%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:06:48 PM UTC 2026
% Result : Theorem 166.18s 39.57s
% Output : CNFRefutation 166.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 18
% Syntax : Number of formulae : 205 ( 113 unt; 0 def)
% Number of atoms : 320 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 214 ( 99 ~; 94 |; 2 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 335 ( 0 sgn 333 !; 2 ?; 269 :)
% 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/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',use_substitution_of_equivalents) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_and_2) ).
fof(f44,negated_conjecture,
~ and_2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ and_2,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( kn3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f47,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f48,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
fof(f49,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1))
=> and_2 ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f50,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f51,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(f54,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f57,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X1))
| and_2 ),
inference(ennf_transformation,[],[f49]) ).
fof(f58,plain,
( ~ kn1
| ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f59,plain,
( ~ kn2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f47]) ).
fof(f60,plain,
( ~ kn3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(ennf_transformation,[],[f46]) ).
fof(f61,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f62,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f63,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f64,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f66,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK1))
| and_2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ and_2,
inference(cnf_transformation,[],[f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_51,plain,
( and_2
| ~ is_a_theorem(implies(and(sK0,sK1),sK1)) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_61,plain,
modus_ponens,
inference(cnf_transformation,[],[f77]) ).
tcf(c_62,plain,
kn1,
inference(cnf_transformation,[],[f78]) ).
tcf(c_63,plain,
kn2,
inference(cnf_transformation,[],[f79]) ).
tcf(c_64,plain,
kn3,
inference(cnf_transformation,[],[f80]) ).
tcf(c_65,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f81]) ).
tcf(c_66,plain,
op_or,
inference(cnf_transformation,[],[f82]) ).
tcf(c_67,plain,
op_implies_and,
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,plain,
op_equiv,
inference(cnf_transformation,[],[f84]) ).
tcf(c_69,negated_conjecture,
~ and_2,
inference(cnf_transformation,[],[f85]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_53,c_63,c_53]) ).
tcf(c_80,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_62,c_52]) ).
tcf(c_83,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK1)),
inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_65,c_50]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_67,c_56]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_61,c_49]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_91]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_66,c_55]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_68,c_57]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))),
inference(global_subsumption_just,[status(thm)],[c_54,c_64,c_54]) ).
tcf(c_152,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_93,c_88]) ).
tcf(c_153,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),or(and(X1,X2),not(and(X2,X0))))),
inference(demodulation,[status(thm)],[c_99,c_152]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_88,c_152]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_77,c_92]) ).
tcf(c_362,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152,c_92]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] : and(or(X0,X1),implies(X1,not(X0))) = equiv(not(X0),X1),
inference(superposition,[status(thm)],[c_152,c_96]) ).
tcf(c_380,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
tcf(c_381,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))),
inference(superposition,[status(thm)],[c_96,c_77]) ).
tcf(c_413,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_361]) ).
tcf(c_430,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(not(X0),X1),or(and(X1,X2),implies(X2,X0)))),
inference(superposition,[status(thm)],[c_88,c_153]) ).
tcf(c_452,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[status(thm)],[c_88,c_349]) ).
tcf(c_519,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(equiv(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_378,c_361]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,X2),implies(X2,X0)))),
inference(light_normalisation,[status(thm)],[c_430,c_152]) ).
tcf(c_743,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),or(and(X1,not(X2)),or(X2,X0)))),
inference(superposition,[status(thm)],[c_152,c_739]) ).
tcf(c_744,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(and(X1,X2),implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_739,c_92]) ).
tcf(c_788,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,X1),implies(implies(X1,X2),or(X2,X0)))),
inference(demodulation,[status(thm)],[c_743,c_349]) ).
tcf(c_792,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_788,c_92]) ).
tcf(c_3696,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_792,c_92]) ).
tcf(c_3812,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(and(X1,X1),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_80,c_3696]) ).
tcf(c_3813,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_3696]) ).
tcf(c_3815,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(equiv(X1,X1),X0))
| ~ is_a_theorem(or(X0,implies(X1,X1))) ),
inference(superposition,[status(thm)],[c_380,c_3696]) ).
tcf(c_3830,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X1),X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_349,c_3812]) ).
tcf(c_3837,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,and(X2,X2)))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_3812,c_3813]) ).
tcf(c_3845,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X1,X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(demodulation,[status(thm)],[c_3830,c_152]) ).
tcf(c_3853,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X1,X1))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_3845,c_92]) ).
tcf(c_3861,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,and(X2,X2)))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_349,c_3837]) ).
tcf(c_3907,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(equiv(X0,X0),and(X1,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_744,c_3815]) ).
tcf(c_3927,plain,
! [X0: $i] : is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))),
inference(superposition,[status(thm)],[c_380,c_3861]) ).
tcf(c_3943,plain,
! [X0: $i] : is_a_theorem(or(equiv(X0,X0),X0)),
inference(superposition,[status(thm)],[c_3927,c_3813]) ).
tcf(c_3950,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_3943,c_3853]) ).
tcf(c_4073,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,equiv(X0,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_3907,c_3813]) ).
tcf(c_4110,plain,
! [X0: $i] :
( is_a_theorem(or(X0,not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_3950,c_519]) ).
tcf(c_4121,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_4110,c_3853]) ).
tcf(c_4132,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(or(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_3812,c_4121]) ).
tcf(c_4191,plain,
! [X0: $i] :
( is_a_theorem(and(equiv(X0,X0),equiv(X0,X0)))
| ~ is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))) ),
inference(superposition,[status(thm)],[c_4073,c_4132]) ).
tcf(c_4196,plain,
! [X0: $i] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_4191,c_3927]) ).
tcf(c_4235,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(superposition,[status(thm)],[c_4196,c_361]) ).
tcf(c_4493,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_4235,c_424]) ).
tcf(c_4495,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_4235,c_519]) ).
tcf(c_4500,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_4493,c_3696]) ).
tcf(c_4777,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_4495,c_4500]) ).
tcf(c_4784,plain,
! [X0: $i] : is_a_theorem(or(X0,equiv(X0,X0))),
inference(superposition,[status(thm)],[c_3943,c_4500]) ).
tcf(c_4913,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_4777]) ).
tcf(c_4917,plain,
! [X0: $i] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_4777,c_3853]) ).
tcf(c_5073,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_4913,c_3813]) ).
tcf(c_5520,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(X0),or(X0,X1))),
inference(superposition,[status(thm)],[c_152,c_5073]) ).
tcf(c_5646,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_5520,c_362]) ).
tcf(c_6859,plain,
! [X0: $i] :
( is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(or(X0,equiv(X0,X0))) ),
inference(superposition,[status(thm)],[c_4073,c_4917]) ).
tcf(c_6863,plain,
! [X0: $i] : is_a_theorem(not(not(equiv(X0,X0)))),
inference(forward_subsumption_resolution,[status(thm)],[c_6859,c_4784]) ).
tcf(c_6905,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(superposition,[status(thm)],[c_6863,c_5646]) ).
tcf(c_6915,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_6905,c_3813]) ).
tcf(c_6929,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,and(equiv(X1,X1),equiv(X1,X1)))),
inference(superposition,[status(thm)],[c_6915,c_3837]) ).
tcf(c_89929,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_4235,c_424]) ).
tcf(c_89930,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_89929]) ).
tcf(c_90092,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_792,c_92]) ).
tcf(c_90283,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(and(X1,X1),X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_80,c_90092]) ).
tcf(c_90284,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_90092]) ).
tcf(c_90287,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X1,X2),X0))
| ~ is_a_theorem(or(X0,equiv(X1,X2))) ),
inference(superposition,[status(thm)],[c_381,c_90092]) ).
tcf(c_90290,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_89929,c_90092]) ).
tcf(c_90303,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_413,c_90290]) ).
tcf(c_90305,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_89930,c_90290]) ).
tcf(c_90306,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X2,X0),and(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_744,c_90290]) ).
tcf(c_90331,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_90305]) ).
tcf(c_90358,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,and(X2,X2)))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_90283,c_90284]) ).
tcf(c_90360,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_90331,c_90284]) ).
tcf(c_90362,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(superposition,[status(thm)],[c_6929,c_90284]) ).
tcf(c_90406,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_90360,c_90290]) ).
tcf(c_90410,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_90362,c_90284]) ).
tcf(c_90474,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_90303,c_152,c_349]) ).
tcf(c_90476,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_90474,c_90092]) ).
tcf(c_90477,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_90474,c_92]) ).
tcf(c_90886,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(or(X0,X0),X1))),
inference(superposition,[status(thm)],[c_90406,c_90476]) ).
tcf(c_90913,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(or(X0,X0),X1),X0)),
inference(superposition,[status(thm)],[c_90886,c_90290]) ).
tcf(c_90924,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(or(and(X0,X1),and(X0,X1)),X2))),
inference(superposition,[status(thm)],[c_90913,c_90284]) ).
tcf(c_92584,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X0),X1)),
inference(superposition,[status(thm)],[c_90410,c_90287]) ).
tcf(c_92627,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_90306,c_90284]) ).
tcf(c_92650,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_92584,c_90476]) ).
tcf(c_92839,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X2,X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_92627,c_90290]) ).
tcf(c_92843,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_92627,c_90477]) ).
tcf(c_92913,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(or(X1,implies(X3,X0)))
| ~ is_a_theorem(or(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_92839,c_90284]) ).
tcf(c_92921,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(or(and(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_744,c_92843]) ).
tcf(c_92943,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(and(X0,X1),and(X0,X1)),X0)),
inference(superposition,[status(thm)],[c_90924,c_92843]) ).
tcf(c_92947,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_92627,c_92843]) ).
tcf(c_93071,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,implies(X1,X0)))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_92839,c_92947]) ).
tcf(c_93229,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(implies(X0,X1),and(X0,not(X1))),X0)),
inference(superposition,[status(thm)],[c_349,c_92943]) ).
tcf(c_94866,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(implies(X0,X1),implies(X0,X1)),X0)),
inference(demodulation,[status(thm)],[c_93229,c_452]) ).
tcf(c_95112,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[status(thm)],[c_94866,c_90290]) ).
tcf(c_95116,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,X0))),
inference(superposition,[status(thm)],[c_94866,c_90358]) ).
tcf(c_95129,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,X0),implies(X0,X1))),
inference(superposition,[status(thm)],[c_95116,c_90290]) ).
tcf(c_97623,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(X2,X0))),
inference(superposition,[status(thm)],[c_95112,c_92913]) ).
tcf(c_97829,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
inference(superposition,[status(thm)],[c_97623,c_90290]) ).
tcf(c_98272,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_97829,c_92843]) ).
tcf(c_98281,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(superposition,[status(thm)],[c_152,c_98272]) ).
tcf(c_99286,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(X1,X1),X0))),
inference(superposition,[status(thm)],[c_92650,c_92921]) ).
tcf(c_99459,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,and(implies(X1,X1),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_99286]) ).
tcf(c_99503,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(implies(X0,X0),not(X1)),X1)),
inference(superposition,[status(thm)],[c_99459,c_90290]) ).
tcf(c_100379,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(or(X1,X1),X1))),
inference(superposition,[status(thm)],[c_90886,c_93071]) ).
tcf(c_100424,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,and(X1,X1)))),
inference(superposition,[status(thm)],[c_95129,c_93071]) ).
tcf(c_100537,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(or(X1,X1),X1))),
inference(superposition,[status(thm)],[c_152,c_100379]) ).
tcf(c_100547,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X1,and(X1,X1)))),
inference(superposition,[status(thm)],[c_152,c_100424]) ).
tcf(c_100644,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(or(X1,X1),X1),X0))),
inference(superposition,[status(thm)],[c_100537,c_92921]) ).
tcf(c_100676,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(X1,and(X1,X1)),X0))),
inference(superposition,[status(thm)],[c_100547,c_92921]) ).
tcf(c_104660,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(demodulation,[status(thm)],[c_99503,c_349]) ).
tcf(c_104670,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_104660,c_92]) ).
tcf(c_114488,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_153,c_104670]) ).
tcf(c_114926,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(and(X0,X1)),and(X1,X0))),
inference(superposition,[status(thm)],[c_114488,c_90290]) ).
tcf(c_126261,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_114926,c_90284]) ).
tcf(c_127664,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(and(X0,X1)),X1)),
inference(superposition,[status(thm)],[c_126261,c_90290]) ).
tcf(c_227663,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,or(X0,X0)),equiv(or(X0,X0),X0))),
inference(superposition,[status(thm)],[c_96,c_100644]) ).
tcf(c_228676,plain,
! [X0: $i] : is_a_theorem(implies(implies(and(X0,X0),X0),equiv(X0,and(X0,X0)))),
inference(superposition,[status(thm)],[c_96,c_100676]) ).
tcf(c_229052,plain,
! [X0: $i] :
( is_a_theorem(equiv(or(X0,X0),X0))
| ~ is_a_theorem(implies(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_227663,c_92]) ).
tcf(c_229053,plain,
! [X0: $i] : is_a_theorem(equiv(or(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_229052,c_98281]) ).
tcf(c_230409,plain,
! [X0: $i] : or(X0,X0) = X0,
inference(superposition,[status(thm)],[c_229053,c_85]) ).
tcf(c_244564,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,and(X0,X0)))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_228676,c_92]) ).
tcf(c_244565,plain,
! [X0: $i] : is_a_theorem(equiv(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_244564,c_77]) ).
tcf(c_244920,plain,
! [X0: $i] : and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_244565,c_85]) ).
tcf(c_245222,plain,
! [X0: $i] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_244920,c_88]) ).
tcf(c_245852,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(demodulation,[status(thm)],[c_245222,c_152,c_230409]) ).
tcf(c_246253,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_245852,c_152]) ).
tcf(c_246720,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X1)),
inference(demodulation,[status(thm)],[c_127664,c_246253]) ).
tcf(c_246766,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_246720]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL507+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.41 % Computer : n020.cluster.edu
% 0.14/10.41 % Model : x86_64 x86_64
% 0.14/10.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.41 % Memory : 8046.5625MB
% 0.14/10.41 % OS : Linux 6.8.0-71-generic
% 0.14/10.41 % CPULimit : 300
% 0.14/10.41 % WCLimit : 300
% 0.14/10.41 % DateTime : Wed Sep 23 23:36:45 UTC 2026
% 0.14/10.42 % CPUTime :
% 0.14/10.42 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/10.48 Running first-order theorem proving
% 0.14/10.48 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/10.50
% 0.19/10.50 % ======== iProver multi-core TPTP/SMT =========
% 0.19/10.50
% 0.19/10.50 % Detected problem language: tptp
% 0.19/10.52 % Proving...
% 166.18/39.57 % SZS status Started for theBenchmark.p
% 166.18/39.57 % SZS status Theorem for theBenchmark.p
% 166.18/39.57
% 166.18/39.57 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 166.18/39.57
% 166.18/39.57 % ------ iProver source info
% 166.18/39.57
% 166.18/39.57 % git: date: 2026-07-19 20:42:38 +0200
% 166.18/39.57 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 166.18/39.57 % git: non_committed_changes: false
% 166.18/39.57
% 166.18/39.57 % ------ Parsing...
% 166.18/39.57 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 166.18/39.57
% 166.18/39.57 % ------ Preprocessing... sup_sim: 2 sf_s rm: 10 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 166.18/39.57
% 166.18/39.57 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 166.18/39.57
% 166.18/39.57 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 166.18/39.57 % ------ Proving...
% 166.18/39.57 % ------ Problem Properties
% 166.18/39.57
% 166.18/39.57 %
% 166.18/39.57 % clauses 9
% 166.18/39.57 % conjectures 0
% 166.18/39.57 % EPR 0
% 166.18/39.57 % Horn 9
% 166.18/39.57 % unary 7
% 166.18/39.57 % binary 1
% 166.18/39.57 % lits 12
% 166.18/39.57 % lits eq 4
% 166.18/39.57 % fd_pure 0
% 166.18/39.57 % fd_pseudo 0
% 166.18/39.57 % fd_cond 0
% 166.18/39.57 % fd_pseudo_cond 1
% 166.18/39.57 % AC symbols 0
% 166.18/39.57
% 166.18/39.57 % ------ Input Options Time Limit: Unbounded
% 166.18/39.57
% 166.18/39.57
% 166.18/39.57 % ------
% 166.18/39.57 % Current options:
% 166.18/39.57 % ------
% 166.18/39.57
% 166.18/39.57
% 166.18/39.57 %
% 166.18/39.57
% 166.18/39.57 % ------ Proving...
% 166.18/39.57 %
% 166.18/39.57
% 166.18/39.57 % SZS status Theorem for theBenchmark.p
% 166.18/39.57
% 166.18/39.57 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 166.18/39.58
% 166.18/39.58
%------------------------------------------------------------------------------