%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL488+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:13:54 PM UTC 2026
% Result : Theorem 27.96s 3.99s
% Output : CNFRefutation 27.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 25 unt; 0 def)
% Number of atoms : 77 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 23 ~; 20 |; 1 &)
% ( 4 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(hilbert_and_2,plain,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(hilbert_and_2_negated,plain,
~ and_2,
inference(negate_conjecture,[status(cth)],[hilbert_and_2]) ).
cnf(73,plain,
~ and_2,
inference(cnf,[status(esa)],[hilbert_and_2_negated]) ).
cnf(l0,plain,
~ and_2,
inference(instantiation,[status(thm)],[73]) ).
fof(and_2,plain,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('Axioms/LCL006+0.ax',and_2) ).
cnf(18,plain,
( ~ is_a_theorem(implies(and(sK16,sK17),sK17))
| and_2 ),
inference(cnf,[status(esa)],[and_2]) ).
cnf(l1,plain,
( ~ is_a_theorem(implies(and(sK16,sK17),sK17))
| and_2 ),
inference(instantiation,[status(thm)],[18]) ).
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(l198,plain,
( ~ op_implies_and
| implies(not(or(not(sK16),not(sK17))),sK17) = not(and(not(or(not(sK16),not(sK17))),not(sK17))) ),
inference(instantiation,[status(thm)],[57]) ).
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(l4,plain,
( ~ modus_ponens
| ~ is_a_theorem(or(sK17,or(not(sK16),not(sK17))))
| ~ is_a_theorem(implies(or(sK17,or(not(sK16),not(sK17))),not(and(not(or(not(sK16),not(sK17))),not(sK17)))))
| is_a_theorem(not(and(not(or(not(sK16),not(sK17))),not(sK17)))) ),
inference(instantiation,[status(thm)],[0]) ).
fof(principia_modus_ponens,plain,
modus_ponens,
file('Axioms/LCL006+4.ax',principia_modus_ponens) ).
cnf(63,plain,
modus_ponens,
inference(cnf,[status(esa)],[principia_modus_ponens]) ).
cnf(l6,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(hilbert_op_implies_and,plain,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
cnf(71,plain,
op_implies_and,
inference(cnf,[status(esa)],[hilbert_op_implies_and]) ).
cnf(l199,plain,
op_implies_and,
inference(instantiation,[status(thm)],[71]) ).
fof(op_and,plain,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('Axioms/LCL006+1.ax',op_and) ).
cnf(56,plain,
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf,[status(esa)],[op_and]) ).
cnf(l197,plain,
( ~ op_and
| and(sK16,sK17) = not(or(not(sK16),not(sK17))) ),
inference(instantiation,[status(thm)],[56]) ).
fof(principia_op_and,plain,
op_and,
file('Axioms/LCL006+4.ax',principia_op_and) ).
cnf(61,plain,
op_and,
inference(cnf,[status(esa)],[principia_op_and]) ).
cnf(l200,plain,
op_and,
inference(instantiation,[status(thm)],[61]) ).
fof(r3,plain,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('Axioms/LCL006+0.ax',r3) ).
cnf(49,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf,[status(esa)],[r3]) ).
cnf(l180,plain,
( ~ r3
| is_a_theorem(implies(or(sK17,or(not(sK16),not(sK17))),or(or(not(sK16),not(sK17)),sK17))) ),
inference(instantiation,[status(thm)],[49]) ).
fof(principia_r3,plain,
r3,
file('Axioms/LCL006+4.ax',principia_r3) ).
cnf(66,plain,
r3,
inference(cnf,[status(esa)],[principia_r3]) ).
cnf(l217,plain,
r3,
inference(instantiation,[status(thm)],[66]) ).
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(l263,plain,
( ~ op_or
| or(or(not(sK16),not(sK17)),sK17) = not(and(not(or(not(sK16),not(sK17))),not(sK17))) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(l86,plain,
( ~ op_implies_and
| implies(not(sK17),or(not(sK16),not(sK17))) = not(and(not(sK17),not(or(not(sK16),not(sK17))))) ),
inference(instantiation,[status(thm)],[57]) ).
fof(hilbert_op_or,plain,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
cnf(70,plain,
op_or,
inference(cnf,[status(esa)],[hilbert_op_or]) ).
cnf(l288,plain,
op_or,
inference(instantiation,[status(thm)],[70]) ).
cnf(l96,plain,
op_implies_and,
inference(instantiation,[status(thm)],[71]) ).
cnf(l81,plain,
( ~ op_or
| or(sK17,or(not(sK16),not(sK17))) = not(and(not(sK17),not(or(not(sK16),not(sK17))))) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(l82,plain,
op_or,
inference(instantiation,[status(thm)],[70]) ).
fof(r2,plain,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('Axioms/LCL006+0.ax',r2) ).
cnf(47,plain,
( ~ r2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf,[status(esa)],[r2]) ).
cnf(l84,plain,
( ~ r2
| is_a_theorem(implies(not(sK17),or(not(sK16),not(sK17)))) ),
inference(instantiation,[status(thm)],[47]) ).
fof(principia_r2,plain,
r2,
file('Axioms/LCL006+4.ax',principia_r2) ).
cnf(65,plain,
r2,
inference(cnf,[status(esa)],[principia_r2]) ).
cnf(l88,plain,
r2,
inference(instantiation,[status(thm)],[65]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l198,l4,l6,l199,l197,l200,l180,l217,l263,l86,l288,l96,l81,l82,l84,l88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL488+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 5 07:12:51 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % launching worker at depth: 1
% 0.09/0.37 % launching worker at depth: 6
% 0.09/0.37 % launching worker at depth: 2
% 0.09/0.37 % launching worker at depth: 4
% 0.09/0.37 % launching worker at depth: 5
% 0.09/0.37 % launching worker at depth: 7
% 0.09/0.37 % launching worker at depth: 3
% 0.09/0.37 % launching worker at depth: 8
% 0.09/0.37 % launching worker at depth: 9
% 0.09/0.37 % launching worker at depth: 10
% 0.09/0.38 % launching worker at depth: 11
% 0.09/0.41 % launching worker at depth: 12
% 4.23/1.00 % launching worker at depth: 13
% 27.96/3.99 % SZS status Theorem for theBenchmark
% 27.96/3.99 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------