TSTP Solution File: LCL486+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : LCL486+1 : TPTP v8.2.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n024.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 : Mon Jun 24 11:05:40 EDT 2024
% Result : Theorem 184.66s 24.87s
% Output : CNFRefutation 184.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 61 ( 25 unt; 0 def)
% Number of atoms : 111 ( 5 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 41 ~; 34 |; 2 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 52 !; 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(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
fof(f25,axiom,
( r4
<=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
fof(f26,axiom,
( r5
<=> ! [X3,X4,X5] : is_a_theorem(implies(implies(X4,X5),implies(or(X3,X4),or(X3,X5)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
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(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r5) ).
fof(f45,conjecture,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
fof(f46,negated_conjecture,
~ implies_3,
inference(negated_conjecture,[],[f45]) ).
fof(f56,plain,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(rectify,[],[f25]) ).
fof(f57,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f58,plain,
~ implies_3,
inference(flattening,[],[f46]) ).
fof(f59,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f57]) ).
fof(f60,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f56]) ).
fof(f64,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> implies_3 ),
inference(unused_predicate_definition_removal,[],[f6]) ).
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,
( implies_3
| ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f74,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f60]) ).
fof(f75,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f59]) ).
fof(f79,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f81,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
=> ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[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,
( implies_3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))) ),
inference(cnf_transformation,[],[f82]) ).
fof(f89,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f74]) ).
fof(f90,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f75]) ).
fof(f94,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f79]) ).
fof(f96,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f99,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f103,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f104,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f109,plain,
~ implies_3,
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(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2))))
| implies_3 ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_55,plain,
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f89]) ).
cnf(c_56,plain,
( ~ r5
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_60,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f96]) ).
cnf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f99]) ).
cnf(c_69,plain,
r4,
inference(cnf_transformation,[],[f103]) ).
cnf(c_70,plain,
r5,
inference(cnf_transformation,[],[f104]) ).
cnf(c_75,negated_conjecture,
~ implies_3,
inference(cnf_transformation,[],[f109]) ).
cnf(c_96,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
cnf(c_105,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_106,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_105]) ).
cnf(c_116,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_70,c_56]) ).
cnf(c_119,plain,
is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_69,c_55]) ).
cnf(c_122,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(implies(sK1,sK2),implies(sK0,sK2)))),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
cnf(c_5591,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(not(X2),X0),implies(X2,X1)))),
inference(superposition,[status(thm)],[c_96,c_116]) ).
cnf(c_5593,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X0),implies(X2,X1)))),
inference(demodulation,[status(thm)],[c_5591,c_96]) ).
cnf(c_5601,plain,
( ~ is_a_theorem(or(X0,or(X1,X2)))
| is_a_theorem(or(X1,or(X0,X2))) ),
inference(superposition,[status(thm)],[c_119,c_106]) ).
cnf(c_5653,plain,
( ~ is_a_theorem(or(X0,implies(X1,X2)))
| is_a_theorem(or(not(X1),or(X0,X2))) ),
inference(superposition,[status(thm)],[c_96,c_5601]) ).
cnf(c_5654,plain,
( ~ is_a_theorem(or(X0,implies(X1,X2)))
| is_a_theorem(implies(X1,or(X0,X2))) ),
inference(demodulation,[status(thm)],[c_5653,c_96]) ).
cnf(c_5881,plain,
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X1,or(not(X0),X2))) ),
inference(superposition,[status(thm)],[c_96,c_5654]) ).
cnf(c_5884,plain,
( ~ is_a_theorem(implies(X0,implies(X1,X2)))
| is_a_theorem(implies(X1,implies(X0,X2))) ),
inference(demodulation,[status(thm)],[c_5881,c_96]) ).
cnf(c_6998,plain,
is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(superposition,[status(thm)],[c_5593,c_5884]) ).
cnf(c_7037,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_122,c_6998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL486+1 : TPTP v8.2.0. Released v3.3.0.
% 0.07/0.12 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Jun 22 12:10:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 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
% 184.66/24.87 % SZS status Started for theBenchmark.p
% 184.66/24.87 % SZS status Theorem for theBenchmark.p
% 184.66/24.87
% 184.66/24.87 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 184.66/24.87
% 184.66/24.87 ------ iProver source info
% 184.66/24.87
% 184.66/24.87 git: date: 2024-06-12 09:56:46 +0000
% 184.66/24.87 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 184.66/24.87 git: non_committed_changes: false
% 184.66/24.87
% 184.66/24.87 ------ Parsing...
% 184.66/24.87 ------ Clausification by vclausify_rel & Parsing by iProver...
% 184.66/24.87
% 184.66/24.87 ------ Preprocessing... sup_sim: 0 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
% 184.66/24.87
% 184.66/24.87 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 184.66/24.87
% 184.66/24.87 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 184.66/24.87 ------ Proving...
% 184.66/24.87 ------ Problem Properties
% 184.66/24.87
% 184.66/24.87
% 184.66/24.87 clauses 13
% 184.66/24.87 conjectures 0
% 184.66/24.87 EPR 0
% 184.66/24.87 Horn 13
% 184.66/24.87 unary 11
% 184.66/24.87 binary 1
% 184.66/24.87 lits 16
% 184.66/24.87 lits eq 6
% 184.66/24.87 fd_pure 0
% 184.66/24.87 fd_pseudo 0
% 184.66/24.87 fd_cond 0
% 184.66/24.87 fd_pseudo_cond 1
% 184.66/24.87 AC symbols 0
% 184.66/24.87
% 184.66/24.87 ------ Input Options Time Limit: Unbounded
% 184.66/24.87
% 184.66/24.87
% 184.66/24.87 ------
% 184.66/24.87 Current options:
% 184.66/24.87 ------
% 184.66/24.87
% 184.66/24.87
% 184.66/24.87
% 184.66/24.87
% 184.66/24.87 ------ Proving...
% 184.66/24.87
% 184.66/24.87
% 184.66/24.87 % SZS status Theorem for theBenchmark.p
% 184.66/24.87
% 184.66/24.87 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 184.66/24.87
% 184.66/24.88
%------------------------------------------------------------------------------