TSTP Solution File: LCL494+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n018.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 02:38:01 EDT 2024
% Result : Theorem 3.88s 1.18s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 19
% Syntax : Number of formulae : 94 ( 46 unt; 0 def)
% Number of atoms : 156 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 111 ( 49 ~; 42 |; 2 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 121 ( 6 sgn 64 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r3) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f44,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f45,conjecture,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
fof(f46,negated_conjecture,
~ equivalence_2,
inference(negated_conjecture,[],[f45]) ).
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(f58,plain,
~ equivalence_2,
inference(flattening,[],[f46]) ).
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(f64,plain,
( ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
=> equivalence_2 ),
inference(unused_predicate_definition_removal,[],[f14]) ).
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(f67,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f66]) ).
fof(f68,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f67]) ).
fof(f70,plain,
( equivalence_2
| ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f72,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f62]) ).
fof(f73,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f76,plain,
( ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(ennf_transformation,[],[f27]) ).
fof(f77,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f78,plain,
( ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(ennf_transformation,[],[f29]) ).
fof(f79,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f80,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f81,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
=> ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f70,f81]) ).
fof(f83,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f68]) ).
fof(f85,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))) ),
inference(cnf_transformation,[],[f82]) ).
fof(f87,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f73]) ).
fof(f91,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[],[f76]) ).
fof(f92,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f77]) ).
fof(f93,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[],[f78]) ).
fof(f94,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f79]) ).
fof(f95,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f80]) ).
fof(f96,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f97,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f99,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f101,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f102,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f106,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f107,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f108,plain,
op_equiv,
inference(cnf_transformation,[],[f44]) ).
fof(f109,plain,
~ equivalence_2,
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,[],[f83]) ).
cnf(c_51,plain,
( ~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0)))
| equivalence_2 ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_53,plain,
( ~ r2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f87]) ).
cnf(c_54,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_57,plain,
( ~ op_or
| not(and(not(X0),not(X1))) = or(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_58,plain,
( ~ op_and
| not(or(not(X0),not(X1))) = and(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_59,plain,
( ~ op_implies_and
| not(and(X0,not(X1))) = implies(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_60,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_61,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f96]) ).
cnf(c_63,plain,
op_and,
inference(cnf_transformation,[],[f97]) ).
cnf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f99]) ).
cnf(c_67,plain,
r2,
inference(cnf_transformation,[],[f101]) ).
cnf(c_68,plain,
r3,
inference(cnf_transformation,[],[f102]) ).
cnf(c_72,plain,
op_or,
inference(cnf_transformation,[],[f106]) ).
cnf(c_73,plain,
op_implies_and,
inference(cnf_transformation,[],[f107]) ).
cnf(c_74,plain,
op_equiv,
inference(cnf_transformation,[],[f108]) ).
cnf(c_75,negated_conjecture,
~ equivalence_2,
inference(cnf_transformation,[],[f109]) ).
cnf(c_87,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_67,c_53]) ).
cnf(c_93,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).
cnf(c_96,plain,
~ is_a_theorem(implies(equiv(sK0,sK1),implies(sK1,sK0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
cnf(c_98,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
cnf(c_104,plain,
not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_73,c_59]) ).
cnf(c_107,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_65,c_49]) ).
cnf(c_108,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_107]) ).
cnf(c_109,plain,
not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_63,c_58]) ).
cnf(c_112,plain,
not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_72,c_57]) ).
cnf(c_115,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_61,c_74,c_61]) ).
cnf(c_190,plain,
implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_112,c_104]) ).
cnf(c_191,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_109,c_98]) ).
cnf(c_420,plain,
is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_98,c_87]) ).
cnf(c_439,plain,
is_a_theorem(or(X0,implies(X1,not(X0)))),
inference(superposition,[status(thm)],[c_190,c_420]) ).
cnf(c_449,plain,
or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_191,c_190]) ).
cnf(c_603,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_93,c_108]) ).
cnf(c_744,plain,
is_a_theorem(or(implies(X0,not(X1)),X1)),
inference(superposition,[status(thm)],[c_439,c_603]) ).
cnf(c_825,plain,
is_a_theorem(implies(and(X0,X1),X1)),
inference(demodulation,[status(thm)],[c_744,c_449]) ).
cnf(c_826,plain,
is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(superposition,[status(thm)],[c_115,c_825]) ).
cnf(c_830,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : LCL494+1 : TPTP v8.1.2. Released v3.3.0.
% 0.04/0.14 % Command : run_iprover %s %d THM
% 0.13/0.36 % Computer : n018.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu May 2 19:25:31 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.88/1.18 % SZS status Started for theBenchmark.p
% 3.88/1.18 % SZS status Theorem for theBenchmark.p
% 3.88/1.18
% 3.88/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.88/1.18
% 3.88/1.18 ------ iProver source info
% 3.88/1.18
% 3.88/1.18 git: date: 2024-05-02 19:28:25 +0000
% 3.88/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.88/1.18 git: non_committed_changes: false
% 3.88/1.18
% 3.88/1.18 ------ Parsing...
% 3.88/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.88/1.18
% 3.88/1.18 ------ Preprocessing... sup_sim: 2 sf_s rm: 14 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 3.88/1.18
% 3.88/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.88/1.18
% 3.88/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.88/1.18 ------ Proving...
% 3.88/1.18 ------ Problem Properties
% 3.88/1.18
% 3.88/1.18
% 3.88/1.18 clauses 13
% 3.88/1.18 conjectures 0
% 3.88/1.18 EPR 0
% 3.88/1.18 Horn 13
% 3.88/1.18 unary 11
% 3.88/1.18 binary 1
% 3.88/1.18 lits 16
% 3.88/1.18 lits eq 6
% 3.88/1.18 fd_pure 0
% 3.88/1.18 fd_pseudo 0
% 3.88/1.18 fd_cond 0
% 3.88/1.18 fd_pseudo_cond 1
% 3.88/1.18 AC symbols 0
% 3.88/1.18
% 3.88/1.18 ------ Schedule dynamic 5 is on
% 3.88/1.18
% 3.88/1.18 ------ no conjectures: strip conj schedule
% 3.88/1.18
% 3.88/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.88/1.18
% 3.88/1.18
% 3.88/1.18 ------
% 3.88/1.18 Current options:
% 3.88/1.18 ------
% 3.88/1.18
% 3.88/1.18
% 3.88/1.18
% 3.88/1.18
% 3.88/1.18 ------ Proving...
% 3.88/1.18
% 3.88/1.18
% 3.88/1.18 % SZS status Theorem for theBenchmark.p
% 3.88/1.18
% 3.88/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.88/1.18
% 3.88/1.19
%------------------------------------------------------------------------------