%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL500+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 : n012.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 12:13:56 PM UTC 2026
% Result : Theorem 259.50s 32.93s
% Output : CNFRefutation 259.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 20
% Syntax : Number of formulae : 74 ( 38 unt; 0 def)
% Number of atoms : 122 ( 14 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 39 ~; 36 |; 1 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(rosser_kn2,plain,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(rosser_kn2_negated,plain,
~ kn2,
inference(negate_conjecture,[status(cth)],[rosser_kn2]) ).
cnf(73,plain,
~ kn2,
inference(cnf,[status(esa)],[rosser_kn2_negated]) ).
cnf(l0,plain,
~ kn2,
inference(instantiation,[status(thm)],[73]) ).
fof(kn2,plain,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('Axioms/LCL006+0.ax',kn2) ).
cnf(36,plain,
( ~ is_a_theorem(implies(and(sK34,sK35),sK34))
| kn2 ),
inference(cnf,[status(esa)],[kn2]) ).
cnf(l1,plain,
( ~ is_a_theorem(implies(and(sK34,sK35),sK34))
| kn2 ),
inference(instantiation,[status(thm)],[36]) ).
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(l5,plain,
( ~ op_implies_and
| implies(not(or(not(sK34),not(sK35))),sK34) = not(and(not(or(not(sK34),not(sK35))),not(sK34))) ),
inference(instantiation,[status(thm)],[57]) ).
fof(rosser_op_implies_and,plain,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).
cnf(71,plain,
op_implies_and,
inference(cnf,[status(esa)],[rosser_op_implies_and]) ).
cnf(l9,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(l13,plain,
( ~ op_and
| and(sK34,sK35) = not(or(not(sK34),not(sK35))) ),
inference(instantiation,[status(thm)],[56]) ).
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(l76,plain,
( ~ modus_ponens
| ~ is_a_theorem(not(and(not(sK34),not(or(not(sK34),not(sK35))))))
| ~ is_a_theorem(implies(not(and(not(sK34),not(or(not(sK34),not(sK35))))),not(and(not(or(not(sK34),not(sK35))),not(sK34)))))
| is_a_theorem(not(and(not(or(not(sK34),not(sK35))),not(sK34)))) ),
inference(instantiation,[status(thm)],[0]) ).
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(l42,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(l171,plain,
( ~ r3
| is_a_theorem(implies(or(sK34,or(not(sK34),not(sK35))),or(or(not(sK34),not(sK35)),sK34))) ),
inference(instantiation,[status(thm)],[49]) ).
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(l78,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l169,plain,
( ~ modus_ponens
| ~ is_a_theorem(or(not(sK34),or(sK34,not(sK35))))
| ~ is_a_theorem(implies(or(not(sK34),or(sK34,not(sK35))),not(and(not(sK34),not(or(not(sK34),not(sK35)))))))
| is_a_theorem(not(and(not(sK34),not(or(not(sK34),not(sK35)))))) ),
inference(instantiation,[status(thm)],[0]) ).
fof(principia_r3,plain,
r3,
file('Axioms/LCL006+4.ax',principia_r3) ).
cnf(66,plain,
r3,
inference(cnf,[status(esa)],[principia_r3]) ).
cnf(l176,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(l271,plain,
( ~ op_or
| or(sK34,or(not(sK34),not(sK35))) = not(and(not(sK34),not(or(not(sK34),not(sK35))))) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(l224,plain,
( ~ op_or
| or(or(not(sK34),not(sK35)),sK34) = not(and(not(or(not(sK34),not(sK35))),not(sK34))) ),
inference(instantiation,[status(thm)],[55]) ).
fof(rosser_op_or,plain,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).
cnf(70,plain,
op_or,
inference(cnf,[status(esa)],[rosser_op_or]) ).
cnf(l282,plain,
op_or,
inference(instantiation,[status(thm)],[70]) ).
cnf(l229,plain,
op_or,
inference(instantiation,[status(thm)],[70]) ).
cnf(l179,plain,
( ~ modus_ponens
| ~ is_a_theorem(or(not(sK34),or(not(sK35),sK34)))
| ~ is_a_theorem(implies(or(not(sK34),or(not(sK35),sK34)),or(not(sK34),or(sK34,not(sK35)))))
| is_a_theorem(or(not(sK34),or(sK34,not(sK35)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l170,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l180,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(or(not(sK35),sK34),or(sK34,not(sK35))))
| ~ is_a_theorem(implies(implies(or(not(sK35),sK34),or(sK34,not(sK35))),implies(or(not(sK34),or(not(sK35),sK34)),or(not(sK34),or(sK34,not(sK35))))))
| is_a_theorem(implies(or(not(sK34),or(not(sK35),sK34)),or(not(sK34),or(sK34,not(sK35))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l311,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(r5,plain,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('Axioms/LCL006+0.ax',r5) ).
cnf(53,plain,
( ~ r5
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(cnf,[status(esa)],[r5]) ).
cnf(l181,plain,
( ~ r5
| is_a_theorem(implies(implies(or(not(sK35),sK34),or(sK34,not(sK35))),implies(or(not(sK34),or(not(sK35),sK34)),or(not(sK34),or(sK34,not(sK35)))))) ),
inference(instantiation,[status(thm)],[53]) ).
fof(principia_r5,plain,
r5,
file('Axioms/LCL006+4.ax',principia_r5) ).
cnf(68,plain,
r5,
inference(cnf,[status(esa)],[principia_r5]) ).
cnf(l571,plain,
r5,
inference(instantiation,[status(thm)],[68]) ).
fof(op_implies_or,plain,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('Axioms/LCL006+1.ax',op_implies_or) ).
cnf(58,plain,
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf,[status(esa)],[op_implies_or]) ).
cnf(l281,plain,
( ~ op_implies_or
| implies(sK34,or(not(sK35),sK34)) = or(not(sK34),or(not(sK35),sK34)) ),
inference(instantiation,[status(thm)],[58]) ).
cnf(l306,plain,
( ~ op_or
| or(sK34,or(not(sK34),not(sK35))) = not(and(not(sK34),not(or(not(sK34),not(sK35))))) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(l182,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(r4,plain,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('Axioms/LCL006+0.ax',r4) ).
cnf(51,plain,
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf,[status(esa)],[r4]) ).
cnf(l304,plain,
( ~ r4
| is_a_theorem(implies(or(not(sK34),or(sK34,not(sK35))),or(sK34,or(not(sK34),not(sK35))))) ),
inference(instantiation,[status(thm)],[51]) ).
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(l278,plain,
( ~ r2
| is_a_theorem(implies(sK34,or(not(sK35),sK34))) ),
inference(instantiation,[status(thm)],[47]) ).
fof(principia_r4,plain,
r4,
file('Axioms/LCL006+4.ax',principia_r4) ).
cnf(67,plain,
r4,
inference(cnf,[status(esa)],[principia_r4]) ).
cnf(l305,plain,
r4,
inference(instantiation,[status(thm)],[67]) ).
fof(principia_op_implies_or,plain,
op_implies_or,
file('Axioms/LCL006+4.ax',principia_op_implies_or) ).
cnf(60,plain,
op_implies_or,
inference(cnf,[status(esa)],[principia_op_implies_or]) ).
cnf(l285,plain,
op_implies_or,
inference(instantiation,[status(thm)],[60]) ).
fof(principia_r2,plain,
r2,
file('Axioms/LCL006+4.ax',principia_r2) ).
cnf(65,plain,
r2,
inference(cnf,[status(esa)],[principia_r2]) ).
cnf(l483,plain,
r2,
inference(instantiation,[status(thm)],[65]) ).
cnf(l569,plain,
op_or,
inference(instantiation,[status(thm)],[70]) ).
cnf(l183,plain,
( ~ r3
| is_a_theorem(implies(or(not(sK35),sK34),or(sK34,not(sK35)))) ),
inference(instantiation,[status(thm)],[49]) ).
cnf(l287,plain,
r3,
inference(instantiation,[status(thm)],[66]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l5,l9,l13,l76,l42,l171,l78,l169,l176,l271,l224,l282,l229,l179,l170,l180,l311,l181,l571,l281,l306,l182,l304,l278,l305,l285,l483,l569,l183,l287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL500+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Fri Sep 4 17:34:12 UTC 2026
% 0.03/0.29 % CPUTime :
% 0.03/0.29 % launching worker at depth: 1
% 0.03/0.29 % launching worker at depth: 2
% 0.03/0.29 % launching worker at depth: 3
% 0.03/0.29 % launching worker at depth: 4
% 0.03/0.29 % launching worker at depth: 5
% 0.03/0.29 % launching worker at depth: 6
% 0.03/0.29 % launching worker at depth: 7
% 0.03/0.29 % launching worker at depth: 8
% 0.03/0.29 % launching worker at depth: 9
% 0.03/0.29 % launching worker at depth: 10
% 0.03/0.30 % launching worker at depth: 11
% 0.03/0.32 % launching worker at depth: 12
% 1.99/0.57 % launching worker at depth: 13
% 259.50/32.93 % SZS status Theorem for theBenchmark
% 259.50/32.93 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------