%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL469+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 : 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 07:54:42 AM UTC 2026
% Result : Theorem 14.96s 4.02s
% Output : CNFRefutation 14.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 16 unt; 0 def)
% Number of atoms : 32 ( 7 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 7 ~; 4 |; 0 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 24 ( 3 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hilbert_op_or,axiom,
'op$uor' ).
fof(hilbert_op_implies_and,axiom,
'op$uimplies$uand' ).
fof(or_1,axiom,
( 'or$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,or(X0,X1))) ) ).
fof(cn2,axiom,
( cn2
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(not(X0),X1))) ) ).
fof(op_or,axiom,
( 'op$uor'
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ) ).
fof(op_implies_and,axiom,
( 'op$uimplies$uand'
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ) ).
fof(luka_cn2,axiom,
cn2 ).
fof(hilbert_or_1,conjecture,
'or$u1' ).
fof(negated_conjecture,negated_conjecture,
~ 'or$u1',
inference(negate_conjecture,[status(cth)],[hilbert_or_1]) ).
cnf(c0,plain,
'op$uor',
inference(clausification,[status(esa)],[hilbert_op_or]) ).
cnf(c1,plain,
'op$uimplies$uand',
inference(clausification,[status(esa)],[hilbert_op_implies_and]) ).
cnf(c25,plain,
( ~ 'is$ua$utheorem'(implies(sK40,or(sK40,sK41)))
| 'or$u1' ),
inference(clausification,[status(esa)],[or_1]) ).
cnf(c44,plain,
( 'is$ua$utheorem'(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(clausification,[status(esa)],[cn2]) ).
cnf(c58,plain,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ 'op$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(c68,plain,
cn2,
inference(clausification,[status(esa)],[luka_cn2]) ).
cnf(c71,plain,
~ 'or$u1',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(sK40,or(sK40,sK41))),
inference(resolution,[status(thm)],[c71,c25]) ).
cnf(d1,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c1,c60]) ).
cnf(d2,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c0,c58]) ).
cnf(d3,plain,
or(X0,X1) = implies(not(X0),X1),
inference(demodulation,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'is$ua$utheorem'(implies(X0,implies(not(X0),X1))),
inference(resolution,[status(thm)],[c68,c44]) ).
cnf(d5,plain,
'is$ua$utheorem'(implies(X0,or(X0,X1))),
inference(demodulation,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL469+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n002.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Fri Sep 25 22:39:35 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.96/4.02 % SZS status Theorem for theBenchmark.p
% 14.96/4.02 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------