%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : LCL520+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 : n026.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 12:13:57 PM UTC 2026
% Result : Theorem 102.80s 13.35s
% Output : CNFRefutation 102.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 16
% Syntax : Number of formulae : 68 ( 35 unt; 0 def)
% Number of atoms : 115 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 87 ( 40 ~; 37 |; 1 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(principia_r3,plain,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(principia_r3_negated,plain,
~ r3,
inference(negate_conjecture,[status(cth)],[principia_r3]) ).
cnf(71,plain,
~ r3,
inference(cnf,[status(esa)],[principia_r3_negated]) ).
cnf(l0,plain,
~ r3,
inference(instantiation,[status(thm)],[71]) ).
fof(r3,plain,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('Axioms/LCL006+0.ax',r3) ).
cnf(50,plain,
( ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48)))
| r3 ),
inference(cnf,[status(esa)],[r3]) ).
cnf(l1,plain,
( ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48)))
| r3 ),
inference(instantiation,[status(thm)],[50]) ).
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(or(not(not(sK48)),not(sK48)))
| ~ is_a_theorem(implies(or(not(not(sK48)),not(sK48)),implies(or(sK48,sK49),or(sK49,sK48))))
| is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48))) ),
inference(instantiation,[status(thm)],[0]) ).
fof(rosser_modus_ponens,plain,
modus_ponens,
file('Axioms/LCL006+5.ax',rosser_modus_ponens) ).
cnf(63,plain,
modus_ponens,
inference(cnf,[status(esa)],[rosser_modus_ponens]) ).
cnf(l3,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(kn3,plain,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('Axioms/LCL006+0.ax',kn3) ).
cnf(37,plain,
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf,[status(esa)],[kn3]) ).
cnf(l121,plain,
( ~ kn3
| is_a_theorem(implies(implies(not(sK48),not(sK48)),implies(not(and(not(sK48),not(sK49))),not(and(not(sK49),not(sK48)))))) ),
inference(instantiation,[status(thm)],[37]) ).
fof(rosser_kn3,plain,
kn3,
file('Axioms/LCL006+5.ax',rosser_kn3) ).
cnf(66,plain,
kn3,
inference(cnf,[status(esa)],[rosser_kn3]) ).
cnf(l123,plain,
kn3,
inference(instantiation,[status(thm)],[66]) ).
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(l10,plain,
( ~ op_implies_or
| implies(not(sK48),not(sK48)) = or(not(not(sK48)),not(sK48)) ),
inference(instantiation,[status(thm)],[58]) ).
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(l413,plain,
( ~ op_or
| or(sK48,sK49) = not(and(not(sK48),not(sK49))) ),
inference(instantiation,[status(thm)],[55]) ).
fof(principia_op_implies_or,plain,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
cnf(68,plain,
op_implies_or,
inference(cnf,[status(esa)],[principia_op_implies_or]) ).
cnf(l12,plain,
op_implies_or,
inference(instantiation,[status(thm)],[68]) ).
fof(rosser_op_or,plain,
op_or,
file('Axioms/LCL006+5.ax',rosser_op_or) ).
cnf(60,plain,
op_or,
inference(cnf,[status(esa)],[rosser_op_or]) ).
cnf(l487,plain,
op_or,
inference(instantiation,[status(thm)],[60]) ).
cnf(l7,plain,
( ~ modus_ponens
| ~ is_a_theorem(and(or(not(not(sK48)),not(sK48)),or(not(not(sK48)),not(sK48))))
| ~ is_a_theorem(implies(and(or(not(not(sK48)),not(sK48)),or(not(not(sK48)),not(sK48))),or(not(not(sK48)),not(sK48))))
| is_a_theorem(or(not(not(sK48)),not(sK48))) ),
inference(instantiation,[status(thm)],[0]) ).
fof(kn2,plain,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('Axioms/LCL006+0.ax',kn2) ).
cnf(35,plain,
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf,[status(esa)],[kn2]) ).
cnf(l37,plain,
( ~ kn2
| is_a_theorem(implies(and(or(not(not(sK48)),not(sK48)),or(not(not(sK48)),not(sK48))),or(not(not(sK48)),not(sK48)))) ),
inference(instantiation,[status(thm)],[35]) ).
cnf(l20,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
fof(rosser_kn2,plain,
kn2,
file('Axioms/LCL006+5.ax',rosser_kn2) ).
cnf(65,plain,
kn2,
inference(cnf,[status(esa)],[rosser_kn2]) ).
cnf(l38,plain,
kn2,
inference(instantiation,[status(thm)],[65]) ).
cnf(l19,plain,
( ~ modus_ponens
| ~ is_a_theorem(not(and(not(not(not(sK48))),not(not(sK48)))))
| ~ is_a_theorem(implies(not(and(not(not(not(sK48))),not(not(sK48)))),and(or(not(not(sK48)),not(sK48)),or(not(not(sK48)),not(sK48)))))
| is_a_theorem(and(or(not(not(sK48)),not(sK48)),or(not(not(sK48)),not(sK48)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l572,plain,
( ~ op_or
| or(sK49,sK48) = not(and(not(sK49),not(sK48))) ),
inference(instantiation,[status(thm)],[55]) ).
cnf(l950,plain,
op_or,
inference(instantiation,[status(thm)],[60]) ).
cnf(l46,plain,
( ~ modus_ponens
| ~ is_a_theorem(not(and(and(not(not(sK48)),not(not(sK48))),not(not(not(sK48))))))
| ~ is_a_theorem(implies(not(and(and(not(not(sK48)),not(not(sK48))),not(not(not(sK48))))),not(and(not(not(not(sK48))),not(not(sK48))))))
| is_a_theorem(not(and(not(not(not(sK48))),not(not(sK48))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l22,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l323,plain,
( ~ kn2
| is_a_theorem(implies(and(not(not(sK48)),not(not(sK48))),not(not(sK48)))) ),
inference(instantiation,[status(thm)],[35]) ).
cnf(l325,plain,
kn2,
inference(instantiation,[status(thm)],[65]) ).
cnf(l63,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l49,plain,
( ~ modus_ponens
| ~ is_a_theorem(implies(not(not(sK48)),and(not(not(sK48)),not(not(sK48)))))
| ~ is_a_theorem(implies(implies(not(not(sK48)),and(not(not(sK48)),not(not(sK48)))),implies(not(and(and(not(not(sK48)),not(not(sK48))),not(not(not(sK48))))),not(and(not(not(not(sK48))),not(not(sK48)))))))
| is_a_theorem(implies(not(and(and(not(not(sK48)),not(not(sK48))),not(not(not(sK48))))),not(and(not(not(not(sK48))),not(not(sK48)))))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l307,plain,
( ~ kn3
| is_a_theorem(implies(implies(not(not(sK48)),and(not(not(sK48)),not(not(sK48)))),implies(not(and(and(not(not(sK48)),not(not(sK48))),not(not(not(sK48))))),not(and(not(not(not(sK48))),not(not(sK48))))))) ),
inference(instantiation,[status(thm)],[37]) ).
cnf(l60,plain,
( ~ op_or
| or(not(not(sK48)),not(sK48)) = not(and(not(not(not(sK48))),not(not(sK48)))) ),
inference(instantiation,[status(thm)],[55]) ).
fof(kn1,plain,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('Axioms/LCL006+0.ax',kn1) ).
cnf(33,plain,
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf,[status(esa)],[kn1]) ).
cnf(l308,plain,
( ~ kn1
| is_a_theorem(implies(not(not(sK48)),and(not(not(sK48)),not(not(sK48))))) ),
inference(instantiation,[status(thm)],[33]) ).
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(l309,plain,
( ~ op_implies_and
| implies(and(not(not(sK48)),not(not(sK48))),not(not(sK48))) = not(and(and(not(not(sK48)),not(not(sK48))),not(not(not(sK48))))) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(l430,plain,
op_or,
inference(instantiation,[status(thm)],[60]) ).
fof(rosser_kn1,plain,
kn1,
file('Axioms/LCL006+5.ax',rosser_kn1) ).
cnf(64,plain,
kn1,
inference(cnf,[status(esa)],[rosser_kn1]) ).
cnf(l314,plain,
kn1,
inference(instantiation,[status(thm)],[64]) ).
cnf(l214,plain,
( ~ kn1
| is_a_theorem(implies(or(not(not(sK48)),not(sK48)),and(or(not(not(sK48)),not(sK48)),or(not(not(sK48)),not(sK48))))) ),
inference(instantiation,[status(thm)],[33]) ).
cnf(l237,plain,
modus_ponens,
inference(instantiation,[status(thm)],[63]) ).
cnf(l219,plain,
kn1,
inference(instantiation,[status(thm)],[64]) ).
fof(rosser_op_implies_and,plain,
op_implies_and,
file('Axioms/LCL006+5.ax',rosser_op_implies_and) ).
cnf(61,plain,
op_implies_and,
inference(cnf,[status(esa)],[rosser_op_implies_and]) ).
cnf(l313,plain,
op_implies_and,
inference(instantiation,[status(thm)],[61]) ).
cnf(l326,plain,
kn3,
inference(instantiation,[status(thm)],[66]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l121,l123,l10,l413,l12,l487,l7,l37,l20,l38,l19,l572,l950,l46,l22,l323,l325,l63,l49,l307,l60,l308,l309,l430,l314,l214,l237,l219,l313,l326]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL520+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
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 4 13:27:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % launching worker at depth: 1
% 0.10/0.39 % launching worker at depth: 6
% 0.10/0.39 % launching worker at depth: 3
% 0.10/0.39 % launching worker at depth: 8
% 0.10/0.39 % launching worker at depth: 5
% 0.10/0.39 % launching worker at depth: 7
% 0.10/0.39 % launching worker at depth: 2
% 0.10/0.39 % launching worker at depth: 4
% 0.10/0.39 % launching worker at depth: 9
% 0.10/0.39 % launching worker at depth: 10
% 0.10/0.39 % launching worker at depth: 11
% 0.10/0.43 % launching worker at depth: 12
% 1.93/0.67 % launching worker at depth: 13
% 102.80/13.35 % SZS status Theorem for theBenchmark
% 102.80/13.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------