%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : LCL494+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 07:54:44 AM UTC 2026
% Result : Theorem 18.73s 3.27s
% Output : CNFRefutation 18.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 19
% Syntax : Number of formulae : 62 ( 38 unt; 0 def)
% Number of atoms : 91 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 51 ( 22 ~; 17 |; 1 &)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 77 ( 7 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hilbert_op_or,axiom,
'op$uor' ).
fof(hilbert_op_implies_and,axiom,
'op$uimplies$uand' ).
fof(hilbert_op_equiv,axiom,
'op$uequiv' ).
fof(modus_ponens,axiom,
( 'modus$uponens'
<=> ! [X0,X1] :
( ( 'is$ua$utheorem'(implies(X0,X1))
& 'is$ua$utheorem'(X0) )
=> 'is$ua$utheorem'(X1) ) ) ).
fof(and_2,axiom,
( 'and$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(and(X0,X1),X1)) ) ).
fof(equivalence_2,axiom,
( 'equivalence$u2'
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(equiv(X0,X1),implies(X1,X0))) ) ).
fof(r2,axiom,
( r2
<=> ! [X0,X1] : 'is$ua$utheorem'(implies(X1,or(X0,X1))) ) ).
fof(r3,axiom,
( r3
<=> ! [X0,X1] : 'is$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_and,axiom,
( 'op$uand'
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ) ).
fof(op_implies_and,axiom,
( 'op$uimplies$uand'
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ) ).
fof(op_implies_or,axiom,
( 'op$uimplies$uor'
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ) ).
fof(op_equiv,axiom,
( 'op$uequiv'
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ) ).
fof(principia_op_implies_or,axiom,
'op$uimplies$uor' ).
fof(principia_op_and,axiom,
'op$uand' ).
fof(principia_modus_ponens,axiom,
'modus$uponens' ).
fof(principia_r2,axiom,
r2 ).
fof(principia_r3,axiom,
r3 ).
fof(hilbert_equivalence_2,conjecture,
'equivalence$u2' ).
fof(negated_conjecture,negated_conjecture,
~ 'equivalence$u2',
inference(negate_conjecture,[status(cth)],[hilbert_equivalence_2]) ).
cnf(c0,plain,
'op$uor',
inference(clausification,[status(esa)],[hilbert_op_or]) ).
cnf(c1,plain,
'op$uimplies$uand',
inference(clausification,[status(esa)],[hilbert_op_implies_and]) ).
cnf(c2,plain,
'op$uequiv',
inference(clausification,[status(esa)],[hilbert_op_equiv]) ).
cnf(c3,plain,
( 'is$ua$utheorem'(X1)
| ~ 'is$ua$utheorem'(implies(X0,X1))
| ~ 'is$ua$utheorem'(X0)
| ~ 'modus$uponens' ),
inference(clausification,[status(esa)],[modus_ponens]) ).
cnf(c20,plain,
( 'is$ua$utheorem'(implies(and(X0,X1),X1))
| ~ 'and$u2' ),
inference(clausification,[status(esa)],[and_2]) ).
cnf(c21,plain,
( ~ 'is$ua$utheorem'(implies(and(sK32,sK33),sK33))
| 'and$u2' ),
inference(clausification,[status(esa)],[and_2]) ).
cnf(c33,plain,
( ~ 'is$ua$utheorem'(implies(equiv(sK58,sK59),implies(sK59,sK58)))
| 'equivalence$u2' ),
inference(clausification,[status(esa)],[equivalence_2]) ).
cnf(c50,plain,
( 'is$ua$utheorem'(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(clausification,[status(esa)],[r2]) ).
cnf(c52,plain,
( 'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(clausification,[status(esa)],[r3]) ).
cnf(c58,plain,
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ 'op$uor' ),
inference(clausification,[status(esa)],[op_or]) ).
cnf(c59,plain,
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ 'op$uand' ),
inference(clausification,[status(esa)],[op_and]) ).
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(c62,plain,
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ 'op$uequiv' ),
inference(clausification,[status(esa)],[op_equiv]) ).
cnf(c63,plain,
'op$uimplies$uor',
inference(clausification,[status(esa)],[principia_op_implies_or]) ).
cnf(c64,plain,
'op$uand',
inference(clausification,[status(esa)],[principia_op_and]) ).
cnf(c66,plain,
'modus$uponens',
inference(clausification,[status(esa)],[principia_modus_ponens]) ).
cnf(c68,plain,
r2,
inference(clausification,[status(esa)],[principia_r2]) ).
cnf(c69,plain,
r3,
inference(clausification,[status(esa)],[principia_r3]) ).
cnf(c73,plain,
~ 'equivalence$u2',
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
~ 'is$ua$utheorem'(implies(equiv(sK58,sK59),implies(sK59,sK58))),
inference(resolution,[status(thm)],[c73,c33]) ).
cnf(d1,plain,
equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c2,c62]) ).
cnf(d2,plain,
( ~ 'and$u2'
| 'is$ua$utheorem'(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(superposition,[status(thm)],[d1,c20]) ).
cnf(d3,plain,
~ 'and$u2',
inference(resolution,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
~ 'is$ua$utheorem'(implies(and(sK32,sK33),sK33)),
inference(resolution,[status(thm)],[d3,c21]) ).
cnf(d5,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c1,c60]) ).
cnf(d6,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c63,c61]) ).
cnf(d7,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c0,c58]) ).
cnf(d8,plain,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(resolution,[status(thm)],[c64,c59]) ).
cnf(d9,plain,
or(or(not(X0),not(X1)),X2) = not(and(and(X0,X1),not(X2))),
inference(superposition,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
or(implies(X0,not(X1)),X2) = not(and(and(X0,X1),not(X2))),
inference(demodulation,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(demodulation,[status(thm)],[d10,d5]) ).
cnf(d12,plain,
'is$ua$utheorem'(implies(or(X0,X1),or(X1,X0))),
inference(resolution,[status(thm)],[c69,c52]) ).
cnf(d13,plain,
( ~ 'is$ua$utheorem'(implies(X1,X0))
| ~ 'is$ua$utheorem'(X1)
| 'is$ua$utheorem'(X0) ),
inference(resolution,[status(thm)],[c66,c3]) ).
cnf(d14,plain,
( 'is$ua$utheorem'(or(X1,X0))
| ~ 'is$ua$utheorem'(or(X0,X1)) ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
'is$ua$utheorem'(implies(X0,or(X1,X0))),
inference(resolution,[status(thm)],[c68,c50]) ).
cnf(d16,plain,
'is$ua$utheorem'(implies(X1,implies(X0,X1))),
inference(superposition,[status(thm)],[d6,d15]) ).
cnf(d17,plain,
or(X0,X1) = implies(not(X0),X1),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d18,plain,
'is$ua$utheorem'(or(X0,implies(X1,not(X0)))),
inference(superposition,[status(thm)],[d17,d16]) ).
cnf(d19,plain,
'is$ua$utheorem'(or(implies(X0,not(X1)),X1)),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
'is$ua$utheorem'(implies(and(X0,X1),X1)),
inference(demodulation,[status(thm)],[d19,d11]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL494+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
% 0.12/0.36 % Computer : n005.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 22:39:33 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.73/3.27 % SZS status Theorem for theBenchmark.p
% 18.73/3.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------