TSTP Solution File: LCL499+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL499+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n009.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 07:44:46 EDT 2023
% Result : Theorem 0.40s 1.14s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 69 ( 32 unt; 0 def)
% Number of atoms : 120 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 91 ( 40 ~; 33 |; 2 &)
% ( 7 <=>; 9 =>; 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 : 73 ( 0 sgn; 40 !; 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(f16,axiom,
( kn1
<=> ! [X3] : is_a_theorem(implies(X3,and(X3,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kn1) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f24,axiom,
( r3
<=> ! [X3,X4] : is_a_theorem(implies(or(X3,X4),or(X4,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3) ).
fof(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_and) ).
fof(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_implies_or) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r1) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f45,conjecture,
kn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn1) ).
fof(f46,negated_conjecture,
~ kn1,
inference(negated_conjecture,[],[f45]) ).
fof(f47,plain,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(rectify,[],[f16]) ).
fof(f53,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f55,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f58,plain,
~ kn1,
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(f63,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f53]) ).
fof(f64,plain,
( ! [X0] : is_a_theorem(implies(X0,and(X0,X0)))
=> kn1 ),
inference(unused_predicate_definition_removal,[],[f47]) ).
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,
( kn1
| ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f71,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f63]) ).
fof(f73,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f61]) ).
fof(f77,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f79,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f81,plain,
( ? [X0] : ~ is_a_theorem(implies(X0,and(X0,X0)))
=> ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
introduced(choice_axiom,[]) ).
fof(f82,plain,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[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,
( kn1
| ~ is_a_theorem(implies(sK0,and(sK0,sK0))) ),
inference(cnf_transformation,[],[f82]) ).
fof(f86,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f71]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f73]) ).
fof(f92,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f77]) ).
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(f97,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f99,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f100,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f102,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f109,plain,
~ kn1,
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(sK0,and(sK0,sK0)))
| kn1 ),
inference(cnf_transformation,[],[f85]) ).
cnf(c_52,plain,
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f86]) ).
cnf(c_54,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f88]) ).
cnf(c_58,plain,
( ~ op_and
| not(or(not(X0),not(X1))) = and(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
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_63,plain,
op_and,
inference(cnf_transformation,[],[f97]) ).
cnf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f99]) ).
cnf(c_66,plain,
r1,
inference(cnf_transformation,[],[f100]) ).
cnf(c_68,plain,
r3,
inference(cnf_transformation,[],[f102]) ).
cnf(c_75,negated_conjecture,
~ kn1,
inference(cnf_transformation,[],[f109]) ).
cnf(c_90,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_66,c_52]) ).
cnf(c_93,plain,
~ is_a_theorem(implies(sK0,and(sK0,sK0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
cnf(c_95,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_98,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
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_191,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_109,c_98]) ).
cnf(c_402,plain,
is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[status(thm)],[c_98,c_90]) ).
cnf(c_435,plain,
implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_191,c_98]) ).
cnf(c_436,plain,
is_a_theorem(or(and(X0,X0),not(X0))),
inference(demodulation,[status(thm)],[c_402,c_435]) ).
cnf(c_587,plain,
( ~ is_a_theorem(or(X0,X1))
| is_a_theorem(or(X1,X0)) ),
inference(superposition,[status(thm)],[c_95,c_108]) ).
cnf(c_736,plain,
is_a_theorem(or(not(X0),and(X0,X0))),
inference(superposition,[status(thm)],[c_436,c_587]) ).
cnf(c_821,plain,
is_a_theorem(implies(X0,and(X0,X0))),
inference(demodulation,[status(thm)],[c_736,c_98]) ).
cnf(c_822,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_93,c_821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : LCL499+1 : TPTP v8.1.2. Released v3.3.0.
% 0.05/0.11 % Command : run_iprover %s %d THM
% 0.10/0.31 % Computer : n009.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Aug 24 18:29:21 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.42 Running first-order theorem proving
% 0.16/0.42 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.40/1.14 % SZS status Started for theBenchmark.p
% 0.40/1.14 % SZS status Theorem for theBenchmark.p
% 0.40/1.14
% 0.40/1.14 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.40/1.14
% 0.40/1.14 ------ iProver source info
% 0.40/1.14
% 0.40/1.14 git: date: 2023-05-31 18:12:56 +0000
% 0.40/1.14 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.40/1.14 git: non_committed_changes: false
% 0.40/1.14 git: last_make_outside_of_git: false
% 0.40/1.14
% 0.40/1.14 ------ Parsing...
% 0.40/1.14 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.40/1.14
% 0.40/1.14 ------ 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
% 0.40/1.14
% 0.40/1.14 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.40/1.14
% 0.40/1.14 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.40/1.14 ------ Proving...
% 0.40/1.14 ------ Problem Properties
% 0.40/1.14
% 0.40/1.14
% 0.40/1.14 clauses 13
% 0.40/1.14 conjectures 0
% 0.40/1.14 EPR 0
% 0.40/1.14 Horn 13
% 0.40/1.14 unary 11
% 0.40/1.14 binary 1
% 0.40/1.14 lits 16
% 0.40/1.14 lits eq 6
% 0.40/1.14 fd_pure 0
% 0.40/1.14 fd_pseudo 0
% 0.40/1.14 fd_cond 0
% 0.40/1.14 fd_pseudo_cond 1
% 0.40/1.14 AC symbols 0
% 0.40/1.14
% 0.40/1.14 ------ Schedule dynamic 5 is on
% 0.40/1.14
% 0.40/1.14 ------ no conjectures: strip conj schedule
% 0.40/1.14
% 0.40/1.14 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 0.40/1.14
% 0.40/1.14
% 0.40/1.14 ------
% 0.40/1.14 Current options:
% 0.40/1.14 ------
% 0.40/1.14
% 0.40/1.14
% 0.40/1.14
% 0.40/1.14
% 0.40/1.14 ------ Proving...
% 0.40/1.14
% 0.40/1.14
% 0.40/1.14 % SZS status Theorem for theBenchmark.p
% 0.40/1.14
% 0.40/1.14 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.40/1.14
% 1.69/1.15
%------------------------------------------------------------------------------