%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL500+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 : n003.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 11.04s 4.36s
% Output : CNFRefutation 11.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 26
% Syntax : Number of formulae : 156 ( 82 unt; 0 def)
% Number of atoms : 250 ( 43 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 166 ( 72 ~; 67 |; 2 &)
% ( 8 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 14 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 220 ( 0 sgn 218 !; 2 ?; 122 :)
% 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(f17,axiom,
( kn2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn2) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
fof(f24,axiom,
( r3
<=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r3) ).
fof(f25,axiom,
( r4
<=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r4) ).
fof(f26,axiom,
( r5
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r5) ).
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(f28,axiom,
( op_and
=> ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_and) ).
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(f30,axiom,
( op_implies_or
=> ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',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/Axioms/LCL006+1.ax',op_equiv) ).
fof(f32,axiom,
op_implies_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_implies_or) ).
fof(f33,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_op_and) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_modus_ponens) ).
fof(f36,axiom,
r1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r1) ).
fof(f37,axiom,
r2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r2) ).
fof(f38,axiom,
r3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r3) ).
fof(f39,axiom,
r4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r4) ).
fof(f40,axiom,
r5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',principia_r5) ).
fof(f41,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax',use_substitution_of_equivalents) ).
fof(f42,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f43,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f44,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).
fof(f45,conjecture,
kn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn2) ).
fof(f46,negated_conjecture,
~ kn2,
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f47,plain,
~ kn2,
inference(flattening,[],[f46]) ).
fof(f48,plain,
( r5
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f26]) ).
fof(f49,plain,
( r4
=> ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f25]) ).
fof(f50,plain,
( r3
=> ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f24]) ).
fof(f51,plain,
( r2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f52,plain,
( r1
=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f53,plain,
( ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0))
=> kn2 ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f54,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f55,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(f56,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f55]) ).
fof(f57,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f59,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(and(X0,X1),X0))
| kn2 ),
inference(ennf_transformation,[],[f53]) ).
fof(f60,plain,
( ~ r1
| ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
inference(ennf_transformation,[],[f52]) ).
fof(f61,plain,
( ~ r2
| ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f51]) ).
fof(f62,plain,
( ~ r3
| ! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(ennf_transformation,[],[f50]) ).
fof(f63,plain,
( ~ r4
| ! [X0,X1,X2] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f64,plain,
( ~ r5
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(ennf_transformation,[],[f48]) ).
fof(f65,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f66,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f67,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f68,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f69,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f70,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| kn2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f59]) ).
fof(f71,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f72,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f58]) ).
fof(f73,plain,
( ~ is_a_theorem(implies(and(sK0,sK1),sK0))
| kn2 ),
inference(cnf_transformation,[],[f70]) ).
fof(f74,plain,
! [X0] :
( ~ r1
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(cnf_transformation,[],[f60]) ).
fof(f75,plain,
! [X0,X1] :
( ~ r2
| is_a_theorem(implies(X1,or(X0,X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f76,plain,
! [X0,X1] :
( ~ r3
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ r4
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(cnf_transformation,[],[f63]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ r5
| is_a_theorem(implies(implies(X1,X2),implies(or(X0,X1),or(X0,X2)))) ),
inference(cnf_transformation,[],[f64]) ).
fof(f79,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f65]) ).
fof(f80,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f66]) ).
fof(f81,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f67]) ).
fof(f82,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f83,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f69]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f32]) ).
fof(f85,plain,
op_and,
inference(cnf_transformation,[],[f33]) ).
fof(f87,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f88,plain,
r1,
inference(cnf_transformation,[],[f36]) ).
fof(f89,plain,
r2,
inference(cnf_transformation,[],[f37]) ).
fof(f90,plain,
r3,
inference(cnf_transformation,[],[f38]) ).
fof(f91,plain,
r4,
inference(cnf_transformation,[],[f39]) ).
fof(f92,plain,
r5,
inference(cnf_transformation,[],[f40]) ).
fof(f93,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f41]) ).
fof(f94,plain,
op_or,
inference(cnf_transformation,[],[f42]) ).
fof(f95,plain,
op_implies_and,
inference(cnf_transformation,[],[f43]) ).
fof(f96,plain,
op_equiv,
inference(cnf_transformation,[],[f44]) ).
fof(f97,plain,
~ kn2,
inference(cnf_transformation,[],[f47]) ).
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,[],[f71]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_51,plain,
( kn2
| ~ is_a_theorem(implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_52,plain,
! [X0: $i] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[],[f76]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
| ~ r5 ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f79]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( not(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_62,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_63,plain,
op_and,
inference(cnf_transformation,[],[f85]) ).
tcf(c_65,plain,
modus_ponens,
inference(cnf_transformation,[],[f87]) ).
tcf(c_66,plain,
r1,
inference(cnf_transformation,[],[f88]) ).
tcf(c_67,plain,
r2,
inference(cnf_transformation,[],[f89]) ).
tcf(c_68,plain,
r3,
inference(cnf_transformation,[],[f90]) ).
tcf(c_69,plain,
r4,
inference(cnf_transformation,[],[f91]) ).
tcf(c_70,plain,
r5,
inference(cnf_transformation,[],[f92]) ).
tcf(c_71,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f93]) ).
tcf(c_72,plain,
op_or,
inference(cnf_transformation,[],[f94]) ).
tcf(c_73,plain,
op_implies_and,
inference(cnf_transformation,[],[f95]) ).
tcf(c_74,plain,
op_equiv,
inference(cnf_transformation,[],[f96]) ).
tcf(c_75,negated_conjecture,
~ kn2,
inference(cnf_transformation,[],[f97]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_53,c_67,c_53]) ).
tcf(c_90,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_66,c_52]) ).
tcf(c_93,plain,
~ is_a_theorem(implies(and(sK0,sK1),sK0)),
inference(global_subsumption_just,[status(thm)],[c_51,c_75,c_51]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_54,c_68,c_54]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_60,c_62,c_60]) ).
tcf(c_101,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_71,c_50]) ).
tcf(c_104,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_73,c_59]) ).
tcf(c_107,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_65,c_49]) ).
tcf(c_108,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_107]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_63,c_58]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_72,c_57]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_61,c_74,c_61]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(global_subsumption_just,[status(thm)],[c_56,c_70,c_56]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_55,c_69,c_55]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_112,c_104]) ).
tcf(c_186,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_109,c_98]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_186,c_98]) ).
tcf(c_1119,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[status(thm)],[c_98,c_90]) ).
tcf(c_1123,plain,
! [X0: $i] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(demodulation,[status(thm)],[c_1119,c_438]) ).
tcf(c_1125,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_185,c_87]) ).
tcf(c_1135,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_90,c_108]) ).
tcf(c_1137,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_108]) ).
tcf(c_1141,plain,
! [X0: $i,X1: $i] : and(implies(X0,not(X1)),or(X1,X0)) = equiv(X0,not(X1)),
inference(superposition,[status(thm)],[c_185,c_115]) ).
tcf(c_1153,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X0,X2)))
| ~ is_a_theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_121,c_108]) ).
tcf(c_1158,plain,
! [X0: $i,X1: $i] : not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[c_185,c_186]) ).
tcf(c_1178,plain,
! [X0: $i,X1: $i,X2: $i] : not(or(and(X0,X1),not(X2))) = and(implies(X0,not(X1)),X2),
inference(superposition,[status(thm)],[c_438,c_186]) ).
tcf(c_1181,plain,
! [X0: $i,X1: $i,X2: $i] : and(implies(X0,not(X1)),X2) = and(not(and(X0,X1)),X2),
inference(demodulation,[status(thm)],[c_1178,c_1158]) ).
tcf(c_1364,plain,
! [X0: $i] : is_a_theorem(or(not(X0),and(X0,X0))),
inference(superposition,[status(thm)],[c_1123,c_1137]) ).
tcf(c_1368,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(demodulation,[status(thm)],[c_1364,c_98]) ).
tcf(c_1403,plain,
! [X0: $i,X1: $i] : and(not(and(X0,X1)),or(X1,X0)) = equiv(X0,not(X1)),
inference(demodulation,[status(thm)],[c_1141,c_1181]) ).
tcf(c_1404,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),or(not(X1),X0)) = equiv(X0,not(not(X1))),
inference(superposition,[status(thm)],[c_104,c_1403]) ).
tcf(c_1412,plain,
! [X0: $i,X1: $i] : equiv(X0,not(not(X1))) = equiv(X0,X1),
inference(demodulation,[status(thm)],[c_1404,c_98,c_115]) ).
tcf(c_1486,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(X1,not(X1)))),
inference(superposition,[status(thm)],[c_1125,c_1153]) ).
tcf(c_1633,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_1368,c_108]) ).
tcf(c_1676,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_1486,c_1135]) ).
tcf(c_1691,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_1676,c_1137]) ).
tcf(c_1692,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(demodulation,[status(thm)],[c_1691,c_98]) ).
tcf(c_2568,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_115,c_1633]) ).
tcf(c_2572,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2568,c_1692]) ).
tcf(c_6327,plain,
! [X0: $i] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(superposition,[status(thm)],[c_1412,c_2572]) ).
tcf(c_6510,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_6327,c_101]) ).
tcf(c_6572,plain,
! [X0: $i,X1: $i] : implies(X0,not(X1)) = not(and(X0,X1)),
inference(superposition,[status(thm)],[c_6510,c_104]) ).
tcf(c_22063,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_185,c_87]) ).
tcf(c_22076,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_108]) ).
tcf(c_22087,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X2,X0),or(X2,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_118,c_108]) ).
tcf(c_22229,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X1))
| ~ is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_22087,c_108]) ).
tcf(c_22783,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X0,or(X2,X1)))
| ~ is_a_theorem(or(X0,or(X1,X2))) ),
inference(superposition,[status(thm)],[c_95,c_22229]) ).
tcf(c_29174,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(not(X0),X1))),
inference(superposition,[status(thm)],[c_22063,c_22783]) ).
tcf(c_29216,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(demodulation,[status(thm)],[c_29174,c_98]) ).
tcf(c_29638,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_29216,c_22076]) ).
tcf(c_29645,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(not(and(X0,X1)),X0)),
inference(superposition,[status(thm)],[c_6572,c_29638]) ).
tcf(c_29662,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(demodulation,[status(thm)],[c_29645,c_98]) ).
tcf(c_29700,plain,
$false,
inference(superposition,[status(thm)],[c_29662,c_93]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL500+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Wed Sep 23 23:36:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.40 Running first-order theorem proving
% 0.08/0.40 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
% 0.08/0.41
% 0.08/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.41
% 0.08/0.41 % Detected problem language: tptp
% 0.08/0.42 % Proving...
% 11.04/4.36 % SZS status Started for theBenchmark.p
% 11.04/4.36 % SZS status Theorem for theBenchmark.p
% 11.04/4.36
% 11.04/4.36 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 11.04/4.36
% 11.04/4.36 % ------ iProver source info
% 11.04/4.36
% 11.04/4.36 % git: date: 2026-07-19 20:42:38 +0200
% 11.04/4.36 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 11.04/4.36 % git: non_committed_changes: false
% 11.04/4.36
% 11.04/4.36 % ------ Parsing...
% 11.04/4.36 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 11.04/4.36
% 11.04/4.36 % ------ Preprocessing... sup_sim: 2 sf_s rm: 14 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 11.04/4.36
% 11.04/4.36 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 11.04/4.36
% 11.04/4.36 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 11.04/4.36 % ------ Proving...
% 11.04/4.36 % ------ Problem Properties
% 11.04/4.36
% 11.04/4.36 %
% 11.04/4.36 % clauses 13
% 11.04/4.36 % conjectures 0
% 11.04/4.36 % EPR 0
% 11.04/4.36 % Horn 13
% 11.04/4.36 % unary 11
% 11.04/4.36 % binary 1
% 11.04/4.36 % lits 16
% 11.04/4.36 % lits eq 6
% 11.04/4.36 % fd_pure 0
% 11.04/4.36 % fd_pseudo 0
% 11.04/4.36 % fd_cond 0
% 11.04/4.36 % fd_pseudo_cond 1
% 11.04/4.36 % AC symbols 0
% 11.04/4.36
% 11.04/4.36 % ------ Input Options Time Limit: Unbounded
% 11.04/4.36
% 11.04/4.36
% 11.04/4.36 % ------
% 11.04/4.36 % Current options:
% 11.04/4.36 % ------
% 11.04/4.36
% 11.04/4.36
% 11.04/4.36 %
% 11.04/4.36
% 11.04/4.36 % ------ Proving...
% 11.04/4.36 %
% 11.04/4.36
% 11.04/4.36 % SZS status Theorem for theBenchmark.p
% 11.04/4.36
% 11.04/4.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 11.04/4.36
% 11.04/4.36
%------------------------------------------------------------------------------