TSTP Solution File: LCL504+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL504+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 02:38:03 EDT 2024
% Result : Theorem 159.91s 21.83s
% Output : CNFRefutation 159.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 17
% Syntax : Number of formulae : 170 ( 63 unt; 0 def)
% Number of atoms : 317 ( 20 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 279 ( 132 ~; 126 |; 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 : 257 ( 10 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/sandbox2/benchmark/theBenchmark.p',modus_ponens) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_2) ).
fof(f16,axiom,
( kn1
<=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X3,X4] : is_a_theorem(implies(and(X3,X4),X3)) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f44,negated_conjecture,
~ implies_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,
~ implies_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(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> implies_2 ),
inference(unused_predicate_definition_removal,[],[f5]) ).
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,
( implies_2
| ? [X0,X1] : ~ is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(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(implies(X0,implies(X0,X1)),implies(X0,X1)))
=> ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(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,
( implies_2
| ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(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,
~ implies_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(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))
| implies_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,
~ implies_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_86,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_86]) ).
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_349,plain,
or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_86,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_380,plain,
and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1),
inference(superposition,[status(thm)],[c_152,c_96]) ).
cnf(c_381,plain,
and(implies(X0,not(X1)),or(X1,X0)) = equiv(X0,not(X1)),
inference(superposition,[status(thm)],[c_152,c_96]) ).
cnf(c_382,plain,
( ~ is_a_theorem(implies(X0,X0))
| is_a_theorem(equiv(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_360]) ).
cnf(c_383,plain,
is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
cnf(c_384,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_96,c_77]) ).
cnf(c_431,plain,
is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_86,c_153]) ).
cnf(c_474,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),not(and(not(X2),X0))))),
inference(superposition,[status(thm)],[c_349,c_153]) ).
cnf(c_646,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_721,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(light_normalisation,[status(thm)],[c_431,c_152]) ).
cnf(c_725,plain,
is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
inference(superposition,[status(thm)],[c_152,c_721]) ).
cnf(c_726,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_721,c_92]) ).
cnf(c_748,plain,
is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(demodulation,[status(thm)],[c_725,c_349]) ).
cnf(c_752,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(implies(implies(X1,X2),or(X2,X0))) ),
inference(superposition,[status(thm)],[c_748,c_92]) ).
cnf(c_799,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X1,X2),not(and(not(X2),X0)))) ),
inference(superposition,[status(thm)],[c_474,c_92]) ).
cnf(c_1888,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_726,c_362]) ).
cnf(c_1902,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_752,c_92]) ).
cnf(c_1918,plain,
and(or(X0,not(X1)),or(X1,not(X0))) = equiv(not(X0),not(X1)),
inference(superposition,[status(thm)],[c_152,c_380]) ).
cnf(c_1932,plain,
( ~ is_a_theorem(equiv(X0,not(X1)))
| is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_381,c_361]) ).
cnf(c_1969,plain,
( ~ is_a_theorem(implies(not(X0),X1))
| is_a_theorem(or(and(X1,X2),implies(X2,X0))) ),
inference(superposition,[status(thm)],[c_86,c_646]) ).
cnf(c_1974,plain,
( ~ is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(not(and(X1,X2))) ),
inference(superposition,[status(thm)],[c_646,c_362]) ).
cnf(c_1987,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(and(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_80,c_1902]) ).
cnf(c_1988,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_1902]) ).
cnf(c_1990,plain,
( ~ is_a_theorem(or(X0,implies(X1,X1)))
| is_a_theorem(or(equiv(X1,X1),X0)) ),
inference(superposition,[status(thm)],[c_383,c_1902]) ).
cnf(c_1991,plain,
( ~ is_a_theorem(or(X0,equiv(X1,X2)))
| is_a_theorem(or(implies(X1,X2),X0)) ),
inference(superposition,[status(thm)],[c_384,c_1902]) ).
cnf(c_2021,plain,
( ~ is_a_theorem(not(and(X0,X0)))
| ~ is_a_theorem(or(X1,X0))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_1987,c_362]) ).
cnf(c_2028,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_1988]) ).
cnf(c_2242,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(implies(not(X1),X2)) ),
inference(superposition,[status(thm)],[c_86,c_1888]) ).
cnf(c_2292,plain,
( ~ is_a_theorem(equiv(not(X0),not(X1)))
| is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_1918,c_361]) ).
cnf(c_2354,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X2,X0))
| is_a_theorem(not(and(not(X1),X2))) ),
inference(superposition,[status(thm)],[c_86,c_1974]) ).
cnf(c_7327,plain,
is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
cnf(c_7619,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(X2,X0))
| is_a_theorem(or(X1,X2)) ),
inference(superposition,[status(thm)],[c_752,c_92]) ).
cnf(c_7683,plain,
( ~ is_a_theorem(or(X0,and(X1,X2)))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_77,c_7619]) ).
cnf(c_7736,plain,
is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_7327,c_7683]) ).
cnf(c_7751,plain,
is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_7736,c_7683]) ).
cnf(c_7757,plain,
is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_86,c_7751]) ).
cnf(c_7760,plain,
( ~ is_a_theorem(not(X0))
| is_a_theorem(not(and(X0,X1))) ),
inference(superposition,[status(thm)],[c_7751,c_362]) ).
cnf(c_7762,plain,
is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[status(thm)],[c_152,c_7757]) ).
cnf(c_7953,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(equiv(X0,X0),and(X1,X0))) ),
inference(superposition,[status(thm)],[c_726,c_1990]) ).
cnf(c_8013,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_7953,c_7683]) ).
cnf(c_8138,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_8013,c_1991]) ).
cnf(c_8163,plain,
( ~ is_a_theorem(or(not(X0),X1))
| is_a_theorem(or(or(X0,not(X0)),X1)) ),
inference(superposition,[status(thm)],[c_152,c_8138]) ).
cnf(c_8280,plain,
( ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_7760,c_2021]) ).
cnf(c_8287,plain,
( ~ is_a_theorem(not(and(not(X0),not(X0))))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_7327,c_8280]) ).
cnf(c_8765,plain,
( ~ is_a_theorem(or(X0,X0))
| is_a_theorem(X0) ),
inference(demodulation,[status(thm)],[c_8287,c_86,c_152]) ).
cnf(c_8775,plain,
( ~ is_a_theorem(or(X0,implies(X0,X0)))
| is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_8138,c_8765]) ).
cnf(c_8776,plain,
( ~ is_a_theorem(or(not(X0),or(X0,not(X0))))
| is_a_theorem(or(X0,not(X0))) ),
inference(superposition,[status(thm)],[c_8163,c_8765]) ).
cnf(c_8778,plain,
is_a_theorem(implies(X0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_8775,c_7757]) ).
cnf(c_8779,plain,
is_a_theorem(or(X0,not(X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_8776,c_7762]) ).
cnf(c_8780,plain,
is_a_theorem(equiv(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_382,c_8778]) ).
cnf(c_8784,plain,
is_a_theorem(or(sK0,not(sK0))),
inference(instantiation,[status(thm)],[c_8779]) ).
cnf(c_178062,plain,
( ~ is_a_theorem(equiv(not(X0),not(X0)))
| is_a_theorem(implies(not(X0),not(X0))) ),
inference(instantiation,[status(thm)],[c_1932]) ).
cnf(c_178063,plain,
is_a_theorem(equiv(not(X0),not(X0))),
inference(instantiation,[status(thm)],[c_8780]) ).
cnf(c_178241,plain,
is_a_theorem(implies(not(X0),and(not(X0),not(X0)))),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_178243,plain,
( ~ is_a_theorem(implies(not(X0),not(X0)))
| is_a_theorem(or(and(not(X0),X1),implies(X1,X0))) ),
inference(instantiation,[status(thm)],[c_1969]) ).
cnf(c_178399,plain,
( ~ is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(or(X0,not(X0)))
| is_a_theorem(implies(not(X1),X0)) ),
inference(instantiation,[status(thm)],[c_2242]) ).
cnf(c_178406,plain,
( ~ is_a_theorem(or(implies(X0,X1),X2))
| ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(not(X3),implies(X0,X1))) ),
inference(instantiation,[status(thm)],[c_2242]) ).
cnf(c_178452,plain,
( ~ is_a_theorem(or(and(not(X0),X1),X2))
| ~ is_a_theorem(not(and(not(X0),X1)))
| is_a_theorem(X2) ),
inference(instantiation,[status(thm)],[c_362]) ).
cnf(c_178515,plain,
( ~ is_a_theorem(implies(implies(X0,X1),and(implies(X0,X1),implies(X0,X1))))
| is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))) ),
inference(instantiation,[status(thm)],[c_2028]) ).
cnf(c_178516,plain,
is_a_theorem(implies(implies(X0,X1),and(implies(X0,X1),implies(X0,X1)))),
inference(instantiation,[status(thm)],[c_80]) ).
cnf(c_180840,plain,
( ~ is_a_theorem(or(and(not(X0),X1),implies(X1,X2)))
| ~ is_a_theorem(not(and(not(X0),X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(instantiation,[status(thm)],[c_178452]) ).
cnf(c_180999,plain,
( ~ is_a_theorem(implies(not(X0),and(not(X0),not(X0))))
| ~ is_a_theorem(or(X0,not(X0)))
| is_a_theorem(implies(not(and(not(X0),not(X0))),X0)) ),
inference(instantiation,[status(thm)],[c_178399]) ).
cnf(c_182708,plain,
( ~ is_a_theorem(equiv(not(X0),not(implies(X1,X2))))
| is_a_theorem(or(X0,not(implies(X1,X2)))) ),
inference(instantiation,[status(thm)],[c_2292]) ).
cnf(c_182821,plain,
( ~ is_a_theorem(implies(not(X0),implies(X1,X2)))
| ~ is_a_theorem(or(X0,not(X0)))
| is_a_theorem(implies(not(implies(X1,X2)),X0)) ),
inference(instantiation,[status(thm)],[c_178399]) ).
cnf(c_183794,plain,
( ~ is_a_theorem(equiv(not(implies(X0,X1)),not(implies(X0,X1))))
| is_a_theorem(or(implies(X0,X1),not(implies(X0,X1)))) ),
inference(instantiation,[status(thm)],[c_182708]) ).
cnf(c_183795,plain,
is_a_theorem(equiv(not(implies(X0,X1)),not(implies(X0,X1)))),
inference(instantiation,[status(thm)],[c_178063]) ).
cnf(c_186072,plain,
( ~ is_a_theorem(or(and(not(X0),implies(sK0,implies(sK0,sK1))),implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))))
| ~ is_a_theorem(not(and(not(X0),implies(sK0,implies(sK0,sK1)))))
| is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_180840]) ).
cnf(c_186550,plain,
( ~ is_a_theorem(or(and(not(implies(sK0,sK1)),implies(sK0,implies(sK0,sK1))),implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))))
| ~ is_a_theorem(not(and(not(implies(sK0,sK1)),implies(sK0,implies(sK0,sK1)))))
| is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_186072]) ).
cnf(c_186551,plain,
( ~ is_a_theorem(implies(not(implies(sK0,sK1)),not(implies(sK0,sK1))))
| is_a_theorem(or(and(not(implies(sK0,sK1)),implies(sK0,implies(sK0,sK1))),implies(implies(sK0,implies(sK0,sK1)),implies(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_178243]) ).
cnf(c_192319,plain,
( ~ is_a_theorem(equiv(not(implies(sK0,sK1)),not(implies(sK0,sK1))))
| is_a_theorem(implies(not(implies(sK0,sK1)),not(implies(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_178062]) ).
cnf(c_192345,plain,
( ~ is_a_theorem(equiv(not(implies(sK0,sK1)),not(implies(sK0,sK1))))
| is_a_theorem(or(implies(sK0,sK1),not(implies(sK0,sK1)))) ),
inference(instantiation,[status(thm)],[c_183794]) ).
cnf(c_198733,plain,
is_a_theorem(equiv(not(implies(sK0,sK1)),not(implies(sK0,sK1)))),
inference(instantiation,[status(thm)],[c_183795]) ).
cnf(c_198796,plain,
( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),X0))
| ~ is_a_theorem(implies(X0,implies(sK0,sK1)))
| is_a_theorem(not(and(not(implies(sK0,sK1)),implies(sK0,implies(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_2354]) ).
cnf(c_199152,plain,
( ~ is_a_theorem(implies(not(implies(sK0,sK1)),and(not(implies(sK0,sK1)),not(implies(sK0,sK1)))))
| ~ is_a_theorem(or(implies(sK0,sK1),not(implies(sK0,sK1))))
| is_a_theorem(implies(not(and(not(implies(sK0,sK1)),not(implies(sK0,sK1)))),implies(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_180999]) ).
cnf(c_200696,plain,
( ~ is_a_theorem(or(implies(sK0,sK1),X0))
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(not(X1),implies(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_178406]) ).
cnf(c_203344,plain,
is_a_theorem(implies(not(implies(sK0,sK1)),and(not(implies(sK0,sK1)),not(implies(sK0,sK1))))),
inference(instantiation,[status(thm)],[c_178241]) ).
cnf(c_203485,plain,
( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),not(and(not(implies(sK0,sK1)),X0))))
| ~ is_a_theorem(implies(not(and(not(implies(sK0,sK1)),X0)),implies(sK0,sK1)))
| is_a_theorem(not(and(not(implies(sK0,sK1)),implies(sK0,implies(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_198796]) ).
cnf(c_203486,plain,
( ~ is_a_theorem(implies(X0,sK0))
| is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),not(and(not(implies(sK0,sK1)),X0)))) ),
inference(instantiation,[status(thm)],[c_799]) ).
cnf(c_214644,plain,
( ~ is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),not(and(not(implies(sK0,sK1)),not(implies(sK0,sK1))))))
| ~ is_a_theorem(implies(not(and(not(implies(sK0,sK1)),not(implies(sK0,sK1)))),implies(sK0,sK1)))
| is_a_theorem(not(and(not(implies(sK0,sK1)),implies(sK0,implies(sK0,sK1))))) ),
inference(instantiation,[status(thm)],[c_203485]) ).
cnf(c_215374,plain,
is_a_theorem(implies(implies(sK0,sK1),and(implies(sK0,sK1),implies(sK0,sK1)))),
inference(instantiation,[status(thm)],[c_178516]) ).
cnf(c_215843,plain,
( ~ is_a_theorem(implies(not(X0),implies(sK0,sK1)))
| ~ is_a_theorem(or(X0,not(X0)))
| is_a_theorem(implies(not(implies(sK0,sK1)),X0)) ),
inference(instantiation,[status(thm)],[c_182821]) ).
cnf(c_215844,plain,
( ~ is_a_theorem(implies(not(sK0),implies(sK0,sK1)))
| ~ is_a_theorem(or(sK0,not(sK0)))
| is_a_theorem(implies(not(implies(sK0,sK1)),sK0)) ),
inference(instantiation,[status(thm)],[c_215843]) ).
cnf(c_224029,plain,
( ~ is_a_theorem(implies(not(implies(sK0,sK1)),sK0))
| is_a_theorem(implies(implies(sK0,implies(sK0,sK1)),not(and(not(implies(sK0,sK1)),not(implies(sK0,sK1)))))) ),
inference(instantiation,[status(thm)],[c_203486]) ).
cnf(c_258303,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),and(implies(sK0,sK1),implies(sK0,sK1))))
| is_a_theorem(or(implies(sK0,sK1),and(sK0,not(sK1)))) ),
inference(instantiation,[status(thm)],[c_178515]) ).
cnf(c_258306,plain,
( ~ is_a_theorem(or(implies(sK0,sK1),and(sK0,not(sK1))))
| ~ is_a_theorem(implies(and(sK0,not(sK1)),X0))
| is_a_theorem(implies(not(X0),implies(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_200696]) ).
cnf(c_258308,plain,
( ~ is_a_theorem(or(implies(sK0,sK1),and(sK0,not(sK1))))
| ~ is_a_theorem(implies(and(sK0,not(sK1)),sK0))
| is_a_theorem(implies(not(sK0),implies(sK0,sK1))) ),
inference(instantiation,[status(thm)],[c_258306]) ).
cnf(c_389051,plain,
is_a_theorem(implies(and(sK0,not(sK1)),sK0)),
inference(instantiation,[status(thm)],[c_77]) ).
cnf(c_389052,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_389051,c_258308,c_258303,c_224029,c_215844,c_215374,c_214644,c_203344,c_199152,c_198733,c_192345,c_192319,c_186551,c_186550,c_8784,c_51,c_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LCL504+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu May 2 19:30:50 EDT 2024
% 0.13/0.33 % 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 --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 159.91/21.83 % SZS status Started for theBenchmark.p
% 159.91/21.83 % SZS status Theorem for theBenchmark.p
% 159.91/21.83
% 159.91/21.83 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 159.91/21.83
% 159.91/21.83 ------ iProver source info
% 159.91/21.83
% 159.91/21.83 git: date: 2024-05-02 19:28:25 +0000
% 159.91/21.83 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 159.91/21.83 git: non_committed_changes: false
% 159.91/21.83
% 159.91/21.83 ------ Parsing...
% 159.91/21.83 ------ Clausification by vclausify_rel & Parsing by iProver...
% 159.91/21.83
% 159.91/21.83 ------ 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
% 159.91/21.83
% 159.91/21.83 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 159.91/21.83
% 159.91/21.83 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 159.91/21.83 ------ Proving...
% 159.91/21.83 ------ Problem Properties
% 159.91/21.83
% 159.91/21.83
% 159.91/21.83 clauses 9
% 159.91/21.83 conjectures 0
% 159.91/21.83 EPR 0
% 159.91/21.83 Horn 9
% 159.91/21.83 unary 7
% 159.91/21.83 binary 1
% 159.91/21.83 lits 12
% 159.91/21.83 lits eq 4
% 159.91/21.83 fd_pure 0
% 159.91/21.83 fd_pseudo 0
% 159.91/21.83 fd_cond 0
% 159.91/21.83 fd_pseudo_cond 1
% 159.91/21.83 AC symbols 0
% 159.91/21.83
% 159.91/21.83 ------ Input Options Time Limit: Unbounded
% 159.91/21.83
% 159.91/21.83
% 159.91/21.83 ------
% 159.91/21.83 Current options:
% 159.91/21.83 ------
% 159.91/21.83
% 159.91/21.83
% 159.91/21.83
% 159.91/21.83
% 159.91/21.83 ------ Proving...
% 159.91/21.83
% 159.91/21.83
% 159.91/21.83 % SZS status Theorem for theBenchmark.p
% 159.91/21.83
% 159.91/21.83 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 159.91/21.83
% 159.91/21.84
%------------------------------------------------------------------------------