%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL461+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 02:06:43 PM UTC 2026
% Result : Theorem 149.67s 21.59s
% Output : CNFRefutation 149.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 34
% Syntax : Number of formulae : 263 ( 142 unt; 0 def)
% Number of atoms : 418 ( 61 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 267 ( 119 ~; 111 |; 2 &)
% ( 14 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 390 ( 0 sgn 387 !; 3 ?; 253 :)
% 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(f3,axiom,
( modus_tollens
<=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',modus_tollens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f6,axiom,
( implies_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',implies_3) ).
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f8,axiom,
( and_2
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_2) ).
fof(f9,axiom,
( and_3
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',and_3) ).
fof(f10,axiom,
( or_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_1) ).
fof(f11,axiom,
( or_2
<=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',or_2) ).
fof(f14,axiom,
( equivalence_2
<=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_2) ).
fof(f15,axiom,
( equivalence_3
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',equivalence_3) ).
fof(f18,axiom,
( kn3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax',kn3) ).
fof(f27,axiom,
( op_or
=> ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_or) ).
fof(f29,axiom,
( op_implies_and
=> ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_implies_and) ).
fof(f31,axiom,
( op_equiv
=> ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax',op_equiv) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_modus_tollens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f39,axiom,
implies_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_implies_3) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_2) ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_and_3) ).
fof(f43,axiom,
or_1,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_1) ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_or_2) ).
fof(f47,axiom,
equivalence_2,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_2) ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',hilbert_equivalence_3) ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax',use_substitution_of_equivalents) ).
fof(f50,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_or) ).
fof(f51,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_implies_and) ).
fof(f52,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_op_equiv) ).
fof(f53,conjecture,
kn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rosser_kn3) ).
fof(f54,negated_conjecture,
~ kn3,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ kn3,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
=> kn3 ),
inference(unused_predicate_definition_removal,[],[f18]) ).
fof(f57,plain,
( equivalence_3
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f15]) ).
fof(f58,plain,
( equivalence_2
=> ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f14]) ).
fof(f61,plain,
( or_2
=> ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f11]) ).
fof(f62,plain,
( or_1
=> ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f63,plain,
( and_3
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(unused_predicate_definition_removal,[],[f9]) ).
fof(f64,plain,
( and_2
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f65,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f66,plain,
( implies_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f68,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f69,plain,
( modus_tollens
=> ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f3]) ).
fof(f70,plain,
( substitution_of_equivalents
=> ! [X0,X1] :
( is_a_theorem(equiv(X0,X1))
=> X0 = X1 ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f71,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(f74,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f75,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
( ~ substitution_of_equivalents
| ! [X0,X1] :
( ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ) ),
inference(ennf_transformation,[],[f70]) ).
fof(f77,plain,
( ~ modus_tollens
| ! [X0,X1] : is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f78,plain,
( ~ implies_1
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f68]) ).
fof(f79,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f80,plain,
( ~ implies_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f81,plain,
( ~ and_1
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f65]) ).
fof(f82,plain,
( ~ and_2
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)) ),
inference(ennf_transformation,[],[f64]) ).
fof(f83,plain,
( ~ and_3
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(ennf_transformation,[],[f63]) ).
fof(f84,plain,
( ~ or_1
| ! [X0,X1] : is_a_theorem(implies(X0,or(X0,X1))) ),
inference(ennf_transformation,[],[f62]) ).
fof(f85,plain,
( ~ or_2
| ! [X0,X1] : is_a_theorem(implies(X1,or(X0,X1))) ),
inference(ennf_transformation,[],[f61]) ).
fof(f88,plain,
( ~ equivalence_2
| ! [X0,X1] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(ennf_transformation,[],[f58]) ).
fof(f89,plain,
( ~ equivalence_3
| ! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(ennf_transformation,[],[f57]) ).
fof(f90,plain,
( ? [X0,X1,X2] : ~ is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| kn3 ),
inference(ennf_transformation,[],[f56]) ).
fof(f91,plain,
( ~ op_or
| ! [X0,X1] : or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(ennf_transformation,[],[f27]) ).
fof(f92,plain,
( ~ op_implies_and
| ! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))) ),
inference(ennf_transformation,[],[f29]) ).
fof(f93,plain,
( ~ op_equiv
| ! [X0,X1] : equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(ennf_transformation,[],[f31]) ).
fof(f94,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))
| kn3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f90]) ).
fof(f95,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f96,plain,
! [X0,X1] :
( ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f76]) ).
fof(f97,plain,
! [X0,X1] :
( ~ modus_tollens
| is_a_theorem(implies(implies(not(X1),not(X0)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f98,plain,
! [X0,X1] :
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f78]) ).
fof(f99,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f79]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ implies_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(cnf_transformation,[],[f80]) ).
fof(f101,plain,
! [X0,X1] :
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f81]) ).
fof(f102,plain,
! [X0,X1] :
( ~ and_2
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(cnf_transformation,[],[f82]) ).
fof(f103,plain,
! [X0,X1] :
( ~ and_3
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(cnf_transformation,[],[f83]) ).
fof(f104,plain,
! [X0,X1] :
( ~ or_1
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f105,plain,
! [X0,X1] :
( ~ or_2
| is_a_theorem(implies(X1,or(X0,X1))) ),
inference(cnf_transformation,[],[f85]) ).
fof(f108,plain,
! [X0,X1] :
( ~ equivalence_2
| is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(cnf_transformation,[],[f88]) ).
fof(f109,plain,
! [X0,X1] :
( ~ equivalence_3
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(cnf_transformation,[],[f89]) ).
fof(f110,plain,
( ~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0)))))
| kn3 ),
inference(cnf_transformation,[],[f94]) ).
fof(f111,plain,
! [X0,X1] :
( ~ op_or
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(cnf_transformation,[],[f91]) ).
fof(f112,plain,
! [X0,X1] :
( ~ op_implies_and
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(cnf_transformation,[],[f92]) ).
fof(f113,plain,
! [X0,X1] :
( ~ op_equiv
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f117,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f118,plain,
modus_tollens,
inference(cnf_transformation,[],[f36]) ).
fof(f119,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f120,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f121,plain,
implies_3,
inference(cnf_transformation,[],[f39]) ).
fof(f122,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f123,plain,
and_2,
inference(cnf_transformation,[],[f41]) ).
fof(f124,plain,
and_3,
inference(cnf_transformation,[],[f42]) ).
fof(f125,plain,
or_1,
inference(cnf_transformation,[],[f43]) ).
fof(f126,plain,
or_2,
inference(cnf_transformation,[],[f44]) ).
fof(f129,plain,
equivalence_2,
inference(cnf_transformation,[],[f47]) ).
fof(f130,plain,
equivalence_3,
inference(cnf_transformation,[],[f48]) ).
fof(f131,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f49]) ).
fof(f132,plain,
op_or,
inference(cnf_transformation,[],[f50]) ).
fof(f133,plain,
op_implies_and,
inference(cnf_transformation,[],[f51]) ).
fof(f134,plain,
op_equiv,
inference(cnf_transformation,[],[f52]) ).
fof(f135,plain,
~ kn3,
inference(cnf_transformation,[],[f55]) ).
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,[],[f95]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ substitution_of_equivalents
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[],[f100]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f101]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[],[f103]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ or_2 ),
inference(cnf_transformation,[],[f105]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[],[f108]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[],[f109]) ).
tcf(c_64,plain,
( kn3
| ~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0))))) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( ( not(and(not(X0),not(X1))) = or(X0,X1) )
| ~ op_or ),
inference(cnf_transformation,[],[f111]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( not(and(X0,not(X1))) = implies(X0,X1) )
| ~ op_implies_and ),
inference(cnf_transformation,[],[f112]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ( and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1) )
| ~ op_equiv ),
inference(cnf_transformation,[],[f113]) ).
tcf(c_71,plain,
modus_ponens,
inference(cnf_transformation,[],[f117]) ).
tcf(c_72,plain,
modus_tollens,
inference(cnf_transformation,[],[f118]) ).
tcf(c_73,plain,
implies_1,
inference(cnf_transformation,[],[f119]) ).
tcf(c_74,plain,
implies_2,
inference(cnf_transformation,[],[f120]) ).
tcf(c_75,plain,
implies_3,
inference(cnf_transformation,[],[f121]) ).
tcf(c_76,plain,
and_1,
inference(cnf_transformation,[],[f122]) ).
tcf(c_77,plain,
and_2,
inference(cnf_transformation,[],[f123]) ).
tcf(c_78,plain,
and_3,
inference(cnf_transformation,[],[f124]) ).
tcf(c_79,plain,
or_1,
inference(cnf_transformation,[],[f125]) ).
tcf(c_80,plain,
or_2,
inference(cnf_transformation,[],[f126]) ).
tcf(c_83,plain,
equivalence_2,
inference(cnf_transformation,[],[f129]) ).
tcf(c_84,plain,
equivalence_3,
inference(cnf_transformation,[],[f130]) ).
tcf(c_85,plain,
substitution_of_equivalents,
inference(cnf_transformation,[],[f131]) ).
tcf(c_86,plain,
op_or,
inference(cnf_transformation,[],[f132]) ).
tcf(c_87,plain,
op_implies_and,
inference(cnf_transformation,[],[f133]) ).
tcf(c_88,plain,
op_equiv,
inference(cnf_transformation,[],[f134]) ).
tcf(c_89,negated_conjecture,
~ kn3,
inference(cnf_transformation,[],[f135]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_59,c_80,c_59]) ).
tcf(c_110,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_58,c_79,c_58]) ).
tcf(c_112,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X1)),
inference(global_subsumption_just,[status(thm)],[c_56,c_77,c_56]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_76,c_55]) ).
tcf(c_117,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_52,c_73,c_52]) ).
tcf(c_120,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_62,c_83,c_62]) ).
tcf(c_125,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_57,c_78,c_57]) ).
tcf(c_128,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_50,c_85,c_50]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] : not(and(X0,not(X1))) = implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_66,c_87,c_66]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_74,c_53]) ).
tcf(c_137,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(global_subsumption_just,[status(thm)],[c_51,c_72,c_51]) ).
tcf(c_140,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_71,c_49]) ).
tcf(c_141,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_140]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] : not(and(not(X0),not(X1))) = or(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_65,c_86,c_65]) ).
tcf(c_145,plain,
! [X0: $i,X1: $i] : and(implies(X0,X1),implies(X1,X0)) = equiv(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_67,c_88,c_67]) ).
tcf(c_148,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(global_subsumption_just,[status(thm)],[c_63,c_84,c_63]) ).
tcf(c_151,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),
inference(global_subsumption_just,[status(thm)],[c_54,c_75,c_54]) ).
tcf(c_154,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(not(and(sK1,sK2)),not(and(sK2,sK0))))),
inference(global_subsumption_just,[status(thm)],[c_64,c_89,c_64]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] : implies(not(X0),X1) = or(X0,X1),
inference(demodulation,[status(thm)],[c_142,c_131]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(demodulation,[status(thm)],[c_137,c_241]) ).
tcf(c_243,plain,
~ is_a_theorem(implies(implies(sK0,sK1),or(and(sK1,sK2),not(and(sK2,sK0))))),
inference(demodulation,[status(thm)],[c_154,c_241]) ).
tcf(c_482,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,and(X1,not(X2))) = not(and(X0,implies(X1,X2))),
inference(superposition,[status(thm)],[c_131,c_131]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
inference(superposition,[status(thm)],[c_241,c_242]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_134,c_141]) ).
tcf(c_556,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_125,c_141]) ).
tcf(c_561,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(or(X0,not(X1))) ),
inference(superposition,[status(thm)],[c_242,c_141]) ).
tcf(c_592,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X1,X0),equiv(X0,X1)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_148,c_141]) ).
tcf(c_1466,plain,
! [X0: $i,X1: $i] : is_a_theorem(or(X0,or(X1,not(X0)))),
inference(superposition,[status(thm)],[c_241,c_107]) ).
tcf(c_1520,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_556,c_141]) ).
tcf(c_1748,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_145,c_1520]) ).
tcf(c_1868,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_125,c_553]) ).
tcf(c_2054,plain,
! [X0: $i] :
( is_a_theorem(equiv(and(X0,X0),X0))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(superposition,[status(thm)],[c_1868,c_1748]) ).
tcf(c_2062,plain,
! [X0: $i] : is_a_theorem(equiv(and(X0,X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_2054,c_115]) ).
tcf(c_2296,plain,
! [X0: $i] : and(X0,X0) = X0,
inference(superposition,[status(thm)],[c_2062,c_128]) ).
tcf(c_2317,plain,
! [X0: $i] : implies(not(X0),X0) = not(not(X0)),
inference(superposition,[status(thm)],[c_2296,c_131]) ).
tcf(c_2331,plain,
! [X0: $i] : or(X0,X0) = not(not(X0)),
inference(demodulation,[status(thm)],[c_2317,c_241]) ).
tcf(c_2759,plain,
! [X0: $i] : is_a_theorem(implies(X0,not(not(X0)))),
inference(superposition,[status(thm)],[c_2331,c_110]) ).
tcf(c_2767,plain,
! [X0: $i] : is_a_theorem(or(X0,not(not(not(X0))))),
inference(superposition,[status(thm)],[c_2331,c_1466]) ).
tcf(c_2841,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(not(X0)),X0))
| ~ is_a_theorem(implies(not(not(X0)),X0)) ),
inference(superposition,[status(thm)],[c_2759,c_1748]) ).
tcf(c_2843,plain,
! [X0: $i] :
( is_a_theorem(equiv(not(not(X0)),X0))
| ~ is_a_theorem(or(not(X0),X0)) ),
inference(demodulation,[status(thm)],[c_2841,c_241]) ).
tcf(c_2876,plain,
! [X0: $i] : is_a_theorem(implies(not(not(X0)),X0)),
inference(superposition,[status(thm)],[c_2767,c_561]) ).
tcf(c_2877,plain,
! [X0: $i] : is_a_theorem(or(not(X0),X0)),
inference(demodulation,[status(thm)],[c_2876,c_241]) ).
tcf(c_2880,plain,
! [X0: $i] : is_a_theorem(equiv(not(not(X0)),X0)),
inference(backward_subsumption_resolution,[status(thm)],[c_2843,c_2877]) ).
tcf(c_2888,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_2880,c_128]) ).
tcf(c_2899,plain,
! [X0: $i,X1: $i] : not(implies(X0,X1)) = and(X0,not(X1)),
inference(superposition,[status(thm)],[c_131,c_2888]) ).
tcf(c_3798,plain,
! [X0: $i,X1: $i] : not(not(implies(X0,X1))) = implies(X0,X1),
inference(demodulation,[status(thm)],[c_131,c_2899]) ).
tcf(c_3801,plain,
! [X0: $i,X1: $i] : not(not(or(X0,X1))) = or(X0,X1),
inference(superposition,[status(thm)],[c_241,c_3798]) ).
tcf(c_3818,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,and(X0,not(X1))))),
inference(superposition,[status(thm)],[c_241,c_125]) ).
tcf(c_3819,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,or(X1,not(implies(X0,X1))))),
inference(demodulation,[status(thm)],[c_3818,c_2899]) ).
tcf(c_3866,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_556,c_141]) ).
tcf(c_3867,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(or(X1,not(implies(X0,X1))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_3819,c_141]) ).
tcf(c_4221,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_145,c_3866]) ).
tcf(c_4385,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_3867,c_561]) ).
tcf(c_4563,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_117,c_553]) ).
tcf(c_4565,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_125,c_553]) ).
tcf(c_4593,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_241,c_4565]) ).
tcf(c_4599,plain,
! [X0: $i] : is_a_theorem(or(X0,not(or(X0,X0)))),
inference(demodulation,[status(thm)],[c_4593,c_241,c_2899]) ).
tcf(c_4740,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(superposition,[status(thm)],[c_4599,c_561]) ).
tcf(c_6733,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,and(X0,X1)))
| ~ is_a_theorem(implies(X0,and(X0,X1))) ),
inference(superposition,[status(thm)],[c_115,c_4221]) ).
tcf(c_6734,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,and(X1,X0)))
| ~ is_a_theorem(implies(X0,and(X1,X0))) ),
inference(superposition,[status(thm)],[c_112,c_4221]) ).
tcf(c_6742,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(implies(X0,X1),or(X1,not(X0))))
| ~ is_a_theorem(implies(implies(X0,X1),or(X1,not(X0)))) ),
inference(superposition,[status(thm)],[c_242,c_4221]) ).
tcf(c_6759,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,implies(X1,X0)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_4385,c_4221]) ).
tcf(c_6782,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,or(X0,X0)))
| ~ is_a_theorem(implies(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_4740,c_4221]) ).
tcf(c_6788,plain,
! [X0: $i] : is_a_theorem(equiv(X0,or(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_6782,c_110]) ).
tcf(c_6791,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X1,implies(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_6759,c_117]) ).
tcf(c_7354,plain,
! [X0: $i] : or(X0,X0) = X0,
inference(superposition,[status(thm)],[c_6788,c_128]) ).
tcf(c_7402,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_7354,c_3801]) ).
tcf(c_7476,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(demodulation,[status(thm)],[c_505,c_7402]) ).
tcf(c_7646,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_7402,c_241]) ).
tcf(c_8763,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(implies(not(X0),X1),or(X1,not(not(X0)))))
| ~ is_a_theorem(implies(implies(not(X0),X1),or(X1,X0))) ),
inference(superposition,[status(thm)],[c_7402,c_6742]) ).
tcf(c_8765,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(or(X0,X1),or(X1,X0)))
| ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(demodulation,[status(thm)],[c_8763,c_241,c_7402]) ).
tcf(c_8766,plain,
! [X0: $i,X1: $i] : is_a_theorem(equiv(or(X0,X1),or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_8765,c_7476]) ).
tcf(c_10110,plain,
! [X0: $i,X1: $i] : or(X0,X1) = or(X1,X0),
inference(superposition,[status(thm)],[c_8766,c_128]) ).
tcf(c_10212,plain,
! [X0: $i,X1: $i] : or(X0,not(X1)) = implies(X1,X0),
inference(superposition,[status(thm)],[c_10110,c_7646]) ).
tcf(c_10389,plain,
! [X0: $i,X1: $i] :
( ( implies(X0,X1) = X1 )
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_6791,c_128]) ).
tcf(c_10658,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_4563,c_10389]) ).
tcf(c_11355,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(X0,implies(X1,X1)))),
inference(superposition,[status(thm)],[c_10658,c_125]) ).
tcf(c_11356,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,and(implies(X1,X1),X0))),
inference(superposition,[status(thm)],[c_10658,c_125]) ).
tcf(c_11749,plain,
! [X0: $i,X1: $i] : is_a_theorem(equiv(X0,and(X0,implies(X1,X1)))),
inference(superposition,[status(thm)],[c_11355,c_6733]) ).
tcf(c_11768,plain,
! [X0: $i,X1: $i] : is_a_theorem(equiv(X0,and(implies(X1,X1),X0))),
inference(superposition,[status(thm)],[c_11356,c_6734]) ).
tcf(c_12186,plain,
! [X0: $i,X1: $i] : and(X0,implies(X1,X1)) = X0,
inference(superposition,[status(thm)],[c_11749,c_128]) ).
tcf(c_12326,plain,
! [X0: $i,X1: $i] : and(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_11768,c_128]) ).
tcf(c_12534,plain,
! [X0: $i,X1: $i] : implies(X0,X0) = implies(X1,X1),
inference(superposition,[status(thm)],[c_12326,c_12186]) ).
tcf(c_12535,plain,
! [X0: $i] : implies(X0,X0) = iPr_def_10,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_12534]) ).
tcf(c_39613,plain,
! [X0: $i,X1: $i] : not(not(implies(X0,X1))) = implies(X0,X1),
inference(demodulation,[status(thm)],[c_131,c_2899]) ).
tcf(c_39618,plain,
! [X0: $i,X1: $i] : not(not(or(X0,X1))) = or(X0,X1),
inference(superposition,[status(thm)],[c_241,c_39613]) ).
tcf(c_39680,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,not(implies(X1,X2))) = not(and(X0,implies(X1,X2))),
inference(demodulation,[status(thm)],[c_482,c_2899]) ).
tcf(c_39682,plain,
! [X0: $i,X1: $i,X2: $i] : implies(X0,not(or(X1,X2))) = not(and(X0,or(X1,X2))),
inference(superposition,[status(thm)],[c_241,c_39680]) ).
tcf(c_39688,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : or(X0,implies(X1,not(implies(X2,X3)))) = implies(and(X1,implies(X2,X3)),X0),
inference(superposition,[status(thm)],[c_39680,c_10212]) ).
tcf(c_39689,plain,
~ is_a_theorem(implies(implies(sK0,sK1),implies(and(sK2,sK0),and(sK1,sK2)))),
inference(demodulation,[status(thm)],[c_243,c_10212]) ).
tcf(c_39693,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(not(X1),not(implies(X0,X1))))
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_2899,c_556]) ).
tcf(c_39702,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,X1),X1))
| ~ is_a_theorem(X0) ),
inference(demodulation,[status(thm)],[c_39693,c_241,c_10212]) ).
tcf(c_39810,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : implies(implies(X0,not(or(X1,X2))),X3) = or(and(X0,or(X1,X2)),X3),
inference(superposition,[status(thm)],[c_39682,c_241]) ).
tcf(c_40149,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_556,c_141]) ).
tcf(c_40693,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_145,c_40149]) ).
tcf(c_40723,plain,
! [X0: $i] : is_a_theorem(implies(X0,X0)),
inference(superposition,[status(thm)],[c_117,c_553]) ).
tcf(c_40725,plain,
! [X0: $i] : is_a_theorem(implies(X0,and(X0,X0))),
inference(superposition,[status(thm)],[c_125,c_553]) ).
tcf(c_40910,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,implies(X1,X0)))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(superposition,[status(thm)],[c_39702,c_40693]) ).
tcf(c_40934,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X1,implies(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_40910,c_117]) ).
tcf(c_40988,plain,
! [X0: $i] : is_a_theorem(or(X0,and(not(X0),not(X0)))),
inference(superposition,[status(thm)],[c_241,c_40725]) ).
tcf(c_40996,plain,
! [X0: $i] : is_a_theorem(implies(or(X0,X0),X0)),
inference(demodulation,[status(thm)],[c_40988,c_241,c_2899,c_10212]) ).
tcf(c_41004,plain,
! [X0: $i] :
( is_a_theorem(equiv(X0,or(X0,X0)))
| ~ is_a_theorem(implies(X0,or(X0,X0))) ),
inference(superposition,[status(thm)],[c_40996,c_40693]) ).
tcf(c_41007,plain,
! [X0: $i] : is_a_theorem(equiv(X0,or(X0,X0))),
inference(forward_subsumption_resolution,[status(thm)],[c_41004,c_110]) ).
tcf(c_41024,plain,
! [X0: $i] : or(X0,X0) = X0,
inference(superposition,[status(thm)],[c_41007,c_128]) ).
tcf(c_41079,plain,
! [X0: $i] : not(not(X0)) = X0,
inference(superposition,[status(thm)],[c_41024,c_39618]) ).
tcf(c_41099,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,not(X1)),X2) = or(and(X0,X1),X2),
inference(superposition,[status(thm)],[c_41024,c_39810]) ).
tcf(c_41300,plain,
! [X0: $i,X1: $i] : or(not(X0),X1) = implies(X0,X1),
inference(superposition,[status(thm)],[c_41079,c_241]) ).
tcf(c_41741,plain,
! [X0: $i,X1: $i] :
( ( implies(X0,X1) = X1 )
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_40934,c_128]) ).
tcf(c_41797,plain,
! [X0: $i,X1: $i] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(superposition,[status(thm)],[c_41300,c_10212]) ).
tcf(c_42167,plain,
! [X0: $i,X1: $i] : implies(implies(X0,X0),X1) = X1,
inference(superposition,[status(thm)],[c_40723,c_41741]) ).
tcf(c_42227,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,equiv(X0,implies(X1,X1))))
| ~ is_a_theorem(implies(X0,implies(X1,X1))) ),
inference(superposition,[status(thm)],[c_42167,c_592]) ).
tcf(c_42236,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(equiv(X0,implies(X1,X1)),X0)),
inference(superposition,[status(thm)],[c_42167,c_120]) ).
tcf(c_42260,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,implies(X1,X1))),
inference(superposition,[status(thm)],[c_42167,c_117]) ).
tcf(c_42297,plain,
! [X0: $i,X1: $i,X2: $i] : or(X0,implies(X1,not(X2))) = implies(and(X1,X2),X0),
inference(superposition,[status(thm)],[c_42167,c_39688]) ).
tcf(c_42322,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(X0,equiv(X0,implies(X1,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_42227,c_42260]) ).
tcf(c_42375,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(equiv(X0,equiv(X0,implies(X1,X1))))
| ~ is_a_theorem(implies(X0,equiv(X0,implies(X1,X1)))) ),
inference(superposition,[status(thm)],[c_42236,c_40693]) ).
tcf(c_42380,plain,
! [X0: $i,X1: $i] : is_a_theorem(equiv(X0,equiv(X0,implies(X1,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[c_42375,c_42322]) ).
tcf(c_42551,plain,
! [X0: $i,X1: $i] : equiv(X0,implies(X1,X1)) = X0,
inference(superposition,[status(thm)],[c_42380,c_128]) ).
tcf(c_42615,plain,
! [X0: $i,X1: $i] :
( ( implies(X1,X1) = X0 )
| ~ is_a_theorem(X0) ),
inference(superposition,[status(thm)],[c_42551,c_128]) ).
tcf(c_42670,plain,
is_a_theorem(iPr_def_10),
inference(demodulation,[status(thm)],[c_40723,c_12535]) ).
tcf(c_42933,plain,
! [X0: $i] :
( ( X0 = iPr_def_10 )
| ~ is_a_theorem(X0) ),
inference(demodulation,[status(thm)],[c_42615,c_12535]) ).
tcf(c_42938,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))) = iPr_def_10,
inference(superposition,[status(thm)],[c_151,c_42933]) ).
tcf(c_46571,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(implies(X1,not(X2)),implies(X2,not(X0)))) = iPr_def_10,
inference(superposition,[status(thm)],[c_41797,c_42938]) ).
tcf(c_46642,plain,
! [X0: $i,X1: $i,X2: $i] : implies(implies(X0,X1),implies(and(X2,X0),and(X1,X2))) = iPr_def_10,
inference(demodulation,[status(thm)],[c_46571,c_41099,c_42297]) ).
tcf(c_46674,plain,
~ is_a_theorem(iPr_def_10),
inference(demodulation,[status(thm)],[c_39689,c_46642]) ).
tcf(c_46675,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_46674,c_42670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL461+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 % Computer : n003.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Wed Sep 23 23:29:50 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 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
% 0.11/0.45
% 0.11/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.45
% 0.11/0.45 % Detected problem language: tptp
% 0.18/0.46 % Proving...
% 149.67/21.59 % SZS status Started for theBenchmark.p
% 149.67/21.59 % SZS status Theorem for theBenchmark.p
% 149.67/21.59
% 149.67/21.59 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 149.67/21.59
% 149.67/21.59 % ------ iProver source info
% 149.67/21.59
% 149.67/21.59 % git: date: 2026-07-19 20:42:38 +0200
% 149.67/21.59 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 149.67/21.59 % git: non_committed_changes: false
% 149.67/21.59
% 149.67/21.59 % ------ Parsing...
% 149.67/21.59 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 149.67/21.59
% 149.67/21.59 % ------ Preprocessing... sup_sim: 3 sf_s rm: 20 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 149.67/21.59
% 149.67/21.59 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 149.67/21.59
% 149.67/21.59 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 149.67/21.59 % ------ Proving...
% 149.67/21.59 % ------ Problem Properties
% 149.67/21.59
% 149.67/21.59 %
% 149.67/21.59 % clauses 19
% 149.67/21.59 % conjectures 0
% 149.67/21.59 % EPR 0
% 149.67/21.59 % Horn 19
% 149.67/21.59 % unary 17
% 149.67/21.59 % binary 1
% 149.67/21.59 % lits 22
% 149.67/21.59 % lits eq 4
% 149.67/21.59 % fd_pure 0
% 149.67/21.59 % fd_pseudo 0
% 149.67/21.59 % fd_cond 0
% 149.67/21.59 % fd_pseudo_cond 1
% 149.67/21.59 % AC symbols 0
% 149.67/21.59
% 149.67/21.59 % ------ Input Options Time Limit: Unbounded
% 149.67/21.59
% 149.67/21.59
% 149.67/21.59 % ------
% 149.67/21.59 % Current options:
% 149.67/21.59 % ------
% 149.67/21.59
% 149.67/21.59
% 149.67/21.59 %
% 149.67/21.59
% 149.67/21.59 % ------ Proving...
% 149.67/21.59 %
% 149.67/21.59
% 149.67/21.59 % SZS status Theorem for theBenchmark.p
% 149.67/21.59
% 149.67/21.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 149.67/21.60
% 149.67/21.60
%------------------------------------------------------------------------------