%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL461+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 07:54:41 AM UTC 2026
% Result : Theorem 201.81s 29.43s
% Output : CNFRefutation 201.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 33
% Syntax : Number of formulae : 156 ( 76 unt; 0 def)
% Number of atoms : 260 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 195 ( 91 ~; 83 |; 1 &)
% ( 16 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 236 ( 21 sgn 37 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rosser_op_or,axiom,
'op$uor' ).
fof(rosser_op_implies_and,axiom,
'op$uimplies$uand' ).
fof(modus_ponens,axiom,
( 'modus$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(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(implies_3,axiom,
( 'implies$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ) ).
fof(and_1,axiom,
( 'and$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(or_1,axiom,
( 'or$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,or(X0,X1))) ) ).
fof(or_2,axiom,
( 'or$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X1,or(X0,X1))) ) ).
fof(or_3,axiom,
( 'or$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ) ).
fof(equivalence_3,axiom,
( 'equivalence$u3'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ) ).
fof(kn3,axiom,
( kn3
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ) ).
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(r3,axiom,
( r3
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(or(X0,X1),or(X1,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$uand'
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ) ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_implies_1,axiom,
'implies$u1' ).
fof(hilbert_implies_2,axiom,
'implies$u2' ).
fof(hilbert_implies_3,axiom,
'implies$u3' ).
fof(hilbert_and_1,axiom,
'and$u1' ).
fof(hilbert_and_2,axiom,
'and$u2' ).
fof(hilbert_and_3,axiom,
'and$u3' ).
fof(hilbert_or_1,axiom,
'or$u1' ).
fof(hilbert_or_2,axiom,
'or$u2' ).
fof(hilbert_or_3,axiom,
'or$u3' ).
fof(hilbert_equivalence_3,axiom,
'equivalence$u3' ).
fof(use_substitution_of_equivalents,axiom,
'substitution$uof$uequivalents' ).
fof(rosser_kn3,conjecture,
kn3 ).
fof(negated_conjecture,negated_conjecture,
~ kn3,
inference(negate_conjecture,[status(cth)],[rosser_kn3]) ).
cnf(c0,plain,
'op$uor',
inference(clausification,[status(esa)],[rosser_op_or]) ).
cnf(c1,plain,
'op$uimplies$uand',
inference(clausification,[status(esa)],[rosser_op_implies_and]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c7,plain,
( X0 = X1
| ~ 'is$ua$utheorem'(equiv(X0,X1))
| ~ 'substitution$uof$uequivalents' ),
inference(clausification,[status(esa)],[substitution_of_equivalents]) ).
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(c16,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ 'implies$u3' ),
inference(clausification,[status(esa)],[implies_3]) ).
cnf(c18,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X0))
| ~ 'and$u1' ),
inference(clausification,[status(esa)],[and_1]) ).
cnf(c20,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X1))
| ~ 'and$u2' ),
inference(clausification,[status(esa)],[and_2]) ).
cnf(c22,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1))))
| ~ 'and$u3' ),
inference(clausification,[status(esa)],[and_3]) ).
cnf(c24,plain,
( 'is$ua$utheorem'(implies(X0,or(X0,X1)))
| ~ 'or$u1' ),
inference(clausification,[status(esa)],[or_1]) ).
cnf(c26,plain,
( 'is$ua$utheorem'(implies(X0,or(X1,X0)))
| ~ 'or$u2' ),
inference(clausification,[status(esa)],[or_2]) ).
cnf(c28,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ 'or$u3' ),
inference(clausification,[status(esa)],[or_3]) ).
cnf(c34,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ 'equivalence$u3' ),
inference(clausification,[status(esa)],[equivalence_3]) ).
cnf(c41,plain,
( ~ 'is$ua$utheorem'(implies(implies(sK73,sK74),implies(not(and(sK74,sK75)),not(and(sK75,sK73)))))
| kn3 ),
inference(clausification,[status(esa)],[kn3]) ).
cnf(c46,plain,
( 'is$ua$utheorem'(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(clausification,[status(esa)],[cn3]) ).
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(c52,plain,
( 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c53,plain,
( ~ 'is$ua$utheorem'(implies(or(sK96,sK97),or(sK97,sK96)))
| r3 ),
inference(clausification,[status(esa)],[r3]) ).
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$uand' ),
inference(clausification,[status(esa)],[op_implies_and]) ).
cnf(c66,plain,
'modus$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(c70,plain,
'implies$u3',
inference(clausification,[status(esa)],[hilbert_implies_3]) ).
cnf(c71,plain,
'and$u1',
inference(clausification,[status(esa)],[hilbert_and_1]) ).
cnf(c72,plain,
'and$u2',
inference(clausification,[status(esa)],[hilbert_and_2]) ).
cnf(c73,plain,
'and$u3',
inference(clausification,[status(esa)],[hilbert_and_3]) ).
cnf(c74,plain,
'or$u1',
inference(clausification,[status(esa)],[hilbert_or_1]) ).
cnf(c75,plain,
'or$u2',
inference(clausification,[status(esa)],[hilbert_or_2]) ).
cnf(c76,plain,
'or$u3',
inference(clausification,[status(esa)],[hilbert_or_3]) ).
cnf(c79,plain,
'equivalence$u3',
inference(clausification,[status(esa)],[hilbert_equivalence_3]) ).
cnf(c80,plain,
'substitution$uof$uequivalents',
inference(clausification,[status(esa)],[use_substitution_of_equivalents]) ).
cnf(c81,plain,
~ kn3,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(resolution,[status(thm)],[c70,c16]) ).
cnf(d1,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d2,plain,
( 'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X1)))),
inference(resolution,[status(thm)],[c73,c22]) ).
cnf(d4,plain,
( 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d5,plain,
( 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,and(X1,X0)),X2)) ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'is$ua$utheorem'(implies(X1,X2))
| 'is$ua$utheorem'(implies(X0,implies(X1,and(X0,X2)))) ),
inference(resolution,[status(thm)],[d5,d2]) ).
cnf(d7,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c1,c60]) ).
cnf(d8,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c0,c58]) ).
cnf(d9,plain,
or(X0,X1) = implies(not(X0),X1),
inference(demodulation,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ 'is$ua$utheorem'(equiv(X0,X1))
| X0 = X1 ),
inference(resolution,[status(thm)],[c80,c7]) ).
cnf(d11,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c76,c28]) ).
cnf(d12,plain,
( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d1,d11]) ).
cnf(d13,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)],[d12,d1]) ).
cnf(d14,plain,
( r1
| ~ 'is$ua$utheorem'(implies(sK89,sK89))
| ~ 'is$ua$utheorem'(implies(sK89,sK89)) ),
inference(resolution,[status(thm)],[d13,c49]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[c68,c12]) ).
cnf(d16,plain,
'is$ua$utheorem'(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(resolution,[status(thm)],[c69,c14]) ).
cnf(d17,plain,
( 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[d1,d16]) ).
cnf(d18,plain,
'is$ua$utheorem'(implies(X0,X0)),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
r1,
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(or(X0,X0),X0)),
inference(resolution,[status(thm)],[d19,c48]) ).
cnf(d21,plain,
'is$ua$utheorem'(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c74,c24]) ).
cnf(d22,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(resolution,[status(thm)],[c79,c34]) ).
cnf(d23,plain,
( 'is$ua$utheorem'(implies(implies(X1,X0),equiv(X0,X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d1,d22]) ).
cnf(d24,plain,
( 'is$ua$utheorem'(equiv(X0,X1))
| ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d23,d1]) ).
cnf(d25,plain,
( 'is$ua$utheorem'(equiv(X0,or(X0,X1)))
| ~ 'is$ua$utheorem'(implies(or(X0,X1),X0)) ),
inference(resolution,[status(thm)],[d24,d21]) ).
cnf(d26,plain,
'is$ua$utheorem'(equiv(X0,or(X0,X0))),
inference(resolution,[status(thm)],[d25,d20]) ).
cnf(d27,plain,
X0 = or(X0,X0),
inference(resolution,[status(thm)],[d26,d10]) ).
cnf(d28,plain,
'is$ua$utheorem'(implies(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d17,d3]) ).
cnf(d29,plain,
( 'is$ua$utheorem'(equiv(X0,and(X0,X0)))
| ~ 'is$ua$utheorem'(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[d24,d28]) ).
cnf(d30,plain,
'is$ua$utheorem'(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c71,c18]) ).
cnf(d31,plain,
'is$ua$utheorem'(equiv(X0,and(X0,X0))),
inference(resolution,[status(thm)],[d30,d29]) ).
cnf(d32,plain,
X0 = and(X0,X0),
inference(resolution,[status(thm)],[d31,d10]) ).
cnf(d33,plain,
implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[d32,d7]) ).
cnf(d34,plain,
or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[d33,d9]) ).
cnf(d35,plain,
X0 = not(not(X0)),
inference(demodulation,[status(thm)],[d34,d27]) ).
cnf(d36,plain,
or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[d35,d9]) ).
cnf(d37,plain,
( ~ r3
| 'is$ua$utheorem'(equiv(or(X1,X0),or(X0,X1)))
| ~ 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[d24,c52]) ).
cnf(d38,plain,
( ~ r3
| ~ r3
| 'is$ua$utheorem'(equiv(or(X0,X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[d37,c52]) ).
cnf(d39,plain,
( r3
| ~ 'is$ua$utheorem'(implies(sK96,or(sK97,sK96)))
| ~ 'is$ua$utheorem'(implies(sK97,or(sK97,sK96))) ),
inference(resolution,[status(thm)],[d13,c53]) ).
cnf(d40,plain,
( r3
| ~ 'is$ua$utheorem'(implies(sK96,or(sK97,sK96))) ),
inference(resolution,[status(thm)],[d21,d39]) ).
cnf(d41,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c75,c26]) ).
cnf(d42,plain,
r3,
inference(resolution,[status(thm)],[d41,d40]) ).
cnf(d43,plain,
'is$ua$utheorem'(equiv(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[d42,d38]) ).
cnf(d44,plain,
or(X0,X1) = or(X1,X0),
inference(resolution,[status(thm)],[d43,d10]) ).
cnf(d45,plain,
or(X1,not(X0)) = implies(X0,X1),
inference(superposition,[status(thm)],[d44,d36]) ).
cnf(d46,plain,
~ 'is$ua$utheorem'(implies(implies(sK73,sK74),implies(not(and(sK74,sK75)),not(and(sK75,sK73))))),
inference(resolution,[status(thm)],[c81,c41]) ).
cnf(d47,plain,
~ 'is$ua$utheorem'(implies(implies(sK73,sK74),or(and(sK74,sK75),not(and(sK75,sK73))))),
inference(demodulation,[status(thm)],[d46,d9]) ).
cnf(d48,plain,
~ 'is$ua$utheorem'(implies(implies(sK73,sK74),implies(and(sK75,sK73),and(sK74,sK75)))),
inference(demodulation,[status(thm)],[d47,d45]) ).
cnf(d49,plain,
or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))),
inference(superposition,[status(thm)],[d8,d8]) ).
cnf(d50,plain,
or(and(not(X0),not(X1)),X2) = implies(or(X0,X1),X2),
inference(demodulation,[status(thm)],[d49,d7]) ).
cnf(d51,plain,
( ~ 'is$ua$utheorem'(implies(and(not(X0),not(X1)),X3))
| ~ 'is$ua$utheorem'(implies(X2,X3))
| 'is$ua$utheorem'(implies(implies(or(X0,X1),X2),X3)) ),
inference(superposition,[status(thm)],[d50,d13]) ).
cnf(d52,plain,
( 'is$ua$utheorem'(implies(implies(or(X0,X0),X2),X1))
| ~ 'is$ua$utheorem'(implies(X2,X1))
| ~ 'is$ua$utheorem'(implies(not(X0),X1)) ),
inference(superposition,[status(thm)],[d32,d51]) ).
cnf(d53,plain,
( ~ 'is$ua$utheorem'(implies(not(X0),X2))
| 'is$ua$utheorem'(implies(implies(X0,X1),X2))
| ~ 'is$ua$utheorem'(implies(X1,X2)) ),
inference(demodulation,[status(thm)],[d52,d27]) ).
cnf(d54,plain,
( ~ 'is$ua$utheorem'(or(X0,X1))
| 'is$ua$utheorem'(implies(implies(X0,X2),X1))
| ~ 'is$ua$utheorem'(implies(X2,X1)) ),
inference(demodulation,[status(thm)],[d53,d9]) ).
cnf(d55,plain,
( ~ 'is$ua$utheorem'(or(sK73,implies(and(sK75,sK73),and(sK74,sK75))))
| ~ 'is$ua$utheorem'(implies(sK74,implies(and(sK75,sK73),and(sK74,sK75)))) ),
inference(resolution,[status(thm)],[d54,d48]) ).
cnf(d56,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(X0,X1))
| ~ r3 ),
inference(resolution,[status(thm)],[c52,d1]) ).
cnf(d57,plain,
implies(X2,and(X0,not(X1))) = not(and(X2,implies(X0,X1))),
inference(superposition,[status(thm)],[d7,d7]) ).
cnf(d58,plain,
or(and(X0,implies(X1,X2)),X3) = implies(implies(X0,and(X1,not(X2))),X3),
inference(superposition,[status(thm)],[d57,d9]) ).
cnf(d59,plain,
( ~ cn3
| 'is$ua$utheorem'(implies(implies(implies(X0,X1),and(X0,not(X1))),and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[d7,c46]) ).
cnf(d60,plain,
( ~ cn3
| 'is$ua$utheorem'(implies(implies(implies(X0,X1),and(X0,not(X1))),X2))
| ~ 'is$ua$utheorem'(implies(and(X0,not(X1)),X2)) ),
inference(resolution,[status(thm)],[d4,d59]) ).
cnf(d61,plain,
( ~ cn3
| ~ 'is$ua$utheorem'(implies(and(X0,not(X1)),X2))
| 'is$ua$utheorem'(or(and(implies(X0,X1),implies(X0,X1)),X2)) ),
inference(demodulation,[status(thm)],[d60,d58]) ).
cnf(d62,plain,
( cn3
| ~ 'is$ua$utheorem'(implies(or(sK87,sK87),sK87)) ),
inference(demodulation,[status(thm)],[c47,d9]) ).
cnf(d63,plain,
cn3,
inference(resolution,[status(thm)],[d20,d62]) ).
cnf(d64,plain,
( ~ 'is$ua$utheorem'(implies(and(X0,not(X1)),X2))
| 'is$ua$utheorem'(or(and(implies(X0,X1),implies(X0,X1)),X2)) ),
inference(resolution,[status(thm)],[d63,d61]) ).
cnf(d65,plain,
( ~ r3
| 'is$ua$utheorem'(or(X2,and(implies(X0,X1),implies(X0,X1))))
| ~ 'is$ua$utheorem'(implies(and(X0,not(X1)),X2)) ),
inference(resolution,[status(thm)],[d64,d56]) ).
cnf(d66,plain,
( ~ r3
| 'is$ua$utheorem'(or(X2,implies(X0,X1)))
| ~ 'is$ua$utheorem'(implies(and(X0,not(X1)),X2)) ),
inference(demodulation,[status(thm)],[d65,d32]) ).
cnf(d67,plain,
( 'is$ua$utheorem'(or(X2,implies(X0,X1)))
| ~ 'is$ua$utheorem'(implies(and(X0,not(X1)),X2)) ),
inference(resolution,[status(thm)],[d42,d66]) ).
cnf(d68,plain,
( 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d4,d15]) ).
cnf(d69,plain,
'is$ua$utheorem'(implies(X0,implies(implies(X0,X1),implies(X2,X1)))),
inference(resolution,[status(thm)],[d68,d0]) ).
cnf(d70,plain,
'is$ua$utheorem'(implies(and(X0,X1),X1)),
inference(resolution,[status(thm)],[c72,c20]) ).
cnf(d71,plain,
( 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d1,d15]) ).
cnf(d72,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),X1))
| ~ 'is$ua$utheorem'(implies(implies(X0,X1),X0)) ),
inference(resolution,[status(thm)],[d2,d17]) ).
cnf(d73,plain,
( ~ 'is$ua$utheorem'(X0)
| 'is$ua$utheorem'(implies(implies(X0,X1),X1)) ),
inference(resolution,[status(thm)],[d72,d71]) ).
cnf(d74,plain,
( 'is$ua$utheorem'(equiv(implies(X0,X1),X1))
| ~ 'is$ua$utheorem'(implies(X1,implies(X0,X1)))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d73,d24]) ).
cnf(d75,plain,
( 'is$ua$utheorem'(equiv(implies(X0,X1),X1))
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d15,d74]) ).
cnf(d76,plain,
( implies(X0,X1) = X1
| ~ 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[d75,d10]) ).
cnf(d77,plain,
implies(implies(and(X0,X1),X1),X2) = X2,
inference(resolution,[status(thm)],[d76,d70]) ).
cnf(d78,plain,
'is$ua$utheorem'(implies(and(X0,X1),implies(X2,X1))),
inference(superposition,[status(thm)],[d77,d69]) ).
cnf(d79,plain,
( 'is$ua$utheorem'(implies(and(X0,X2),X1))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d4,d30]) ).
cnf(d80,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X2))
| ~ 'is$ua$utheorem'(implies(X0,implies(and(X0,X1),X2))) ),
inference(resolution,[status(thm)],[d79,d17]) ).
cnf(d81,plain,
'is$ua$utheorem'(implies(and(and(X0,X1),X2),X1)),
inference(resolution,[status(thm)],[d80,d78]) ).
cnf(d82,plain,
'is$ua$utheorem'(or(X0,implies(and(X1,X0),X2))),
inference(resolution,[status(thm)],[d81,d67]) ).
cnf(d83,plain,
~ 'is$ua$utheorem'(implies(sK74,implies(and(sK75,sK73),and(sK74,sK75)))),
inference(resolution,[status(thm)],[d82,d55]) ).
cnf(d84,plain,
~ 'is$ua$utheorem'(implies(and(sK75,sK73),sK75)),
inference(resolution,[status(thm)],[d83,d6]) ).
cnf(d85,plain,
$false,
inference(resolution,[status(thm)],[d30,d84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL461+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 22:38:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 201.81/29.43 % SZS status Theorem for theBenchmark.p
% 201.81/29.43 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------