%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL509+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 : n014.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 80.59s 18.96s
% Output : CNFRefutation 80.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 140 ( 64 unt; 0 def)
% Number of atoms : 237 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 182 ( 85 ~; 80 |; 2 &)
% ( 5 <=>; 10 =>; 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 : 11 ( 9 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 227 ( 0 sgn 225 !; 2 ?; 169 :)
% 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(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
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(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,
or_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hilbert_or_1) ).
fof(f44,negated_conjecture,
~ or_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ or_1,
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(X0,or(X0,X1)))
=> or_1 ),
inference(unused_predicate_definition_removal,[],[f10]) ).
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(f57,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X0,or(X0,X1)))
| or_1 ),
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(sK0,or(sK0,sK1)))
| or_1 ),
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(f67,plain,
( ~ is_a_theorem(implies(sK0,or(sK0,sK1)))
| or_1 ),
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(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,
~ or_1,
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_51,plain,
( or_1
| ~ is_a_theorem(implies(sK0,or(sK0,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_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,
~ or_1,
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(sK0,or(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).
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_347,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_358,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_372,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
tcf(c_373,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_380,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_383,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_380,c_152]) ).
tcf(c_415,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(not(X0),X1),or(X0,X1))),
inference(superposition,[status(thm)],[c_152,c_373]) ).
tcf(c_435,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(equiv(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_415,c_92]) ).
tcf(c_465,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_383]) ).
tcf(c_466,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_383,c_92]) ).
tcf(c_575,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_465,c_347]) ).
tcf(c_579,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_575,c_92]) ).
tcf(c_657,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_579,c_92]) ).
tcf(c_1103,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_657]) ).
tcf(c_1104,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_657]) ).
tcf(c_1106,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_372,c_657]) ).
tcf(c_1190,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_347,c_1103]) ).
tcf(c_1208,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_1103,c_1104]) ).
tcf(c_1250,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_466,c_1106]) ).
tcf(c_1283,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_1190,c_152]) ).
tcf(c_1293,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_1283,c_92]) ).
tcf(c_1377,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_347,c_1208]) ).
tcf(c_1445,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,equiv(X0,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_1250,c_1104]) ).
tcf(c_1696,plain,
! [X0: $i] : is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))),
inference(superposition,[status(thm)],[c_372,c_1377]) ).
tcf(c_1763,plain,
! [X0: $i] : is_a_theorem(or(equiv(X0,X0),X0)),
inference(superposition,[status(thm)],[c_1696,c_1104]) ).
tcf(c_1784,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_1763,c_1293]) ).
tcf(c_1924,plain,
! [X0: $i] :
( is_a_theorem(or(X0,not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_1784,c_435]) ).
tcf(c_1958,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_1924,c_1293]) ).
tcf(c_2009,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(or(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_1103,c_1958]) ).
tcf(c_2440,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_1445,c_2009]) ).
tcf(c_2449,plain,
! [X0: $i] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_2440,c_1696]) ).
tcf(c_2457,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(superposition,[status(thm)],[c_2449,c_358]) ).
tcf(c_151586,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_151799,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_151586]) ).
tcf(c_153629,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
tcf(c_153634,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_153637,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_153639,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_153637,c_152]) ).
tcf(c_153661,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(and(X1,X2),not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_153,c_92]) ).
tcf(c_153662,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_153629,c_92]) ).
tcf(c_153667,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_153696,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(global_subsumption_just,[status(thm)],[c_153662,c_2457]) ).
tcf(c_153698,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_153696,c_151799]) ).
tcf(c_153700,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_153698]) ).
tcf(c_153735,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_153639]) ).
tcf(c_153736,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_153639,c_92]) ).
tcf(c_153757,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_153735,c_153634]) ).
tcf(c_153761,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_153757,c_92]) ).
tcf(c_153780,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(not(and(X0,X1))) ),
inference(superposition,[status(thm)],[c_153736,c_153667]) ).
tcf(c_153803,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_153761,c_92]) ).
tcf(c_154369,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(not(and(X1,X2)))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(not(and(X0,X1))) ),
inference(superposition,[status(thm)],[c_153661,c_153667]) ).
tcf(c_155338,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_153803]) ).
tcf(c_155345,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_153698,c_153803]) ).
tcf(c_155903,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_153700,c_155345]) ).
tcf(c_156004,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_155903]) ).
tcf(c_156727,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_156004,c_155338]) ).
tcf(c_158871,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_156727,c_155345]) ).
tcf(c_159092,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(or(X0,X1),not(X0))),
inference(superposition,[status(thm)],[c_152,c_158871]) ).
tcf(c_161506,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(not(and(not(X1),X2)))
| ~ is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_88,c_154369]) ).
tcf(c_181769,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(not(and(not(X1),X0)))
| ~ is_a_theorem(implies(X0,and(X1,X2))) ),
inference(superposition,[status(thm)],[c_77,c_161506]) ).
tcf(c_184734,plain,
! [X0: $i] : is_a_theorem(not(and(not(X0),X0))),
inference(superposition,[status(thm)],[c_80,c_181769]) ).
tcf(c_185111,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_184734,c_153780]) ).
tcf(c_188444,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X0,X1))),
inference(superposition,[status(thm)],[c_159092,c_185111]) ).
tcf(c_188483,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_188444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL509+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/5.38 % Computer : n014.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Wed Sep 23 23:36:12 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/5.42 Running first-order theorem proving
% 0.14/5.42 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
% 0.14/5.43
% 0.14/5.43 % ======== iProver multi-core TPTP/SMT =========
% 0.14/5.43
% 0.14/5.44 % Detected problem language: tptp
% 0.14/5.45 % Proving...
% 80.59/18.96 % SZS status Started for theBenchmark.p
% 80.59/18.96 % SZS status Theorem for theBenchmark.p
% 80.59/18.96
% 80.59/18.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 80.59/18.96
% 80.59/18.96 % ------ iProver source info
% 80.59/18.96
% 80.59/18.96 % git: date: 2026-07-19 20:42:38 +0200
% 80.59/18.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 80.59/18.96 % git: non_committed_changes: false
% 80.59/18.96
% 80.59/18.96 % ------ Parsing...
% 80.59/18.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 80.59/18.96
% 80.59/18.96 % ------ 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 %
% 80.59/18.96
% 80.59/18.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 80.59/18.96
% 80.59/18.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 80.59/18.96 % ------ Proving...
% 80.59/18.96 % ------ Problem Properties
% 80.59/18.96
% 80.59/18.96 %
% 80.59/18.96 % clauses 9
% 80.59/18.96 % conjectures 0
% 80.59/18.96 % EPR 0
% 80.59/18.96 % Horn 9
% 80.59/18.96 % unary 7
% 80.59/18.96 % binary 1
% 80.59/18.96 % lits 12
% 80.59/18.96 % lits eq 4
% 80.59/18.96 % fd_pure 0
% 80.59/18.96 % fd_pseudo 0
% 80.59/18.96 % fd_cond 0
% 80.59/18.96 % fd_pseudo_cond 1
% 80.59/18.96 % AC symbols 0
% 80.59/18.96
% 80.59/18.96 % ------ Schedule dynamic 5 is on
% 80.59/18.96
% 80.59/18.96 % ------ no conjectures: strip conj schedule
% 80.59/18.96
% 80.59/18.96 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 80.59/18.96
% 80.59/18.96
% 80.59/18.96 % ------
% 80.59/18.96 % Current options:
% 80.59/18.96 % ------
% 80.59/18.96
% 80.59/18.96
% 80.59/18.96 %
% 80.59/18.96
% 80.59/18.96 % ------ Proving...
% 80.59/18.96 % Proof_search_loop: time out after: 3490 full_loop iterations
% 80.59/18.96
% 80.59/18.96 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" stripped conjectures Time Limit: 15.
% 80.59/18.96
% 80.59/18.96
% 80.59/18.96 % ------
% 80.59/18.96 % Current options:
% 80.59/18.96 % ------
% 80.59/18.96
% 80.59/18.96
% 80.59/18.96 %
% 80.59/18.96
% 80.59/18.96 % ------ Proving...
% 80.59/18.96 %
% 80.59/18.96
% 80.59/18.96 % SZS status Theorem for theBenchmark.p
% 80.59/18.96
% 80.59/18.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 80.59/18.97
% 80.59/18.97
%------------------------------------------------------------------------------