%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL546+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 : 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 : Mon Sep 7 12:13:59 PM UTC 2026
% Result : Theorem 43.97s 5.97s
% Output : CNFRefutation 43.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 46 ( 24 unt; 0 def)
% Number of atoms : 79 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 26 ~; 23 |; 1 &)
% ( 6 <=>; 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 : 21 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_m6s3m9b_axiom_m6,plain,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(s1_0_m6s3m9b_axiom_m6_negated,plain,
~ axiom_m6,
inference(negate_conjecture,[status(cth)],[s1_0_m6s3m9b_axiom_m6]) ).
cnf(146,plain,
~ axiom_m6,
inference(cnf,[status(esa)],[s1_0_m6s3m9b_axiom_m6_negated]) ).
cnf(l0,plain,
~ axiom_m6,
inference(instantiation,[status(thm)],[146]) ).
fof(axiom_m6,plain,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(X))) ),
file('Axioms/LCL007+0.ax',axiom_m6) ).
cnf(121,plain,
( ~ is_a_theorem(strict_implies(sK88,possibly(sK88)))
| axiom_m6 ),
inference(cnf,[status(esa)],[axiom_m6]) ).
cnf(l1,plain,
( ~ is_a_theorem(strict_implies(sK88,possibly(sK88)))
| axiom_m6 ),
inference(instantiation,[status(thm)],[121]) ).
fof(op_strict_implies,plain,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('Axioms/LCL007+1.ax',op_strict_implies) ).
cnf(132,plain,
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf,[status(esa)],[op_strict_implies]) ).
cnf(l102,plain,
( ~ op_strict_implies
| strict_implies(sK88,possibly(sK88)) = necessarily(implies(sK88,possibly(sK88))) ),
inference(instantiation,[status(thm)],[132]) ).
fof(s1_0_op_strict_implies,plain,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
cnf(143,plain,
op_strict_implies,
inference(cnf,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(l105,plain,
op_strict_implies,
inference(instantiation,[status(thm)],[143]) ).
fof(necessitation,plain,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('Axioms/LCL007+0.ax',necessitation) ).
cnf(78,plain,
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf,[status(esa)],[necessitation]) ).
cnf(l11,plain,
( ~ necessitation
| ~ is_a_theorem(implies(sK88,possibly(sK88)))
| is_a_theorem(necessarily(implies(sK88,possibly(sK88)))) ),
inference(instantiation,[status(thm)],[78]) ).
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(l75,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(necessarily(possibly(sK88)),possibly(sK88)))
| ~ is_a_theorem(implies(implies(necessarily(possibly(sK88)),possibly(sK88)),implies(sK88,possibly(sK88))))
| is_a_theorem(implies(sK88,possibly(sK88))) ),
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(l76,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(km4b_necessitation,plain,
necessitation,
file('Axioms/LCL007+3.ax',km4b_necessitation) ).
cnf(135,plain,
necessitation,
inference(cnf,[status(esa)],[km4b_necessitation]) ).
cnf(l19,plain,
necessitation,
inference(instantiation,[status(thm)],[135]) ).
cnf(l81,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(sK88,necessarily(possibly(sK88))))
| ~ is_a_theorem(implies(implies(sK88,necessarily(possibly(sK88))),implies(implies(necessarily(possibly(sK88)),possibly(sK88)),implies(sK88,possibly(sK88)))))
| is_a_theorem(implies(implies(necessarily(possibly(sK88)),possibly(sK88)),implies(sK88,possibly(sK88)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l251,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(implies_3,plain,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('Axioms/LCL006+0.ax',implies_3) ).
cnf(13,plain,
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf,[status(esa)],[implies_3]) ).
cnf(l89,plain,
( ~ implies_3
| is_a_theorem(implies(implies(sK88,necessarily(possibly(sK88))),implies(implies(necessarily(possibly(sK88)),possibly(sK88)),implies(sK88,possibly(sK88))))) ),
inference(instantiation,[status(thm)],[13]) ).
fof(hilbert_implies_3,plain,
implies_3,
file('Axioms/LCL006+2.ax',hilbert_implies_3) ).
cnf(67,plain,
implies_3,
inference(cnf,[status(esa)],[hilbert_implies_3]) ).
cnf(l372,plain,
implies_3,
inference(instantiation,[status(thm)],[67]) ).
fof(axiom_B,plain,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('Axioms/LCL007+0.ax',axiom_B) ).
cnf(98,plain,
( ~ axiom_B
| is_a_theorem(implies(X0,necessarily(possibly(X0)))) ),
inference(cnf,[status(esa)],[axiom_B]) ).
cnf(l93,plain,
( ~ axiom_B
| is_a_theorem(implies(sK88,necessarily(possibly(sK88)))) ),
inference(instantiation,[status(thm)],[98]) ).
fof(km4b_axiom_B,plain,
axiom_B,
file('Axioms/LCL007+3.ax',km4b_axiom_B) ).
cnf(139,plain,
axiom_B,
inference(cnf,[status(esa)],[km4b_axiom_B]) ).
cnf(l94,plain,
axiom_B,
inference(instantiation,[status(thm)],[139]) ).
fof(axiom_M,plain,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('Axioms/LCL007+0.ax',axiom_M) ).
cnf(94,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf,[status(esa)],[axiom_M]) ).
cnf(l293,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(possibly(sK88)),possibly(sK88))) ),
inference(instantiation,[status(thm)],[94]) ).
fof(km4b_axiom_M,plain,
axiom_M,
file('Axioms/LCL007+3.ax',km4b_axiom_M) ).
cnf(137,plain,
axiom_M,
inference(cnf,[status(esa)],[km4b_axiom_M]) ).
cnf(l296,plain,
axiom_M,
inference(instantiation,[status(thm)],[137]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l102,l105,l11,l75,l76,l19,l81,l251,l89,l372,l93,l94,l293,l296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL546+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 5 08:28:50 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % launching worker at depth: 1
% 0.10/0.37 % launching worker at depth: 5
% 0.10/0.37 % launching worker at depth: 2
% 0.10/0.37 % launching worker at depth: 6
% 0.10/0.37 % launching worker at depth: 4
% 0.10/0.37 % launching worker at depth: 3
% 0.10/0.37 % launching worker at depth: 7
% 0.10/0.37 % launching worker at depth: 8
% 0.10/0.37 % launching worker at depth: 9
% 0.10/0.37 % launching worker at depth: 10
% 0.10/0.37 % launching worker at depth: 11
% 0.10/0.43 % launching worker at depth: 12
% 14.56/2.25 % launching worker at depth: 13
% 43.97/5.97 % SZS status Theorem for theBenchmark
% 43.97/5.97 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------