%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL502+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 142.31s 35.51s
% Output : CNFRefutation 142.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 18
% Syntax : Number of formulae : 224 ( 117 unt; 0 def)
% Number of atoms : 359 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 255 ( 120 ~; 114 |; 2 &)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 10 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 390 ( 0 sgn 388 !; 2 ?; 324 :)
% 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(f2,axiom,
( substitution_of_equivalents
<=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',substitution_of_equivalents) ).
fof(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
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(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax',use_substitution_of_equivalents) ).
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,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
fof(f44,negated_conjecture,
~ modus_tollens,
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f45,plain,
~ modus_tollens,
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(implies(not(X1),not(X0)),implies(X0,X1)))
=> modus_tollens ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f50,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f51,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f54,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f51]) ).
fof(f55,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f50]) ).
fof(f57,plain,
( ? [X0,X1] : ~ is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1)))
| modus_tollens ),
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(implies(not(sK1),not(sK0)),implies(sK0,sK1)))
| modus_tollens ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f57]) ).
fof(f65,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f66,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f56]) ).
fof(f67,plain,
( ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1)))
| modus_tollens ),
inference(cnf_transformation,[],[f64]) ).
fof(f68,plain,
! [X0] :
( ~ kn1
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(cnf_transformation,[],[f58]) ).
fof(f69,plain,
! [X0,X1] :
( ~ kn2
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f70,plain,
! [X2,X0,X1] :
( ~ kn3
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f71,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f61]) ).
fof(f72,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f62]) ).
fof(f73,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f77,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f78,plain,
kn1,
inference(cnf_transformation,[],[f36]) ).
fof(f79,plain,
kn2,
inference(cnf_transformation,[],[f37]) ).
fof(f80,plain,
kn3,
inference(cnf_transformation,[],[f38]) ).
fof(f81,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f39]) ).
fof(f82,plain,
op_or,
inference(cnf_transformation,[],[f40]) ).
fof(f83,plain,
op_implies_and,
inference(cnf_transformation,[],[f41]) ).
fof(f84,plain,
op_equiv,
inference(cnf_transformation,[],[f42]) ).
fof(f85,plain,
~ modus_tollens,
inference(cnf_transformation,[],[f45]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_51,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(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_65,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f81]) ).
tcf(c_66,plain,
op_or,
inference(cnf_transformation,[],[f82]) ).
tcf(c_67,plain,
op_implies_and,
inference(cnf_transformation,[],[f83]) ).
tcf(c_68,plain,
op_equiv,
inference(cnf_transformation,[],[f84]) ).
tcf(c_69,negated_conjecture,
~ modus_tollens,
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,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_65,c_50]) ).
tcf(c_86,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_89,plain,
~ is_a_theorem(implies(implies(not(sK1),not(sK0)),implies(sK0,sK1))),
inference(global_subsumption_just,[status(thm)],[c_51,c_69,c_51]) ).
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_86]) ).
tcf(c_153,plain,
~ is_a_theorem(implies(or(sK1,not(sK0)),implies(sK0,sK1))),
inference(demodulation,[status(thm)],[c_89,c_152]) ).
tcf(c_154,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] : implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
inference(superposition,[status(thm)],[c_86,c_86]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i,X2: $i] : or(and(X0,not(X1)),X2) = implies(implies(X0,X1),X2),
inference(superposition,[status(thm)],[c_86,c_152]) ).
tcf(c_361,plain,
! [X0: $i] :
( is_a_theorem(and(X0,X0))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_80,c_92]) ).
tcf(c_362,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_363,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_383,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,X0))
| ~ is_a_theorem(implies(X0,X0)) ),
inference(superposition,[status(thm)],[c_96,c_361]) ).
tcf(c_384,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,X0),equiv(X0,X0))),
inference(superposition,[status(thm)],[c_96,c_80]) ).
tcf(c_385,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_427,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(superposition,[status(thm)],[c_96,c_362]) ).
tcf(c_432,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_86,c_154]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : implies(implies(X0,and(X1,not(X2))),X3) = or(and(X0,implies(X1,X2)),X3),
inference(superposition,[status(thm)],[c_86,c_350]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,and(not(X1),not(X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[c_152,c_347]) ).
tcf(c_722,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_432,c_152]) ).
tcf(c_726,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_722]) ).
tcf(c_727,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_722,c_92]) ).
tcf(c_749,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_726,c_350]) ).
tcf(c_751,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(or(X1,X2),or(X2,X0)))),
inference(superposition,[status(thm)],[c_152,c_749]) ).
tcf(c_753,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_749,c_92]) ).
tcf(c_919,plain,
! [X0: $i] : is_a_theorem(not(and(not(X0),or(X0,X0)))),
inference(superposition,[status(thm)],[c_492,c_80]) ).
tcf(c_1231,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_753,c_92]) ).
tcf(c_1767,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_384,c_1231]) ).
tcf(c_7690,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
tcf(c_7818,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(or(X1,X2),or(X2,X0)))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_751,c_92]) ).
tcf(c_7869,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_727,c_363]) ).
tcf(c_7874,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_753,c_92]) ).
tcf(c_7959,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X1,X1),X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_919,c_7869]) ).
tcf(c_7969,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_7959,c_92]) ).
tcf(c_7994,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(or(X1,X2))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_7818,c_92]) ).
tcf(c_7999,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_7874]) ).
tcf(c_8000,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_7874]) ).
tcf(c_8030,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_7690,c_8000]) ).
tcf(c_8119,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,not(and(X0,X1)))),
inference(superposition,[status(thm)],[c_8030,c_8000]) ).
tcf(c_8127,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_86,c_8119]) ).
tcf(c_8133,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(and(X0,X1),and(X0,X1))) ),
inference(superposition,[status(thm)],[c_8119,c_7969]) ).
tcf(c_8237,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_7999,c_8133]) ).
tcf(c_8250,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_7999,c_8237]) ).
tcf(c_8664,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,X0))
| ~ is_a_theorem(or(and(X0,X1),X2)) ),
inference(superposition,[status(thm)],[c_8119,c_7994]) ).
tcf(c_8722,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_727,c_8664]) ).
tcf(c_8886,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_8722,c_8250]) ).
tcf(c_10396,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_8127,c_8886]) ).
tcf(c_10405,plain,
! [X0: $i] : is_a_theorem(equiv(X0,X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_383,c_10396]) ).
tcf(c_16341,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
tcf(c_16366,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_10405,c_427]) ).
tcf(c_16367,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_16366]) ).
tcf(c_16560,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_753,c_92]) ).
tcf(c_16788,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_16560]) ).
tcf(c_16790,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_16366,c_16560]) ).
tcf(c_16809,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_16341,c_16790]) ).
tcf(c_16810,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_16367,c_16790]) ).
tcf(c_16812,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X2,X0),and(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_727,c_16790]) ).
tcf(c_16832,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_86,c_16810]) ).
tcf(c_16840,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_16809,c_152,c_350]) ).
tcf(c_16843,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_16840,c_16560]) ).
tcf(c_16870,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_16832,c_16788]) ).
tcf(c_17127,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_16812,c_16788]) ).
tcf(c_17230,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(X2,X0))
| ~ is_a_theorem(not(X1))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_17127,c_363]) ).
tcf(c_17663,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,not(X0)))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[status(thm)],[c_16810,c_17230]) ).
tcf(c_17758,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,not(X0)))
| ~ is_a_theorem(not(X0)) ),
inference(superposition,[status(thm)],[c_152,c_17663]) ).
tcf(c_17766,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,implies(X0,X1)))
| ~ is_a_theorem(not(and(X0,not(X1)))) ),
inference(superposition,[status(thm)],[c_86,c_17758]) ).
tcf(c_17858,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,implies(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_17766,c_86]) ).
tcf(c_17864,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,or(X0,X1)))
| ~ is_a_theorem(implies(not(X0),X1)) ),
inference(superposition,[status(thm)],[c_152,c_17858]) ).
tcf(c_17876,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,or(X0,X1)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(light_normalisation,[status(thm)],[c_17864,c_152]) ).
tcf(c_17887,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X0,X1))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_17876,c_16843]) ).
tcf(c_17964,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X1,X0),X2))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_17127,c_17887]) ).
tcf(c_18544,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X0),X1)),
inference(superposition,[status(thm)],[c_16870,c_17964]) ).
tcf(c_18582,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_18544,c_16788]) ).
tcf(c_89815,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_80]) ).
tcf(c_89851,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_10405,c_427]) ).
tcf(c_89852,plain,
! [X0: $i] : is_a_theorem(or(X0,not(X0))),
inference(superposition,[status(thm)],[c_152,c_89851]) ).
tcf(c_90045,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_753,c_92]) ).
tcf(c_90353,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_90045]) ).
tcf(c_90354,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_90045]) ).
tcf(c_90356,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_89851,c_90045]) ).
tcf(c_90357,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_384,c_90045]) ).
tcf(c_90358,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X1,X2),X0))
| ~ is_a_theorem(or(X0,equiv(X1,X2))) ),
inference(superposition,[status(thm)],[c_385,c_90045]) ).
tcf(c_90377,plain,
! [X0: $i] : is_a_theorem(or(and(not(X0),not(X0)),X0)),
inference(superposition,[status(thm)],[c_89815,c_90356]) ).
tcf(c_90378,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(superposition,[status(thm)],[c_89852,c_90356]) ).
tcf(c_90380,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(implies(X2,X0),and(X1,X2)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_727,c_90356]) ).
tcf(c_90398,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,not(X1)))),
inference(superposition,[status(thm)],[c_86,c_90378]) ).
tcf(c_90433,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_90353,c_90354]) ).
tcf(c_90435,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X0,X1))),
inference(superposition,[status(thm)],[c_90398,c_90354]) ).
tcf(c_90460,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_90377,c_152,c_350]) ).
tcf(c_90463,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X1))) ),
inference(superposition,[status(thm)],[c_90460,c_90045]) ).
tcf(c_90464,plain,
! [X0: $i] :
( is_a_theorem(X0)
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_90460,c_92]) ).
tcf(c_90465,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(equiv(X1,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_90357,c_1767,c_18582]) ).
tcf(c_90466,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(equiv(X0,X0),X1)),
inference(renaming,[status(thm)],[c_90465]) ).
tcf(c_90469,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,equiv(X1,X1))),
inference(superposition,[status(thm)],[c_90466,c_90354]) ).
tcf(c_90477,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),X0)),
inference(superposition,[status(thm)],[c_90435,c_90356]) ).
tcf(c_90908,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(or(X0,X0),X1))),
inference(superposition,[status(thm)],[c_90477,c_90463]) ).
tcf(c_90999,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(or(X0,X0),X1),X0)),
inference(superposition,[status(thm)],[c_90908,c_90356]) ).
tcf(c_91011,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(X0,implies(or(and(X0,X1),and(X0,X1)),X2))),
inference(superposition,[status(thm)],[c_90999,c_90354]) ).
tcf(c_92458,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,implies(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_90380,c_90354]) ).
tcf(c_92513,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X1,or(X2,X0)))
| ~ is_a_theorem(or(X0,X1)) ),
inference(superposition,[status(thm)],[c_152,c_92458]) ).
tcf(c_92517,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_92458,c_90356]) ).
tcf(c_92521,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_92458,c_90464]) ).
tcf(c_92665,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,or(X1,X0))) ),
inference(superposition,[status(thm)],[c_92513,c_90464]) ).
tcf(c_92677,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_92517,c_90354]) ).
tcf(c_92684,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(or(and(X0,X1),X0)) ),
inference(superposition,[status(thm)],[c_727,c_92521]) ).
tcf(c_92703,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(and(X0,X1),and(X0,X1)),X0)),
inference(superposition,[status(thm)],[c_91011,c_92521]) ).
tcf(c_92971,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(implies(X0,X1),and(X0,not(X1))),X0)),
inference(superposition,[status(thm)],[c_350,c_92703]) ).
tcf(c_93155,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,X0))
| ~ is_a_theorem(or(X0,X0)) ),
inference(superposition,[status(thm)],[c_92513,c_92665]) ).
tcf(c_93168,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(or(X2,implies(X1,X0)))
| ~ is_a_theorem(or(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_92458,c_93155]) ).
tcf(c_93893,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X0),X1)),
inference(superposition,[status(thm)],[c_90469,c_90358]) ).
tcf(c_93937,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_93893,c_92665]) ).
tcf(c_95062,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(implies(X0,X1),implies(X0,X1)),X0)),
inference(demodulation,[status(thm)],[c_92971,c_473]) ).
tcf(c_95307,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,and(implies(X0,X1),implies(X0,X1)))),
inference(superposition,[status(thm)],[c_95062,c_90356]) ).
tcf(c_95311,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(implies(X0,X1),and(X0,X0))),
inference(superposition,[status(thm)],[c_95062,c_90433]) ).
tcf(c_95325,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,X0),implies(X0,X1))),
inference(superposition,[status(thm)],[c_95311,c_90356]) ).
tcf(c_98057,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(X2,X0))),
inference(superposition,[status(thm)],[c_95307,c_92677]) ).
tcf(c_98226,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(or(implies(X0,X1),implies(X1,X2))),
inference(superposition,[status(thm)],[c_98057,c_90356]) ).
tcf(c_98561,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(X1,X1),X0))),
inference(superposition,[status(thm)],[c_93937,c_92684]) ).
tcf(c_99361,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(superposition,[status(thm)],[c_98226,c_92521]) ).
tcf(c_99371,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(superposition,[status(thm)],[c_152,c_99361]) ).
tcf(c_100257,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(or(X1,X1),X1))),
inference(superposition,[status(thm)],[c_90908,c_93168]) ).
tcf(c_100297,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,implies(X1,and(X1,X1)))),
inference(superposition,[status(thm)],[c_95325,c_93168]) ).
tcf(c_100443,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,and(implies(X1,X1),not(X0)))),
inference(superposition,[status(thm)],[c_152,c_98561]) ).
tcf(c_100522,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(implies(X0,X0),not(X1)),X1)),
inference(superposition,[status(thm)],[c_100443,c_90356]) ).
tcf(c_100697,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(or(X1,X1),X1),X0))),
inference(superposition,[status(thm)],[c_100257,c_92684]) ).
tcf(c_100728,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(X1,and(X1,X1)),X0))),
inference(superposition,[status(thm)],[c_100297,c_92684]) ).
tcf(c_112552,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(implies(X0,X0),X1),X1)),
inference(demodulation,[status(thm)],[c_100522,c_350]) ).
tcf(c_112562,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(X0,X0),X1)) ),
inference(superposition,[status(thm)],[c_112552,c_92]) ).
tcf(c_118864,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(X0,X1),not(and(X1,X0)))),
inference(superposition,[status(thm)],[c_154,c_112562]) ).
tcf(c_120110,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(not(X0),X1),implies(X1,X0))),
inference(superposition,[status(thm)],[c_86,c_118864]) ).
tcf(c_121784,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(and(not(X0),not(X1)),or(X1,X0))),
inference(superposition,[status(thm)],[c_152,c_120110]) ).
tcf(c_124511,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[c_121784,c_152,c_350]) ).
tcf(c_216622,plain,
! [X0: $i] : is_a_theorem(implies(implies(X0,or(X0,X0)),equiv(or(X0,X0),X0))),
inference(superposition,[status(thm)],[c_96,c_100697]) ).
tcf(c_230725,plain,
! [X0: $i] : is_a_theorem(implies(implies(and(X0,X0),X0),equiv(X0,and(X0,X0)))),
inference(superposition,[status(thm)],[c_96,c_100728]) ).
tcf(c_231147,plain,
! [X0: $i] :
( is_a_theorem(equiv(or(X0,X0),X0))
| ~ is_a_theorem(implies(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_216622,c_92]) ).
tcf(c_231148,plain,
! [X0: $i] : is_a_theorem(equiv(or(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_231147,c_99371]) ).
tcf(c_233013,plain,
! [X0: $i] : or(X0,X0) = X0,
inference(superposition,[status(thm)],[c_231148,c_83]) ).
tcf(c_250880,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,and(X0,X0)))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_230725,c_92]) ).
tcf(c_250881,plain,
! [X0: $i] : is_a_theorem(equiv(X0,and(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_250880,c_77]) ).
tcf(c_251227,plain,
! [X0: $i] : and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_250881,c_83]) ).
tcf(c_251561,plain,
! [X0: $i] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_251227,c_86]) ).
tcf(c_252372,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(demodulation,[status(thm)],[c_251561,c_152,c_233013]) ).
tcf(c_252778,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_252372,c_152]) ).
tcf(c_255228,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(superposition,[status(thm)],[c_252778,c_124511]) ).
tcf(c_255600,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_153,c_255228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL502+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.73 % Computer : n020.cluster.edu
% 0.10/5.73 % Model : x86_64 x86_64
% 0.10/5.73 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.73 % Memory : 8046.5625MB
% 0.10/5.73 % OS : Linux 6.8.0-71-generic
% 0.10/5.73 % CPULimit : 300
% 0.10/5.73 % WCLimit : 300
% 0.10/5.73 % DateTime : Wed Sep 23 23:35:41 UTC 2026
% 0.10/5.73 % CPUTime :
% 0.10/5.73 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.77 Running first-order theorem proving
% 0.10/5.77 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
% 0.10/5.79
% 0.10/5.79 % ======== iProver multi-core TPTP/SMT =========
% 0.10/5.79
% 0.10/5.79 % Detected problem language: tptp
% 0.13/5.80 % Proving...
% 142.31/35.51 % SZS status Started for theBenchmark.p
% 142.31/35.51 % SZS status Theorem for theBenchmark.p
% 142.31/35.51
% 142.31/35.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 142.31/35.51
% 142.31/35.51 % ------ iProver source info
% 142.31/35.51
% 142.31/35.51 % git: date: 2026-07-19 20:42:38 +0200
% 142.31/35.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 142.31/35.51 % git: non_committed_changes: false
% 142.31/35.51
% 142.31/35.51 % ------ Parsing...
% 142.31/35.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 142.31/35.51
% 142.31/35.51 % ------ Preprocessing... sup_sim: 3 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 %
% 142.31/35.51
% 142.31/35.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 142.31/35.51
% 142.31/35.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 142.31/35.51 % ------ Proving...
% 142.31/35.51 % ------ Problem Properties
% 142.31/35.51
% 142.31/35.51 %
% 142.31/35.51 % clauses 9
% 142.31/35.51 % conjectures 0
% 142.31/35.51 % EPR 0
% 142.31/35.51 % Horn 9
% 142.31/35.51 % unary 7
% 142.31/35.51 % binary 1
% 142.31/35.51 % lits 12
% 142.31/35.51 % lits eq 4
% 142.31/35.51 % fd_pure 0
% 142.31/35.51 % fd_pseudo 0
% 142.31/35.51 % fd_cond 0
% 142.31/35.51 % fd_pseudo_cond 1
% 142.31/35.51 % AC symbols 0
% 142.31/35.51
% 142.31/35.51 % ------ Input Options Time Limit: Unbounded
% 142.31/35.51
% 142.31/35.51
% 142.31/35.51 % ------
% 142.31/35.51 % Current options:
% 142.31/35.51 % ------
% 142.31/35.51
% 142.31/35.51
% 142.31/35.51 %
% 142.31/35.51
% 142.31/35.51 % ------ Proving...
% 142.31/35.51 %
% 142.31/35.51
% 142.31/35.51 % SZS status Theorem for theBenchmark.p
% 142.31/35.51
% 142.31/35.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 142.31/35.52
% 142.31/35.52
%------------------------------------------------------------------------------