TSTP Solution File: LCL509+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL509+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 : Mon Jun 24 11:05:43 EDT 2024
% Result : Theorem 129.71s 18.27s
% Output : CNFRefutation 129.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 165 ( 65 unt; 0 def)
% Number of atoms : 292 ( 42 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 240 ( 113 ~; 106 |; 2 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 271 ( 11 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(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
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_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,negated_conjecture,
~ or_1,
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_1,
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(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
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_1
| ? [X0,X1] : ~ is_a_theorem(implies(X0,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(X0,or(X0,X1)))
=> ~ is_a_theorem(implies(sK0,or(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( or_1
| ~ is_a_theorem(implies(sK0,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_1
| ~ is_a_theorem(implies(sK0,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_1,
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(sK0,or(sK0,sK1)))
| or_1 ),
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_1,
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(sK0,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_184,plain,
X0 = X0,
theory(equality) ).
cnf(c_186,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_187,plain,
( X0 != X1
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ),
theory(equality) ).
cnf(c_188,plain,
( X0 != X1
| X2 != X3
| implies(X0,X2) = implies(X1,X3) ),
theory(equality) ).
cnf(c_191,plain,
( X0 != X1
| not(X0) = not(X1) ),
theory(equality) ).
cnf(c_329,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(and(X0,X0)) ),
inference(superposition,[status(thm)],[c_80,c_92]) ).
cnf(c_342,plain,
implies(not(X0),X1) = or(X0,X1),
inference(superposition,[status(thm)],[c_93,c_88]) ).
cnf(c_349,plain,
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(equiv(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_329]) ).
cnf(c_350,plain,
is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
cnf(c_352,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_96,c_77]) ).
cnf(c_358,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),not(and(not(X2),X0))))),
inference(superposition,[status(thm)],[c_88,c_99]) ).
cnf(c_385,plain,
or(and(not(X0),not(X1)),X2) = implies(or(X0,X1),X2),
inference(superposition,[status(thm)],[c_93,c_342]) ).
cnf(c_392,plain,
is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_342,c_80]) ).
cnf(c_393,plain,
is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(superposition,[status(thm)],[c_342,c_99]) ).
cnf(c_424,plain,
is_a_theorem(or(and(X0,not(X1)),and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[status(thm)],[c_88,c_392]) ).
cnf(c_531,plain,
is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_88,c_393]) ).
cnf(c_569,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c_92,c_77]) ).
cnf(c_573,plain,
is_a_theorem(or(and(X0,not(X0)),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_424]) ).
cnf(c_629,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(and(X0,not(X1)))) ),
inference(resolution,[status(thm)],[c_187,c_88]) ).
cnf(c_656,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(not(and(not(X0),not(X1)))) ),
inference(resolution,[status(thm)],[c_93,c_187]) ).
cnf(c_668,plain,
( X0 != X1
| ~ is_a_theorem(not(X1))
| is_a_theorem(not(X0)) ),
inference(resolution,[status(thm)],[c_191,c_187]) ).
cnf(c_696,plain,
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(and(implies(X0,X1),implies(X1,X0))) ),
inference(resolution,[status(thm)],[c_96,c_187]) ).
cnf(c_713,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_342,c_531]) ).
cnf(c_732,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(not(and(X1,X2)),not(and(X2,X0)))) ),
inference(resolution,[status(thm)],[c_99,c_92]) ).
cnf(c_745,plain,
( X0 != X1
| X1 = X0 ),
inference(resolution,[status(thm)],[c_186,c_184]) ).
cnf(c_756,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_713,c_92]) ).
cnf(c_863,plain,
( X0 != X1
| X2 != X3
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[status(thm)],[c_188,c_187]) ).
cnf(c_868,plain,
is_a_theorem(implies(implies(not(X0),X1),implies(implies(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_93,c_358]) ).
cnf(c_898,plain,
is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_342,c_868]) ).
cnf(c_970,plain,
or(X0,X1) = not(and(not(X0),not(X1))),
inference(resolution,[status(thm)],[c_745,c_93]) ).
cnf(c_972,plain,
implies(X0,X1) = not(and(X0,not(X1))),
inference(resolution,[status(thm)],[c_745,c_88]) ).
cnf(c_974,plain,
equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c_745,c_96]) ).
cnf(c_984,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(implies(X1,X2),or(X2,X0))) ),
inference(superposition,[status(thm)],[c_898,c_92]) ).
cnf(c_1086,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_984,c_92]) ).
cnf(c_1090,plain,
( ~ is_a_theorem(not(and(X0,not(X1))))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_972,c_187]) ).
cnf(c_1198,plain,
( ~ is_a_theorem(not(and(not(X0),not(X1))))
| is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_970,c_187]) ).
cnf(c_1262,plain,
( X0 != X1
| ~ is_a_theorem(not(not(X1)))
| is_a_theorem(not(not(X0))) ),
inference(resolution,[status(thm)],[c_668,c_191]) ).
cnf(c_1574,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_656,c_1090]) ).
cnf(c_1590,plain,
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X0))
| is_a_theorem(X1) ),
inference(resolution,[status(thm)],[c_1574,c_92]) ).
cnf(c_2625,plain,
( ~ is_a_theorem(equiv(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_696,c_569]) ).
cnf(c_2681,plain,
( X0 != X1
| X2 != and(X1,X1)
| is_a_theorem(implies(X0,X2)) ),
inference(resolution,[status(thm)],[c_863,c_80]) ).
cnf(c_3082,plain,
( ~ is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(not(and(X1,X2))) ),
inference(resolution,[status(thm)],[c_732,c_92]) ).
cnf(c_4514,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_80,c_1086]) ).
cnf(c_4515,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_1086]) ).
cnf(c_4517,plain,
( ~ is_a_theorem(or(X0,implies(X1,X1)))
| is_a_theorem(or(equiv(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_350,c_1086]) ).
cnf(c_4518,plain,
( ~ is_a_theorem(or(X0,equiv(X1,X2)))
| is_a_theorem(or(implies(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_352,c_1086]) ).
cnf(c_4807,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(or(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_385,c_4514]) ).
cnf(c_4823,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_392,c_4515]) ).
cnf(c_4828,plain,
( ~ is_a_theorem(or(and(X0,X1),X2))
| is_a_theorem(or(X0,and(X2,X2))) ),
inference(superposition,[status(thm)],[c_4514,c_4515]) ).
cnf(c_4932,plain,
is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_4823,c_4515]) ).
cnf(c_6337,plain,
( X0 != X1
| is_a_theorem(implies(X0,and(X1,X1))) ),
inference(resolution,[status(thm)],[c_2681,c_184]) ).
cnf(c_6345,plain,
( X0 != implies(X1,X1)
| is_a_theorem(implies(X0,equiv(X1,X1))) ),
inference(resolution,[status(thm)],[c_2681,c_974]) ).
cnf(c_7691,plain,
is_a_theorem(implies(not(and(X0,not(X0))),equiv(X0,X0))),
inference(resolution,[status(thm)],[c_6345,c_88]) ).
cnf(c_8030,plain,
( ~ is_a_theorem(not(and(X0,not(X0))))
| is_a_theorem(equiv(X0,X0)) ),
inference(resolution,[status(thm)],[c_7691,c_92]) ).
cnf(c_8550,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| ~ is_a_theorem(or(X1,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_4807,c_92]) ).
cnf(c_13027,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(equiv(X0,X0),and(X1,X0))) ),
inference(superposition,[status(thm)],[c_756,c_4517]) ).
cnf(c_14282,plain,
is_a_theorem(or(implies(X0,X0),and(X0,not(X0)))),
inference(superposition,[status(thm)],[c_573,c_4518]) ).
cnf(c_14331,plain,
is_a_theorem(or(X0,implies(X0,X0))),
inference(superposition,[status(thm)],[c_14282,c_4515]) ).
cnf(c_16994,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(not(and(not(X2),X0))) ),
inference(resolution,[status(thm)],[c_3082,c_629]) ).
cnf(c_20610,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,and(X0,X0))) ),
inference(superposition,[status(thm)],[c_4514,c_4828]) ).
cnf(c_26336,plain,
( ~ is_a_theorem(implies(X0,and(X1,X2)))
| is_a_theorem(not(and(not(X1),X0))) ),
inference(resolution,[status(thm)],[c_16994,c_77]) ).
cnf(c_27042,plain,
is_a_theorem(not(and(not(X0),X0))),
inference(resolution,[status(thm)],[c_26336,c_80]) ).
cnf(c_27048,plain,
( X0 != X1
| is_a_theorem(not(and(not(X1),X0))) ),
inference(resolution,[status(thm)],[c_26336,c_6337]) ).
cnf(c_27225,plain,
is_a_theorem(or(not(X0),X0)),
inference(resolution,[status(thm)],[c_27042,c_1198]) ).
cnf(c_27228,plain,
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(not(and(X1,X0))) ),
inference(resolution,[status(thm)],[c_27042,c_3082]) ).
cnf(c_27559,plain,
( ~ is_a_theorem(not(not(X0)))
| is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c_27225,c_1590]) ).
cnf(c_30997,plain,
( not(X0) != X1
| is_a_theorem(implies(not(X1),X0)) ),
inference(resolution,[status(thm)],[c_27048,c_1090]) ).
cnf(c_33614,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(not(and(X1,not(X0)))) ),
inference(resolution,[status(thm)],[c_27228,c_1574]) ).
cnf(c_34376,plain,
( ~ is_a_theorem(not(not(implies(X0,X1))))
| is_a_theorem(not(not(not(and(X0,not(X1)))))) ),
inference(resolution,[status(thm)],[c_1262,c_88]) ).
cnf(c_37593,plain,
( ~ is_a_theorem(not(not(implies(X0,X1))))
| is_a_theorem(not(and(X0,not(X1)))) ),
inference(resolution,[status(thm)],[c_34376,c_27559]) ).
cnf(c_37733,plain,
is_a_theorem(implies(not(or(X0,X1)),and(not(X0),not(X1)))),
inference(resolution,[status(thm)],[c_30997,c_93]) ).
cnf(c_40706,plain,
is_a_theorem(not(and(not(not(X0)),not(or(X0,X1))))),
inference(resolution,[status(thm)],[c_37733,c_26336]) ).
cnf(c_40713,plain,
is_a_theorem(implies(not(not(X0)),or(X0,X1))),
inference(resolution,[status(thm)],[c_40706,c_1090]) ).
cnf(c_50997,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(resolution,[status(thm)],[c_33614,c_1090]) ).
cnf(c_63954,plain,
( ~ is_a_theorem(or(and(X0,X1),and(X0,X1)))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_4932,c_8550]) ).
cnf(c_65655,plain,
( ~ is_a_theorem(or(X0,and(X0,X0)))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_20610,c_63954]) ).
cnf(c_66722,plain,
( ~ is_a_theorem(or(implies(X0,X0),equiv(X0,X0)))
| is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_65655]) ).
cnf(c_87175,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_13027,c_4515]) ).
cnf(c_87370,plain,
( ~ is_a_theorem(or(X0,implies(X0,X0)))
| is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_87175,c_66722]) ).
cnf(c_95758,plain,
( ~ is_a_theorem(not(not(implies(X0,X0))))
| is_a_theorem(equiv(X0,X0)) ),
inference(resolution,[status(thm)],[c_37593,c_8030]) ).
cnf(c_95994,plain,
is_a_theorem(equiv(X0,X0)),
inference(global_subsumption_just,[status(thm)],[c_95758,c_349,c_14331,c_87370]) ).
cnf(c_96004,plain,
is_a_theorem(implies(X0,X0)),
inference(resolution,[status(thm)],[c_95994,c_2625]) ).
cnf(c_96124,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(not(and(not(X1),X0))) ),
inference(resolution,[status(thm)],[c_96004,c_16994]) ).
cnf(c_106049,plain,
( ~ is_a_theorem(implies(not(X0),X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[status(thm)],[c_96124,c_1198]) ).
cnf(c_106682,plain,
is_a_theorem(or(or(X0,X1),not(X0))),
inference(resolution,[status(thm)],[c_106049,c_40713]) ).
cnf(c_107783,plain,
is_a_theorem(implies(X0,or(X0,X1))),
inference(resolution,[status(thm)],[c_106682,c_50997]) ).
cnf(c_109622,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_107783]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL509+1 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Jun 22 12:55:39 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 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
% 129.71/18.27 % SZS status Started for theBenchmark.p
% 129.71/18.27 % SZS status Theorem for theBenchmark.p
% 129.71/18.27
% 129.71/18.27 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 129.71/18.27
% 129.71/18.27 ------ iProver source info
% 129.71/18.27
% 129.71/18.27 git: date: 2024-06-12 09:56:46 +0000
% 129.71/18.27 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 129.71/18.27 git: non_committed_changes: false
% 129.71/18.27
% 129.71/18.27 ------ Parsing...
% 129.71/18.27 ------ Clausification by vclausify_rel & Parsing by iProver...
% 129.71/18.27
% 129.71/18.27 ------ Preprocessing... sup_sim: 0 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
% 129.71/18.27
% 129.71/18.27 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 129.71/18.27
% 129.71/18.27 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 129.71/18.27 ------ Proving...
% 129.71/18.27 ------ Problem Properties
% 129.71/18.27
% 129.71/18.27
% 129.71/18.27 clauses 9
% 129.71/18.27 conjectures 0
% 129.71/18.27 EPR 0
% 129.71/18.27 Horn 9
% 129.71/18.27 unary 7
% 129.71/18.27 binary 1
% 129.71/18.27 lits 12
% 129.71/18.27 lits eq 4
% 129.71/18.27 fd_pure 0
% 129.71/18.27 fd_pseudo 0
% 129.71/18.27 fd_cond 0
% 129.71/18.27 fd_pseudo_cond 1
% 129.71/18.27 AC symbols 0
% 129.71/18.27
% 129.71/18.27 ------ Input Options Time Limit: Unbounded
% 129.71/18.27
% 129.71/18.27
% 129.71/18.27 ------
% 129.71/18.27 Current options:
% 129.71/18.27 ------
% 129.71/18.27
% 129.71/18.27
% 129.71/18.27
% 129.71/18.27
% 129.71/18.27 ------ Proving...
% 129.71/18.27
% 129.71/18.27
% 129.71/18.27 % SZS status Theorem for theBenchmark.p
% 129.71/18.27
% 129.71/18.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 129.71/18.27
% 129.71/18.27
%------------------------------------------------------------------------------