TSTP Solution File: LCL510+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL510+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n017.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 02:38:04 EDT 2024
% Result : Theorem 77.43s 11.25s
% Output : CNFRefutation 77.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 17
% Syntax : Number of formulae : 228 ( 100 unt; 0 def)
% Number of atoms : 381 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 292 ( 139 ~; 132 |; 2 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 422 ( 58 sgn 62 !; 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(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
fof(f16,axiom,
( kn1
<=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(not(and(X4,X5)),not(and(X5,X3))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
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(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(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
fof(f44,negated_conjecture,
~ or_2,
inference(negated_conjecture,[],[f43]) ).
fof(f45,plain,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(rectify,[],[f16]) ).
fof(f46,plain,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(rectify,[],[f17]) ).
fof(f47,plain,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(rectify,[],[f18]) ).
fof(f56,plain,
~ or_2,
inference(flattening,[],[f44]) ).
fof(f57,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f47]) ).
fof(f58,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f46]) ).
fof(f59,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f45]) ).
fof(f60,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> or_2 ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f62,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(f65,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f62]) ).
fof(f66,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f65]) ).
fof(f68,plain,
( or_2
| ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f69,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(ennf_transformation,[],[f59]) ).
fof(f70,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(ennf_transformation,[],[f58]) ).
fof(f71,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(ennf_transformation,[],[f57]) ).
fof(f72,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f73,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f74,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f75,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
=> ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f68,f75]) ).
fof(f77,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f66]) ).
fof(f79,plain,
( or_2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f80,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f69]) ).
fof(f81,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f82,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f71]) ).
fof(f83,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f72]) ).
fof(f84,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f73]) ).
fof(f85,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f90,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f91,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f92,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f94,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f96,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f97,plain,
~ or_2,
inference(cnf_transformation,[],[f56]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(sK1,or(sK0,sK1)))
| or_2 ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_52,plain,
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f80]) ).
cnf(c_53,plain,
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_54,plain,
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_55,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
cnf(c_56,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
cnf(c_57,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_61,plain,
modus_ponens,
inference(cnf_transformation,[],[f89]) ).
cnf(c_62,plain,
kn1,
inference(cnf_transformation,[],[f90]) ).
cnf(c_63,plain,
kn2,
inference(cnf_transformation,[],[f91]) ).
cnf(c_64,plain,
kn3,
inference(cnf_transformation,[],[f92]) ).
cnf(c_66,plain,
op_or,
inference(cnf_transformation,[],[f94]) ).
cnf(c_67,plain,
op_implies_and,
inference(cnf_transformation,[],[f95]) ).
cnf(c_68,plain,
op_equiv,
inference(cnf_transformation,[],[f96]) ).
cnf(c_69,negated_conjecture,
~ or_2,
inference(cnf_transformation,[],[f97]) ).
cnf(c_77,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_53,c_63,c_53]) ).
cnf(c_80,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_62,c_52]) ).
cnf(c_83,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).
cnf(c_88,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_67,c_56]) ).
cnf(c_91,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).
cnf(c_92,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_91]) ).
cnf(c_93,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_66,c_55]) ).
cnf(c_96,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_68,c_57]) ).
cnf(c_99,plain,
is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(global_subsumption_just,[status(thm)],[c_54,c_64,c_54]) ).
cnf(c_152,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_93,c_88]) ).
cnf(c_153,plain,
is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(demodulation,[status(thm)],[c_99,c_152]) ).
cnf(c_346,plain,
implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
inference(superposition,[status(thm)],[c_88,c_88]) ).
cnf(c_349,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_88,c_152]) ).
cnf(c_360,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(and(X0,X0)) ),
inference(superposition,[status(thm)],[c_80,c_92]) ).
cnf(c_361,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_77,c_92]) ).
cnf(c_362,plain,
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_152,c_92]) ).
cnf(c_378,plain,
and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1),
inference(superposition,[status(thm)],[c_152,c_96]) ).
cnf(c_380,plain,
is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
cnf(c_381,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_96,c_77]) ).
cnf(c_413,plain,
is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
cnf(c_422,plain,
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(equiv(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_360]) ).
cnf(c_424,plain,
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_361]) ).
cnf(c_430,plain,
is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_88,c_153]) ).
cnf(c_472,plain,
implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[c_152,c_346]) ).
cnf(c_519,plain,
( ~ is_a_theorem(equiv(not(X0),X1))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_378,c_361]) ).
cnf(c_717,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(and(X1,X2),not(and(X2,X0)))) ),
inference(superposition,[status(thm)],[c_153,c_92]) ).
cnf(c_739,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(light_normalisation,[status(thm)],[c_430,c_152]) ).
cnf(c_743,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
inference(superposition,[status(thm)],[c_152,c_739]) ).
cnf(c_744,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_739,c_92]) ).
cnf(c_779,plain,
is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(demodulation,[status(thm)],[c_743,c_349]) ).
cnf(c_781,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(or(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_152,c_779]) ).
cnf(c_783,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(implies(X1,X2),or(X2,X0))) ),
inference(superposition,[status(thm)],[c_779,c_92]) ).
cnf(c_3743,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_783,c_92]) ).
cnf(c_3890,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_80,c_3743]) ).
cnf(c_3891,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_3743]) ).
cnf(c_3893,plain,
( ~ is_a_theorem(or(X0,implies(X1,X1)))
| is_a_theorem(or(equiv(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_380,c_3743]) ).
cnf(c_3894,plain,
( ~ is_a_theorem(or(X0,equiv(X1,X2)))
| is_a_theorem(or(implies(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_381,c_3743]) ).
cnf(c_3911,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(implies(not(X1),X1),X0)) ),
inference(superposition,[status(thm)],[c_349,c_3890]) ).
cnf(c_3918,plain,
( ~ is_a_theorem(or(and(X0,X1),X2))
| is_a_theorem(or(X0,and(X2,X2))) ),
inference(superposition,[status(thm)],[c_3890,c_3891]) ).
cnf(c_3919,plain,
( ~ is_a_theorem(implies(implies(X0,X1),and(X2,X3)))
| is_a_theorem(or(X2,and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[c_349,c_3891]) ).
cnf(c_3926,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(equiv(X0,X0),and(X1,X0))) ),
inference(superposition,[status(thm)],[c_744,c_3893]) ).
cnf(c_3937,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(or(X1,X1),X0)) ),
inference(demodulation,[status(thm)],[c_3911,c_152]) ).
cnf(c_3944,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_3937,c_92]) ).
cnf(c_4012,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(or(X0,and(X2,X2))) ),
inference(superposition,[status(thm)],[c_349,c_3918]) ).
cnf(c_4033,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_3926,c_3891]) ).
cnf(c_4056,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_4033,c_3894]) ).
cnf(c_4110,plain,
is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))),
inference(superposition,[status(thm)],[c_380,c_4012]) ).
cnf(c_4215,plain,
is_a_theorem(or(equiv(X0,X0),X0)),
inference(superposition,[status(thm)],[c_4110,c_3891]) ).
cnf(c_4221,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(equiv(not(X0),not(X0))) ),
inference(superposition,[status(thm)],[c_4215,c_3944]) ).
cnf(c_4969,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(or(X0,not(X0))) ),
inference(superposition,[status(thm)],[c_4221,c_519]) ).
cnf(c_4980,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_4969,c_3944]) ).
cnf(c_5048,plain,
( ~ is_a_theorem(or(X0,implies(X0,X0)))
| is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_4056,c_4980]) ).
cnf(c_5518,plain,
is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_80,c_3919]) ).
cnf(c_5657,plain,
is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_5518,c_3891]) ).
cnf(c_5659,plain,
is_a_theorem(implies(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_5048,c_5657]) ).
cnf(c_5660,plain,
is_a_theorem(equiv(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_422,c_5659]) ).
cnf(c_8016,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_5660,c_424]) ).
cnf(c_8017,plain,
is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_8016]) ).
cnf(c_8128,plain,
( ~ is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(implies(X1,X2)) ),
inference(superposition,[status(thm)],[c_744,c_362]) ).
cnf(c_8133,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_783,c_92]) ).
cnf(c_8289,plain,
is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[status(thm)],[c_472,c_80]) ).
cnf(c_8311,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(or(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_8289,c_8128]) ).
cnf(c_8349,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_8311,c_92]) ).
cnf(c_8372,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_80,c_8133]) ).
cnf(c_8373,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_8133]) ).
cnf(c_8379,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_8016,c_8133]) ).
cnf(c_8393,plain,
is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_413,c_8379]) ).
cnf(c_8395,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_8017,c_8379]) ).
cnf(c_8396,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(implies(X2,X0),and(X1,X2))) ),
inference(superposition,[status(thm)],[c_744,c_8379]) ).
cnf(c_8405,plain,
is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_8395]) ).
cnf(c_8428,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X0,and(X1,X1))) ),
inference(superposition,[status(thm)],[c_8372,c_8379]) ).
cnf(c_8437,plain,
is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_8405,c_8373]) ).
cnf(c_8563,plain,
is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_8437,c_8379]) ).
cnf(c_8565,plain,
is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[status(thm)],[c_152,c_8563]) ).
cnf(c_8597,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_8565,c_8349]) ).
cnf(c_8609,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_8393,c_152,c_349]) ).
cnf(c_8612,plain,
( ~ is_a_theorem(or(X0,or(X1,X1)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_8609,c_8133]) ).
cnf(c_8890,plain,
( ~ is_a_theorem(or(X0,implies(X1,X1)))
| is_a_theorem(or(X0,equiv(X1,X1))) ),
inference(superposition,[status(thm)],[c_96,c_8428]) ).
cnf(c_9025,plain,
is_a_theorem(or(X0,equiv(X0,X0))),
inference(superposition,[status(thm)],[c_8437,c_8890]) ).
cnf(c_11585,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_8396,c_8373]) ).
cnf(c_12773,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_11585,c_8890]) ).
cnf(c_13059,plain,
( ~ is_a_theorem(or(X0,equiv(X0,X0)))
| is_a_theorem(or(equiv(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_12773,c_8597]) ).
cnf(c_13066,plain,
is_a_theorem(or(equiv(X0,X0),X1)),
inference(forward_subsumption_resolution,[status(thm)],[c_13059,c_9025]) ).
cnf(c_13085,plain,
is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_13066,c_8612]) ).
cnf(c_16776,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_5660,c_424]) ).
cnf(c_16777,plain,
is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_16776]) ).
cnf(c_16916,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_783,c_92]) ).
cnf(c_17071,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_80,c_16916]) ).
cnf(c_17072,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_16916]) ).
cnf(c_17075,plain,
( ~ is_a_theorem(or(X0,equiv(X1,X2)))
| is_a_theorem(or(implies(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_381,c_16916]) ).
cnf(c_17078,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_16776,c_16916]) ).
cnf(c_17099,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_413,c_17072]) ).
cnf(c_17100,plain,
( ~ is_a_theorem(or(and(X0,X1),X2))
| is_a_theorem(or(X0,and(X2,X2))) ),
inference(superposition,[status(thm)],[c_17071,c_17072]) ).
cnf(c_17149,plain,
is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_17099,c_17072]) ).
cnf(c_17157,plain,
is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_88,c_17149]) ).
cnf(c_17229,plain,
is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_413,c_17078]) ).
cnf(c_17239,plain,
is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_17157,c_17078]) ).
cnf(c_17252,plain,
is_a_theorem(or(X0,implies(and(X0,X1),X2))),
inference(superposition,[status(thm)],[c_17239,c_17072]) ).
cnf(c_17276,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_17229,c_152,c_349]) ).
cnf(c_17278,plain,
( ~ is_a_theorem(or(X0,or(X1,X1)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_17276,c_16916]) ).
cnf(c_17338,plain,
is_a_theorem(or(implies(and(X0,X1),X2),X0)),
inference(superposition,[status(thm)],[c_17252,c_17078]) ).
cnf(c_17418,plain,
is_a_theorem(or(X0,and(not(and(X0,X1)),not(and(X0,X1))))),
inference(superposition,[status(thm)],[c_16777,c_17100]) ).
cnf(c_17828,plain,
is_a_theorem(or(X0,implies(and(or(X0,X0),X1),X2))),
inference(superposition,[status(thm)],[c_17338,c_17278]) ).
cnf(c_18108,plain,
is_a_theorem(or(X0,implies(equiv(not(X0),X0),X1))),
inference(superposition,[status(thm)],[c_378,c_17828]) ).
cnf(c_18118,plain,
is_a_theorem(or(implies(equiv(not(X0),X0),X1),X0)),
inference(superposition,[status(thm)],[c_18108,c_17078]) ).
cnf(c_18128,plain,
is_a_theorem(or(implies(X0,X1),implies(equiv(not(equiv(X0,X1)),equiv(X0,X1)),X2))),
inference(superposition,[status(thm)],[c_18118,c_17075]) ).
cnf(c_39380,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_5660,c_424]) ).
cnf(c_39559,plain,
( ~ is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(implies(X1,X2)) ),
inference(superposition,[status(thm)],[c_744,c_362]) ).
cnf(c_39564,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_783,c_92]) ).
cnf(c_40019,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_80,c_39564]) ).
cnf(c_40020,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_39564]) ).
cnf(c_40026,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_39380,c_39564]) ).
cnf(c_40043,plain,
is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_413,c_40026]) ).
cnf(c_40044,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(not(and(X2,X0)),and(X1,X2))) ),
inference(superposition,[status(thm)],[c_717,c_40026]) ).
cnf(c_40046,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(implies(X2,X0),and(X1,X2))) ),
inference(superposition,[status(thm)],[c_744,c_40026]) ).
cnf(c_40071,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(or(X2,and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[c_349,c_40026]) ).
cnf(c_40087,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_40043,c_152,c_349]) ).
cnf(c_40091,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_40087,c_92]) ).
cnf(c_40115,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(implies(not(X1),X1),X0)) ),
inference(superposition,[status(thm)],[c_349,c_40019]) ).
cnf(c_40117,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X0,and(X1,X1))) ),
inference(superposition,[status(thm)],[c_40019,c_40026]) ).
cnf(c_40129,plain,
is_a_theorem(or(not(and(X0,X1)),X0)),
inference(superposition,[status(thm)],[c_17418,c_40020]) ).
cnf(c_40182,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_40046,c_40020]) ).
cnf(c_40764,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(or(X1,X1),X0)) ),
inference(demodulation,[status(thm)],[c_40115,c_152]) ).
cnf(c_40770,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_40764,c_92]) ).
cnf(c_40800,plain,
( ~ is_a_theorem(or(X0,implies(X1,X1)))
| is_a_theorem(or(X0,equiv(X1,X1))) ),
inference(superposition,[status(thm)],[c_96,c_40117]) ).
cnf(c_40817,plain,
is_a_theorem(or(X0,equiv(X1,X1))),
inference(global_subsumption_just,[status(thm)],[c_40800,c_13085]) ).
cnf(c_41061,plain,
( ~ is_a_theorem(or(X0,implies(X1,X0)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_40182,c_40091]) ).
cnf(c_41384,plain,
is_a_theorem(implies(equiv(not(equiv(X0,X1)),equiv(X0,X1)),implies(X0,X1))),
inference(superposition,[status(thm)],[c_18128,c_41061]) ).
cnf(c_41838,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(not(and(not(X0),X1))) ),
inference(superposition,[status(thm)],[c_40129,c_40770]) ).
cnf(c_41965,plain,
is_a_theorem(not(and(not(equiv(X0,X0)),X1))),
inference(superposition,[status(thm)],[c_40817,c_41838]) ).
cnf(c_42771,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X1,not(and(X2,X0)))) ),
inference(superposition,[status(thm)],[c_40044,c_40020]) ).
cnf(c_42892,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(or(X0,X2)) ),
inference(superposition,[status(thm)],[c_40071,c_40020]) ).
cnf(c_49359,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| is_a_theorem(or(X2,not(equiv(X1,X0)))) ),
inference(superposition,[status(thm)],[c_96,c_42771]) ).
cnf(c_53858,plain,
( ~ is_a_theorem(or(X0,not(equiv(X1,X1))))
| is_a_theorem(implies(X2,X0)) ),
inference(superposition,[status(thm)],[c_41965,c_39559]) ).
cnf(c_75860,plain,
( ~ is_a_theorem(implies(implies(X0,X0),X1))
| is_a_theorem(implies(X2,X1)) ),
inference(superposition,[status(thm)],[c_49359,c_53858]) ).
cnf(c_80151,plain,
( ~ is_a_theorem(implies(or(X0,not(X0)),X1))
| is_a_theorem(implies(X2,X1)) ),
inference(superposition,[status(thm)],[c_152,c_75860]) ).
cnf(c_83874,plain,
is_a_theorem(implies(X0,implies(or(X1,X2),or(X2,X1)))),
inference(superposition,[status(thm)],[c_781,c_80151]) ).
cnf(c_85643,plain,
is_a_theorem(or(X0,implies(or(X1,X2),or(X2,X1)))),
inference(superposition,[status(thm)],[c_83874,c_42892]) ).
cnf(c_89400,plain,
is_a_theorem(implies(equiv(not(equiv(not(X0),X1)),equiv(not(X0),X1)),or(X0,X1))),
inference(superposition,[status(thm)],[c_152,c_41384]) ).
cnf(c_89441,plain,
( ~ is_a_theorem(not(X0))
| is_a_theorem(implies(or(X1,X2),or(X2,X1))) ),
inference(superposition,[status(thm)],[c_85643,c_362]) ).
cnf(c_89485,plain,
is_a_theorem(or(X0,and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[status(thm)],[c_88,c_17418]) ).
cnf(c_89545,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(X2,X3),or(X3,X2))) ),
inference(superposition,[status(thm)],[c_88,c_89441]) ).
cnf(c_89617,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_783,c_92]) ).
cnf(c_89646,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(superposition,[status(thm)],[c_89400,c_89545]) ).
cnf(c_89719,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_89646,c_92]) ).
cnf(c_89722,plain,
is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_413,c_89719]) ).
cnf(c_89724,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(implies(X2,X0),and(X1,X2))) ),
inference(superposition,[status(thm)],[c_744,c_89719]) ).
cnf(c_89749,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_89722,c_152,c_349]) ).
cnf(c_89751,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_89749,c_92]) ).
cnf(c_91127,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_89617]) ).
cnf(c_91217,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_89724,c_91127]) ).
cnf(c_92390,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(implies(X2,X0),X1)) ),
inference(superposition,[status(thm)],[c_91217,c_89719]) ).
cnf(c_92393,plain,
( ~ is_a_theorem(or(X0,implies(X1,X0)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_91217,c_89751]) ).
cnf(c_94017,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,implies(X3,X0))) ),
inference(superposition,[status(thm)],[c_92390,c_91127]) ).
cnf(c_98929,plain,
is_a_theorem(or(implies(X0,X1),implies(X2,X0))),
inference(superposition,[status(thm)],[c_89485,c_94017]) ).
cnf(c_99741,plain,
is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
inference(superposition,[status(thm)],[c_98929,c_89719]) ).
cnf(c_100111,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_99741,c_92393]) ).
cnf(c_100118,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(superposition,[status(thm)],[c_152,c_100111]) ).
cnf(c_100123,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_100118]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LCL510+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.12 % Command : run_iprover %s %d THM
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu May 2 18:39:21 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.17/0.44 Running first-order theorem proving
% 0.17/0.44 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
% 77.43/11.25 % SZS status Started for theBenchmark.p
% 77.43/11.25 % SZS status Theorem for theBenchmark.p
% 77.43/11.25
% 77.43/11.25 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 77.43/11.25
% 77.43/11.25 ------ iProver source info
% 77.43/11.25
% 77.43/11.25 git: date: 2024-05-02 19:28:25 +0000
% 77.43/11.25 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 77.43/11.25 git: non_committed_changes: false
% 77.43/11.25
% 77.43/11.25 ------ Parsing...
% 77.43/11.25 ------ Clausification by vclausify_rel & Parsing by iProver...
% 77.43/11.25
% 77.43/11.25 ------ Preprocessing... sup_sim: 2 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 77.43/11.25
% 77.43/11.25 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 77.43/11.25
% 77.43/11.25 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 77.43/11.25 ------ Proving...
% 77.43/11.25 ------ Problem Properties
% 77.43/11.25
% 77.43/11.25
% 77.43/11.25 clauses 9
% 77.43/11.25 conjectures 0
% 77.43/11.25 EPR 0
% 77.43/11.25 Horn 9
% 77.43/11.25 unary 7
% 77.43/11.25 binary 1
% 77.43/11.25 lits 12
% 77.43/11.25 lits eq 4
% 77.43/11.25 fd_pure 0
% 77.43/11.25 fd_pseudo 0
% 77.43/11.25 fd_cond 0
% 77.43/11.25 fd_pseudo_cond 1
% 77.43/11.25 AC symbols 0
% 77.43/11.25
% 77.43/11.25 ------ Input Options Time Limit: Unbounded
% 77.43/11.25
% 77.43/11.25
% 77.43/11.25 ------
% 77.43/11.25 Current options:
% 77.43/11.25 ------
% 77.43/11.25
% 77.43/11.25
% 77.43/11.25
% 77.43/11.25
% 77.43/11.25 ------ Proving...
% 77.43/11.25
% 77.43/11.25
% 77.43/11.25 % SZS status Theorem for theBenchmark.p
% 77.43/11.25
% 77.43/11.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 77.43/11.25
% 77.43/11.25
%------------------------------------------------------------------------------