%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL458+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 : n013.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 07:54:40 AM UTC 2026
% Result : Theorem 32.17s 16.83s
% Output : CNFRefutation 32.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 81 ( 39 unt; 0 def)
% Number of atoms : 140 ( 10 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 118 ( 59 ~; 46 |; 1 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 117 ( 14 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(principia_op_implies_or,axiom,
'op$uimplies$uor' ).
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(implies_1,axiom,
( 'implies$u1'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X0,implies(X1,X0))) ) ).
fof(implies_3,axiom,
( 'implies$u3'
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ) ).
fof(or_1,axiom,
( 'or$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(r4,axiom,
( r4
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ) ).
fof(r5,axiom,
( r5
<=> ! [X0,X1,X2] : 'is$ua$utheorem'(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ) ).
fof(op_or,axiom,
( 'op$uor'
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ) ).
fof(op_implies_and,axiom,
( 'op$uimplies$uand'
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ) ).
fof(op_implies_or,axiom,
( 'op$uimplies$uor'
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ) ).
fof(hilbert_op_or,axiom,
'op$uor' ).
fof(hilbert_op_implies_and,axiom,
'op$uimplies$uand' ).
fof(hilbert_modus_ponens,axiom,
'modus$uponens' ).
fof(hilbert_implies_1,axiom,
'implies$u1' ).
fof(hilbert_implies_3,axiom,
'implies$u3' ).
fof(hilbert_or_1,axiom,
'or$u1' ).
fof(hilbert_or_2,axiom,
'or$u2' ).
fof(hilbert_or_3,axiom,
'or$u3' ).
fof(principia_r5,conjecture,
r5 ).
fof(negated_conjecture,negated_conjecture,
~ r5,
inference(negate_conjecture,[status(cth)],[principia_r5]) ).
cnf(c0,plain,
'op$uimplies$uor',
inference(clausification,[status(esa)],[principia_op_implies_or]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c12,plain,
( 'is$ua$utheorem'(implies(X0,implies(X1,X0)))
| ~ 'implies$u1' ),
inference(clausification,[status(esa)],[implies_1]) ).
cnf(c16,plain,
( 'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ 'implies$u3' ),
inference(clausification,[status(esa)],[implies_3]) ).
cnf(c24,plain,
( 'is$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(c54,plain,
( 'is$ua$utheorem'(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(clausification,[status(esa)],[r4]) ).
cnf(c55,plain,
( ~ 'is$ua$utheorem'(implies(or(sK101,or(sK102,sK103)),or(sK102,or(sK101,sK103))))
| r4 ),
inference(clausification,[status(esa)],[r4]) ).
cnf(c57,plain,
( ~ 'is$ua$utheorem'(implies(implies(sK108,sK109),implies(or(sK107,sK108),or(sK107,sK109))))
| r5 ),
inference(clausification,[status(esa)],[r5]) ).
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$uand' ),
inference(clausification,[status(esa)],[op_implies_and]) ).
cnf(c61,plain,
( implies(X0,X1) = or(not(X0),X1)
| ~ 'op$uimplies$uor' ),
inference(clausification,[status(esa)],[op_implies_or]) ).
cnf(c63,plain,
'op$uor',
inference(clausification,[status(esa)],[hilbert_op_or]) ).
cnf(c64,plain,
'op$uimplies$uand',
inference(clausification,[status(esa)],[hilbert_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(c70,plain,
'implies$u3',
inference(clausification,[status(esa)],[hilbert_implies_3]) ).
cnf(c74,plain,
'or$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(c81,plain,
~ r5,
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d1,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(resolution,[status(thm)],[c76,c28]) ).
cnf(d2,plain,
( 'is$ua$utheorem'(implies(implies(X2,X1),implies(or(X0,X2),X1)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d0,d1]) ).
cnf(d3,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)],[d2,d0]) ).
cnf(d4,plain,
~ 'is$ua$utheorem'(implies(implies(sK108,sK109),implies(or(sK107,sK108),or(sK107,sK109)))),
inference(resolution,[status(thm)],[c81,c57]) ).
cnf(d5,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c64,c60]) ).
cnf(d6,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c63,c58]) ).
cnf(d7,plain,
or(X0,X1) = implies(not(X0),X1),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c0,c61]) ).
cnf(d9,plain,
( ~ 'is$ua$utheorem'(implies(not(X0),X2))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| 'is$ua$utheorem'(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[d8,d3]) ).
cnf(d10,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)],[d9,d7]) ).
cnf(d11,plain,
( ~ 'is$ua$utheorem'(or(sK108,implies(or(sK107,sK108),or(sK107,sK109))))
| ~ 'is$ua$utheorem'(implies(sK109,implies(or(sK107,sK108),or(sK107,sK109)))) ),
inference(resolution,[status(thm)],[d10,d4]) ).
cnf(d12,plain,
( 'is$ua$utheorem'(or(X1,or(X0,X2)))
| ~ 'is$ua$utheorem'(or(X0,or(X1,X2)))
| ~ r4 ),
inference(resolution,[status(thm)],[c54,d0]) ).
cnf(d13,plain,
( ~ r4
| 'is$ua$utheorem'(or(X1,or(not(X0),X2)))
| ~ 'is$ua$utheorem'(implies(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[d8,d12]) ).
cnf(d14,plain,
( ~ r4
| 'is$ua$utheorem'(or(X2,implies(X0,X1)))
| ~ 'is$ua$utheorem'(implies(X0,or(X2,X1))) ),
inference(demodulation,[status(thm)],[d13,d8]) ).
cnf(d15,plain,
( ~ 'is$ua$utheorem'(implies(X1,or(X0,X3)))
| ~ 'is$ua$utheorem'(implies(X2,or(X0,X3)))
| ~ r4
| 'is$ua$utheorem'(or(X0,implies(or(X1,X2),X3))) ),
inference(resolution,[status(thm)],[d14,d3]) ).
cnf(d16,plain,
( ~ 'is$ua$utheorem'(implies(sK109,implies(or(sK107,sK108),or(sK107,sK109))))
| ~ r4
| ~ 'is$ua$utheorem'(implies(sK107,or(sK108,or(sK107,sK109))))
| ~ 'is$ua$utheorem'(implies(sK108,or(sK108,or(sK107,sK109)))) ),
inference(resolution,[status(thm)],[d15,d11]) ).
cnf(d17,plain,
'is$ua$utheorem'(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c74,c24]) ).
cnf(d18,plain,
( ~ r4
| ~ 'is$ua$utheorem'(implies(sK107,or(sK108,or(sK107,sK109))))
| ~ 'is$ua$utheorem'(implies(sK109,implies(or(sK107,sK108),or(sK107,sK109)))) ),
inference(resolution,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c75,c26]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(resolution,[status(thm)],[c70,c16]) ).
cnf(d21,plain,
( 'is$ua$utheorem'(implies(implies(X1,X2),implies(X0,X2)))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d0,d20]) ).
cnf(d22,plain,
( 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(X0,X1)) ),
inference(resolution,[status(thm)],[d21,d0]) ).
cnf(d23,plain,
( 'is$ua$utheorem'(implies(X0,X2))
| ~ 'is$ua$utheorem'(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d22,d17]) ).
cnf(d24,plain,
'is$ua$utheorem'(implies(X0,or(X1,or(X0,X2)))),
inference(resolution,[status(thm)],[d23,d19]) ).
cnf(d25,plain,
( ~ r4
| ~ 'is$ua$utheorem'(implies(sK109,implies(or(sK107,sK108),or(sK107,sK109)))) ),
inference(resolution,[status(thm)],[d24,d18]) ).
cnf(d26,plain,
'is$ua$utheorem'(implies(X0,implies(X1,X0))),
inference(resolution,[status(thm)],[c68,c12]) ).
cnf(d27,plain,
( 'is$ua$utheorem'(implies(X1,X2))
| ~ 'is$ua$utheorem'(implies(or(X0,X1),X2)) ),
inference(resolution,[status(thm)],[d22,d19]) ).
cnf(d28,plain,
'is$ua$utheorem'(implies(X0,implies(X1,or(X2,X0)))),
inference(resolution,[status(thm)],[d27,d26]) ).
cnf(d29,plain,
~ r4,
inference(resolution,[status(thm)],[d28,d25]) ).
cnf(d30,plain,
~ 'is$ua$utheorem'(implies(or(sK101,or(sK102,sK103)),or(sK102,or(sK101,sK103)))),
inference(resolution,[status(thm)],[d29,c55]) ).
cnf(d31,plain,
( ~ 'is$ua$utheorem'(implies(sK101,or(sK102,or(sK101,sK103))))
| ~ 'is$ua$utheorem'(implies(or(sK102,sK103),or(sK102,or(sK101,sK103)))) ),
inference(resolution,[status(thm)],[d30,d3]) ).
cnf(d32,plain,
~ 'is$ua$utheorem'(implies(or(sK102,sK103),or(sK102,or(sK101,sK103)))),
inference(resolution,[status(thm)],[d24,d31]) ).
cnf(d33,plain,
( ~ 'is$ua$utheorem'(implies(sK102,or(sK102,or(sK101,sK103))))
| ~ 'is$ua$utheorem'(implies(sK103,or(sK102,or(sK101,sK103)))) ),
inference(resolution,[status(thm)],[d32,d3]) ).
cnf(d34,plain,
~ 'is$ua$utheorem'(implies(sK103,or(sK102,or(sK101,sK103)))),
inference(resolution,[status(thm)],[d17,d33]) ).
cnf(d35,plain,
'is$ua$utheorem'(implies(X0,or(X1,or(X2,X0)))),
inference(resolution,[status(thm)],[d27,d19]) ).
cnf(d36,plain,
$false,
inference(resolution,[status(thm)],[d35,d34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL458+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n013.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Fri Sep 25 22:36:17 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.17/16.83 % SZS status Theorem for theBenchmark.p
% 32.17/16.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------