%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL503+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/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 02:06:47 PM UTC 2026
% Result : Theorem 53.32s 9.39s
% Output : CNFRefutation 53.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 16
% Syntax : Number of formulae : 135 ( 59 unt; 0 def)
% Number of atoms : 228 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 174 ( 81 ~; 76 |; 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 : 218 ( 0 sgn 216 !; 2 ?; 160 :)
% 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/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(f16,axiom,
( kn1
<=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',kn1) ).
fof(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_modus_ponens) ).
fof(f36,axiom,
kn1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn1) ).
fof(f37,axiom,
kn2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn2) ).
fof(f38,axiom,
kn3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',rosser_kn3) ).
fof(f40,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
fof(f41,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
fof(f43,conjecture,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
fof(f44,negated_conjecture,
~ implies_1,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ implies_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,implies(X1,X0)))
=> implies_1 ),
inference(unused_predicate_definition_removal,[],[f4]) ).
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,implies(X1,X0)))
| implies_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,implies(sK1,sK0)))
| implies_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,implies(sK1,sK0)))
| implies_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,
~ implies_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,
( implies_1
| ~ is_a_theorem(implies(sK0,implies(sK1,sK0))) ),
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,
~ implies_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,implies(sK1,sK0))),
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_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_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_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_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_717,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_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_3679,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_3795,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_3679]) ).
tcf(c_3796,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_3679]) ).
tcf(c_3798,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_3679]) ).
tcf(c_3813,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_3795]) ).
tcf(c_3820,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_3795,c_3796]) ).
tcf(c_3828,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_3813,c_152]) ).
tcf(c_3836,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_3828,c_92]) ).
tcf(c_3844,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_3820]) ).
tcf(c_3889,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_3798]) ).
tcf(c_3909,plain,
! [X0: $i] : is_a_theorem(or(X0,and(equiv(X0,X0),equiv(X0,X0)))),
inference(superposition,[status(thm)],[c_380,c_3844]) ).
tcf(c_3925,plain,
! [X0: $i] : is_a_theorem(or(equiv(X0,X0),X0)),
inference(superposition,[status(thm)],[c_3909,c_3796]) ).
tcf(c_3931,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_3925,c_3836]) ).
tcf(c_4053,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,equiv(X0,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_3889,c_3796]) ).
tcf(c_4090,plain,
! [X0: $i] :
( is_a_theorem(or(X0,not(X0)))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_3931,c_519]) ).
tcf(c_4101,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_4090,c_3836]) ).
tcf(c_4112,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(or(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_3795,c_4101]) ).
tcf(c_4190,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_4053,c_4112]) ).
tcf(c_4195,plain,
! [X0: $i] : is_a_theorem(and(equiv(X0,X0),equiv(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_4190,c_3909]) ).
tcf(c_4214,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(superposition,[status(thm)],[c_4195,c_361]) ).
tcf(c_39194,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_4214,c_424]) ).
tcf(c_39195,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_39194]) ).
tcf(c_39322,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_39483,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_39322]) ).
tcf(c_39489,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_39194,c_39322]) ).
tcf(c_39505,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_413,c_39489]) ).
tcf(c_39506,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(not(and(X2,X0)),and(X1,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_717,c_39489]) ).
tcf(c_39507,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_39195,c_39489]) ).
tcf(c_39517,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_88,c_39507]) ).
tcf(c_39525,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_39505,c_152,c_349]) ).
tcf(c_39527,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_39525,c_39322]) ).
tcf(c_39528,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_39525,c_92]) ).
tcf(c_39659,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,not(and(X2,X0))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_39506,c_39483]) ).
tcf(c_42203,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_88,c_39659]) ).
tcf(c_42254,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_42203,c_152]) ).
tcf(c_42264,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_42254,c_39489]) ).
tcf(c_42272,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_42254,c_39528]) ).
tcf(c_42483,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_42264,c_39483]) ).
tcf(c_42485,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_42264,c_39527]) ).
tcf(c_45008,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_39517,c_42483]) ).
tcf(c_49501,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,or(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_152,c_45008]) ).
tcf(c_49803,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(X2,X0))),
inference(superposition,[status(thm)],[c_49501,c_42485]) ).
tcf(c_49862,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
inference(superposition,[status(thm)],[c_49803,c_39489]) ).
tcf(c_50255,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_49862,c_42272]) ).
tcf(c_50256,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_83,c_50255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL503+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.18/0.66 % Computer : n020.cluster.edu
% 0.18/0.66 % Model : x86_64 x86_64
% 0.18/0.66 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.66 % Memory : 8046.5625MB
% 0.18/0.66 % OS : Linux 6.8.0-71-generic
% 0.18/0.66 % CPULimit : 300
% 0.18/0.66 % WCLimit : 300
% 0.18/0.66 % DateTime : Wed Sep 23 23:36:20 UTC 2026
% 0.18/0.66 % CPUTime :
% 0.18/0.66 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.23/0.73 Running first-order theorem proving
% 0.23/0.73 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.74
% 0.23/0.74 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.74
% 0.23/0.74 % Detected problem language: tptp
% 0.23/0.76 % Proving...
% 53.32/9.39 % SZS status Started for theBenchmark.p
% 53.32/9.39 % SZS status Theorem for theBenchmark.p
% 53.32/9.39
% 53.32/9.39 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 53.32/9.39
% 53.32/9.39 % ------ iProver source info
% 53.32/9.39
% 53.32/9.39 % git: date: 2026-07-19 20:42:38 +0200
% 53.32/9.39 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 53.32/9.39 % git: non_committed_changes: false
% 53.32/9.39
% 53.32/9.39 % ------ Parsing...
% 53.32/9.39 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 53.32/9.39
% 53.32/9.39 % ------ 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 %
% 53.32/9.39
% 53.32/9.39 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 53.32/9.39
% 53.32/9.39 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 53.32/9.39 % ------ Proving...
% 53.32/9.39 % ------ Problem Properties
% 53.32/9.39
% 53.32/9.39 %
% 53.32/9.39 % clauses 9
% 53.32/9.39 % conjectures 0
% 53.32/9.39 % EPR 0
% 53.32/9.39 % Horn 9
% 53.32/9.39 % unary 7
% 53.32/9.39 % binary 1
% 53.32/9.39 % lits 12
% 53.32/9.39 % lits eq 4
% 53.32/9.39 % fd_pure 0
% 53.32/9.39 % fd_pseudo 0
% 53.32/9.39 % fd_cond 0
% 53.32/9.39 % fd_pseudo_cond 1
% 53.32/9.39 % AC symbols 0
% 53.32/9.39
% 53.32/9.39 % ------ Input Options Time Limit: Unbounded
% 53.32/9.39
% 53.32/9.39
% 53.32/9.39 % ------
% 53.32/9.39 % Current options:
% 53.32/9.39 % ------
% 53.32/9.39
% 53.32/9.39
% 53.32/9.39 %
% 53.32/9.39
% 53.32/9.39 % ------ Proving...
% 53.32/9.39 %
% 53.32/9.39
% 53.32/9.39 % SZS status Theorem for theBenchmark.p
% 53.32/9.39
% 53.32/9.39 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 53.32/9.39
% 53.32/9.39
%------------------------------------------------------------------------------