%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : LCL523+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 01:07:54 PM UTC 2026
% Result : Theorem 1.33s 0.57s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 71
% Syntax : Number of formulae : 268 ( 47 unt; 39 def)
% Number of atoms : 815 ( 45 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 974 ( 427 ~; 444 |; 41 &)
% ( 55 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 59 ( 57 usr; 57 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 23 con; 0-2 aty)
% Number of variables : 242 ( 217 !; 25 ?)
% 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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f77,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
axiom_5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,conjecture,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,negated_conjecture,
~ axiom_4,
inference(negated_conjecture,[status(cth)],[f82]) ).
fof(f84,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(f85,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)],[f84]) ).
fof(f86,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)],[f85]) ).
fof(f87,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)],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f92,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f93,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)],[f92]) ).
fof(f94,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)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f102,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(f103,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)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,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(f107,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)],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f114,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(f115,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)],[f114]) ).
fof(f116,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f122,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(f123,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)],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f132,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ or_2 ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| or_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(NNF_transformation,[status(thm)],[f12]) ).
fof(f135,plain,
( ( ~ is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl))))
| or_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23_skl,sK24_skl,sK25_skl]),skolemize(X,sK23_skl),skolemize(Y,sK24_skl),skolemize(Z,sK25_skl)],[f134]) ).
fof(f136,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ or_3 ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f174,plain,
( ( ? [P] : ~ is_a_theorem(implies(or(P,P),P))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f175,plain,
( ( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44_skl]),skolemize(P,sK44_skl)],[f174]) ).
fof(f176,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f177,plain,
( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 ),
inference(cnf_transformation,[status(thm)],[f175]) ).
fof(f194,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f195,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f198,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f199,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f202,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f203,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f205,plain,
op_implies_and,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f206,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f207,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f209,plain,
implies_1,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f210,plain,
implies_2,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f212,plain,
and_1,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f214,plain,
and_3,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f216,plain,
or_2,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f217,plain,
or_3,
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f221,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f236,plain,
( adjunction
<=> ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f237,plain,
( ( ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(NNF_transformation,[status(thm)],[f236]) ).
fof(f238,plain,
( ( ( ~ is_a_theorem(and(sK58_skl,sK59_skl))
& is_a_theorem(sK59_skl)
& is_a_theorem(sK58_skl) )
| adjunction )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58_skl,sK59_skl]),skolemize(X,sK58_skl),skolemize(Y,sK59_skl)],[f237]) ).
fof(f239,plain,
! [X0,X1] :
( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ adjunction ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
( is_a_theorem(sK58_skl)
| adjunction ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f241,plain,
( is_a_theorem(sK59_skl)
| adjunction ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f242,plain,
( ~ is_a_theorem(and(sK58_skl,sK59_skl))
| adjunction ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f253,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(f254,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)],[f253]) ).
fof(f255,plain,
! [X0] :
( is_a_theorem(implies(necessarily(X0),X0))
| ~ axiom_M ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f257,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(f258,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)],[f257]) ).
fof(f260,plain,
( ~ is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl))))
| axiom_4 ),
inference(cnf_transformation,[status(thm)],[f258]) ).
fof(f265,plain,
( ( ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| axiom_5 )
& ( ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_5 ) ),
inference(NNF_transformation,[status(thm)],[f58]) ).
fof(f266,plain,
( ( ~ is_a_theorem(implies(possibly(sK67_skl),necessarily(possibly(sK67_skl))))
| axiom_5 )
& ( ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67_skl]),skolemize(X,sK67_skl)],[f265]) ).
fof(f267,plain,
! [X0] :
( is_a_theorem(implies(possibly(X0),necessarily(possibly(X0))))
| ~ axiom_5 ),
inference(cnf_transformation,[status(thm)],[f266]) ).
fof(f325,plain,
( ! [X] : possibly(X) = not(necessarily(not(X)))
| ~ op_possibly ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f326,plain,
! [X0] :
( possibly(X0) = not(necessarily(not(X0)))
| ~ op_possibly ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f333,plain,
op_possibly,
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f336,plain,
axiom_M,
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f337,plain,
axiom_5,
inference(cnf_transformation,[status(thm)],[f81]) ).
fof(f338,plain,
~ axiom_4,
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f339,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,definition,
! [X0,X1] :
( sQ1_spl
<=> ( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f343,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f88,f339,f342]) ).
fof(f358,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f362,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f95,f358,f361]) ).
fof(f384,definition,
( sQ12_spl
<=> implies_1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ12_spl
| ~ implies_1 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
! [X0,X1] :
( sQ13_spl
<=> is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f388,plain,
! [X0,X1] :
( ~ sQ13_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f104,f384,f387]) ).
fof(f395,definition,
( sQ15_spl
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ15_spl
| ~ implies_2 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f398,definition,
! [X0,X1] :
( sQ16_spl
<=> is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f399,plain,
! [X0,X1] :
( ~ sQ16_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f398]) ).
fof(f401,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f108,f395,f398]) ).
fof(f417,definition,
( sQ21_spl
<=> and_1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ21_spl
| ~ and_1 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f421,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f116,f417,f420]) ).
fof(f439,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
! [X0,X1] :
( sQ28_spl
<=> is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f443,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f124,f439,f442]) ).
fof(f461,definition,
( sQ33_spl
<=> or_2 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ33_spl
| ~ or_2 ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f465,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f132,f461,f464]) ).
fof(f472,definition,
( sQ36_spl
<=> or_3 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ36_spl
| ~ or_3 ),
inference(component_clause,[status(thm)],[f472]) ).
fof(f475,definition,
! [X0,X1,X2] :
( sQ37_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f476,plain,
! [X0,X1,X2] :
( ~ sQ37_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))) ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f136,f472,f475]) ).
fof(f519,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f520,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f576,definition,
( sQ64_spl
<=> r1 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f579,definition,
! [X0] :
( sQ65_spl
<=> is_a_theorem(implies(or(X0,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f580,plain,
! [X0] :
( ~ sQ65_spl
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(component_clause,[status(thm)],[f579]) ).
fof(f582,plain,
( sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f176,f576,f579]) ).
fof(f583,definition,
( sQ66_spl
<=> is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ66_spl
| ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( ~ sQ66_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f177,f576,f583]) ).
fof(f628,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f628]) ).
fof(f631,definition,
! [X0,X1] :
( sQ79_spl
<=> or(X0,X1) = not(and(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f632,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f634,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f195,f628,f631]) ).
fof(f642,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f642]) ).
fof(f645,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f646,plain,
! [X0,X1] :
( ~ sQ83_spl
| implies(X0,X1) = not(and(X0,not(X1))) ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f648,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f199,f642,f645]) ).
fof(f656,definition,
( sQ86_spl
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f658,plain,
( sQ86_spl
| ~ op_equiv ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,definition,
! [X0,X1] :
( sQ87_spl
<=> equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f660,plain,
! [X0,X1] :
( ~ sQ87_spl
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f662,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f203,f656,f659]) ).
fof(f697,definition,
( sQ97_spl
<=> adjunction ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f700,definition,
! [X0,X1] :
( sQ98_spl
<=> ( is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f701,plain,
! [X0,X1] :
( ~ sQ98_spl
| is_a_theorem(and(X0,X1))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f700]) ).
fof(f703,plain,
( sQ98_spl
| ~ sQ97_spl ),
inference(split_clause,[status(thm)],[f239,f697,f700]) ).
fof(f704,definition,
( sQ99_spl
<=> is_a_theorem(sK58_skl) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f707,plain,
( sQ99_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f240,f697,f704]) ).
fof(f708,definition,
( sQ100_spl
<=> is_a_theorem(sK59_skl) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( sQ100_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f241,f697,f708]) ).
fof(f712,definition,
( sQ101_spl
<=> is_a_theorem(and(sK58_skl,sK59_skl)) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f714,plain,
( sQ101_spl
| ~ is_a_theorem(and(sK58_skl,sK59_skl)) ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,plain,
( ~ sQ101_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f242,f697,f712]) ).
fof(f742,definition,
( sQ109_spl
<=> axiom_M ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f744,plain,
( sQ109_spl
| ~ axiom_M ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f745,definition,
! [X0] :
( sQ110_spl
<=> is_a_theorem(implies(necessarily(X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f746,plain,
! [X0] :
( ~ sQ110_spl
| is_a_theorem(implies(necessarily(X0),X0)) ),
inference(component_clause,[status(thm)],[f745]) ).
fof(f748,plain,
( sQ110_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f255,f742,f745]) ).
fof(f753,definition,
( sQ112_spl
<=> axiom_4 ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ112_spl
| axiom_4 ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f760,definition,
( sQ114_spl
<=> is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f762,plain,
( sQ114_spl
| ~ is_a_theorem(implies(necessarily(sK65_skl),necessarily(necessarily(sK65_skl)))) ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f763,plain,
( ~ sQ114_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f260,f753,f760]) ).
fof(f775,definition,
( sQ118_spl
<=> axiom_5 ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f777,plain,
( sQ118_spl
| ~ axiom_5 ),
inference(component_clause,[status(thm)],[f775]) ).
fof(f778,definition,
! [X0] :
( sQ119_spl
<=> is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f779,plain,
! [X0] :
( ~ sQ119_spl
| is_a_theorem(implies(possibly(X0),necessarily(possibly(X0)))) ),
inference(component_clause,[status(thm)],[f778]) ).
fof(f781,plain,
( sQ119_spl
| ~ sQ118_spl ),
inference(split_clause,[status(thm)],[f267,f775,f778]) ).
fof(f940,definition,
( sQ163_spl
<=> op_possibly ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( sQ163_spl
| ~ op_possibly ),
inference(component_clause,[status(thm)],[f940]) ).
fof(f943,definition,
! [X0] :
( sQ164_spl
<=> possibly(X0) = not(necessarily(not(X0))) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f944,plain,
! [X0] :
( ~ sQ164_spl
| possibly(X0) = not(necessarily(not(X0))) ),
inference(component_clause,[status(thm)],[f943]) ).
fof(f946,plain,
( sQ164_spl
| ~ sQ163_spl ),
inference(split_clause,[status(thm)],[f326,f940,f943]) ).
fof(f968,plain,
( sQ163_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f942,f333]) ).
fof(f969,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f970,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f207]) ).
fof(f971,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f974,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f360,f221]) ).
fof(f975,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f974]) ).
fof(f976,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f206]) ).
fof(f977,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f976]) ).
fof(f978,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f644,f205]) ).
fof(f979,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f978]) ).
fof(f980,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f630,f204]) ).
fof(f981,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f980]) ).
fof(f988,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f744,f336]) ).
fof(f989,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f988]) ).
fof(f1007,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f216]) ).
fof(f1008,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f1007]) ).
fof(f1013,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f212]) ).
fof(f1014,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f1013]) ).
fof(f1029,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f209]) ).
fof(f1030,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f1029]) ).
fof(f1042,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ1_spl
| is_a_theorem(implies(X1,and(X0,X1)))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f343,f443]) ).
fof(f1114,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ sQ1_spl
| ~ is_a_theorem(X1)
| is_a_theorem(and(X1,X0))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f343,f1042]) ).
fof(f1125,plain,
( sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f337]) ).
fof(f1126,plain,
sQ118_spl,
inference(contradiction_clause,[status(thm)],[f1125]) ).
fof(f1146,plain,
( sQ101_spl
| ~ sQ28_spl
| ~ sQ1_spl
| ~ is_a_theorem(sK58_skl)
| ~ is_a_theorem(sK59_skl) ),
inference(resolution,[status(thm)],[f1114,f714]) ).
fof(f1153,plain,
( sQ101_spl
| ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ99_spl
| ~ sQ100_spl ),
inference(split_clause,[status(thm)],[f1146,f708,f704,f342,f442,f712]) ).
fof(f1156,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f441,f214]) ).
fof(f1157,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f1156]) ).
fof(f1300,plain,
( sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f217]) ).
fof(f1301,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f1300]) ).
fof(f1333,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(resolution,[status(thm)],[f399,f343]) ).
fof(f1335,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f397,f210]) ).
fof(f1336,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f1335]) ).
fof(f1348,plain,
! [X0,X1] :
( ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(X0,X1))
| ~ is_a_theorem(implies(X1,X0))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(paramodulation,[status(thm)],[f660,f701]) ).
fof(f1357,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ83_spl
| or(X0,X1) = implies(not(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f646,f632]) ).
fof(f1999,plain,
! [X0,X1] :
( ~ sQ37_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))) ),
inference(resolution,[status(thm)],[f1333,f476]) ).
fof(f2001,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(resolution,[status(thm)],[f1333,f443]) ).
fof(f2002,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ16_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f1333,f388]) ).
fof(f2007,plain,
( ~ sQ28_spl
| ~ sQ1_spl
| ~ sQ16_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f2001,f519,f398,f342,f442]) ).
fof(f3231,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ37_spl
| ~ sQ16_spl
| is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f1999,f343]) ).
fof(f3299,plain,
( sQ66_spl
| ~ sQ1_spl
| ~ sQ37_spl
| ~ sQ16_spl
| ~ is_a_theorem(implies(sK44_skl,sK44_skl)) ),
inference(resolution,[status(thm)],[f3231,f585]) ).
fof(f3305,plain,
( sQ66_spl
| ~ sQ1_spl
| ~ sQ37_spl
| ~ sQ16_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3299,f2002]) ).
fof(f3306,plain,
( sQ66_spl
| ~ sQ1_spl
| ~ sQ37_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f3305]) ).
fof(f3323,plain,
! [X0] :
( ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0)))
| ~ is_a_theorem(implies(necessarily(possibly(X0)),possibly(X0))) ),
inference(resolution,[status(thm)],[f1348,f779]) ).
fof(f3344,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(X0,or(X0,X0)))
| ~ is_a_theorem(implies(X0,or(X0,X0))) ),
inference(resolution,[status(thm)],[f1348,f580]) ).
fof(f3352,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| is_a_theorem(equiv(and(X0,X0),X0))
| ~ is_a_theorem(implies(and(X0,X0),X0)) ),
inference(resolution,[status(thm)],[f1348,f520]) ).
fof(f3357,plain,
! [X0] :
( ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| is_a_theorem(equiv(necessarily(possibly(X0)),possibly(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3323,f746]) ).
fof(f3361,plain,
! [X0] :
( ~ sQ65_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ34_spl
| is_a_theorem(equiv(X0,or(X0,X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[f3344,f465]) ).
fof(f3363,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| is_a_theorem(equiv(and(X0,X0),X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3352,f421]) ).
fof(f3461,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ65_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ34_spl
| X0 = or(X0,X0) ),
inference(resolution,[status(thm)],[f3361,f362]) ).
fof(f3503,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| and(X0,X0) = X0 ),
inference(resolution,[status(thm)],[f3363,f362]) ).
fof(f3549,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| implies(not(X0),X0) = not(not(X0)) ),
inference(paramodulation,[status(thm)],[f3503,f646]) ).
fof(f3567,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| or(X0,X0) = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f1357,f3549]) ).
fof(f3568,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| X0 = not(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f3461,f3567]) ).
fof(f3576,plain,
! [X0] :
( ~ sQ164_spl
| ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| necessarily(not(X0)) = not(possibly(X0)) ),
inference(paramodulation,[status(thm)],[f944,f3568]) ).
fof(f3603,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ164_spl
| possibly(not(X0)) = not(necessarily(X0)) ),
inference(paramodulation,[status(thm)],[f3568,f944]) ).
fof(f4164,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| necessarily(possibly(X0)) = possibly(X0) ),
inference(resolution,[status(thm)],[f3357,f362]) ).
fof(f4170,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ164_spl
| possibly(not(possibly(X0))) = not(possibly(X0)) ),
inference(paramodulation,[status(thm)],[f4164,f3603]) ).
fof(f4179,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ164_spl
| possibly(necessarily(not(X0))) = not(possibly(X0)) ),
inference(forward_demodulation,[status(thm)],[f3576,f4170]) ).
fof(f4180,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ119_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ110_spl
| ~ sQ49_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ164_spl
| possibly(necessarily(not(X0))) = necessarily(not(X0)) ),
inference(forward_demodulation,[status(thm)],[f3576,f4179]) ).
fof(f5311,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| possibly(necessarily(X0)) = necessarily(not(not(X0))) ),
inference(paramodulation,[status(thm)],[f3568,f4180]) ).
fof(f5327,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| possibly(necessarily(X0)) = necessarily(X0) ),
inference(forward_demodulation,[status(thm)],[f3568,f5311]) ).
fof(f5373,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| necessarily(necessarily(X0)) = possibly(necessarily(X0)) ),
inference(paramodulation,[status(thm)],[f5327,f4164]) ).
fof(f5391,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| necessarily(necessarily(X0)) = necessarily(X0) ),
inference(forward_demodulation,[status(thm)],[f5327,f5373]) ).
fof(f5427,plain,
( sQ114_spl
| ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| ~ is_a_theorem(implies(necessarily(sK65_skl),necessarily(sK65_skl))) ),
inference(backward_demodulation,[status(thm)],[f5391,f762]) ).
fof(f5446,plain,
( sQ114_spl
| ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5427,f2002]) ).
fof(f5447,plain,
( sQ114_spl
| ~ sQ6_spl
| ~ sQ49_spl
| ~ sQ87_spl
| ~ sQ98_spl
| ~ sQ22_spl
| ~ sQ83_spl
| ~ sQ79_spl
| ~ sQ65_spl
| ~ sQ34_spl
| ~ sQ119_spl
| ~ sQ110_spl
| ~ sQ164_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f5446]) ).
fof(f5464,plain,
( ~ sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f754,f338]) ).
fof(f5465,plain,
~ sQ112_spl,
inference(contradiction_clause,[status(thm)],[f5464]) ).
fof(f5466,plain,
$false,
inference(sat_refutation,[status(thm)],[f345,f364,f390,f401,f423,f445,f467,f478,f582,f586,f634,f648,f662,f703,f707,f711,f715,f748,f763,f781,f946,f969,f971,f975,f977,f979,f981,f989,f1008,f1014,f1030,f1126,f1153,f1157,f1301,f1336,f2007,f3306,f5447,f5465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL523+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Mon Sep 21 00:36:38 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.32 % Drodi V4.1.1
% 1.33/0.57 % Refutation found
% 1.33/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.33/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.33/0.61 % Elapsed time: 0.279515 seconds
% 1.33/0.61 % CPU time: 1.994610 seconds
% 1.33/0.61 % Total memory used: 143.018 MB
% 1.33/0.61 % Net memory used: 137.050 MB
%------------------------------------------------------------------------------