TSTP Solution File: LCL538+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL538+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 2.77s 1.17s
% Output : CNFRefutation 2.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 20 unt; 0 def)
% Number of atoms : 114 ( 5 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 100 ( 38 ~; 36 |; 14 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn; 24 !; 6 ?)
% 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(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f51,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/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
fof(f55,axiom,
( axiom_M
<=> ! [X0] : is_a_theorem(implies(necessarily(X0),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_M) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
fof(f90,negated_conjecture,
~ modus_ponens_strict_implies,
inference(negated_conjecture,[],[f89]) ).
fof(f105,plain,
~ modus_ponens_strict_implies,
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_implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) )
=> modus_ponens_strict_implies ),
inference(unused_predicate_definition_removal,[],[f51]) ).
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(f151,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) ) ),
inference(ennf_transformation,[],[f110]) ).
fof(f152,plain,
( modus_ponens_strict_implies
| ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) ) ),
inference(flattening,[],[f151]) ).
fof(f154,plain,
( ! [X0] : is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(ennf_transformation,[],[f108]) ).
fof(f158,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f160,plain,
( ? [X0,X1] :
( ~ is_a_theorem(X1)
& is_a_theorem(strict_implies(X0,X1))
& is_a_theorem(X0) )
=> ( ~ is_a_theorem(sK1)
& is_a_theorem(strict_implies(sK0,sK1))
& is_a_theorem(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f161,plain,
( modus_ponens_strict_implies
| ( ~ is_a_theorem(sK1)
& is_a_theorem(strict_implies(sK0,sK1))
& is_a_theorem(sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f152,f160]) ).
fof(f162,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f132]) ).
fof(f183,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f199,plain,
( modus_ponens_strict_implies
| is_a_theorem(sK0) ),
inference(cnf_transformation,[],[f161]) ).
fof(f200,plain,
( modus_ponens_strict_implies
| is_a_theorem(strict_implies(sK0,sK1)) ),
inference(cnf_transformation,[],[f161]) ).
fof(f201,plain,
( modus_ponens_strict_implies
| ~ is_a_theorem(sK1) ),
inference(cnf_transformation,[],[f161]) ).
fof(f203,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[],[f154]) ).
fof(f207,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f158]) ).
fof(f212,plain,
axiom_M,
inference(cnf_transformation,[],[f80]) ).
fof(f217,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f220,plain,
~ modus_ponens_strict_implies,
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,[],[f162]) ).
cnf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f183]) ).
cnf(c_86,plain,
( ~ is_a_theorem(sK1)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f201]) ).
cnf(c_87,plain,
( is_a_theorem(strict_implies(sK0,sK1))
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f200]) ).
cnf(c_88,plain,
( is_a_theorem(sK0)
| modus_ponens_strict_implies ),
inference(cnf_transformation,[],[f199]) ).
cnf(c_90,plain,
( ~ axiom_M
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(cnf_transformation,[],[f203]) ).
cnf(c_94,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f207]) ).
cnf(c_99,plain,
axiom_M,
inference(cnf_transformation,[],[f212]) ).
cnf(c_104,plain,
op_strict_implies,
inference(cnf_transformation,[],[f217]) ).
cnf(c_107,negated_conjecture,
~ modus_ponens_strict_implies,
inference(cnf_transformation,[],[f220]) ).
cnf(c_137,plain,
is_a_theorem(strict_implies(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_87,c_107,c_87]) ).
cnf(c_139,plain,
is_a_theorem(implies(necessarily(X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_90,c_99,c_90]) ).
cnf(c_175,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_94,c_104,c_94]) ).
cnf(c_190,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_191,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_190]) ).
cnf(c_696,plain,
is_a_theorem(implies(strict_implies(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_175,c_139]) ).
cnf(c_777,plain,
( ~ is_a_theorem(implies(X0,sK1))
| ~ is_a_theorem(X0)
| is_a_theorem(sK1) ),
inference(instantiation,[status(thm)],[c_191]) ).
cnf(c_778,plain,
( ~ is_a_theorem(implies(sK0,sK1))
| ~ is_a_theorem(sK0)
| is_a_theorem(sK1) ),
inference(instantiation,[status(thm)],[c_777]) ).
cnf(c_1094,plain,
( ~ is_a_theorem(strict_implies(X0,X1))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_696,c_191]) ).
cnf(c_1459,plain,
is_a_theorem(implies(sK0,sK1)),
inference(superposition,[status(thm)],[c_137,c_1094]) ).
cnf(c_1485,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1459,c_778,c_86,c_88,c_107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL538+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 06:54:32 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.77/1.17 % SZS status Started for theBenchmark.p
% 2.77/1.17 % SZS status Theorem for theBenchmark.p
% 2.77/1.17
% 2.77/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.77/1.17
% 2.77/1.17 ------ iProver source info
% 2.77/1.17
% 2.77/1.17 git: date: 2023-05-31 18:12:56 +0000
% 2.77/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.77/1.17 git: non_committed_changes: false
% 2.77/1.17 git: last_make_outside_of_git: false
% 2.77/1.17
% 2.77/1.17 ------ Parsing...
% 2.77/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.77/1.17
% 2.77/1.17 ------ Preprocessing... sup_sim: 3 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e
% 2.77/1.17
% 2.77/1.17 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.77/1.17
% 2.77/1.17 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.77/1.17 ------ Proving...
% 2.77/1.17 ------ Problem Properties
% 2.77/1.17
% 2.77/1.17
% 2.77/1.17 clauses 29
% 2.77/1.17 conjectures 0
% 2.77/1.17 EPR 2
% 2.77/1.17 Horn 29
% 2.77/1.17 unary 26
% 2.77/1.17 binary 2
% 2.77/1.17 lits 33
% 2.77/1.17 lits eq 7
% 2.77/1.17 fd_pure 0
% 2.77/1.17 fd_pseudo 0
% 2.77/1.17 fd_cond 0
% 2.77/1.17 fd_pseudo_cond 1
% 2.77/1.17 AC symbols 0
% 2.77/1.17
% 2.77/1.17 ------ Schedule dynamic 5 is on
% 2.77/1.17
% 2.77/1.17 ------ no conjectures: strip conj schedule
% 2.77/1.17
% 2.77/1.17 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.77/1.17
% 2.77/1.17
% 2.77/1.17 ------
% 2.77/1.17 Current options:
% 2.77/1.17 ------
% 2.77/1.17
% 2.77/1.17
% 2.77/1.17
% 2.77/1.17
% 2.77/1.17 ------ Proving...
% 2.77/1.17
% 2.77/1.17
% 2.77/1.17 % SZS status Theorem for theBenchmark.p
% 2.77/1.17
% 2.77/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.77/1.17
% 2.77/1.17
%------------------------------------------------------------------------------