%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL541+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 01:07:57 PM UTC 2026
% Result : Theorem 17.57s 2.67s
% Output : CNFRefutation 17.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 37
% Syntax : Number of formulae : 200 ( 104 unt; 0 def)
% Number of atoms : 395 ( 60 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 333 ( 138 ~; 128 |; 42 &)
% ( 18 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 20 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 27 con; 0-2 aty)
% Number of variables : 299 ( 270 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
modus_tollens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
and_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
equivalence_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
( axiom_m1
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
axiom_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f88,axiom,
op_strict_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f89,conjecture,
axiom_m1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f90,negated_conjecture,
~ axiom_m1,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
( modus_ponens
<=> ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f92,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
| modus_ponens )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(NNF_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( ( ? [Y] :
( ~ is_a_theorem(Y)
& ? [X] :
( is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(miniscoping,[status(thm)],[f92]) ).
fof(f94,plain,
( ( ( ~ is_a_theorem(sK0_skl)
& is_a_theorem(implies(sK1_skl,sK0_skl))
& is_a_theorem(sK1_skl) )
| modus_ponens )
& ( ! [Y] :
( is_a_theorem(Y)
| ! [X] :
( ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) ) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(X,sK1_skl)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f99,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f100,plain,
( ( ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(NNF_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
( ( ( sK2_skl != sK3_skl
& is_a_theorem(equiv(sK2_skl,sK3_skl)) )
| substitution_of_equivalents )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f105,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f106,plain,
( ( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(X,sK4_skl),skolemize(Y,sK5_skl)],[f105]) ).
fof(f107,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f109,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X)))
| implies_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f110,plain,
( ( ~ is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl)))
| implies_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl]),skolemize(X,sK6_skl),skolemize(Y,sK7_skl)],[f109]) ).
fof(f111,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[status(thm)],[f110]) ).
fof(f113,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f114,plain,
( ( ~ is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))
| implies_2 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(X,sK8_skl),skolemize(Y,sK9_skl)],[f113]) ).
fof(f115,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f121,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f122,plain,
( ( ~ is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl))
| and_1 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl,sK14_skl]),skolemize(X,sK13_skl),skolemize(Y,sK14_skl)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(thm)],[f122]) ).
fof(f125,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y))
| and_2 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f126,plain,
( ( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
| and_2 )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl]),skolemize(X,sK15_skl),skolemize(Y,sK16_skl)],[f125]) ).
fof(f127,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[status(thm)],[f126]) ).
fof(f129,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(NNF_transformation,[status(thm)],[f9]) ).
fof(f130,plain,
( ( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl]),skolemize(X,sK17_skl),skolemize(Y,sK18_skl)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f130]) ).
fof(f137,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f138,plain,
( ( ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl)))
| or_2 )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl,sK22_skl]),skolemize(X,sK21_skl),skolemize(Y,sK22_skl)],[f137]) ).
fof(f139,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ or_2 ),
inference(cnf_transformation,[status(thm)],[f138]) ).
fof(f153,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f154,plain,
( ( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))
| equivalence_3 )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(X,sK30_skl),skolemize(Y,sK31_skl)],[f153]) ).
fof(f155,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f201,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f202,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f205,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f206,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f211,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f212,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f214,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f215,plain,
modus_tollens,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f216,plain,
implies_1,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f217,plain,
implies_2,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f219,plain,
and_1,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f220,plain,
and_2,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f221,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f223,plain,
or_2,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f227,plain,
equivalence_3,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f228,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f229,plain,
( necessitation
<=> ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f230,plain,
( ( ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(NNF_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
( ( ( ~ is_a_theorem(necessarily(sK55_skl))
& is_a_theorem(sK55_skl) )
| necessitation )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X,sK55_skl)],[f230]) ).
fof(f232,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0)
| ~ necessitation ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f260,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),X))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(NNF_transformation,[status(thm)],[f55]) ).
fof(f261,plain,
( ( ~ is_a_theorem(implies(necessarily(sK64_skl),sK64_skl))
| axiom_M )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64_skl]),skolemize(X,sK64_skl)],[f260]) ).
fof(f262,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(thm)],[f261]) ).
fof(f264,plain,
( ( ? [X] : ~ is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(NNF_transformation,[status(thm)],[f56]) ).
fof(f265,plain,
( ( ~ is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))
| axiom_4 )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65_skl]),skolemize(X,sK65_skl)],[f264]) ).
fof(f266,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0))))
| ~ axiom_4 ),
inference(cnf_transformation,[status(thm)],[f265]) ).
fof(f292,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| axiom_m1 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(NNF_transformation,[status(thm)],[f63]) ).
fof(f293,plain,
( ( ~ is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))
| axiom_m1 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76_skl,sK77_skl]),skolemize(X,sK76_skl),skolemize(Y,sK77_skl)],[f292]) ).
fof(f295,plain,
( ~ is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl)))
| axiom_m1 ),
inference(cnf_transformation,[status(thm)],[f293]) ).
fof(f296,plain,
( ( ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(NNF_transformation,[status(thm)],[f64]) ).
fof(f297,plain,
( ( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78_skl,sK79_skl]),skolemize(X,sK78_skl),skolemize(Y,sK79_skl)],[f296]) ).
fof(f298,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f299,plain,
( ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl))
| axiom_m2 ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f336,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f337,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(implies(X0,X1))
| ~ op_strict_implies ),
inference(cnf_transformation,[status(thm)],[f336]) ).
fof(f338,plain,
( ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))
| ~ op_strict_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f339,plain,
! [X0,X1] :
( strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0))
| ~ op_strict_equiv ),
inference(cnf_transformation,[status(thm)],[f338]) ).
fof(f341,plain,
necessitation,
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f343,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f344,plain,
axiom_4,
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f349,plain,
op_strict_implies,
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f351,plain,
op_strict_equiv,
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f352,plain,
~ axiom_m1,
inference(cnf_transformation,[status(thm)],[f90]) ).
fof(f353,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f95,f214]) ).
fof(f354,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f228]) ).
fof(f355,plain,
! [X0,X1] : is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f107,f215]) ).
fof(f356,plain,
! [X0] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f341]) ).
fof(f357,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f111,f216]) ).
fof(f358,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f262,f343]) ).
fof(f359,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f123,f219]) ).
fof(f360,plain,
! [X0,X1] : is_a_theorem(implies(and(X0,X1),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f127,f220]) ).
fof(f362,plain,
! [X0,X1] : is_a_theorem(implies(X0,or(X1,X0))),
inference(forward_subsumption_resolution,[status(thm)],[f139,f223]) ).
fof(f364,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(forward_subsumption_resolution,[status(thm)],[f115,f217]) ).
fof(f369,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f337,f349]) ).
fof(f371,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f369,f356]) ).
fof(f374,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ is_a_theorem(implies(X0,equiv(X1,X2)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f353,f354]) ).
fof(f378,plain,
! [X0,X1] : is_a_theorem(implies(X0,implies(X1,and(X0,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f131,f221]) ).
fof(f385,plain,
! [X0,X1] : implies(X0,X1) = not(and(X0,not(X1))),
inference(forward_subsumption_resolution,[status(thm)],[f206,f212]) ).
fof(f394,plain,
! [X0] : is_a_theorem(implies(necessarily(X0),necessarily(necessarily(X0)))),
inference(forward_subsumption_resolution,[status(thm)],[f266,f344]) ).
fof(f395,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),necessarily(necessarily(implies(X0,X1))))),
inference(paramodulation,[status(thm)],[f369,f394]) ).
fof(f397,plain,
! [X0,X1] : is_a_theorem(implies(strict_implies(X0,X1),necessarily(strict_implies(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f369,f395]) ).
fof(f400,plain,
! [X0,X1] :
( is_a_theorem(strict_implies(and(X0,X1),X0))
| ~ is_a_theorem(strict_implies(and(sK78_skl,sK79_skl),sK78_skl)) ),
inference(resolution,[status(thm)],[f299,f298]) ).
fof(f410,plain,
! [X0,X1,X2,X3] :
( ~ is_a_theorem(implies(X3,implies(X0,equiv(X1,X2))))
| ~ is_a_theorem(X3)
| X1 = X2
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f374,f353]) ).
fof(f426,plain,
! [X0,X1] :
( or(X0,X1) = implies(not(X0),X1)
| ~ op_or ),
inference(forward_demodulation,[status(thm)],[f385,f202]) ).
fof(f429,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(X1)),implies(X1,X0))),
inference(backward_demodulation,[status(thm)],[f432,f355]) ).
fof(f432,plain,
! [X0,X1] : or(X0,X1) = implies(not(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f426,f211]) ).
fof(f442,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,implies(not(X0),X1)),implies(not(X0),X1))),
inference(paramodulation,[status(thm)],[f432,f364]) ).
fof(f457,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),implies(not(X0),X1))),
inference(forward_demodulation,[status(thm)],[f432,f442]) ).
fof(f458,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,or(X0,X1)),or(X0,X1))),
inference(forward_demodulation,[status(thm)],[f432,f457]) ).
fof(f465,plain,
! [X0,X1] : is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))),
inference(forward_subsumption_resolution,[status(thm)],[f155,f227]) ).
fof(f491,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,not(not(X1))),or(X1,X0))),
inference(paramodulation,[status(thm)],[f432,f429]) ).
fof(f588,plain,
! [X0,X1] : strict_equiv(X0,X1) = and(strict_implies(X0,X1),strict_implies(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f339,f351]) ).
fof(f591,plain,
! [X0,X1] : is_a_theorem(implies(strict_equiv(X0,X1),strict_implies(X1,X0))),
inference(paramodulation,[status(thm)],[f588,f360]) ).
fof(f750,plain,
~ is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f295,f352]) ).
fof(f752,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,strict_implies(and(sK76_skl,sK77_skl),and(sK77_skl,sK76_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f750,f353]) ).
fof(f942,plain,
~ is_a_theorem(strict_equiv(and(sK77_skl,sK76_skl),and(sK76_skl,sK77_skl))),
inference(resolution,[status(thm)],[f752,f591]) ).
fof(f950,plain,
! [X0] :
( ~ is_a_theorem(implies(X0,strict_equiv(and(sK77_skl,sK76_skl),and(sK76_skl,sK77_skl))))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f942,f353]) ).
fof(f1142,plain,
~ is_a_theorem(necessarily(strict_equiv(and(sK77_skl,sK76_skl),and(sK76_skl,sK77_skl)))),
inference(resolution,[status(thm)],[f950,f358]) ).
fof(f1848,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(and(sK78_skl,sK79_skl),sK78_skl))
| is_a_theorem(strict_implies(and(X0,X1),X0)) ),
inference(resolution,[status(thm)],[f400,f371]) ).
fof(f1850,plain,
! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1848,f359]) ).
fof(f2297,plain,
! [X0,X1] :
( ~ is_a_theorem(implies(X1,X0))
| X1 = X0
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f410,f465]) ).
fof(f2503,plain,
! [X0,X1] :
( or(X0,or(X0,X1)) = or(X0,X1)
| ~ is_a_theorem(implies(or(X0,X1),or(X0,or(X0,X1)))) ),
inference(resolution,[status(thm)],[f2297,f458]) ).
fof(f2514,plain,
! [X0,X1] :
( strict_implies(X0,X1) = necessarily(strict_implies(X0,X1))
| ~ is_a_theorem(implies(necessarily(strict_implies(X0,X1)),strict_implies(X0,X1))) ),
inference(resolution,[status(thm)],[f2297,f397]) ).
fof(f2532,plain,
! [X0,X1] :
( implies(X0,implies(X0,X1)) = implies(X0,X1)
| ~ is_a_theorem(implies(implies(X0,X1),implies(X0,implies(X0,X1)))) ),
inference(resolution,[status(thm)],[f2297,f364]) ).
fof(f2547,plain,
! [X0,X1] : or(X0,or(X0,X1)) = or(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f2503,f362]) ).
fof(f2548,plain,
! [X0,X1] : strict_implies(X0,X1) = necessarily(strict_implies(X0,X1)),
inference(forward_subsumption_resolution,[status(thm)],[f2514,f358]) ).
fof(f2552,plain,
! [X0,X1] : implies(X0,implies(X0,X1)) = implies(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f2532,f357]) ).
fof(f2742,plain,
! [X0] : is_a_theorem(implies(X0,and(X0,X0))),
inference(paramodulation,[status(thm)],[f2552,f378]) ).
fof(f2744,plain,
! [X0] : is_a_theorem(implies(X0,X0)),
inference(paramodulation,[status(thm)],[f2552,f357]) ).
fof(f2991,plain,
! [X0] :
( X0 = and(X0,X0)
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f2742,f2297]) ).
fof(f2997,plain,
! [X0] : X0 = and(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f2991,f360]) ).
fof(f3002,plain,
! [X0] : strict_implies(X0,X0) = strict_equiv(X0,X0),
inference(paramodulation,[status(thm)],[f588,f2997]) ).
fof(f3167,plain,
! [X0] : implies(not(X0),X0) = not(not(X0)),
inference(paramodulation,[status(thm)],[f2997,f385]) ).
fof(f3170,plain,
! [X0] : is_a_theorem(strict_implies(X0,X0)),
inference(paramodulation,[status(thm)],[f2997,f1850]) ).
fof(f3201,plain,
! [X0] : or(X0,X0) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f432,f3167]) ).
fof(f3341,plain,
! [X0] : or(X0,not(not(X0))) = or(X0,X0),
inference(paramodulation,[status(thm)],[f3201,f2547]) ).
fof(f3370,plain,
! [X0] : is_a_theorem(implies(X0,not(not(X0)))),
inference(paramodulation,[status(thm)],[f3201,f362]) ).
fof(f3398,plain,
! [X0] : or(X0,not(not(X0))) = not(not(X0)),
inference(forward_demodulation,[status(thm)],[f3201,f3341]) ).
fof(f3565,plain,
! [X0] :
( X0 = not(not(X0))
| ~ is_a_theorem(implies(not(not(X0)),X0)) ),
inference(resolution,[status(thm)],[f3370,f2297]) ).
fof(f3574,plain,
! [X0] :
( X0 = not(not(X0))
| ~ is_a_theorem(or(not(X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f432,f3565]) ).
fof(f4214,plain,
! [X0] : is_a_theorem(implies(or(not(not(X0)),not(not(X0))),not(not(X0)))),
inference(paramodulation,[status(thm)],[f3398,f491]) ).
fof(f4276,plain,
! [X0] : is_a_theorem(implies(not(not(not(not(X0)))),not(not(X0)))),
inference(forward_demodulation,[status(thm)],[f3201,f4214]) ).
fof(f4277,plain,
! [X0] : is_a_theorem(or(not(not(not(X0))),not(not(X0)))),
inference(forward_demodulation,[status(thm)],[f432,f4276]) ).
fof(f5969,plain,
! [X0] : not(not(X0)) = not(not(not(not(X0)))),
inference(resolution,[status(thm)],[f4277,f3574]) ).
fof(f6172,plain,
! [X0,X1] : implies(X0,not(not(not(X1)))) = not(and(X0,not(not(X1)))),
inference(paramodulation,[status(thm)],[f5969,f385]) ).
fof(f6250,plain,
! [X0,X1] : implies(X0,not(not(not(X1)))) = implies(X0,not(X1)),
inference(forward_demodulation,[status(thm)],[f385,f6172]) ).
fof(f7757,plain,
! [X0] : is_a_theorem(implies(not(not(not(X0))),not(X0))),
inference(paramodulation,[status(thm)],[f6250,f2744]) ).
fof(f7850,plain,
! [X0] : is_a_theorem(or(not(not(X0)),not(X0))),
inference(forward_demodulation,[status(thm)],[f432,f7757]) ).
fof(f7883,plain,
! [X0] : not(X0) = not(not(not(X0))),
inference(resolution,[status(thm)],[f7850,f3574]) ).
fof(f8118,plain,
! [X0,X1] : implies(X0,not(not(X1))) = not(and(X0,not(X1))),
inference(paramodulation,[status(thm)],[f7883,f385]) ).
fof(f8208,plain,
! [X0,X1] : implies(X0,not(not(X1))) = implies(X0,X1),
inference(forward_demodulation,[status(thm)],[f385,f8118]) ).
fof(f9403,plain,
! [X0] : is_a_theorem(implies(not(not(X0)),X0)),
inference(paramodulation,[status(thm)],[f8208,f2744]) ).
fof(f9484,plain,
! [X0] : is_a_theorem(or(not(X0),X0)),
inference(forward_demodulation,[status(thm)],[f432,f9403]) ).
fof(f9519,plain,
! [X0] : X0 = not(not(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f3574,f9484]) ).
fof(f9576,plain,
! [X0,X1] : is_a_theorem(implies(or(X0,X1),or(X1,X0))),
inference(backward_demodulation,[status(thm)],[f9519,f491]) ).
fof(f9582,plain,
! [X0,X1] : and(X0,not(X1)) = not(implies(X0,X1)),
inference(paramodulation,[status(thm)],[f385,f9519]) ).
fof(f9701,plain,
! [X0,X1] : or(not(X0),X1) = implies(X0,X1),
inference(paramodulation,[status(thm)],[f9519,f432]) ).
fof(f9857,plain,
! [X0,X1] :
( or(X1,X0) = or(X0,X1)
| ~ is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(resolution,[status(thm)],[f9576,f2297]) ).
fof(f9866,plain,
! [X0,X1] : or(X0,X1) = or(X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[f9857,f9576]) ).
fof(f10842,plain,
! [X0,X1] : or(X0,not(X1)) = implies(X1,X0),
inference(paramodulation,[status(thm)],[f9866,f9701]) ).
fof(f11528,plain,
! [X0,X1] : implies(X0,not(X1)) = implies(X1,not(X0)),
inference(paramodulation,[status(thm)],[f9701,f10842]) ).
fof(f15749,plain,
! [X0,X1] : and(X0,not(not(X1))) = not(implies(X1,not(X0))),
inference(paramodulation,[status(thm)],[f11528,f9582]) ).
fof(f15951,plain,
! [X0,X1] : and(X0,X1) = not(implies(X1,not(X0))),
inference(forward_demodulation,[status(thm)],[f9519,f15749]) ).
fof(f15952,plain,
! [X0,X1] : and(X0,X1) = and(X1,not(not(X0))),
inference(forward_demodulation,[status(thm)],[f9582,f15951]) ).
fof(f15953,plain,
! [X0,X1] : and(X0,X1) = and(X1,X0),
inference(forward_demodulation,[status(thm)],[f9519,f15952]) ).
fof(f16156,plain,
~ is_a_theorem(necessarily(strict_equiv(and(sK76_skl,sK77_skl),and(sK76_skl,sK77_skl)))),
inference(paramodulation,[status(thm)],[f15953,f1142]) ).
fof(f16825,plain,
~ is_a_theorem(necessarily(strict_implies(and(sK76_skl,sK77_skl),and(sK76_skl,sK77_skl)))),
inference(forward_demodulation,[status(thm)],[f3002,f16156]) ).
fof(f16826,plain,
~ is_a_theorem(strict_implies(and(sK76_skl,sK77_skl),and(sK76_skl,sK77_skl))),
inference(forward_demodulation,[status(thm)],[f2548,f16825]) ).
fof(f16827,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16826,f3170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL541+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 00:37:56 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 17.57/2.67 % Refutation found
% 17.57/2.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.57/2.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.41/2.77 % Elapsed time: 2.370092 seconds
% 9.41/2.77 % CPU time: 18.364723 seconds
% 9.41/2.77 % Total memory used: 342.919 MB
% 9.41/2.77 % Net memory used: 327.220 MB
%------------------------------------------------------------------------------