%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL519+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 : n007.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 02:06:49 PM UTC 2026
% Result : Theorem 96.78s 15.37s
% Output : CNFRefutation 96.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 25
% Syntax : Number of formulae : 252 ( 121 unt; 0 def)
% Number of atoms : 414 ( 58 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 310 ( 148 ~; 143 |; 2 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 11 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 426 ( 0 sgn 424 !; 2 ?; 356 :)
% 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(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(f23,axiom,
( r2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',r2) ).
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_or,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_or) ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+5.ax',rosser_op_implies_and) ).
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_implies_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_implies_or) ).
fof(f41,axiom,
op_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_and) ).
fof(f42,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_op_equiv) ).
fof(f43,conjecture,
r2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',principia_r2) ).
fof(f44,negated_conjecture,
~ r2,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ r2,
inference(flattening,[],[f44]) ).
fof(f46,plain,
( ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1)))
=> r2 ),
inference(unused_predicate_definition_removal,[],[f23]) ).
fof(f47,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(f48,plain,
( kn2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f17]) ).
fof(f49,plain,
( kn1
=> ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(unused_predicate_definition_removal,[],[f16]) ).
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(f52,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f53,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f52]) ).
fof(f55,plain,
( ~ kn1
| ! [X0] : is_a_theorem(implies(X0,and(X0,X0))) ),
inference(ennf_transformation,[],[f49]) ).
fof(f56,plain,
( ~ kn2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f48]) ).
fof(f57,plain,
( ~ kn3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(ennf_transformation,[],[f47]) ).
fof(f58,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(X1,or(X0,X1)))
| r2 ),
inference(ennf_transformation,[],[f46]) ).
fof(f59,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f60,plain,
( ~ op_and
| ! [X0,X1] : and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f28]) ).
fof(f61,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f62,plain,
( ~ op_implies_or
| ! [X0,X1] : implies(X0,X1) = or(not(X0),X1) ),
inference(ennf_transformation,[],[f30]) ).
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(sK1,or(sK0,sK1)))
| r2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f58]) ).
fof(f65,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f67,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f68,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f56]) ).
fof(f69,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f57]) ).
fof(f70,plain,
( ~ is_a_theorem(implies(sK1,or(sK0,sK1)))
| r2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f71,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f59]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_and
| and(X0,X1) = not(or(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f74,plain,
! [X0,X1] :
( ~ op_implies_or
| implies(X0,X1) = or(not(X0),X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f75,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f76,plain,
op_or,
inference(cnf_transformation,[],[f32]) ).
fof(f77,plain,
op_implies_and,
inference(cnf_transformation,[],[f33]) ).
fof(f79,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f80,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f81,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f82,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f84,plain,
op_implies_or,
inference(cnf_transformation,[],[f40]) ).
fof(f85,plain,
op_and,
inference(cnf_transformation,[],[f41]) ).
fof(f86,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f87,plain,
~ r2,
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,
! [X0: $i] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_53,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,[],[f69]) ).
tcf(c_54,plain,
( r2
| ~ is_a_theorem(implies(sK1,or(sK0,sK1))) ),
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(or(not(X0),not(X1))) = and(X0,X1) )
| ~ op_and ),
inference(cnf_transformation,[],[f72]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( or(not(X0),X1) = implies(X0,X1) )
| ~ op_implies_or ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f75]) ).
tcf(c_60,plain,
op_or,
inference(cnf_transformation,[],[f76]) ).
tcf(c_61,plain,
op_implies_and,
inference(cnf_transformation,[],[f77]) ).
tcf(c_63,plain,
modus_ponens,
inference(cnf_transformation,[],[f79]) ).
tcf(c_64,plain,
kn1,
inference(cnf_transformation,[],[f80]) ).
tcf(c_65,plain,
kn2,
inference(cnf_transformation,[],[f81]) ).
tcf(c_66,plain,
kn3,
inference(cnf_transformation,[],[f82]) ).
tcf(c_68,plain,
op_implies_or,
inference(cnf_transformation,[],[f84]) ).
tcf(c_69,plain,
op_and,
inference(cnf_transformation,[],[f85]) ).
tcf(c_70,plain,
op_equiv,
inference(cnf_transformation,[],[f86]) ).
tcf(c_71,negated_conjecture,
~ r2,
inference(cnf_transformation,[],[f87]) ).
tcf(c_81,plain,
~ is_a_theorem(implies(sK1,or(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_54,c_71,c_54]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_52,c_65,c_52]) ).
tcf(c_86,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_64,c_51]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_58,c_68,c_58]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_57,c_61,c_57]) ).
tcf(c_98,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_63,c_49]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_98]) ).
tcf(c_100,plain,
! [X0: $i,X1: $i] : not(or(not(X0),not(X1))) = and(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_56,c_69,c_56]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_55,c_60,c_55]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_59,c_70,c_59]) ).
tcf(c_109,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_53,c_66,c_53]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_103,c_95]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] : not(implies(X0,not(X1))) = and(X0,X1),
inference(demodulation,[status(thm)],[c_100,c_89]) ).
tcf(c_172,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_109,c_170]) ).
tcf(c_228,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_232,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( implies(X0,X2) = implies(X1,X3) )
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_234,plain,
! [X0: $i,X1: $i] :
( ( not(X0) = not(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_387,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_95,c_170]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i,X2: $i] : implies(and(X0,not(X1)),X2) = or(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_95,c_89]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i] : not(or(X0,not(X1))) = and(not(X0),X1),
inference(superposition,[status(thm)],[c_170,c_171]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i] : or(implies(X0,not(X1)),X2) = implies(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_171,c_170]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_171,c_89]) ).
tcf(c_447,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_106,c_86]) ).
tcf(c_471,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_170,c_86]) ).
tcf(c_472,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,not(X0)),equiv(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_170,c_447]) ).
tcf(c_492,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_95,c_172]) ).
tcf(c_523,plain,
! [X0: $i,X1: $i] : and(not(not(X0)),X1) = not(implies(X0,not(X1))),
inference(superposition,[status(thm)],[c_89,c_405]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(not(X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_231,c_89]) ).
tcf(c_627,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_231,c_170]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(resolution,[status(thm)],[c_627,c_99]) ).
tcf(c_759,plain,
! [X0: $i,X1: $i] :
( ( X1 = X0 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_230,c_228]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i] : and(not(not(X0)),X1) = and(X0,X1),
inference(light_normalisation,[status(thm)],[c_523,c_171]) ).
tcf(c_797,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),not(not(X0)))),
inference(superposition,[status(thm)],[c_791,c_83]) ).
tcf(c_799,plain,
! [X0: $i] : is_a_theorem(or(not(X0),and(X0,not(not(X0))))),
inference(superposition,[status(thm)],[c_791,c_471]) ).
tcf(c_838,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),not(not(implies(X0,X1))))),
inference(superposition,[status(thm)],[c_106,c_797]) ).
tcf(c_839,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),not(not(not(not(X0)))))),
inference(superposition,[status(thm)],[c_791,c_797]) ).
tcf(c_846,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,not(not(X0))))),
inference(demodulation,[status(thm)],[c_799,c_89]) ).
tcf(c_860,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(X1,X3))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_232,c_231]) ).
tcf(c_874,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_86,c_99]) ).
tcf(c_879,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(X0),not(X0)))
| ~ is_a_theorem(or(X0,not(X0))) ),
inference(superposition,[status(thm)],[c_472,c_99]) ).
tcf(c_880,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_797,c_99]) ).
tcf(c_881,plain,
! [X0: $i] :
( is_a_theorem(and(X0,not(not(X0))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_846,c_99]) ).
tcf(c_882,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_170,c_99]) ).
tcf(c_910,plain,
! [X0: $i,X1: $i] : implies(X0,X1) = or(not(X0),X1),
inference(resolution,[status(thm)],[c_759,c_89]) ).
tcf(c_912,plain,
! [X0: $i,X1: $i] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)),
inference(resolution,[status(thm)],[c_759,c_106]) ).
tcf(c_914,plain,
! [X0: $i,X1: $i] : or(X0,X1) = implies(not(X0),X1),
inference(resolution,[status(thm)],[c_759,c_170]) ).
tcf(c_949,plain,
! [X0: $i] :
( is_a_theorem(and(X0,not(not(X0))))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_791,c_874]) ).
tcf(c_963,plain,
! [X0: $i] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_874,c_880]) ).
tcf(c_965,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(not(not(X0)))))
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_791,c_880]) ).
tcf(c_993,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_910,c_231]) ).
tcf(c_1022,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(implies(X0,X1)))
| ~ is_a_theorem(and(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_95,c_963]) ).
tcf(c_1032,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(and(X0,X1)))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_171,c_963]) ).
tcf(c_1057,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_914,c_231]) ).
tcf(c_1070,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X0,X1)) ),
inference(superposition,[status(thm)],[c_83,c_99]) ).
tcf(c_1154,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,not(X1)),not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_171,c_838]) ).
tcf(c_1161,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,not(not(X1))),implies(X0,X1))),
inference(superposition,[status(thm)],[c_95,c_1154]) ).
tcf(c_1205,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(resolution,[status(thm)],[c_1057,c_86]) ).
tcf(c_1216,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(not(not(X0)),not(not(X0))))),
inference(resolution,[status(thm)],[c_1205,c_993]) ).
tcf(c_1236,plain,
! [X0: $i] :
( is_a_theorem(and(not(not(X0)),not(not(X0))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[c_1216,c_99]) ).
tcf(c_1261,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_89,c_882]) ).
tcf(c_1298,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(not(not(X0)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[c_673,c_625]) ).
tcf(c_1303,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_949,c_1070]) ).
tcf(c_1337,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,not(X1)))
| ~ is_a_theorem(not(and(X0,X1))) ),
inference(superposition,[status(thm)],[c_171,c_1303]) ).
tcf(c_1359,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(equiv(X0,not(not(X1)))) ),
inference(superposition,[status(thm)],[c_1161,c_99]) ).
tcf(c_1551,plain,
! [X0: $i] :
( is_a_theorem(not(not(not(not(X0)))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_881,c_965]) ).
tcf(c_1572,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(not(and(X0,X1)))))
| ~ is_a_theorem(implies(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_171,c_1551]) ).
tcf(c_1581,plain,
! [X0: $i] :
( is_a_theorem(not(implies(X0,not(X0))))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_949,c_1022]) ).
tcf(c_1631,plain,
! [X0: $i,X1: $i] : is_a_theorem(not(and(and(X0,X1),not(not(not(X0)))))),
inference(superposition,[status(thm)],[c_839,c_1032]) ).
tcf(c_1832,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(and(implies(X0,X1),implies(X1,X0))) ),
inference(resolution,[status(thm)],[c_912,c_231]) ).
tcf(c_1994,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(not(not(X0))) ),
inference(resolution,[status(thm)],[c_1298,c_86]) ).
tcf(c_2506,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_1337]) ).
tcf(c_2831,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_2506,c_99]) ).
tcf(c_3017,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(X0,X1))
| ~ is_a_theorem(not(not(not(X0)))) ),
inference(superposition,[status(thm)],[c_170,c_1261]) ).
tcf(c_3274,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( is_a_theorem(implies(X0,X3))
| ( X3 != X1 )
| ( X0 != and(X1,X2) ) ),
inference(resolution,[status(thm)],[c_860,c_83]) ).
tcf(c_8329,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(and(X1,X2),X0))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_3274,c_228]) ).
tcf(c_8545,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),not(not(X0)))),
inference(demodulation,[status(thm)],[c_1631,c_95]) ).
tcf(c_8650,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(not(not(X0))) ),
inference(demodulation,[status(thm)],[c_1581,c_171]) ).
tcf(c_8894,plain,
! [X0: $i] :
( is_a_theorem(implies(not(not(X0)),X0))
| ~ is_a_theorem(or(not(X0),not(not(X0)))) ),
inference(superposition,[status(thm)],[c_879,c_1359]) ).
tcf(c_8939,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(implies(X0,not(not(X0)))) ),
inference(demodulation,[status(thm)],[c_8894,c_89,c_170]) ).
tcf(c_9192,plain,
! [X0: $i] :
( is_a_theorem(not(not(and(X0,X0))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_86,c_2831]) ).
tcf(c_9195,plain,
! [X0: $i] :
( is_a_theorem(not(not(equiv(X0,X0))))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_447,c_2831]) ).
tcf(c_9230,plain,
! [X0: $i] :
( is_a_theorem(and(and(X0,X0),and(X0,X0)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_9192,c_8650]) ).
tcf(c_9249,plain,
! [X0: $i] :
( is_a_theorem(not(not(not(not(and(X0,X0))))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_9230,c_965]) ).
tcf(c_9256,plain,
! [X0: $i] :
( is_a_theorem(not(not(not(not(equiv(X0,X0))))))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_106,c_9249]) ).
tcf(c_9424,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_388,c_83]) ).
tcf(c_9585,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(or(and(X0,X1),X2),implies(X0,not(X1)))),
inference(superposition,[status(thm)],[c_412,c_9424]) ).
tcf(c_9770,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(implies(X0,X1),X2),implies(X0,not(not(X1))))),
inference(superposition,[status(thm)],[c_387,c_9585]) ).
tcf(c_9895,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_492,c_170]) ).
tcf(c_9902,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_170,c_9895]) ).
tcf(c_9922,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(and(X1,X2))
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_8329,c_99]) ).
tcf(c_10148,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(and(implies(X0,X1),X2),implies(X0,not(not(X1))))),
inference(superposition,[status(thm)],[c_411,c_9770]) ).
tcf(c_10448,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X0,not(not(X1))))),
inference(superposition,[status(thm)],[c_106,c_10148]) ).
tcf(c_10618,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(not(not(equiv(X0,X1)))) ),
inference(superposition,[status(thm)],[c_10448,c_1261]) ).
tcf(c_10619,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_10448,c_99]) ).
tcf(c_10971,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(equiv(X0,X0)) ),
inference(superposition,[status(thm)],[c_10619,c_8939]) ).
tcf(c_11021,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(X1)
| ( X0 != not(not(X1)) ) ),
inference(resolution,[status(thm)],[c_9922,c_1236]) ).
tcf(c_11170,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(implies(X0,X1))))
| ~ is_a_theorem(implies(X0,not(not(X1)))) ),
inference(superposition,[status(thm)],[c_95,c_1572]) ).
tcf(c_11574,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X0))
| ~ is_a_theorem(or(not(equiv(X0,X0)),X1)) ),
inference(superposition,[status(thm)],[c_9256,c_3017]) ).
tcf(c_12876,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(X0))
| ~ is_a_theorem(X1)
| ( X0 != not(X1) ) ),
inference(resolution,[status(thm)],[c_11021,c_234]) ).
tcf(c_13071,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(X0)))
| ~ is_a_theorem(X1)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_12876,c_234]) ).
tcf(c_13370,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(implies(X0,X1))))
| ~ is_a_theorem(or(not(X0),X1)) ),
inference(resolution,[status(thm)],[c_13071,c_910]) ).
tcf(c_14129,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_9902,c_387]) ).
tcf(c_14142,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_14129,c_99]) ).
tcf(c_16036,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(not(not(implies(X0,X0)))) ),
inference(resolution,[status(thm)],[c_1832,c_1994]) ).
tcf(c_16060,plain,
! [X0: $i] :
( is_a_theorem(implies(X0,not(not(X0))))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_9195,c_10618]) ).
tcf(c_16166,plain,
! [X0: $i,X1: $i] : is_a_theorem(not(not(implies(and(X0,X1),X0)))),
inference(superposition,[status(thm)],[c_8545,c_11170]) ).
tcf(c_16456,plain,
! [X0: $i,X1: $i] : is_a_theorem(and(implies(and(X0,X1),X0),implies(and(X0,X1),X0))),
inference(superposition,[status(thm)],[c_16166,c_8650]) ).
tcf(c_17661,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(or(not(X0),X0)) ),
inference(resolution,[status(thm)],[c_16036,c_13370]) ).
tcf(c_18402,plain,
! [X0: $i,X1: $i] : is_a_theorem(not(not(not(not(implies(and(X0,X1),X0)))))),
inference(superposition,[status(thm)],[c_16456,c_965]) ).
tcf(c_18504,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(not(implies(and(X0,X1),X0)),X2)) ),
inference(superposition,[status(thm)],[c_18402,c_3017]) ).
tcf(c_19688,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(and(X0,X1),X0),X2)) ),
inference(demodulation,[status(thm)],[c_18504,c_89]) ).
tcf(c_24137,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_14142,c_19688]) ).
tcf(c_24274,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_471,c_24137]) ).
tcf(c_101665,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(global_subsumption_just,[status(thm)],[c_10971,c_10971,c_17661,c_24274]) ).
tcf(c_101667,plain,
! [X0: $i] : is_a_theorem(implies(X0,not(not(X0)))),
inference(backward_subsumption_resolution,[status(thm)],[c_16060,c_101665]) ).
tcf(c_101672,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(not(equiv(X0,X0)),X1)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_11574,c_101665]) ).
tcf(c_101749,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,not(X1)),not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_171,c_101667]) ).
tcf(c_101838,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(equiv(X0,X0),X1)) ),
inference(demodulation,[status(thm)],[c_101672,c_89]) ).
tcf(c_101951,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,not(not(X1))),implies(X0,X1))),
inference(superposition,[status(thm)],[c_95,c_101749]) ).
tcf(c_102002,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(not(X1))),implies(not(X0),X1))),
inference(superposition,[status(thm)],[c_170,c_101951]) ).
tcf(c_102126,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(not(X1))),or(X0,X1))),
inference(light_normalisation,[status(thm)],[c_102002,c_170]) ).
tcf(c_102132,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,not(not(X1)))) ),
inference(superposition,[status(thm)],[c_102126,c_99]) ).
tcf(c_102215,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,not(not(X1))))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_95,c_1337]) ).
tcf(c_102743,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(equiv(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_102215,c_101838]) ).
tcf(c_102831,plain,
! [X0: $i] : is_a_theorem(not(not(not(not(implies(X0,X0)))))),
inference(superposition,[status(thm)],[c_838,c_102743]) ).
tcf(c_103820,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(and(X0,X1),X0),X2)) ),
inference(demodulation,[status(thm)],[c_18504,c_89]) ).
tcf(c_105081,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(or(implies(X0,X1),X0),X2)) ),
inference(superposition,[status(thm)],[c_388,c_103820]) ).
tcf(c_106632,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_492,c_170]) ).
tcf(c_106645,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(and(X0,X1),implies(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_106632,c_105081]) ).
tcf(c_106707,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(and(X0,not(X1)),or(X1,implies(X0,X2)))),
inference(superposition,[status(thm)],[c_170,c_106645]) ).
tcf(c_106792,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),or(X1,implies(X0,X2)))),
inference(demodulation,[status(thm)],[c_106707,c_387]) ).
tcf(c_107315,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(or(not(implies(X0,X0)),X1)) ),
inference(superposition,[status(thm)],[c_102831,c_3017]) ).
tcf(c_107341,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(demodulation,[status(thm)],[c_107315,c_89]) ).
tcf(c_107347,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_172,c_107341]) ).
tcf(c_107353,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_102215,c_107341]) ).
tcf(c_107360,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_106792,c_107341]) ).
tcf(c_107403,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(not(X0),X1))),
inference(superposition,[status(thm)],[c_89,c_107360]) ).
tcf(c_107411,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X0,X1))),
inference(light_normalisation,[status(thm)],[c_107403,c_170]) ).
tcf(c_107420,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_107411,c_99]) ).
tcf(c_107463,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(not(X0),X1),implies(X1,X0))),
inference(superposition,[status(thm)],[c_95,c_107347]) ).
tcf(c_107468,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(X0),X1),implies(not(X1),X0))),
inference(superposition,[status(thm)],[c_387,c_107463]) ).
tcf(c_107477,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),implies(not(X1),X0))),
inference(light_normalisation,[status(thm)],[c_107468,c_170]) ).
tcf(c_107478,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[c_107477,c_170]) ).
tcf(c_107479,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_89,c_107478]) ).
tcf(c_107482,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(superposition,[status(thm)],[c_89,c_107478]) ).
tcf(c_107487,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_107478,c_99]) ).
tcf(c_107597,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_107482,c_99]) ).
tcf(c_107825,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_471,c_107487]) ).
tcf(c_107826,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_107420,c_107487]) ).
tcf(c_107974,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_107825,c_170,c_387]) ).
tcf(c_107975,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,not(X0)),not(X0))),
inference(superposition,[status(thm)],[c_89,c_107974]) ).
tcf(c_108038,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(not(not(X0))) ),
inference(superposition,[status(thm)],[c_107826,c_102132]) ).
tcf(c_108147,plain,
! [X0: $i] : is_a_theorem(or(and(X0,X0),not(X0))),
inference(demodulation,[status(thm)],[c_107975,c_412]) ).
tcf(c_108148,plain,
! [X0: $i] : is_a_theorem(implies(implies(not(X0),X0),not(not(X0)))),
inference(superposition,[status(thm)],[c_387,c_108147]) ).
tcf(c_108985,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),not(not(X0)))),
inference(demodulation,[status(thm)],[c_108148,c_170]) ).
tcf(c_108992,plain,
! [X0: $i] :
( is_a_theorem(not(not(not(not(X0)))))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_108985,c_2831]) ).
tcf(c_111396,plain,
! [X0: $i,X1: $i] : is_a_theorem(not(not(or(X0,implies(X0,X1))))),
inference(superposition,[status(thm)],[c_106792,c_107353]) ).
tcf(c_111468,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,or(X1,implies(X1,X2)))),
inference(superposition,[status(thm)],[c_111396,c_108038]) ).
tcf(c_114208,plain,
! [X0: $i,X1: $i] : is_a_theorem(not(not(not(not(or(X0,implies(X0,X1))))))),
inference(superposition,[status(thm)],[c_111468,c_108992]) ).
tcf(c_114291,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(or(not(or(X0,implies(X0,X1))),X2)) ),
inference(superposition,[status(thm)],[c_114208,c_3017]) ).
tcf(c_261770,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_9902,c_387]) ).
tcf(c_305529,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(X2)
| ~ is_a_theorem(implies(or(X0,implies(X0,X1)),X2)) ),
inference(demodulation,[status(thm)],[c_114291,c_89]) ).
tcf(c_305549,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(implies(X0,X1),X2),or(X2,X0))),
inference(superposition,[status(thm)],[c_261770,c_305529]) ).
tcf(c_307881,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_305549,c_99]) ).
tcf(c_309015,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(or(X0,not(X1)),X1)),
inference(superposition,[status(thm)],[c_107479,c_307881]) ).
tcf(c_309268,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,not(X1)),X1)),
inference(superposition,[status(thm)],[c_89,c_309015]) ).
tcf(c_309659,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X1)),
inference(demodulation,[status(thm)],[c_309268,c_411]) ).
tcf(c_309660,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),not(X1))),
inference(superposition,[status(thm)],[c_388,c_309659]) ).
tcf(c_310745,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_309660,c_107597]) ).
tcf(c_311528,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(superposition,[status(thm)],[c_170,c_310745]) ).
tcf(c_311553,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_81,c_311528]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL519+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 23:36:08 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 96.78/15.37 % SZS status Started for theBenchmark.p
% 96.78/15.37 % SZS status Theorem for theBenchmark.p
% 96.78/15.37
% 96.78/15.37 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 96.78/15.37
% 96.78/15.37 % ------ iProver source info
% 96.78/15.37
% 96.78/15.37 % git: date: 2026-07-19 20:42:38 +0200
% 96.78/15.37 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 96.78/15.37 % git: non_committed_changes: false
% 96.78/15.37
% 96.78/15.37 % ------ Parsing...
% 96.78/15.37 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 96.78/15.37
% 96.78/15.37 % ------ Preprocessing... sup_sim: 3 sf_s rm: 12 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 96.78/15.37
% 96.78/15.37 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 96.78/15.37
% 96.78/15.37 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 96.78/15.37 % ------ Proving...
% 96.78/15.37 % ------ Problem Properties
% 96.78/15.37
% 96.78/15.37 %
% 96.78/15.37 % clauses 11
% 96.78/15.37 % conjectures 0
% 96.78/15.37 % EPR 0
% 96.78/15.37 % Horn 11
% 96.78/15.37 % unary 9
% 96.78/15.37 % binary 1
% 96.78/15.37 % lits 14
% 96.78/15.37 % lits eq 6
% 96.78/15.37 % fd_pure 0
% 96.78/15.37 % fd_pseudo 0
% 96.78/15.37 % fd_cond 0
% 96.78/15.37 % fd_pseudo_cond 1
% 96.78/15.37 % AC symbols 0
% 96.78/15.37
% 96.78/15.37 % ------ Input Options Time Limit: Unbounded
% 96.78/15.37
% 96.78/15.37
% 96.78/15.37 % ------
% 96.78/15.37 % Current options:
% 96.78/15.37 % ------
% 96.78/15.37
% 96.78/15.37
% 96.78/15.37 %
% 96.78/15.37
% 96.78/15.37 % ------ Proving...
% 96.78/15.37 %
% 96.78/15.37
% 96.78/15.37 % SZS status Theorem for theBenchmark.p
% 96.78/15.37
% 96.78/15.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 96.78/15.38
% 96.78/15.38
%------------------------------------------------------------------------------