TSTP Solution File: LCL567+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL567+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n008.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 07:45:02 EDT 2023
% Result : CounterSatisfiable 278.38s 35.76s
% Output : Saturation 278.38s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_or) ).
fof(f3,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(f5,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(f7,axiom,
( modus_ponens_strict_implies
<=> ! [X0,X1] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f8,axiom,
( adjunction
<=> ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(X0) )
=> is_a_theorem(and(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',adjunction) ).
fof(f9,axiom,
( substitution_strict_equiv
<=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_strict_equiv) ).
fof(f14,axiom,
( axiom_5
<=> ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
fof(f17,axiom,
( axiom_s3
<=> ! [X0,X1] : is_a_theorem(strict_implies(strict_implies(X0,X1),strict_implies(not(possibly(X1)),not(possibly(X0))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_s3) ).
fof(f19,axiom,
( axiom_m1
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m1) ).
fof(f20,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m2) ).
fof(f21,axiom,
( axiom_m3
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m3) ).
fof(f22,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m4) ).
fof(f23,axiom,
( axiom_m5
<=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m5) ).
fof(f24,axiom,
( axiom_m6
<=> ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m6) ).
fof(f27,axiom,
( axiom_m9
<=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m9) ).
fof(f29,axiom,
( op_possibly
=> ! [X0] : possibly(X0) = not(necessarily(not(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_possibly) ).
fof(f31,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f32,axiom,
( op_strict_equiv
=> ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_strict_equiv) ).
fof(f33,axiom,
op_possibly,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_possibly) ).
fof(f34,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_or) ).
fof(f36,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f37,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_equiv) ).
fof(f38,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f39,axiom,
modus_ponens_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f40,axiom,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f41,axiom,
adjunction,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_adjunction) ).
fof(f42,axiom,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m1) ).
fof(f43,axiom,
axiom_m2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f44,axiom,
axiom_m3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m3) ).
fof(f45,axiom,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f46,axiom,
axiom_m5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m5) ).
fof(f47,axiom,
axiom_m6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m6) ).
fof(f48,axiom,
axiom_s3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_s3) ).
fof(f49,axiom,
axiom_m9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_m6s3m9b_axiom_m9) ).
fof(f51,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f52,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f53,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f55,conjecture,
axiom_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km5_axiom_5) ).
fof(f56,negated_conjecture,
~ axiom_5,
inference(negated_conjecture,[],[f55]) ).
fof(f60,plain,
~ axiom_5,
inference(flattening,[],[f56]) ).
fof(f61,plain,
( axiom_m9
=> ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(unused_predicate_definition_removal,[],[f27]) ).
fof(f62,plain,
( axiom_m6
=> ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f63,plain,
( axiom_m5
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f64,plain,
( axiom_m4
=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f65,plain,
( axiom_m3
=> ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f66,plain,
( axiom_m2
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f67,plain,
( axiom_m1
=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f19]) ).
fof(f68,plain,
( axiom_s3
=> ! [X0,X1] : is_a_theorem(strict_implies(strict_implies(X0,X1),strict_implies(not(possibly(X1)),not(possibly(X0))))) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f69,plain,
( ! [X0] : is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
=> axiom_5 ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f70,plain,
( substitution_strict_equiv
=> ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f71,plain,
( adjunction
=> ! [X0,X1] :
( ( is_a_theorem(X1)
& is_a_theorem(X0) )
=> is_a_theorem(and(X0,X1)) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f72,plain,
( modus_ponens_strict_implies
=> ! [X0,X1] :
( ( is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f79,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f1]) ).
fof(f80,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f3]) ).
fof(f81,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f5]) ).
fof(f82,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens_strict_implies ),
inference(ennf_transformation,[],[f72]) ).
fof(f83,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens_strict_implies ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ adjunction ),
inference(ennf_transformation,[],[f71]) ).
fof(f85,plain,
( ! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) )
| ~ adjunction ),
inference(flattening,[],[f84]) ).
fof(f86,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1)) )
| ~ substitution_strict_equiv ),
inference(ennf_transformation,[],[f70]) ).
fof(f87,plain,
( axiom_5
| ? [X0] : ~ is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f88,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(strict_implies(X0,X1),strict_implies(not(possibly(X1)),not(possibly(X0)))))
| ~ axiom_s3 ),
inference(ennf_transformation,[],[f68]) ).
fof(f89,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(ennf_transformation,[],[f67]) ).
fof(f90,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(ennf_transformation,[],[f66]) ).
fof(f91,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(ennf_transformation,[],[f65]) ).
fof(f92,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(ennf_transformation,[],[f64]) ).
fof(f93,plain,
( ! [X0,X1,X2] : is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(ennf_transformation,[],[f63]) ).
fof(f94,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ),
inference(ennf_transformation,[],[f62]) ).
fof(f95,plain,
( ! [X0] : is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ),
inference(ennf_transformation,[],[f61]) ).
fof(f96,plain,
( ! [X0] : possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(ennf_transformation,[],[f29]) ).
fof(f97,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f31]) ).
fof(f98,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f32]) ).
fof(f99,plain,
( ? [X0] : ~ is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
=> ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))) ),
introduced(choice_axiom,[]) ).
fof(f100,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f87,f99]) ).
fof(f101,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f79]) ).
fof(f102,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f80]) ).
fof(f103,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f81]) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f83]) ).
fof(f105,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ adjunction ),
inference(cnf_transformation,[],[f85]) ).
fof(f106,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv ),
inference(cnf_transformation,[],[f86]) ).
fof(f107,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))) ),
inference(cnf_transformation,[],[f100]) ).
fof(f108,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(strict_implies(X0,X1),strict_implies(not(possibly(X1)),not(possibly(X0)))))
| ~ axiom_s3 ),
inference(cnf_transformation,[],[f88]) ).
fof(f109,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),and(X1,X0)))
| ~ axiom_m1 ),
inference(cnf_transformation,[],[f89]) ).
fof(f110,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[],[f90]) ).
fof(f111,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2))))
| ~ axiom_m3 ),
inference(cnf_transformation,[],[f91]) ).
fof(f112,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,and(X0,X0)))
| ~ axiom_m4 ),
inference(cnf_transformation,[],[f92]) ).
fof(f113,plain,
! [X2,X0,X1] :
( is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2)))
| ~ axiom_m5 ),
inference(cnf_transformation,[],[f93]) ).
fof(f114,plain,
! [X0] :
( is_a_theorem(strict_implies(X0,possibly(X0)))
| ~ axiom_m6 ),
inference(cnf_transformation,[],[f94]) ).
fof(f115,plain,
! [X0] :
( is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0)))
| ~ axiom_m9 ),
inference(cnf_transformation,[],[f95]) ).
fof(f116,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[],[f96]) ).
fof(f117,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f97]) ).
fof(f118,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f98]) ).
fof(f119,plain,
op_possibly,
inference(cnf_transformation,[],[f33]) ).
fof(f120,plain,
op_or,
inference(cnf_transformation,[],[f34]) ).
fof(f121,plain,
op_strict_implies,
inference(cnf_transformation,[],[f36]) ).
fof(f122,plain,
op_equiv,
inference(cnf_transformation,[],[f37]) ).
fof(f123,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f38]) ).
fof(f124,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f39]) ).
fof(f125,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f40]) ).
fof(f126,plain,
adjunction,
inference(cnf_transformation,[],[f41]) ).
fof(f127,plain,
axiom_m1,
inference(cnf_transformation,[],[f42]) ).
fof(f128,plain,
axiom_m2,
inference(cnf_transformation,[],[f43]) ).
fof(f129,plain,
axiom_m3,
inference(cnf_transformation,[],[f44]) ).
fof(f130,plain,
axiom_m4,
inference(cnf_transformation,[],[f45]) ).
fof(f131,plain,
axiom_m5,
inference(cnf_transformation,[],[f46]) ).
fof(f132,plain,
axiom_m6,
inference(cnf_transformation,[],[f47]) ).
fof(f133,plain,
axiom_s3,
inference(cnf_transformation,[],[f48]) ).
fof(f134,plain,
axiom_m9,
inference(cnf_transformation,[],[f49]) ).
fof(f135,plain,
op_or,
inference(cnf_transformation,[],[f51]) ).
fof(f136,plain,
op_implies_and,
inference(cnf_transformation,[],[f52]) ).
fof(f137,plain,
op_equiv,
inference(cnf_transformation,[],[f53]) ).
fof(f138,plain,
~ axiom_5,
inference(cnf_transformation,[],[f60]) ).
cnf(c_49,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f101]) ).
cnf(c_50,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_51,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
cnf(c_52,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens_strict_implies
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f104]) ).
cnf(c_53,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ~ adjunction
| is_a_theorem(and(X0,X1)) ),
inference(cnf_transformation,[],[f105]) ).
cnf(c_54,plain,
( ~ is_a_theorem(strict_equiv(X0,X1))
| ~ substitution_strict_equiv
| X0 = X1 ),
inference(cnf_transformation,[],[f106]) ).
cnf(c_55,plain,
( ~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0))))
| axiom_5 ),
inference(cnf_transformation,[],[f107]) ).
cnf(c_56,plain,
( ~ axiom_s3
| is_a_theorem(strict_implies(strict_implies(X0,X1),strict_implies(not(possibly(X1)),not(possibly(X0))))) ),
inference(cnf_transformation,[],[f108]) ).
cnf(c_57,plain,
( ~ axiom_m1
| is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))) ),
inference(cnf_transformation,[],[f109]) ).
cnf(c_58,plain,
( ~ axiom_m2
| is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f110]) ).
cnf(c_59,plain,
( ~ axiom_m3
| is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))) ),
inference(cnf_transformation,[],[f111]) ).
cnf(c_60,plain,
( ~ axiom_m4
| is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_61,plain,
( ~ axiom_m5
| is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_62,plain,
( ~ axiom_m6
| is_a_theorem(strict_implies(X0,possibly(X0))) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_63,plain,
( ~ axiom_m9
| is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_64,plain,
( ~ op_possibly
| not(necessarily(not(X0))) = possibly(X0) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_65,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_66,plain,
( ~ op_strict_equiv
| and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
cnf(c_67,plain,
op_possibly,
inference(cnf_transformation,[],[f119]) ).
cnf(c_68,plain,
op_or,
inference(cnf_transformation,[],[f120]) ).
cnf(c_69,plain,
op_strict_implies,
inference(cnf_transformation,[],[f121]) ).
cnf(c_70,plain,
op_equiv,
inference(cnf_transformation,[],[f122]) ).
cnf(c_71,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f123]) ).
cnf(c_72,plain,
modus_ponens_strict_implies,
inference(cnf_transformation,[],[f124]) ).
cnf(c_73,plain,
substitution_strict_equiv,
inference(cnf_transformation,[],[f125]) ).
cnf(c_74,plain,
adjunction,
inference(cnf_transformation,[],[f126]) ).
cnf(c_75,plain,
axiom_m1,
inference(cnf_transformation,[],[f127]) ).
cnf(c_76,plain,
axiom_m2,
inference(cnf_transformation,[],[f128]) ).
cnf(c_77,plain,
axiom_m3,
inference(cnf_transformation,[],[f129]) ).
cnf(c_78,plain,
axiom_m4,
inference(cnf_transformation,[],[f130]) ).
cnf(c_79,plain,
axiom_m5,
inference(cnf_transformation,[],[f131]) ).
cnf(c_80,plain,
axiom_m6,
inference(cnf_transformation,[],[f132]) ).
cnf(c_81,plain,
axiom_s3,
inference(cnf_transformation,[],[f133]) ).
cnf(c_82,plain,
axiom_m9,
inference(cnf_transformation,[],[f134]) ).
cnf(c_83,plain,
op_or,
inference(cnf_transformation,[],[f135]) ).
cnf(c_84,plain,
op_implies_and,
inference(cnf_transformation,[],[f136]) ).
cnf(c_85,plain,
op_equiv,
inference(cnf_transformation,[],[f137]) ).
cnf(c_86,negated_conjecture,
~ axiom_5,
inference(cnf_transformation,[],[f138]) ).
cnf(c_103,plain,
is_a_theorem(strict_implies(X0,possibly(X0))),
inference(global_subsumption_just,[status(thm)],[c_62,c_80,c_62]) ).
cnf(c_106,plain,
is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_60,c_78,c_60]) ).
cnf(c_109,plain,
is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_58,c_76,c_58]) ).
cnf(c_112,plain,
is_a_theorem(strict_implies(possibly(possibly(X0)),possibly(X0))),
inference(global_subsumption_just,[status(thm)],[c_63,c_82,c_63]) ).
cnf(c_115,plain,
~ is_a_theorem(implies(possibly(sK0),necessarily(possibly(sK0)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_86,c_55]) ).
cnf(c_117,plain,
not(necessarily(not(X0))) = possibly(X0),
inference(global_subsumption_just,[status(thm)],[c_64,c_67,c_64]) ).
cnf(c_120,plain,
is_a_theorem(strict_implies(and(X0,X1),and(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_57,c_75,c_57]) ).
cnf(c_123,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_69,c_65]) ).
cnf(c_126,plain,
( ~ is_a_theorem(strict_equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_54,c_73,c_54]) ).
cnf(c_129,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| is_a_theorem(and(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_53,c_74,c_53]) ).
cnf(c_130,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(X1)
| is_a_theorem(and(X0,X1)) ),
inference(renaming,[status(thm)],[c_129]) ).
cnf(c_132,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_72,c_52]) ).
cnf(c_133,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_132]) ).
cnf(c_134,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
cnf(c_137,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_49,c_83,c_49]) ).
cnf(c_140,plain,
and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_71,c_66]) ).
cnf(c_143,plain,
is_a_theorem(strict_implies(and(strict_implies(X0,X1),strict_implies(X1,X2)),strict_implies(X0,X2))),
inference(global_subsumption_just,[status(thm)],[c_61,c_79,c_61]) ).
cnf(c_146,plain,
is_a_theorem(strict_implies(and(and(X0,X1),X2),and(X0,and(X1,X2)))),
inference(global_subsumption_just,[status(thm)],[c_59,c_77,c_59]) ).
cnf(c_149,plain,
is_a_theorem(strict_implies(strict_implies(X0,X1),strict_implies(not(possibly(X1)),not(possibly(X0))))),
inference(global_subsumption_just,[status(thm)],[c_56,c_81,c_56]) ).
cnf(c_152,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_51,c_85,c_51]) ).
cnf(c_237,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_137,c_134]) ).
cnf(c_306,plain,
X0_1 = X0_1,
theory(equality) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL567+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n008.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 06:12:18 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 278.38/35.76 % SZS status Started for theBenchmark.p
% 278.38/35.76 % SZS status CounterSatisfiable for theBenchmark.p
% 278.38/35.76
% 278.38/35.76 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 278.38/35.76
% 278.38/35.76 ------ iProver source info
% 278.38/35.76
% 278.38/35.76 git: date: 2023-05-31 18:12:56 +0000
% 278.38/35.76 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 278.38/35.76 git: non_committed_changes: false
% 278.38/35.76 git: last_make_outside_of_git: false
% 278.38/35.76
% 278.38/35.76 ------ Parsing...
% 278.38/35.76 ------ Clausification by vclausify_rel & Parsing by iProver...
% 278.38/35.76
% 278.38/35.76 ------ Preprocessing... sup_sim: 1 sf_s rm: 19 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 278.38/35.76
% 278.38/35.76 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 278.38/35.76
% 278.38/35.76 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 278.38/35.76 ------ Proving...
% 278.38/35.76 ------ Problem Properties
% 278.38/35.76
% 278.38/35.76
% 278.38/35.76 clauses 18
% 278.38/35.76 conjectures 0
% 278.38/35.76 EPR 0
% 278.38/35.76 Horn 18
% 278.38/35.76 unary 15
% 278.38/35.76 binary 1
% 278.38/35.76 lits 23
% 278.38/35.76 lits eq 7
% 278.38/35.76 fd_pure 0
% 278.38/35.76 fd_pseudo 0
% 278.38/35.76 fd_cond 0
% 278.38/35.76 fd_pseudo_cond 1
% 278.38/35.76 AC symbols 0
% 278.38/35.76
% 278.38/35.76 ------ Input Options Time Limit: Unbounded
% 278.38/35.76
% 278.38/35.76
% 278.38/35.76 ------
% 278.38/35.76 Current options:
% 278.38/35.76 ------
% 278.38/35.76
% 278.38/35.76
% 278.38/35.76
% 278.38/35.76
% 278.38/35.76 ------ Proving...
% 278.38/35.76
% 278.38/35.76
% 278.38/35.76 % SZS status CounterSatisfiable for theBenchmark.p
% 278.38/35.76
% 278.38/35.76 % SZS output start Saturation for theBenchmark.p
% See solution above
% 278.38/35.76
% 278.38/35.78
%------------------------------------------------------------------------------