TSTP Solution File: LCL498+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 : Thu Aug 31 07:44:46 EDT 2023
% Result : Theorem 38.57s 6.23s
% Output : CNFRefutation 38.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 18
% Syntax : Number of formulae : 144 ( 50 unt; 0 def)
% Number of atoms : 270 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 232 ( 106 ~; 100 |; 2 &)
% ( 13 <=>; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 201 ( 3 sgn; 74 !; 2 ?)
% 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/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f21,axiom,
( cn3
<=> ! [X3] : is_a_theorem(implies(implies(not(X3),X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn3) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',r5) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).
fof(f45,conjecture,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',luka_cn3) ).
fof(f46,negated_conjecture,
~ cn3,
inference(negated_conjecture,[],[f45]) ).
fof(f52,plain,
( cn3
<=> ! [X0] : is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(rectify,[],[f21]) ).
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,
~ cn3,
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] : is_a_theorem(implies(implies(not(X0),X0),X0))
=> cn3 ),
inference(unused_predicate_definition_removal,[],[f52]) ).
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(f69,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f66]) ).
fof(f70,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f69]) ).
fof(f72,plain,
( cn3
| ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f73,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f74,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f75,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f76,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f60]) ).
fof(f77,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f59]) ).
fof(f80,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f82,plain,
( ? [X0] : ~ is_a_theorem(implies(implies(not(X0),X0),X0))
=> ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f72,f82]) ).
fof(f84,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f70]) ).
fof(f86,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(cnf_transformation,[],[f83]) ).
fof(f87,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f74]) ).
fof(f89,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f75]) ).
fof(f90,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f76]) ).
fof(f91,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f77]) ).
fof(f94,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f80]) ).
fof(f96,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
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(f108,plain,
~ cn3,
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,[],[f84]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(implies(not(sK0),sK0),sK0))
| cn3 ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_52,plain,
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_53,plain,
( ~ r2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_54,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_55,plain,
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_56,plain,
( ~ r5
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_59,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_61,plain,
op_implies_or,
inference(cnf_transformation,[],[f96]) ).
cnf(c_64,plain,
modus_ponens,
inference(cnf_transformation,[],[f99]) ).
cnf(c_65,plain,
r1,
inference(cnf_transformation,[],[f100]) ).
cnf(c_66,plain,
r2,
inference(cnf_transformation,[],[f101]) ).
cnf(c_67,plain,
r3,
inference(cnf_transformation,[],[f102]) ).
cnf(c_68,plain,
r4,
inference(cnf_transformation,[],[f103]) ).
cnf(c_69,plain,
r5,
inference(cnf_transformation,[],[f104]) ).
cnf(c_73,negated_conjecture,
~ cn3,
inference(cnf_transformation,[],[f108]) ).
cnf(c_74,plain,
( ~ r2
| is_a_theorem(implies(sK0,or(sK0,sK0))) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_75,plain,
( ~ r1
| is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_52]) ).
cnf(c_84,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_66,c_53]) ).
cnf(c_87,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).
cnf(c_92,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_67,c_54]) ).
cnf(c_95,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_61,c_59]) ).
cnf(c_101,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_64,c_49]) ).
cnf(c_102,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_101]) ).
cnf(c_112,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).
cnf(c_115,plain,
is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_68,c_55]) ).
cnf(c_221,plain,
( X0 != X1
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ),
theory(equality) ).
cnf(c_373,plain,
( X0 != implies(X1,or(X2,X1))
| ~ is_a_theorem(implies(X1,or(X2,X1)))
| is_a_theorem(X0) ),
inference(instantiation,[status(thm)],[c_221]) ).
cnf(c_404,plain,
( or(not(X0),or(X1,X0)) != implies(X0,or(X1,X0))
| ~ is_a_theorem(implies(X0,or(X1,X0)))
| is_a_theorem(or(not(X0),or(X1,X0))) ),
inference(instantiation,[status(thm)],[c_373]) ).
cnf(c_405,plain,
( or(not(sK0),or(sK0,sK0)) != implies(sK0,or(sK0,sK0))
| ~ is_a_theorem(implies(sK0,or(sK0,sK0)))
| is_a_theorem(or(not(sK0),or(sK0,sK0))) ),
inference(instantiation,[status(thm)],[c_404]) ).
cnf(c_510,plain,
is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(superposition,[status(thm)],[c_95,c_92]) ).
cnf(c_527,plain,
or(not(X0),or(X1,X0)) = implies(X0,or(X1,X0)),
inference(instantiation,[status(thm)],[c_95]) ).
cnf(c_528,plain,
or(not(sK0),or(sK0,sK0)) = implies(sK0,or(sK0,sK0)),
inference(instantiation,[status(thm)],[c_527]) ).
cnf(c_716,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),or(not(X2),X1)))),
inference(superposition,[status(thm)],[c_95,c_112]) ).
cnf(c_717,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(not(X2),X0),implies(X2,X1)))),
inference(superposition,[status(thm)],[c_95,c_112]) ).
cnf(c_736,plain,
is_a_theorem(implies(implies(X0,not(X1)),implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_95,c_510]) ).
cnf(c_903,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(resolution,[status(thm)],[c_102,c_92]) ).
cnf(c_986,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_221,c_95]) ).
cnf(c_1053,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(or(X1,not(X0))) ),
inference(resolution,[status(thm)],[c_986,c_903]) ).
cnf(c_1054,plain,
( ~ is_a_theorem(implies(sK0,sK0))
| is_a_theorem(or(sK0,not(sK0))) ),
inference(instantiation,[status(thm)],[c_1053]) ).
cnf(c_1199,plain,
( ~ is_a_theorem(implies(implies(X0,X1),implies(or(not(X2),X0),implies(X2,X1))))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(not(X2),X0),implies(X2,X1))) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_1527,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(superposition,[status(thm)],[c_95,c_716]) ).
cnf(c_1563,plain,
( ~ is_a_theorem(implies(implies(or(X0,X0),X0),implies(or(not(X1),or(X0,X0)),implies(X1,X0))))
| ~ is_a_theorem(implies(or(X0,X0),X0))
| is_a_theorem(implies(or(not(X1),or(X0,X0)),implies(X1,X0))) ),
inference(instantiation,[status(thm)],[c_1199]) ).
cnf(c_1564,plain,
( ~ is_a_theorem(implies(implies(or(sK0,sK0),sK0),implies(or(not(sK0),or(sK0,sK0)),implies(sK0,sK0))))
| ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| is_a_theorem(implies(or(not(sK0),or(sK0,sK0)),implies(sK0,sK0))) ),
inference(instantiation,[status(thm)],[c_1563]) ).
cnf(c_1638,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(or(X2,X0),or(X2,X1))) ),
inference(superposition,[status(thm)],[c_112,c_102]) ).
cnf(c_1640,plain,
( ~ is_a_theorem(or(X0,not(X1)))
| is_a_theorem(implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_510,c_102]) ).
cnf(c_1643,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X2,X0),or(not(X2),X1))) ),
inference(superposition,[status(thm)],[c_716,c_102]) ).
cnf(c_1645,plain,
( ~ is_a_theorem(implies(X0,not(X1)))
| is_a_theorem(implies(X1,not(X0))) ),
inference(superposition,[status(thm)],[c_736,c_102]) ).
cnf(c_1780,plain,
is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,or(not(X0),X2)))),
inference(superposition,[status(thm)],[c_95,c_115]) ).
cnf(c_1914,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X2,X0),implies(X2,X1))) ),
inference(superposition,[status(thm)],[c_1527,c_102]) ).
cnf(c_2268,plain,
is_a_theorem(implies(implies(or(X0,X0),X0),implies(or(not(X1),or(X0,X0)),implies(X1,X0)))),
inference(instantiation,[status(thm)],[c_717]) ).
cnf(c_2269,plain,
is_a_theorem(implies(implies(or(sK0,sK0),sK0),implies(or(not(sK0),or(sK0,sK0)),implies(sK0,sK0)))),
inference(instantiation,[status(thm)],[c_2268]) ).
cnf(c_3272,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X2,X1)) ),
inference(superposition,[status(thm)],[c_1638,c_102]) ).
cnf(c_4354,plain,
( ~ is_a_theorem(implies(or(not(X0),or(X1,X1)),implies(X0,X1)))
| ~ is_a_theorem(or(not(X0),or(X1,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_4355,plain,
( ~ is_a_theorem(implies(or(not(sK0),or(sK0,sK0)),implies(sK0,sK0)))
| ~ is_a_theorem(or(not(sK0),or(sK0,sK0)))
| is_a_theorem(implies(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_4354]) ).
cnf(c_5945,plain,
( ~ is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X2) ),
inference(instantiation,[status(thm)],[c_102]) ).
cnf(c_5967,plain,
( ~ is_a_theorem(implies(or(not(X0),not(X0)),not(X0)))
| is_a_theorem(implies(X0,not(or(not(X0),not(X0))))) ),
inference(instantiation,[status(thm)],[c_1645]) ).
cnf(c_6655,plain,
( ~ is_a_theorem(or(X0,not(or(not(X1),not(X2)))))
| is_a_theorem(implies(or(not(X1),not(X2)),X0)) ),
inference(instantiation,[status(thm)],[c_1640]) ).
cnf(c_6925,plain,
( ~ is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(or(X2,not(X0)))
| is_a_theorem(or(X2,X1)) ),
inference(instantiation,[status(thm)],[c_3272]) ).
cnf(c_7427,plain,
( ~ is_a_theorem(implies(implies(X0,X1),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(X0,X2)) ),
inference(instantiation,[status(thm)],[c_5945]) ).
cnf(c_8059,plain,
( ~ is_a_theorem(implies(not(X0),not(or(not(not(X0)),not(not(X0))))))
| ~ is_a_theorem(or(X1,not(X0)))
| is_a_theorem(or(X1,not(or(not(not(X0)),not(not(X0)))))) ),
inference(instantiation,[status(thm)],[c_6925]) ).
cnf(c_8060,plain,
( ~ is_a_theorem(implies(not(sK0),not(or(not(not(sK0)),not(not(sK0))))))
| ~ is_a_theorem(or(sK0,not(sK0)))
| is_a_theorem(or(sK0,not(or(not(not(sK0)),not(not(sK0)))))) ),
inference(instantiation,[status(thm)],[c_8059]) ).
cnf(c_12169,plain,
( ~ is_a_theorem(implies(implies(implies(not(sK0),sK0),X0),implies(implies(not(sK0),sK0),sK0)))
| ~ is_a_theorem(implies(implies(not(sK0),sK0),X0))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_7427]) ).
cnf(c_13432,plain,
is_a_theorem(implies(implies(X0,or(X1,X2)),or(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_95,c_1780]) ).
cnf(c_13890,plain,
( ~ is_a_theorem(implies(or(not(not(X0)),not(not(X0))),not(not(X0))))
| is_a_theorem(implies(not(X0),not(or(not(not(X0)),not(not(X0)))))) ),
inference(instantiation,[status(thm)],[c_5967]) ).
cnf(c_13891,plain,
( ~ is_a_theorem(implies(or(not(not(sK0)),not(not(sK0))),not(not(sK0))))
| is_a_theorem(implies(not(sK0),not(or(not(not(sK0)),not(not(sK0)))))) ),
inference(instantiation,[status(thm)],[c_13890]) ).
cnf(c_13930,plain,
( ~ is_a_theorem(implies(X0,or(X1,X2)))
| is_a_theorem(or(X1,implies(X0,X2))) ),
inference(superposition,[status(thm)],[c_13432,c_102]) ).
cnf(c_14605,plain,
( ~ is_a_theorem(implies(X0,sK0))
| is_a_theorem(implies(implies(implies(not(sK0),sK0),X0),implies(implies(not(sK0),sK0),sK0))) ),
inference(instantiation,[status(thm)],[c_1914]) ).
cnf(c_16262,plain,
is_a_theorem(implies(or(not(not(X0)),not(not(X0))),not(not(X0)))),
inference(instantiation,[status(thm)],[c_87]) ).
cnf(c_16263,plain,
is_a_theorem(implies(or(not(not(sK0)),not(not(sK0))),not(not(sK0)))),
inference(instantiation,[status(thm)],[c_16262]) ).
cnf(c_17103,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_87,c_102]) ).
cnf(c_20918,plain,
( ~ is_a_theorem(implies(implies(implies(not(sK0),sK0),or(not(not(sK0)),X0)),implies(implies(not(sK0),sK0),sK0)))
| ~ is_a_theorem(implies(implies(not(sK0),sK0),or(not(not(sK0)),X0)))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_12169]) ).
cnf(c_21248,plain,
( ~ is_a_theorem(or(X0,not(or(not(not(X1)),not(not(X1))))))
| is_a_theorem(implies(or(not(not(X1)),not(not(X1))),X0)) ),
inference(instantiation,[status(thm)],[c_6655]) ).
cnf(c_21249,plain,
( ~ is_a_theorem(or(sK0,not(or(not(not(sK0)),not(not(sK0))))))
| is_a_theorem(implies(or(not(not(sK0)),not(not(sK0))),sK0)) ),
inference(instantiation,[status(thm)],[c_21248]) ).
cnf(c_22114,plain,
is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_84,c_13930]) ).
cnf(c_22519,plain,
is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_22114,c_17103]) ).
cnf(c_22586,plain,
is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_22519,c_1645]) ).
cnf(c_22591,plain,
is_a_theorem(implies(sK0,not(not(sK0)))),
inference(instantiation,[status(thm)],[c_22586]) ).
cnf(c_26812,plain,
( ~ is_a_theorem(implies(or(not(not(sK0)),X0),sK0))
| is_a_theorem(implies(implies(implies(not(sK0),sK0),or(not(not(sK0)),X0)),implies(implies(not(sK0),sK0),sK0))) ),
inference(instantiation,[status(thm)],[c_14605]) ).
cnf(c_26913,plain,
( ~ is_a_theorem(implies(sK0,X0))
| is_a_theorem(implies(implies(not(sK0),sK0),or(not(not(sK0)),X0))) ),
inference(instantiation,[status(thm)],[c_1643]) ).
cnf(c_37702,plain,
( ~ is_a_theorem(implies(or(not(not(sK0)),not(not(sK0))),sK0))
| is_a_theorem(implies(implies(implies(not(sK0),sK0),or(not(not(sK0)),not(not(sK0)))),implies(implies(not(sK0),sK0),sK0))) ),
inference(instantiation,[status(thm)],[c_26812]) ).
cnf(c_37751,plain,
( ~ is_a_theorem(implies(sK0,not(X0)))
| is_a_theorem(implies(implies(not(sK0),sK0),or(not(not(sK0)),not(X0)))) ),
inference(instantiation,[status(thm)],[c_26913]) ).
cnf(c_49545,plain,
( ~ is_a_theorem(implies(implies(implies(not(sK0),sK0),or(not(not(sK0)),not(not(sK0)))),implies(implies(not(sK0),sK0),sK0)))
| ~ is_a_theorem(implies(implies(not(sK0),sK0),or(not(not(sK0)),not(not(sK0)))))
| is_a_theorem(implies(implies(not(sK0),sK0),sK0)) ),
inference(instantiation,[status(thm)],[c_20918]) ).
cnf(c_50376,plain,
( ~ is_a_theorem(implies(sK0,not(not(X0))))
| is_a_theorem(implies(implies(not(sK0),sK0),or(not(not(sK0)),not(not(X0))))) ),
inference(instantiation,[status(thm)],[c_37751]) ).
cnf(c_50377,plain,
( ~ is_a_theorem(implies(sK0,not(not(sK0))))
| is_a_theorem(implies(implies(not(sK0),sK0),or(not(not(sK0)),not(not(sK0))))) ),
inference(instantiation,[status(thm)],[c_50376]) ).
cnf(c_50378,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_50377,c_49545,c_37702,c_22591,c_21249,c_16263,c_13891,c_8060,c_4355,c_2269,c_1564,c_1054,c_528,c_405,c_51,c_75,c_74,c_73,c_65,c_66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LCL498+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 05:54:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 38.57/6.23 % SZS status Started for theBenchmark.p
% 38.57/6.23 % SZS status Theorem for theBenchmark.p
% 38.57/6.23
% 38.57/6.23 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 38.57/6.23
% 38.57/6.23 ------ iProver source info
% 38.57/6.23
% 38.57/6.23 git: date: 2023-05-31 18:12:56 +0000
% 38.57/6.23 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 38.57/6.23 git: non_committed_changes: false
% 38.57/6.23 git: last_make_outside_of_git: false
% 38.57/6.23
% 38.57/6.23 ------ Parsing...
% 38.57/6.23 ------ Clausification by vclausify_rel & Parsing by iProver...
% 38.57/6.23
% 38.57/6.23 ------ Preprocessing... sup_sim: 0 sf_s rm: 13 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 38.57/6.23
% 38.57/6.23 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 38.57/6.23
% 38.57/6.23 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 38.57/6.23 ------ Proving...
% 38.57/6.23 ------ Problem Properties
% 38.57/6.23
% 38.57/6.23
% 38.57/6.23 clauses 12
% 38.57/6.23 conjectures 0
% 38.57/6.23 EPR 0
% 38.57/6.23 Horn 12
% 38.57/6.23 unary 10
% 38.57/6.23 binary 1
% 38.57/6.23 lits 15
% 38.57/6.23 lits eq 5
% 38.57/6.23 fd_pure 0
% 38.57/6.23 fd_pseudo 0
% 38.57/6.23 fd_cond 0
% 38.57/6.23 fd_pseudo_cond 1
% 38.57/6.23 AC symbols 0
% 38.57/6.23
% 38.57/6.23 ------ Input Options Time Limit: Unbounded
% 38.57/6.23
% 38.57/6.23
% 38.57/6.23 ------
% 38.57/6.23 Current options:
% 38.57/6.23 ------
% 38.57/6.23
% 38.57/6.23
% 38.57/6.23
% 38.57/6.23
% 38.57/6.23 ------ Proving...
% 38.57/6.23
% 38.57/6.23
% 38.57/6.23 % SZS status Theorem for theBenchmark.p
% 38.57/6.23
% 38.57/6.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 38.57/6.23
% 38.57/6.24
%------------------------------------------------------------------------------