%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL531+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 : n015.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 12:13:58 PM UTC 2026
% Result : Theorem 1.06s 0.59s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 14
% Syntax : Number of formulae : 50 ( 26 unt; 0 def)
% Number of atoms : 87 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 67 ( 30 ~; 27 |; 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 : 23 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(s1_0_axiom_m4,plain,
axiom_m4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(s1_0_axiom_m4_negated,plain,
~ axiom_m4,
inference(negate_conjecture,[status(cth)],[s1_0_axiom_m4]) ).
cnf(145,plain,
~ axiom_m4,
inference(cnf,[status(esa)],[s1_0_axiom_m4_negated]) ).
cnf(l0,plain,
~ axiom_m4,
inference(instantiation,[status(thm)],[145]) ).
fof(axiom_m4,plain,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('Axioms/LCL007+0.ax',axiom_m4) ).
cnf(117,plain,
( ~ is_a_theorem(strict_implies(sK84,and(sK84,sK84)))
| axiom_m4 ),
inference(cnf,[status(esa)],[axiom_m4]) ).
cnf(l1,plain,
( ~ is_a_theorem(strict_implies(sK84,and(sK84,sK84)))
| axiom_m4 ),
inference(instantiation,[status(thm)],[117]) ).
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(l2,plain,
( ~ modus_ponens
| ~ is_a_theorem(necessarily(implies(sK84,and(sK84,sK84))))
| ~ is_a_theorem(implies(necessarily(implies(sK84,and(sK84,sK84))),strict_implies(sK84,and(sK84,sK84))))
| is_a_theorem(strict_implies(sK84,and(sK84,sK84))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l7,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(strict_implies(sK84,and(sK84,sK84)),implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84)))))
| ~ is_a_theorem(implies(implies(strict_implies(sK84,and(sK84,sK84)),implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84)))),implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84)))))
| is_a_theorem(implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84)))) ),
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(l46,plain,
( ~ implies_2
| is_a_theorem(implies(implies(strict_implies(sK84,and(sK84,sK84)),implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84)))),implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84))))) ),
inference(instantiation,[status(thm)],[11]) ).
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(l3,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
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(l33,plain,
( ~ op_strict_implies
| strict_implies(sK84,and(sK84,sK84)) = necessarily(implies(sK84,and(sK84,sK84))) ),
inference(instantiation,[status(thm)],[132]) ).
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(l97,plain,
implies_2,
inference(instantiation,[status(thm)],[66]) ).
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(sK84,and(sK84,sK84)))
| is_a_theorem(necessarily(implies(sK84,and(sK84,sK84)))) ),
inference(instantiation,[status(thm)],[78]) ).
fof(km5_necessitation,plain,
necessitation,
file('Axioms/LCL007+2.ax',km5_necessitation) ).
cnf(135,plain,
necessitation,
inference(cnf,[status(esa)],[km5_necessitation]) ).
cnf(l16,plain,
necessitation,
inference(instantiation,[status(thm)],[135]) ).
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(l34,plain,
( ~ implies_1
| is_a_theorem(implies(strict_implies(sK84,and(sK84,sK84)),implies(strict_implies(sK84,and(sK84,sK84)),strict_implies(sK84,and(sK84,sK84))))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l27,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
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(l35,plain,
implies_1,
inference(instantiation,[status(thm)],[65]) ).
cnf(l15,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(sK84,implies(sK84,and(sK84,sK84))))
| ~ is_a_theorem(implies(implies(sK84,implies(sK84,and(sK84,sK84))),implies(sK84,and(sK84,sK84))))
| is_a_theorem(implies(sK84,and(sK84,sK84))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l31,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l30,plain,
( ~ implies_2
| is_a_theorem(implies(implies(sK84,implies(sK84,and(sK84,sK84))),implies(sK84,and(sK84,sK84)))) ),
inference(instantiation,[status(thm)],[11]) ).
fof(and_3,plain,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('Axioms/LCL006+0.ax',and_3) ).
cnf(19,plain,
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf,[status(esa)],[and_3]) ).
cnf(l67,plain,
( ~ and_3
| is_a_theorem(implies(sK84,implies(sK84,and(sK84,sK84)))) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(l68,plain,
implies_2,
inference(instantiation,[status(thm)],[66]) ).
fof(hilbert_and_3,plain,
and_3,
file('Axioms/LCL006+2.ax',hilbert_and_3) ).
cnf(70,plain,
and_3,
inference(cnf,[status(esa)],[hilbert_and_3]) ).
cnf(l70,plain,
and_3,
inference(instantiation,[status(thm)],[70]) ).
fof(s1_0_op_strict_implies,plain,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
cnf(142,plain,
op_strict_implies,
inference(cnf,[status(esa)],[s1_0_op_strict_implies]) ).
cnf(l49,plain,
op_strict_implies,
inference(instantiation,[status(thm)],[142]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l7,l46,l3,l33,l97,l11,l16,l34,l27,l35,l15,l31,l30,l67,l68,l70,l49]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+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
% 0.10/0.36 % Computer : n015.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 : Fri Sep 4 18:30:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % launching worker at depth: 1
% 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: 5
% 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
% 0.10/0.38 % launching worker at depth: 11
% 0.10/0.39 % launching worker at depth: 12
% 1.06/0.59 % SZS status Theorem for theBenchmark
% 1.06/0.59 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------