TSTP Solution File: LCL909+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : LCL909+1 : TPTP v8.1.2. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n001.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 07:52:57 EDT 2023
% Result : Satisfiable 1.38s 1.16s
% Output : Saturation 1.38s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f22,axiom,
( r1
<=> ! [X3] : is_a_theorem(implies(or(X3,X3),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r1) ).
fof(f23,axiom,
( r2
<=> ! [X3,X4] : is_a_theorem(implies(X4,or(X3,X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2) ).
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(f25,axiom,
( r4
<=> ! [X3,X4,X5] : is_a_theorem(implies(or(X3,or(X4,X5)),or(X4,or(X3,X5)))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',r5) ).
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(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',op_equiv) ).
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(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
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(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r5) ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',substitution_of_equivalents) ).
fof(f48,plain,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(rectify,[],[f22]) ).
fof(f49,plain,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(rectify,[],[f23]) ).
fof(f50,plain,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(rectify,[],[f24]) ).
fof(f51,plain,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(rectify,[],[f25]) ).
fof(f52,plain,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(rectify,[],[f26]) ).
fof(f53,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f52]) ).
fof(f54,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f51]) ).
fof(f55,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f56,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f49]) ).
fof(f57,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f48]) ).
fof(f58,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f59,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(f62,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(ennf_transformation,[],[f59]) ).
fof(f63,plain,
( ! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) )
| ~ modus_ponens ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
( ! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) )
| ~ substitution_of_equivalents ),
inference(ennf_transformation,[],[f58]) ).
fof(f65,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(ennf_transformation,[],[f57]) ).
fof(f66,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(ennf_transformation,[],[f56]) ).
fof(f67,plain,
( ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(ennf_transformation,[],[f55]) ).
fof(f68,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(ennf_transformation,[],[f54]) ).
fof(f69,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(ennf_transformation,[],[f53]) ).
fof(f70,plain,
( ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(ennf_transformation,[],[f28]) ).
fof(f71,plain,
( ! [X0,X1] : implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(ennf_transformation,[],[f30]) ).
fof(f72,plain,
( ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(ennf_transformation,[],[f31]) ).
fof(f73,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[],[f63]) ).
fof(f74,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[],[f64]) ).
fof(f75,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(X1,or(X0,X1)))
| ~ r2 ),
inference(cnf_transformation,[],[f66]) ).
fof(f77,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f67]) ).
fof(f78,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f68]) ).
fof(f79,plain,
! [X2,X0,X1] :
( is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2))))
| ~ r5 ),
inference(cnf_transformation,[],[f69]) ).
fof(f80,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[],[f70]) ).
fof(f81,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[],[f71]) ).
fof(f82,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[],[f72]) ).
fof(f83,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f84,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f85,plain,
op_equiv,
inference(cnf_transformation,[],[f34]) ).
fof(f86,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f87,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f88,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f89,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f90,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f91,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f92,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f41]) ).
cnf(c_49,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f73]) ).
cnf(c_50,plain,
( ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents
| X0 = X1 ),
inference(cnf_transformation,[],[f74]) ).
cnf(c_51,plain,
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f75]) ).
cnf(c_52,plain,
( ~ r2
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(cnf_transformation,[],[f76]) ).
cnf(c_53,plain,
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f77]) ).
cnf(c_54,plain,
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f78]) ).
cnf(c_55,plain,
( ~ r5
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(cnf_transformation,[],[f79]) ).
cnf(c_56,plain,
( ~ op_and
| not(or(not(X0),not(X1))) = and(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
cnf(c_57,plain,
( ~ op_implies_or
| or(not(X0),X1) = implies(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
cnf(c_58,plain,
( ~ op_equiv
| and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
cnf(c_59,plain,
op_implies_or,
inference(cnf_transformation,[],[f83]) ).
cnf(c_60,plain,
op_and,
inference(cnf_transformation,[],[f84]) ).
cnf(c_61,plain,
op_equiv,
inference(cnf_transformation,[],[f85]) ).
cnf(c_62,plain,
modus_ponens,
inference(cnf_transformation,[],[f86]) ).
cnf(c_63,plain,
r1,
inference(cnf_transformation,[],[f87]) ).
cnf(c_64,plain,
r2,
inference(cnf_transformation,[],[f88]) ).
cnf(c_65,plain,
r3,
inference(cnf_transformation,[],[f89]) ).
cnf(c_66,plain,
r4,
inference(cnf_transformation,[],[f90]) ).
cnf(c_67,plain,
r5,
inference(cnf_transformation,[],[f91]) ).
cnf(c_68,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f92]) ).
cnf(c_78,plain,
is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_64,c_52]) ).
cnf(c_81,plain,
is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_51,c_63,c_51]) ).
cnf(c_84,plain,
is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_65,c_53]) ).
cnf(c_87,plain,
or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_59,c_57]) ).
cnf(c_90,plain,
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_50,c_68,c_50]) ).
cnf(c_93,plain,
( ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1))
| is_a_theorem(X1) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_62,c_49]) ).
cnf(c_94,plain,
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(renaming,[status(thm)],[c_93]) ).
cnf(c_95,plain,
not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_60,c_56]) ).
cnf(c_98,plain,
and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_61,c_58]) ).
cnf(c_101,plain,
is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_67,c_55]) ).
cnf(c_104,plain,
is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_54,c_66,c_54]) ).
cnf(c_161,plain,
not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_95,c_87]) ).
cnf(c_162,plain,
X0 = X0,
theory(equality) ).
cnf(c_163,plain,
X0_1 = X0_1,
theory(equality) ).
cnf(c_164,plain,
( X0 != X1
| X2 != X1
| X2 = X0 ),
theory(equality) ).
cnf(c_165,plain,
( X0 != X1
| ~ is_a_theorem(X1)
| is_a_theorem(X0) ),
theory(equality) ).
cnf(c_166,plain,
( X0 != X1
| X2 != X3
| implies(X0,X2) = implies(X1,X3) ),
theory(equality) ).
cnf(c_167,plain,
( X0 != X1
| X2 != X3
| or(X0,X2) = or(X1,X3) ),
theory(equality) ).
cnf(c_168,plain,
( X0 != X1
| X2 != X3
| and(X0,X2) = and(X1,X3) ),
theory(equality) ).
cnf(c_169,plain,
( X0 != X1
| not(X0) = not(X1) ),
theory(equality) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL909+1 : TPTP v8.1.2. Released v6.4.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n001.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 : Fri Aug 25 07:47:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.48 Running first-order theorem proving
% 0.19/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.61 WARNING - Could not infer the problem pformat. Setting FOF as default
% 1.38/1.16 % SZS status Started for theBenchmark.p
% 1.38/1.16 % SZS status Satisfiable for theBenchmark.p
% 1.38/1.16
% 1.38/1.16 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.38/1.16
% 1.38/1.16 ------ iProver source info
% 1.38/1.16
% 1.38/1.16 git: date: 2023-05-31 18:12:56 +0000
% 1.38/1.16 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.38/1.16 git: non_committed_changes: false
% 1.38/1.16 git: last_make_outside_of_git: false
% 1.38/1.16
% 1.38/1.16 ------ Parsing...
% 1.38/1.16 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.38/1.16
% 1.38/1.16 ------ Preprocessing... sup_sim: 1 sf_s rm: 28 0s sf_e pe_s pe_e sf_s rm: 8 0s sf_e pe_s pe_e
% 1.38/1.16
% 1.38/1.16 ------ Preprocessing...------ preprocesses with Option_epr_horn
% 1.38/1.16 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.38/1.16 ------ Proving...
% 1.38/1.16 ------ Problem Properties
% 1.38/1.16
% 1.38/1.16
% 1.38/1.16 clauses 0
% 1.38/1.16 conjectures 0
% 1.38/1.16 EPR 0
% 1.38/1.16 Horn 0
% 1.38/1.16 unary 0
% 1.38/1.16 binary 0
% 1.38/1.16 lits 0
% 1.38/1.16 lits eq 0
% 1.38/1.16 fd_pure 0
% 1.38/1.16 fd_pseudo 0
% 1.38/1.16 fd_cond 0
% 1.38/1.16 fd_pseudo_cond 0
% 1.38/1.16 AC symbols 0
% 1.38/1.16
% 1.38/1.16 ------ Schedule EPR Horn non eq is on
% 1.38/1.16
% 1.38/1.16 ------ no conjectures: strip conj schedule
% 1.38/1.16
% 1.38/1.16 ------ no equalities: superposition off
% 1.38/1.16
% 1.38/1.16 ------ Option_epr_horn stripped conjectures Time Limit: Unbounded
% 1.38/1.16
% 1.38/1.16
% 1.38/1.16
% 1.38/1.16
% 1.38/1.16 % SZS status Satisfiable for theBenchmark.p
% 1.38/1.16
% 1.38/1.16 % SZS output start Saturation for theBenchmark.p
% See solution above
% 1.38/1.16
% 1.38/1.16
%------------------------------------------------------------------------------