TSTP Solution File: LCL500+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 3 02:38:02 EDT 2024
% Result : Theorem 102.61s 14.81s
% Output : CNFRefutation 102.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 29
% Syntax : Number of formulae : 155 ( 62 unt; 0 def)
% Number of atoms : 276 ( 56 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 220 ( 99 ~; 92 |; 2 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 254 ( 9 sgn 95 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f17,axiom,
( kn2
<=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f25,axiom,
( r4
<=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
fof(f26,axiom,
( r5
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f45,conjecture,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f46,negated_conjecture,
~ kn2,
inference(negated_conjecture,[],[f45]) ).
fof(f48,plain,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(rectify,[],[f17]) ).
fof(f53,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f54,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f55,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f56,plain,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(rectify,[],[f25]) ).
fof(f57,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f58,plain,
~ kn2,
inference(flattening,[],[f46]) ).
fof(f59,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f60,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f61,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f62,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f54]) ).
fof(f63,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f64,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> kn2 ),
inference(unused_predicate_definition_removal,[],[f48]) ).
fof(f66,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f67,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f66]) ).
fof(f68,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f67]) ).
fof(f70,plain,
( kn2
| ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f71,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f72,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f73,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f74,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f60]) ).
fof(f75,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f59]) ).
fof(f76,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f77,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f78,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f79,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f81,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
=> ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( kn2
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f70,f81]) ).
fof(f83,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f68]) ).
fof(f85,plain,
( kn2
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f86,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f71]) ).
fof(f87,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f73]) ).
fof(f89,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f75]) ).
fof(f91,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f76]) ).
fof(f92,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f77]) ).
fof(f93,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f78]) ).
fof(f94,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f79]) ).
fof(f96,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f97,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f99,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f100,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f101,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f102,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f103,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f104,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f106,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f107,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f109,plain,
~ kn2,
inference(cnf_transformation,[],[f58]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| kn2 ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_52,plain,
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_53,plain,
( ~ r2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_54,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_55,plain,
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_56,plain,
( ~ r5
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_57,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_58,plain,
( ~ op_and
| not(or(not(X0),not(X1))) = and(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_59,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_60,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f96]) ).
cnf(c_63,plain,
op_and,
inference(cnf_transformation,[],[f97]) ).
cnf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f99]) ).
cnf(c_66,plain,
r1,
inference(cnf_transformation,[],[f100]) ).
cnf(c_67,plain,
r2,
inference(cnf_transformation,[],[f101]) ).
cnf(c_68,plain,
r3,
inference(cnf_transformation,[],[f102]) ).
cnf(c_69,plain,
r4,
inference(cnf_transformation,[],[f103]) ).
cnf(c_70,plain,
r5,
inference(cnf_transformation,[],[f104]) ).
cnf(c_72,plain,
op_or,
inference(cnf_transformation,[],[f106]) ).
cnf(c_73,plain,
op_implies_and,
inference(cnf_transformation,[],[f107]) ).
cnf(c_75,negated_conjecture,
~ kn2,
inference(cnf_transformation,[],[f109]) ).
cnf(c_87,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_67,c_53]) ).
cnf(c_90,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_66,c_52]) ).
cnf(c_93,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
cnf(c_95,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).
cnf(c_98,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
cnf(c_104,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_73,c_59]) ).
cnf(c_107,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_65,c_49]) ).
cnf(c_108,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_107]) ).
cnf(c_109,plain,
not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_63,c_58]) ).
cnf(c_112,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_72,c_57]) ).
cnf(c_118,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_70,c_56]) ).
cnf(c_121,plain,
is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_69,c_55]) ).
cnf(c_140,plain,
X0 = X0,
theory(equality) ).
cnf(c_142,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_143,plain,
( X0 != X1
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ),
theory(equality) ).
cnf(c_144,plain,
( X0 != X1
| X2 != X3
| implies(X0,X2) = implies(X1,X3) ),
theory(equality) ).
cnf(c_146,plain,
( X0 != X1
| X2 != X3
| or(X0,X2) = or(X1,X3) ),
theory(equality) ).
cnf(c_147,plain,
( X0 != X1
| not(X0) = not(X1) ),
theory(equality) ).
cnf(c_446,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c_108,c_90]) ).
cnf(c_450,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[status(thm)],[c_108,c_95]) ).
cnf(c_557,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(and(X0,not(X1)))) ),
inference(resolution,[status(thm)],[c_143,c_104]) ).
cnf(c_559,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_143,c_98]) ).
cnf(c_581,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(X2,X0),or(X2,X1))) ),
inference(resolution,[status(thm)],[c_118,c_108]) ).
cnf(c_588,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X1,not(X0))) ),
inference(resolution,[status(thm)],[c_559,c_450]) ).
cnf(c_606,plain,
( ~ is_a_theorem(or(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(X0,X2))) ),
inference(resolution,[status(thm)],[c_121,c_108]) ).
cnf(c_722,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X2,X1)) ),
inference(resolution,[status(thm)],[c_581,c_108]) ).
cnf(c_895,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_142,c_140]) ).
cnf(c_896,plain,
( X0 != X1
| X2 != not(X1)
| not(X0) = X2 ),
inference(resolution,[status(thm)],[c_142,c_147]) ).
cnf(c_936,plain,
( X0 != X1
| X2 != X3
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[status(thm)],[c_144,c_143]) ).
cnf(c_984,plain,
( X0 != X1
| X2 != X3
| ~ is_a_theorem(or(X1,X3))
| is_a_theorem(or(X0,X2)) ),
inference(resolution,[status(thm)],[c_146,c_143]) ).
cnf(c_1007,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c_895,c_112]) ).
cnf(c_1009,plain,
and(X0,X1) = not(or(not(X0),not(X1))),
inference(resolution,[status(thm)],[c_895,c_109]) ).
cnf(c_1013,plain,
implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c_895,c_98]) ).
cnf(c_1077,plain,
( ~ is_a_theorem(or(not(X0),X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_1013,c_143]) ).
cnf(c_1128,plain,
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(implies(X1,not(X0))) ),
inference(resolution,[status(thm)],[c_1077,c_588]) ).
cnf(c_1255,plain,
( ~ is_a_theorem(not(and(not(X0),not(X1))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_1007,c_143]) ).
cnf(c_1528,plain,
( X0 != or(not(X1),not(X2))
| not(X0) = and(X1,X2) ),
inference(resolution,[status(thm)],[c_896,c_1009]) ).
cnf(c_1982,plain,
( X0 != or(X1,X2)
| X3 != or(X2,X1)
| is_a_theorem(implies(X0,X3)) ),
inference(resolution,[status(thm)],[c_936,c_95]) ).
cnf(c_2215,plain,
( X0 != not(X1)
| X2 != X3
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(or(X0,X2)) ),
inference(resolution,[status(thm)],[c_984,c_559]) ).
cnf(c_3301,plain,
( ~ is_a_theorem(implies(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_1255,c_557]) ).
cnf(c_3405,plain,
is_a_theorem(or(X0,or(X1,not(X0)))),
inference(resolution,[status(thm)],[c_3301,c_87]) ).
cnf(c_3532,plain,
is_a_theorem(or(X0,or(X1,not(X1)))),
inference(resolution,[status(thm)],[c_3405,c_606]) ).
cnf(c_3662,plain,
is_a_theorem(or(X0,not(X0))),
inference(resolution,[status(thm)],[c_3532,c_446]) ).
cnf(c_3676,plain,
is_a_theorem(or(not(X0),X0)),
inference(resolution,[status(thm)],[c_3662,c_450]) ).
cnf(c_3723,plain,
is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[c_3676,c_1077]) ).
cnf(c_7788,plain,
( X0 != or(X1,not(X2))
| is_a_theorem(implies(X0,implies(X2,X1))) ),
inference(resolution,[status(thm)],[c_1982,c_1013]) ).
cnf(c_9788,plain,
( X0 != X1
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(or(not(X2),X0)) ),
inference(resolution,[status(thm)],[c_2215,c_140]) ).
cnf(c_21910,plain,
( ~ is_a_theorem(implies(or(X0,not(X1)),X2))
| is_a_theorem(or(X1,X2)) ),
inference(resolution,[status(thm)],[c_722,c_3405]) ).
cnf(c_30431,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(resolution,[status(thm)],[c_7788,c_140]) ).
cnf(c_30559,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[status(thm)],[c_30431,c_108]) ).
cnf(c_37164,plain,
( X0 != X1
| is_a_theorem(or(not(X1),X0)) ),
inference(resolution,[status(thm)],[c_9788,c_3723]) ).
cnf(c_37905,plain,
( X0 != X1
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[status(thm)],[c_37164,c_1077]) ).
cnf(c_41779,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(resolution,[status(thm)],[c_1528,c_1013]) ).
cnf(c_46966,plain,
is_a_theorem(implies(and(X0,X1),not(implies(X0,not(X1))))),
inference(resolution,[status(thm)],[c_41779,c_37905]) ).
cnf(c_48663,plain,
is_a_theorem(implies(implies(X0,not(X1)),not(and(X0,X1)))),
inference(resolution,[status(thm)],[c_46966,c_1128]) ).
cnf(c_195821,plain,
is_a_theorem(or(X0,implies(X0,X1))),
inference(resolution,[status(thm)],[c_21910,c_30431]) ).
cnf(c_196341,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(or(X0,X2)) ),
inference(resolution,[status(thm)],[c_195821,c_722]) ).
cnf(c_246881,plain,
is_a_theorem(or(X0,not(and(X0,X1)))),
inference(resolution,[status(thm)],[c_196341,c_48663]) ).
cnf(c_250156,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(resolution,[status(thm)],[c_246881,c_30559]) ).
cnf(c_250325,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_250156]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL500+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu May 2 19:31:06 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 102.61/14.81 % SZS status Started for theBenchmark.p
% 102.61/14.81 % SZS status Theorem for theBenchmark.p
% 102.61/14.81
% 102.61/14.81 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 102.61/14.81
% 102.61/14.81 ------ iProver source info
% 102.61/14.81
% 102.61/14.81 git: date: 2024-05-02 19:28:25 +0000
% 102.61/14.81 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 102.61/14.81 git: non_committed_changes: false
% 102.61/14.81
% 102.61/14.81 ------ Parsing...
% 102.61/14.81 ------ Clausification by vclausify_rel & Parsing by iProver...
% 102.61/14.81
% 102.61/14.81 ------ Preprocessing... sf_s rm: 14 0s sf_e sf_s rm: 1 0s sf_e
% 102.61/14.81
% 102.61/14.81 ------ Preprocessing...
% 102.61/14.81
% 102.61/14.81 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 102.61/14.81 ------ Proving...
% 102.61/14.81 ------ Problem Properties
% 102.61/14.81
% 102.61/14.81
% 102.61/14.81 clauses 13
% 102.61/14.81 conjectures 0
% 102.61/14.81 EPR 0
% 102.61/14.81 Horn 13
% 102.61/14.81 unary 11
% 102.61/14.81 binary 1
% 102.61/14.81 lits 16
% 102.61/14.81 lits eq 6
% 102.61/14.81 fd_pure 0
% 102.61/14.81 fd_pseudo 0
% 102.61/14.81 fd_cond 0
% 102.61/14.81 fd_pseudo_cond 1
% 102.61/14.81 AC symbols 0
% 102.61/14.81
% 102.61/14.81 ------ Input Options Time Limit: Unbounded
% 102.61/14.81
% 102.61/14.81
% 102.61/14.81 ------
% 102.61/14.81 Current options:
% 102.61/14.81 ------
% 102.61/14.81
% 102.61/14.81
% 102.61/14.81
% 102.61/14.81
% 102.61/14.81 ------ Proving...
% 102.61/14.81
% 102.61/14.81
% 102.61/14.81 % SZS status Theorem for theBenchmark.p
% 102.61/14.81
% 102.61/14.81 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 102.61/14.82
% 102.61/14.82
%------------------------------------------------------------------------------