%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL526+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 : n005.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 07:54:47 AM UTC 2026
% Result : Theorem 17.76s 2.89s
% Output : CNFRefutation 17.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of formulae : 81 ( 40 unt; 0 def)
% Number of atoms : 138 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 44 ~; 40 |; 2 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 74 ( 6 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_op_strict_implies,axiom,
'op$ustrict$uimplies' ).
fof(s1_0_op_equiv,axiom,
'op$uequiv' ).
fof(s1_0_op_strict_equiv,axiom,
'op$ustrict$uequiv' ).
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(substitution_of_equivalents,axiom,
( 'substitution$uof$uequivalents'
<=> ! [X0,X1] :
( 'is$ua$utheorem'(equiv(X0,X1))
=> X0 = X1 ) ) ).
fof(and_1,axiom,
( 'and$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(and(X0,X1),X0)) ) ).
fof(and_2,axiom,
( 'and$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(and(X0,X1),X1)) ) ).
fof(and_3,axiom,
( 'and$u3'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))) ) ).
fof(op_equiv,axiom,
( 'op$uequiv'
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_and_1,axiom,
'and$u1' ).
fof(hilbert_and_2,axiom,
'and$u2' ).
fof(hilbert_and_3,axiom,
'and$u3' ).
fof(use_substitution_of_equivalents,axiom,
'substitution$uof$uequivalents' ).
fof(adjunction,axiom,
( adjunction
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(X1)
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(and(X0,X1)) ) ) ).
fof(substitution_strict_equiv,axiom,
( 'substitution$ustrict$uequiv'
<=> ! [X0,X1] :
( 'is$ua$utheorem'('strict$uequiv'(X0,X1))
=> X0 = X1 ) ) ).
fof(axiom_M,axiom,
( 'axiom$uM'
<=> ! [X0] : 'is$ua$utheorem'(implies(necessarily(X0),X0)) ) ).
fof(op_strict_implies,axiom,
( 'op$ustrict$uimplies'
=> ! [X0,X1] : 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)) ) ).
fof(op_strict_equiv,axiom,
( 'op$ustrict$uequiv'
=> ! [X0,X1] : 'strict$uequiv'(X0,X1) = and('strict$uimplies'(X0,X1),'strict$uimplies'(X1,X0)) ) ).
fof(km5_axiom_M,axiom,
'axiom$uM' ).
fof(s1_0_substitution_strict_equiv,conjecture,
'substitution$ustrict$uequiv' ).
fof(negated_conjecture,negated_conjecture,
~ 'substitution$ustrict$uequiv',
inference(negate_conjecture,[status(cth)],[s1_0_substitution_strict_equiv]) ).
cnf(c3,plain,
'op$ustrict$uimplies',
inference(clausification,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(c4,plain,
'op$uequiv',
inference(clausification,[status(esa)],[s1_0_op_equiv]) ).
cnf(c5,plain,
'op$ustrict$uequiv',
inference(clausification,[status(esa)],[s1_0_op_strict_equiv]) ).
cnf(c6,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c10,plain,
( X0 = X1
| ~ 'is$ua$utheorem'(equiv(X0,X1))
| ~ 'substitution$uof$uequivalents' ),
inference(clausification,[status(esa)],[substitution_of_equivalents]) ).
cnf(c21,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X0))
| ~ 'and$u1' ),
inference(clausification,[status(esa)],[and_1]) ).
cnf(c23,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X1))
| ~ 'and$u2' ),
inference(clausification,[status(esa)],[and_2]) ).
cnf(c25,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1))))
| ~ 'and$u3' ),
inference(clausification,[status(esa)],[and_3]) ).
cnf(c65,plain,
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ 'op$uequiv' ),
inference(clausification,[status(esa)],[op_equiv]) ).
cnf(c69,plain,
'modus$uponens',
inference(clausification,[status(esa)],[hilbert_modus_ponens]) ).
cnf(c74,plain,
'and$u1',
inference(clausification,[status(esa)],[hilbert_and_1]) ).
cnf(c75,plain,
'and$u2',
inference(clausification,[status(esa)],[hilbert_and_2]) ).
cnf(c76,plain,
'and$u3',
inference(clausification,[status(esa)],[hilbert_and_3]) ).
cnf(c83,plain,
'substitution$uof$uequivalents',
inference(clausification,[status(esa)],[use_substitution_of_equivalents]) ).
cnf(c91,plain,
( 'is$ua$utheorem'(and(X0,X1))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0)
| ~ adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c92,plain,
( 'is$ua$utheorem'(sK128)
| adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c93,plain,
( 'is$ua$utheorem'(sK129)
| adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c94,plain,
( ~ 'is$ua$utheorem'(and(sK128,sK129))
| adjunction ),
inference(clausification,[status(esa)],[adjunction]) ).
cnf(c96,plain,
( 'is$ua$utheorem'('strict$uequiv'(sK132,sK133))
| 'substitution$ustrict$uequiv' ),
inference(clausification,[status(esa)],[substitution_strict_equiv]) ).
cnf(c97,plain,
( sK132 != sK133
| 'substitution$ustrict$uequiv' ),
inference(clausification,[status(esa)],[substitution_strict_equiv]) ).
cnf(c100,plain,
( 'is$ua$utheorem'(implies(necessarily(X0),X0))
| ~ 'axiom$uM' ),
inference(clausification,[status(esa)],[axiom_M]) ).
cnf(c138,plain,
( 'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1))
| ~ 'op$ustrict$uimplies' ),
inference(clausification,[status(esa)],[op_strict_implies]) ).
cnf(c139,plain,
( 'strict$uequiv'(X0,X1) = and('strict$uimplies'(X0,X1),'strict$uimplies'(X1,X0))
| ~ 'op$ustrict$uequiv' ),
inference(clausification,[status(esa)],[op_strict_equiv]) ).
cnf(c143,plain,
'axiom$uM',
inference(clausification,[status(esa)],[km5_axiom_M]) ).
cnf(c145,plain,
~ 'substitution$ustrict$uequiv',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(equiv(X0,X1))
| X0 = X1 ),
inference(resolution,[status(thm)],[c83,c10]) ).
cnf(d1,plain,
equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c4,c65]) ).
cnf(d2,plain,
( ~ adjunction
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X1,X0))
| 'is$ua$utheorem'(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[d1,c91]) ).
cnf(d3,plain,
'is$ua$utheorem'(implies(necessarily(X0),X0)),
inference(resolution,[status(thm)],[c143,c100]) ).
cnf(d4,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c69,c6]) ).
cnf(d5,plain,
( 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(necessarily(X0)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'strict$uimplies'(X0,X1) = necessarily(implies(X0,X1)),
inference(resolution,[status(thm)],[c3,c138]) ).
cnf(d7,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'('strict$uimplies'(X0,X1)) ),
inference(superposition,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
'is$ua$utheorem'('strict$uequiv'(sK132,sK133)),
inference(resolution,[status(thm)],[c145,c96]) ).
cnf(d9,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c74,c21]) ).
cnf(d10,plain,
( 'is$ua$utheorem'(X0)
| ~ 'is$ua$utheorem'(and(X0,X1)) ),
inference(resolution,[status(thm)],[d4,d9]) ).
cnf(d11,plain,
'strict$uequiv'(X0,X1) = and('strict$uimplies'(X0,X1),'strict$uimplies'(X1,X0)),
inference(resolution,[status(thm)],[c5,c139]) ).
cnf(d12,plain,
( 'is$ua$utheorem'('strict$uimplies'(X0,X1))
| ~ 'is$ua$utheorem'('strict$uequiv'(X0,X1)) ),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
'is$ua$utheorem'('strict$uimplies'(sK132,sK133)),
inference(resolution,[status(thm)],[d12,d8]) ).
cnf(d14,plain,
'is$ua$utheorem'(implies(sK132,sK133)),
inference(resolution,[status(thm)],[d13,d7]) ).
cnf(d15,plain,
( ~ adjunction
| 'is$ua$utheorem'(equiv(sK132,sK133))
| ~ 'is$ua$utheorem'(implies(sK133,sK132)) ),
inference(resolution,[status(thm)],[d14,d2]) ).
cnf(d16,plain,
'is$ua$utheorem'(implies(and(X0,X1),X1)),
inference(resolution,[status(thm)],[c75,c23]) ).
cnf(d17,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(and(X0,X1)) ),
inference(resolution,[status(thm)],[d4,d16]) ).
cnf(d18,plain,
( 'is$ua$utheorem'('strict$uimplies'(X1,X0))
| ~ 'is$ua$utheorem'('strict$uequiv'(X0,X1)) ),
inference(superposition,[status(thm)],[d11,d17]) ).
cnf(d19,plain,
'is$ua$utheorem'('strict$uimplies'(sK133,sK132)),
inference(resolution,[status(thm)],[d18,d8]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(sK133,sK132)),
inference(resolution,[status(thm)],[d19,d7]) ).
cnf(d21,plain,
( ~ adjunction
| 'is$ua$utheorem'(equiv(sK132,sK133)) ),
inference(resolution,[status(thm)],[d20,d15]) ).
cnf(d22,plain,
( sK132 = sK133
| ~ adjunction ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
sK132 != sK133,
inference(resolution,[status(thm)],[c145,c97]) ).
cnf(d24,plain,
~ adjunction,
inference(resolution,[status(thm)],[d23,d22]) ).
cnf(d25,plain,
~ 'is$ua$utheorem'(and(sK128,sK129)),
inference(resolution,[status(thm)],[d24,c94]) ).
cnf(d26,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c76,c25]) ).
cnf(d27,plain,
( 'is$ua$utheorem'(implies(X1,and(X0,X1)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d4,d26]) ).
cnf(d28,plain,
( 'is$ua$utheorem'(and(X0,X1))
| ~ 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d27,d4]) ).
cnf(d29,plain,
( ~ 'is$ua$utheorem'(sK128)
| ~ 'is$ua$utheorem'(sK129) ),
inference(resolution,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
'is$ua$utheorem'(sK129),
inference(resolution,[status(thm)],[d24,c93]) ).
cnf(d31,plain,
~ 'is$ua$utheorem'(sK128),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
'is$ua$utheorem'(sK128),
inference(resolution,[status(thm)],[d24,c92]) ).
cnf(d33,plain,
$false,
inference(resolution,[status(thm)],[d32,d31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL526+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
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 22:41:47 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.76/2.89 % SZS status Theorem for theBenchmark.p
% 17.76/2.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------