%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 07:54:39 AM UTC 2026
% Result : Theorem 14.83s 7.46s
% Output : CNFRefutation 14.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 49 ( 27 unt; 0 def)
% Number of atoms : 77 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 25 ~; 18 |; 1 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(luka_op_or,axiom,
'op$uor' ).
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(implies_1,axiom,
( 'implies$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,X0))) ) ).
fof(implies_2,axiom,
( 'implies$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ) ).
fof(or_3,axiom,
( 'or$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ) ).
fof(cn3,axiom,
( cn3
<=> ! [X0] : 'is$ua$utheorem'(implies(implies(not(X0),X0),X0)) ) ).
fof(r1,axiom,
( r1
<=> ! [X0] : 'is$ua$utheorem'(implies(or(X0,X0),X0)) ) ).
fof(op_or,axiom,
( 'op$uor'
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ) ).
fof(op_implies_and,axiom,
( 'op$uimplies$uand'
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ) ).
fof(hilbert_op_implies_and,axiom,
'op$uimplies$uand' ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_implies_1,axiom,
'implies$u1' ).
fof(hilbert_implies_2,axiom,
'implies$u2' ).
fof(hilbert_or_3,axiom,
'or$u3' ).
fof(luka_cn3,conjecture,
cn3 ).
fof(negated_conjecture,negated_conjecture,
~ cn3,
inference(negate_conjecture,[status(cth)],[luka_cn3]) ).
cnf(c0,plain,
'op$uor',
inference(clausification,[status(esa)],[luka_op_or]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c12,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,X0)))
| ~ 'implies$u1' ),
inference(clausification,[status(esa)],[implies_1]) ).
cnf(c14,plain,
( 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ 'implies$u2' ),
inference(clausification,[status(esa)],[implies_2]) ).
cnf(c28,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ 'or$u3' ),
inference(clausification,[status(esa)],[or_3]) ).
cnf(c47,plain,
( ~ 'is$ua$utheorem'(implies(implies(not(sK87),sK87),sK87))
| cn3 ),
inference(clausification,[status(esa)],[cn3]) ).
cnf(c48,plain,
( 'is$ua$utheorem'(implies(or(X0,X0),X0))
| ~ r1 ),
inference(clausification,[status(esa)],[r1]) ).
cnf(c49,plain,
( ~ 'is$ua$utheorem'(implies(or(sK89,sK89),sK89))
| r1 ),
inference(clausification,[status(esa)],[r1]) ).
cnf(c58,plain,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ 'op$uor' ),
inference(clausification,[status(esa)],[op_or]) ).
cnf(c60,plain,
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ 'op$uimplies$uand' ),
inference(clausification,[status(esa)],[op_implies_and]) ).
cnf(c64,plain,
'op$uimplies$uand',
inference(clausification,[status(esa)],[hilbert_op_implies_and]) ).
cnf(c66,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c68,plain,
'implies$u1',
inference(clausification,[status(esa)],[hilbert_implies_1]) ).
cnf(c69,plain,
'implies$u2',
inference(clausification,[status(esa)],[hilbert_implies_2]) ).
cnf(c76,plain,
'or$u3',
inference(clausification,[status(esa)],[hilbert_or_3]) ).
cnf(c81,plain,
~ cn3,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c64,c60]) ).
cnf(d1,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c0,c58]) ).
cnf(d2,plain,
or(X0,X1) = implies(not(X0),X1),
inference(demodulation,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
~ 'is$ua$utheorem'(implies(implies(not(sK87),sK87),sK87)),
inference(resolution,[status(thm)],[c81,c47]) ).
cnf(d4,plain,
~ 'is$ua$utheorem'(implies(or(sK87,sK87),sK87)),
inference(demodulation,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
~ r1,
inference(resolution,[status(thm)],[d4,c48]) ).
cnf(d6,plain,
~ 'is$ua$utheorem'(implies(or(sK89,sK89),sK89)),
inference(resolution,[status(thm)],[d5,c49]) ).
cnf(d7,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d8,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c76,c28]) ).
cnf(d9,plain,
( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d7,d8]) ).
cnf(d10,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)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(implies(sK89,sK89))
| ~ 'is$ua$utheorem'(implies(sK89,sK89)) ),
inference(resolution,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[c68,c12]) ).
cnf(d13,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c69,c14]) ).
cnf(d14,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[d7,d13]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d14,d12]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n016.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 22:40:35 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.83/7.46 % SZS status Theorem for theBenchmark.p
% 14.83/7.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------