
( 'or$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,or(X0,X1))) ) ).
fof(or_2,axiom,
( 'or$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X1,or(X0,X1))) ) ).
fof(or_3,axiom,
( 'or$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ) ).
fof(r3,axiom,
( r3
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_or_1,axiom,
'or$u1' ).
fof(hilbert_or_2,axiom,
'or$u2' ).
fof(hilbert_or_3,axiom,
'or$u3' ).
fof(principia_r3,conjecture,
r3 ).
fof(negated_conjecture,negated_conjecture,
~ r3,
inference(negate_conjecture,[status(cth)],[principia_r3]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c24,plain,
( 'is$ua$utheorem'(implies(X0,or(X0,X1)))
| ~ 'or$u1' ),
inference(clausification,[status(esa)],[or_1]) ).
cnf(c26,plain,
( 'is$ua$utheorem'(implies(X0,or(X1,X0)))
| ~ 'or$u2' ),
inference(clausification,[status(esa)],[or_2]) ).
cnf(c28,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ 'or$u3' ),
inference(clausification,[status(esa)],[or_3]) ).
cnf(c53,plain,
( ~ 'is$ua$utheorem'(implies(or(sK96,sK97),or(sK97,sK96)))
| r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c66,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c74,plain,
'or$u1',
inference(clausification,[status(esa)],[hilbert_or_1]) ).
cnf(c75,plain,
'or$u2',
inference(clausification,[status(esa)],[hilbert_or_2]) ).
cnf(c76,plain,
'or$u3',
inference(clausification,[status(esa)],[hilbert_or_3]) ).
cnf(c81,plain,
~ r3,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(or(sK96,sK97),or(sK97,sK96))),
inference(resolution,[status(thm)],[c81,c53]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d2,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c76,c28]) ).
cnf(d3,plain,
( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
( 'is$ua$utheorem'(implies(or(X0,X2),X1))
| ~ 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
( ~ 'is$ua$utheorem'(implies(sK96,or(sK97,sK96)))
| ~ 'is$ua$utheorem'(implies(sK97,or(sK97,sK96))) ),
inference(resolution,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
'is$ua$utheorem'(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c74,c24]) ).
cnf(d7,plain,
~ 'is$ua$utheorem'(implies(sK96,or(sK97,sK96))),
inference(resolution,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c75,c26]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL456+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
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 22:41:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.09/2.44 % SZS status Theorem for theBenchmark.p
% 10.09/2.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------