%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL542+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 07:54:49 AM UTC 2026
% Result : Theorem 15.39s 22.60s
% Output : CNFRefutation 15.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 36 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 7 |; 0 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 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 : 21 ( 3 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_op_strict_implies,axiom,
'op$ustrict$uimplies' ).
fof(and_1,axiom,
( 'and$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(and(X0,X1),X0)) ) ).
fof(hilbert_and_1,axiom,
'and$u1' ).
fof(necessitation,axiom,
( necessitation
<=> ! [X0] :
( 'is$ua$utheorem'(X0)
=> 'is$ua$utheorem'(necessarily(X0)) ) ) ).
fof(axiom_m2,axiom,
( 'axiom$um2'
<=> ! [X0,X1] : 'is$ua$utheorem'('strict$uimplies'(and(X0,X1),X0)) ) ).
fof(op_strict_implies,axiom,
( 'op$ustrict$uimplies'
=> ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).
fof(km4b_necessitation,axiom,
necessitation ).
fof(s1_0_axiom_m2,conjecture,
'axiom$um2' ).
fof(negated_conjecture,negated_conjecture,
~ 'axiom$um2',
inference(negate_conjecture,[status(cth)],[s1_0_axiom_m2]) ).
cnf(c3,plain,
'op$ustrict$uimplies',
inference(clausification,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(c21,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X0))
| ~ 'and$u1' ),
inference(clausification,[status(esa)],[and_1]) ).
cnf(c74,plain,
'and$u1',
inference(clausification,[status(esa)],[hilbert_and_1]) ).
cnf(c84,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0)
| ~ necessitation ),
inference(clausification,[status(esa)],[necessitation]) ).
cnf(c119,plain,
( ~ 'is$ua$utheorem'('strict$uimplies'(and(sK168,sK169),sK168))
| 'axiom$um2' ),
inference(clausification,[status(esa)],[axiom_m2]) ).
cnf(c138,plain,
( 'strict$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)],[km4b_necessitation]) ).
cnf(c146,plain,
~ 'axiom$um2',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'('strict$uimplies'(and(sK168,sK169),sK168)),
inference(resolution,[status(thm)],[c146,c119]) ).
cnf(d1,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c74,c21]) ).
cnf(d2,plain,
( 'is$ua$utheorem'(necessarily(X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c141,c84]) ).
cnf(d3,plain,
'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(implies(X0,X1))
| 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
'is$ua$utheorem'('strict$uimplies'(and(X0,X1),X0)),
inference(resolution,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[d5,d0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+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
% 0.10/20.39 % Computer : n002.cluster.edu
% 0.10/20.39 % Model : x86_64 x86_64
% 0.10/20.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/20.39 % Memory : 8046.5625MB
% 0.10/20.39 % OS : Linux 6.8.0-71-generic
% 0.10/20.39 % CPULimit : 300
% 0.10/20.39 % WCLimit : 300
% 0.10/20.39 % DateTime : Fri Sep 25 22:45:55 UTC 2026
% 0.10/20.39 % CPUTime :
% 0.10/20.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.39/22.60 % SZS status Theorem for theBenchmark.p
% 15.39/22.60 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------