%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Mon Sep 7 12:13:51 PM UTC 2026
% Result : Theorem 38.50s 5.25s
% Output : CNFRefutation 38.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 26 unt; 0 def)
% Number of atoms : 84 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 28 ~; 25 |; 1 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 27 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(luka_cn3,plain,
cn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn3) ).
fof(luka_cn3_negated,plain,
~ cn3,
inference(negate_conjecture,[status(cth)],[luka_cn3]) ).
cnf(81,plain,
~ cn3,
inference(cnf,[status(esa)],[luka_cn3_negated]) ).
cnf(l0,plain,
~ cn3,
inference(instantiation,[status(thm)],[81]) ).
fof(cn3,plain,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('Axioms/LCL006+0.ax',cn3) ).
cnf(44,plain,
( ~ is_a_theorem(implies(implies(not(sK44),sK44),sK44))
| cn3 ),
inference(cnf,[status(esa)],[cn3]) ).
cnf(l1,plain,
( ~ is_a_theorem(implies(implies(not(sK44),sK44),sK44))
| cn3 ),
inference(instantiation,[status(thm)],[44]) ).
fof(op_implies_and,plain,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('Axioms/LCL006+1.ax',op_implies_and) ).
cnf(57,plain,
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf,[status(esa)],[op_implies_and]) ).
cnf(l41,plain,
( ~ op_implies_and
| implies(not(sK44),sK44) = not(and(not(sK44),not(sK44))) ),
inference(instantiation,[status(thm)],[57]) ).
fof(hilbert_op_implies_and,plain,
op_implies_and,
file('Axioms/LCL006+2.ax',hilbert_op_implies_and) ).
cnf(61,plain,
op_implies_and,
inference(cnf,[status(esa)],[hilbert_op_implies_and]) ).
cnf(l42,plain,
op_implies_and,
inference(instantiation,[status(thm)],[61]) ).
fof(modus_ponens,plain,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(X)
& is_a_theorem(implies(X,Y)) )
=> is_a_theorem(Y) ) ),
file('Axioms/LCL006+0.ax',modus_ponens) ).
cnf(0,plain,
( ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(cnf,[status(esa)],[modus_ponens]) ).
cnf(l10,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(sK44,sK44))
| ~ is_a_theorem(implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44)))
| is_a_theorem(implies(or(sK44,sK44),sK44)) ),
inference(instantiation,[status(thm)],[0]) ).
fof(hilbert_modus_ponens,plain,
modus_ponens,
file('Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
cnf(63,plain,
modus_ponens,
inference(cnf,[status(esa)],[hilbert_modus_ponens]) ).
cnf(l17,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(op_or,plain,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('Axioms/LCL006+1.ax',op_or) ).
cnf(55,plain,
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf,[status(esa)],[op_or]) ).
cnf(l13,plain,
( ~ op_or
| or(sK44,sK44) = not(and(not(sK44),not(sK44))) ),
inference(instantiation,[status(thm)],[55]) ).
fof(luka_op_or,plain,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
cnf(78,plain,
op_or,
inference(cnf,[status(esa)],[luka_op_or]) ).
cnf(l20,plain,
op_or,
inference(instantiation,[status(thm)],[78]) ).
cnf(l32,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(implies(sK44,sK44),implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44))))
| ~ is_a_theorem(implies(implies(implies(sK44,sK44),implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44))),implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44))))
| is_a_theorem(implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l33,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l28,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(sK44,implies(sK44,sK44)))
| ~ is_a_theorem(implies(implies(sK44,implies(sK44,sK44)),implies(sK44,sK44)))
| is_a_theorem(implies(sK44,sK44)) ),
inference(instantiation,[status(thm)],[0]) ).
fof(implies_2,plain,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('Axioms/LCL006+0.ax',implies_2) ).
cnf(11,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf,[status(esa)],[implies_2]) ).
cnf(l113,plain,
( ~ implies_2
| is_a_theorem(implies(implies(implies(sK44,sK44),implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44))),implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44)))) ),
inference(instantiation,[status(thm)],[11]) ).
fof(hilbert_implies_2,plain,
implies_2,
file('Axioms/LCL006+2.ax',hilbert_implies_2) ).
cnf(66,plain,
implies_2,
inference(cnf,[status(esa)],[hilbert_implies_2]) ).
cnf(l114,plain,
implies_2,
inference(instantiation,[status(thm)],[66]) ).
fof(or_3,plain,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('Axioms/LCL006+0.ax',or_3) ).
cnf(25,plain,
( ~ or_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
inference(cnf,[status(esa)],[or_3]) ).
cnf(l112,plain,
( ~ or_3
| is_a_theorem(implies(implies(sK44,sK44),implies(implies(sK44,sK44),implies(or(sK44,sK44),sK44)))) ),
inference(instantiation,[status(thm)],[25]) ).
fof(implies_1,plain,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('Axioms/LCL006+0.ax',implies_1) ).
cnf(9,plain,
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf,[status(esa)],[implies_1]) ).
cnf(l103,plain,
( ~ implies_1
| is_a_theorem(implies(sK44,implies(sK44,sK44))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l29,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l107,plain,
( ~ implies_2
| is_a_theorem(implies(implies(sK44,implies(sK44,sK44)),implies(sK44,sK44))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l109,plain,
implies_2,
inference(instantiation,[status(thm)],[66]) ).
fof(hilbert_or_3,plain,
or_3,
file('Axioms/LCL006+2.ax',hilbert_or_3) ).
cnf(73,plain,
or_3,
inference(cnf,[status(esa)],[hilbert_or_3]) ).
cnf(l115,plain,
or_3,
inference(instantiation,[status(thm)],[73]) ).
fof(hilbert_implies_1,plain,
implies_1,
file('Axioms/LCL006+2.ax',hilbert_implies_1) ).
cnf(65,plain,
implies_1,
inference(cnf,[status(esa)],[hilbert_implies_1]) ).
cnf(l104,plain,
implies_1,
inference(instantiation,[status(thm)],[65]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l41,l42,l10,l17,l13,l20,l32,l33,l28,l113,l114,l112,l103,l29,l107,l109,l115,l104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL453+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n010.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Sat Sep 5 12:38:53 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 % launching worker at depth: 1
% 0.11/0.35 % launching worker at depth: 5
% 0.11/0.35 % launching worker at depth: 2
% 0.11/0.35 % launching worker at depth: 4
% 0.11/0.35 % launching worker at depth: 3
% 0.11/0.35 % launching worker at depth: 8
% 0.11/0.35 % launching worker at depth: 6
% 0.11/0.35 % launching worker at depth: 7
% 0.11/0.36 % launching worker at depth: 9
% 0.11/0.36 % launching worker at depth: 10
% 0.13/0.36 % launching worker at depth: 11
% 0.13/0.43 % launching worker at depth: 12
% 38.50/5.25 % SZS status Theorem for theBenchmark
% 38.50/5.25 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------