%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL531+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 07:54:48 AM UTC 2026
% Result : Theorem 19.19s 3.07s
% Output : CNFRefutation 19.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 36 ( 20 unt; 0 def)
% Number of atoms : 59 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 17 ~; 14 |; 1 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_op_strict_implies,axiom,
'op$ustrict$uimplies' ).
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$utheorem'(implies(X0,implies(X1,and(X0,X1)))) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_implies_2,axiom,
'implies$u2' ).
fof(hilbert_and_3,axiom,
'and$u3' ).
fof(necessitation,axiom,
( necessitation
<=> ! [X0] :
( 'is$ua$utheorem'(X0)
=> 'is$ua$utheorem'(necessarily(X0)) ) ) ).
fof(axiom_m4,axiom,
( 'axiom$um4'
<=> ! [X0] : 'is$ua$utheorem'('strict$uimplies'(X0,and(X0,X0))) ) ).
fof(op_strict_implies,axiom,
( 'op$ustrict$uimplies'
=> ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).
fof(km5_necessitation,axiom,
necessitation ).
fof(s1_0_axiom_m4,conjecture,
'axiom$um4' ).
fof(negated_conjecture,negated_conjecture,
~ 'axiom$um4',
inference(negate_conjecture,[status(cth)],[s1_0_axiom_m4]) ).
cnf(c3,plain,
'op$ustrict$uimplies',
inference(clausification,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(c6,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c17,plain,
( 'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ 'implies$u2' ),
inference(clausification,[status(esa)],[implies_2]) ).
cnf(c25,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1))))
| ~ 'and$u3' ),
inference(clausification,[status(esa)],[and_3]) ).
cnf(c69,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c72,plain,
'implies$u2',
inference(clausification,[status(esa)],[hilbert_implies_2]) ).
cnf(c76,plain,
'and$u3',
inference(clausification,[status(esa)],[hilbert_and_3]) ).
cnf(c84,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0)
| ~ necessitation ),
inference(clausification,[status(esa)],[necessitation]) ).
cnf(c123,plain,
( ~ 'is$ua$utheorem'('strict$uimplies'(sK177,and(sK177,sK177)))
| 'axiom$um4' ),
inference(clausification,[status(esa)],[axiom_m4]) ).
cnf(c138,plain,
( 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1))
| ~ 'op$ustrict$uimplies' ),
inference(clausification,[status(esa)],[op_strict_implies]) ).
cnf(c141,plain,
necessitation,
inference(clausification,[status(esa)],[km5_necessitation]) ).
cnf(c145,plain,
~ 'axiom$um4',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'('strict$uimplies'(sK177,and(sK177,sK177))),
inference(resolution,[status(thm)],[c145,c123]) ).
cnf(d1,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c76,c25]) ).
cnf(d2,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c72,c17]) ).
cnf(d3,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c69,c6]) ).
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,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c141,c84]) ).
cnf(d7,plain,
'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d8,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
'is$ua$utheorem'('strict$uimplies'(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+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
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 22:45:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.19/3.07 % SZS status Theorem for theBenchmark.p
% 19.19/3.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------