TSTP Solution File: LCL544+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 02:38:10 EDT 2024
% Result : Theorem 3.55s 1.18s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 64 ( 27 unt; 0 def)
% Number of atoms : 120 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 101 ( 45 ~; 38 |; 2 &)
% ( 5 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 38 !; 2 ?)
% 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(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_3) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_implies_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_3) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',necessitation) ).
fof(f66,axiom,
( axiom_m4
<=> ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_m4) ).
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(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',km4b_necessitation) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_0_axiom_m4) ).
fof(f90,negated_conjecture,
~ axiom_m4,
inference(negated_conjecture,[],[f89]) ).
fof(f105,plain,
~ axiom_m4,
inference(flattening,[],[f90]) ).
fof(f106,plain,
( ! [X0] : is_a_theorem(strict_implies(X0,and(X0,X0)))
=> axiom_m4 ),
inference(unused_predicate_definition_removal,[],[f66]) ).
fof(f111,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f118,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f122,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
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(f136,plain,
( ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(ennf_transformation,[],[f122]) ).
fof(f140,plain,
( ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(ennf_transformation,[],[f118]) ).
fof(f150,plain,
( ! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) )
| ~ necessitation ),
inference(ennf_transformation,[],[f111]) ).
fof(f155,plain,
( axiom_m4
| ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f106]) ).
fof(f157,plain,
( ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(ennf_transformation,[],[f75]) ).
fof(f159,plain,
( ? [X0] : ~ is_a_theorem(strict_implies(X0,and(X0,X0)))
=> ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f155,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(f165,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f136]) ).
fof(f169,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f140]) ).
fof(f182,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f185,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f189,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f197,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[],[f150]) ).
fof(f202,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f160]) ).
fof(f204,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f157]) ).
fof(f207,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f214,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f217,plain,
~ axiom_m4,
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_53,plain,
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f165]) ).
cnf(c_57,plain,
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f169]) ).
cnf(c_70,plain,
modus_ponens,
inference(cnf_transformation,[],[f182]) ).
cnf(c_73,plain,
implies_2,
inference(cnf_transformation,[],[f185]) ).
cnf(c_77,plain,
and_3,
inference(cnf_transformation,[],[f189]) ).
cnf(c_85,plain,
( ~ is_a_theorem(X0)
| ~ necessitation
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f197]) ).
cnf(c_90,plain,
( ~ is_a_theorem(strict_implies(sK0,and(sK0,sK0)))
| axiom_m4 ),
inference(cnf_transformation,[],[f202]) ).
cnf(c_92,plain,
( ~ op_strict_implies
| necessarily(implies(X0,X1)) = strict_implies(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
cnf(c_95,plain,
necessitation,
inference(cnf_transformation,[],[f207]) ).
cnf(c_102,plain,
op_strict_implies,
inference(cnf_transformation,[],[f214]) ).
cnf(c_105,negated_conjecture,
~ axiom_m4,
inference(cnf_transformation,[],[f217]) ).
cnf(c_134,plain,
~ is_a_theorem(strict_implies(sK0,and(sK0,sK0))),
inference(global_subsumption_just,[status(thm)],[c_90,c_105,c_90]) ).
cnf(c_139,plain,
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_95,c_85]) ).
cnf(c_166,plain,
is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_77,c_57]) ).
cnf(c_169,plain,
necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_92,c_102,c_92]) ).
cnf(c_178,plain,
is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_73,c_53]) ).
cnf(c_184,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_185,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_184]) ).
cnf(c_673,plain,
( ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(strict_implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_139]) ).
cnf(c_1043,plain,
( ~ is_a_theorem(implies(X0,implies(X0,X1)))
| is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_178,c_185]) ).
cnf(c_2512,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_166,c_1043]) ).
cnf(c_2625,plain,
is_a_theorem(strict_implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_2512,c_673]) ).
cnf(c_2628,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_134,c_2625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL544+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n026.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 : Thu May 2 19:26:06 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.21/0.47 Running first-order theorem proving
% 0.21/0.47 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
% 3.55/1.18 % SZS status Started for theBenchmark.p
% 3.55/1.18 % SZS status Theorem for theBenchmark.p
% 3.55/1.18
% 3.55/1.18 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 3.55/1.18
% 3.55/1.18 ------ iProver source info
% 3.55/1.18
% 3.55/1.18 git: date: 2024-05-02 19:28:25 +0000
% 3.55/1.18 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 3.55/1.18 git: non_committed_changes: false
% 3.55/1.18
% 3.55/1.18 ------ Parsing...
% 3.55/1.18 ------ Clausification by vclausify_rel & Parsing by iProver...
% 3.55/1.18
% 3.55/1.18 ------ 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
% 3.55/1.18
% 3.55/1.18 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.55/1.18
% 3.55/1.18 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.55/1.18 ------ Proving...
% 3.55/1.18 ------ Problem Properties
% 3.55/1.18
% 3.55/1.18
% 3.55/1.18 clauses 27
% 3.55/1.18 conjectures 0
% 3.55/1.18 EPR 0
% 3.55/1.18 Horn 27
% 3.55/1.18 unary 24
% 3.55/1.18 binary 2
% 3.55/1.18 lits 31
% 3.55/1.18 lits eq 7
% 3.55/1.18 fd_pure 0
% 3.55/1.18 fd_pseudo 0
% 3.55/1.18 fd_cond 0
% 3.55/1.18 fd_pseudo_cond 1
% 3.55/1.18 AC symbols 0
% 3.55/1.18
% 3.55/1.18 ------ Schedule dynamic 5 is on
% 3.55/1.18
% 3.55/1.18 ------ no conjectures: strip conj schedule
% 3.55/1.18
% 3.55/1.18 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 3.55/1.18
% 3.55/1.18
% 3.55/1.18 ------
% 3.55/1.18 Current options:
% 3.55/1.18 ------
% 3.55/1.18
% 3.55/1.18
% 3.55/1.18
% 3.55/1.18
% 3.55/1.18 ------ Proving...
% 3.55/1.18
% 3.55/1.18
% 3.55/1.18 % SZS status Theorem for theBenchmark.p
% 3.55/1.18
% 3.55/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.55/1.18
% 3.55/1.19
%------------------------------------------------------------------------------