TSTP Solution File: LCL539+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL539+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 07:44:57 EDT 2023
% Result : Theorem 11.91s 2.69s
% Output : CNFRefutation 11.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 104 ( 44 unt; 0 def)
% Number of atoms : 190 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 148 ( 62 ~; 57 |; 6 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 113 ( 6 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(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_2) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f53,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(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_M) ).
fof(f75,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(f76,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(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
fof(f89,conjecture,
substitution_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f90,negated_conjecture,
~ substitution_strict_equiv,
inference(negated_conjecture,[],[f89]) ).
fof(f105,plain,
~ substitution_strict_equiv,
inference(flattening,[],[f90]) ).
fof(f108,plain,
( axiom_M
=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f55]) ).
fof(f110,plain,
( ! [X0,X1] :
( is_a_theorem(strict_equiv(X0,X1))
=> X0 = X1 )
=> substitution_strict_equiv ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f112,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f119,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f120,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f125,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f126,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(f131,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f126]) ).
fof(f132,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f131]) ).
fof(f133,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f125]) ).
fof(f138,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(ennf_transformation,[],[f120]) ).
fof(f139,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(ennf_transformation,[],[f119]) ).
fof(f146,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(ennf_transformation,[],[f112]) ).
fof(f151,plain,
( substitution_strict_equiv
| ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f153,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f108]) ).
fof(f157,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f158,plain,
( ! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(ennf_transformation,[],[f76]) ).
fof(f159,plain,
( ? [X0,X1] :
( X0 != X1
& is_a_theorem(strict_equiv(X0,X1)) )
=> ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
( substitution_strict_equiv
| ( sK0 != sK1
& is_a_theorem(strict_equiv(sK0,sK1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f151,f159]) ).
fof(f161,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f132]) ).
fof(f162,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f133]) ).
fof(f167,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f138]) ).
fof(f168,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f139]) ).
fof(f175,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f146]) ).
fof(f182,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f187,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f188,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f195,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f196,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f198,plain,
( substitution_strict_equiv
| is_a_theorem(strict_equiv(sK0,sK1)) ),
inference(cnf_transformation,[],[f160]) ).
fof(f199,plain,
( substitution_strict_equiv
| sK0 != sK1 ),
inference(cnf_transformation,[],[f160]) ).
fof(f201,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f153]) ).
fof(f205,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f157]) ).
fof(f206,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[],[f158]) ).
fof(f210,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f215,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f217,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f88]) ).
fof(f218,plain,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f105]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f161]) ).
cnf(c_50,plain,
( ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents
| X0 = X1 ),
inference(cnf_transformation,[],[f162]) ).
cnf(c_55,plain,
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f167]) ).
cnf(c_56,plain,
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f168]) ).
cnf(c_63,plain,
( ~ equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(cnf_transformation,[],[f175]) ).
cnf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f182]) ).
cnf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f187]) ).
cnf(c_76,plain,
and_2,
inference(cnf_transformation,[],[f188]) ).
cnf(c_83,plain,
equivalence_3,
inference(cnf_transformation,[],[f195]) ).
cnf(c_84,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f196]) ).
cnf(c_86,plain,
( sK0 != sK1
| substitution_strict_equiv ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_87,plain,
( is_a_theorem(strict_equiv(sK0,sK1))
| substitution_strict_equiv ),
inference(cnf_transformation,[],[f198]) ).
cnf(c_89,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_93,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
cnf(c_94,plain,
( ~ op_strict_equiv
| and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1) ),
inference(cnf_transformation,[],[f206]) ).
cnf(c_98,plain,
axiom_M,
inference(cnf_transformation,[],[f210]) ).
cnf(c_103,plain,
op_strict_implies,
inference(cnf_transformation,[],[f215]) ).
cnf(c_105,plain,
op_strict_equiv,
inference(cnf_transformation,[],[f217]) ).
cnf(c_106,negated_conjecture,
~ substitution_strict_equiv,
inference(cnf_transformation,[],[f218]) ).
cnf(c_132,plain,
is_a_theorem(strict_equiv(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_87,c_106,c_87]) ).
cnf(c_134,plain,
sK0 != sK1,
inference(global_subsumption_just,[status(thm)],[c_86,c_106,c_86]) ).
cnf(c_136,plain,
is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_89,c_98,c_89]) ).
cnf(c_150,plain,
is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption_just,[status(thm)],[c_56,c_76,c_56]) ).
cnf(c_153,plain,
is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
cnf(c_172,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_93,c_103,c_93]) ).
cnf(c_175,plain,
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_50,c_84,c_50]) ).
cnf(c_187,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_70,c_49]) ).
cnf(c_188,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_187]) ).
cnf(c_195,plain,
and(strict_implies(X0,X1),strict_implies(X1,X0)) = strict_equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_94,c_105,c_94]) ).
cnf(c_201,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_63,c_83,c_63]) ).
cnf(c_2532,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_153,c_188]) ).
cnf(c_2533,plain,
( ~ is_a_theorem(and(X0,X1))
| is_a_theorem(X1) ),
inference(superposition,[status(thm)],[c_150,c_188]) ).
cnf(c_2539,plain,
( ~ is_a_theorem(necessarily(X0))
| is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_136,c_188]) ).
cnf(c_2548,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(implies(implies(X1,X0),equiv(X0,X1))) ),
inference(superposition,[status(thm)],[c_201,c_188]) ).
cnf(c_2554,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_172,c_2539]) ).
cnf(c_2561,plain,
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_195,c_2532]) ).
cnf(c_2565,plain,
( ~ is_a_theorem(strict_equiv(X0,X1))
| is_a_theorem(strict_implies(X1,X0)) ),
inference(superposition,[status(thm)],[c_195,c_2533]) ).
cnf(c_2776,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_2548,c_188]) ).
cnf(c_2816,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(superposition,[status(thm)],[c_132,c_2561]) ).
cnf(c_2819,plain,
is_a_theorem(strict_implies(sK1,sK0)),
inference(superposition,[status(thm)],[c_132,c_2565]) ).
cnf(c_2947,plain,
is_a_theorem(implies(sK0,sK1)),
inference(superposition,[status(thm)],[c_2816,c_2554]) ).
cnf(c_2948,plain,
is_a_theorem(implies(sK1,sK0)),
inference(superposition,[status(thm)],[c_2819,c_2554]) ).
cnf(c_5532,plain,
( ~ is_a_theorem(implies(sK0,sK1))
| is_a_theorem(equiv(sK0,sK1)) ),
inference(superposition,[status(thm)],[c_2948,c_2776]) ).
cnf(c_5536,plain,
is_a_theorem(equiv(sK0,sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_5532,c_2947]) ).
cnf(c_5923,plain,
sK0 = sK1,
inference(superposition,[status(thm)],[c_5536,c_175]) ).
cnf(c_5924,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5923,c_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL539+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 03:19:03 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 11.91/2.69 % SZS status Started for theBenchmark.p
% 11.91/2.69 % SZS status Theorem for theBenchmark.p
% 11.91/2.69
% 11.91/2.69 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 11.91/2.69
% 11.91/2.69 ------ iProver source info
% 11.91/2.69
% 11.91/2.69 git: date: 2023-05-31 18:12:56 +0000
% 11.91/2.69 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 11.91/2.69 git: non_committed_changes: false
% 11.91/2.69 git: last_make_outside_of_git: false
% 11.91/2.69
% 11.91/2.69 ------ Parsing...
% 11.91/2.69 ------ Clausification by vclausify_rel & Parsing by iProver...
% 11.91/2.69
% 11.91/2.69 ------ Preprocessing... sup_sim: 2 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e
% 11.91/2.69
% 11.91/2.69 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 11.91/2.69
% 11.91/2.69 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.91/2.69 ------ Proving...
% 11.91/2.69 ------ Problem Properties
% 11.91/2.69
% 11.91/2.69
% 11.91/2.69 clauses 28
% 11.91/2.69 conjectures 0
% 11.91/2.69 EPR 1
% 11.91/2.69 Horn 28
% 11.91/2.69 unary 25
% 11.91/2.69 binary 2
% 11.91/2.69 lits 32
% 11.91/2.69 lits eq 8
% 11.91/2.69 fd_pure 0
% 11.91/2.69 fd_pseudo 0
% 11.91/2.69 fd_cond 0
% 11.91/2.69 fd_pseudo_cond 1
% 11.91/2.69 AC symbols 0
% 11.91/2.69
% 11.91/2.69 ------ Input Options Time Limit: Unbounded
% 11.91/2.69
% 11.91/2.69
% 11.91/2.69 ------
% 11.91/2.69 Current options:
% 11.91/2.69 ------
% 11.91/2.69
% 11.91/2.69
% 11.91/2.69
% 11.91/2.69
% 11.91/2.69 ------ Proving...
% 11.91/2.69
% 11.91/2.69
% 11.91/2.69 % SZS status Theorem for theBenchmark.p
% 11.91/2.69
% 11.91/2.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.91/2.69
% 11.91/2.69
%------------------------------------------------------------------------------