%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LCL908+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 01:11:20 PM UTC 2026
% Result : Satisfiable 0.17s 0.51s
% Output : Saturation 0.17s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f6,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
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(f10,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(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(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/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
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(f16,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
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(f28,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(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(f30,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
op_or,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
op_implies,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
op_equiv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
cn1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
cn2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
cn3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,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(f41,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)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f43,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)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| ~ modus_ponens ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f48,plain,
( substitution_of_equivalents
<=> ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f49]) ).
fof(f51,plain,
! [X0,X1] :
( X0 = X1
| ~ is_a_theorem(equiv(X0,X1))
| ~ substitution_of_equivalents ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,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(f55,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)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0)))
| ~ modus_tollens ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
( ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl)))
| modus_tollens ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f58,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(f59,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)],[f58]) ).
fof(f60,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
( ~ is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl)))
| implies_1 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f62,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(f63,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)],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
( ~ is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl)))
| implies_2 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f66,plain,
( ( ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f67,plain,
( ( ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))
| implies_3 )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl,sK11_skl,sK12_skl]),skolemize(X,sK10_skl),skolemize(Y,sK11_skl),skolemize(Z,sK12_skl)],[f66]) ).
fof(f68,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ implies_3 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f69,plain,
( ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl))))
| implies_3 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f70,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(f71,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)],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f73,plain,
( ~ is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl))
| and_1 ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f74,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(f75,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)],[f74]) ).
fof(f76,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X1))
| ~ and_2 ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f77,plain,
( ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl))
| and_2 ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f78,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(f79,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)],[f78]) ).
fof(f80,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(X1,and(X0,X1))))
| ~ and_3 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f81,plain,
( ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl))))
| and_3 ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(NNF_transformation,[status(thm)],[f10]) ).
fof(f83,plain,
( ( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl]),skolemize(X,sK19_skl),skolemize(Y,sK20_skl)],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X0,X1)))
| ~ or_1 ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f85,plain,
( ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl)))
| or_1 ),
inference(cnf_transformation,[status(thm)],[f83]) ).
fof(f86,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(f87,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)],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ or_2 ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
( ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl)))
| or_2 ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f90,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(f91,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)],[f90]) ).
fof(f92,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)],[f91]) ).
fof(f93,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 ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f94,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| equivalence_1 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f95,plain,
( ( ~ is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl)))
| equivalence_1 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(X,sK26_skl),skolemize(Y,sK27_skl)],[f94]) ).
fof(f96,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X0,X1)))
| ~ equivalence_1 ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
( ~ is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl)))
| equivalence_1 ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f98,plain,
( ( ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| equivalence_2 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f99,plain,
( ( ~ is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))
| equivalence_2 )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl,sK29_skl]),skolemize(X,sK28_skl),skolemize(Y,sK29_skl)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( is_a_theorem(implies(equiv(X0,X1),implies(X1,X0)))
| ~ equivalence_2 ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
( ~ is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl)))
| equivalence_2 ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,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(f103,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)],[f102]) ).
fof(f104,plain,
! [X0,X1] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1))))
| ~ equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
( ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl))))
| equivalence_3 ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f106,plain,
( ( ? [P] : ~ is_a_theorem(implies(P,and(P,P)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(NNF_transformation,[status(thm)],[f16]) ).
fof(f107,plain,
( ( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(P,sK32_skl)],[f106]) ).
fof(f108,plain,
! [X0] :
( is_a_theorem(implies(X0,and(X0,X0)))
| ~ kn1 ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f109,plain,
( ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl)))
| kn1 ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f110,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(NNF_transformation,[status(thm)],[f17]) ).
fof(f111,plain,
( ( ~ is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl))
| kn2 )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33_skl,sK34_skl]),skolemize(P,sK33_skl),skolemize(Q,sK34_skl)],[f110]) ).
fof(f112,plain,
! [X0,X1] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ kn2 ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f113,plain,
( ~ is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl))
| kn2 ),
inference(cnf_transformation,[status(thm)],[f111]) ).
fof(f114,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| kn3 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f115,plain,
( ( ~ is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl)))))
| kn3 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl]),skolemize(P,sK35_skl),skolemize(Q,sK36_skl),skolemize(R,sK37_skl)],[f114]) ).
fof(f116,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0)))))
| ~ kn3 ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
( ~ is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl)))))
| kn3 ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| cn1 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(NNF_transformation,[status(thm)],[f19]) ).
fof(f119,plain,
( ( ~ is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl))))
| cn1 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38_skl,sK39_skl,sK40_skl]),skolemize(P,sK38_skl),skolemize(Q,sK39_skl),skolemize(R,sK40_skl)],[f118]) ).
fof(f120,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))
| ~ cn1 ),
inference(cnf_transformation,[status(thm)],[f119]) ).
fof(f122,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f123,plain,
( ( ~ is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl)))
| cn2 )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41_skl,sK42_skl]),skolemize(P,sK41_skl),skolemize(Q,sK42_skl)],[f122]) ).
fof(f124,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,implies(not(X0),X1)))
| ~ cn2 ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f126,plain,
( ( ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(NNF_transformation,[status(thm)],[f21]) ).
fof(f127,plain,
( ( ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl))
| cn3 )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl]),skolemize(P,sK43_skl)],[f126]) ).
fof(f128,plain,
! [X0] :
( is_a_theorem(implies(implies(not(X0),X0),X0))
| ~ cn3 ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,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(f131,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)],[f130]) ).
fof(f132,plain,
! [X0] :
( is_a_theorem(implies(or(X0,X0),X0))
| ~ r1 ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl))
| r1 ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f134,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(NNF_transformation,[status(thm)],[f23]) ).
fof(f135,plain,
( ( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl]),skolemize(P,sK45_skl),skolemize(Q,sK46_skl)],[f134]) ).
fof(f136,plain,
! [X0,X1] :
( is_a_theorem(implies(X0,or(X1,X0)))
| ~ r2 ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f137,plain,
( ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl)))
| r2 ),
inference(cnf_transformation,[status(thm)],[f135]) ).
fof(f138,plain,
( ( ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(NNF_transformation,[status(thm)],[f24]) ).
fof(f139,plain,
( ( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl]),skolemize(P,sK47_skl),skolemize(Q,sK48_skl)],[f138]) ).
fof(f140,plain,
! [X0,X1] :
( is_a_theorem(implies(or(X0,X1),or(X1,X0)))
| ~ r3 ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl)))
| r3 ),
inference(cnf_transformation,[status(thm)],[f139]) ).
fof(f142,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(NNF_transformation,[status(thm)],[f25]) ).
fof(f143,plain,
( ( ~ is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl))))
| r4 )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49_skl,sK50_skl,sK51_skl]),skolemize(P,sK49_skl),skolemize(Q,sK50_skl),skolemize(R,sK51_skl)],[f142]) ).
fof(f144,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2))))
| ~ r4 ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f145,plain,
( ~ is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl))))
| r4 ),
inference(cnf_transformation,[status(thm)],[f143]) ).
fof(f146,plain,
( ( ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f147,plain,
( ( ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl))))
| r5 )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl]),skolemize(P,sK52_skl),skolemize(Q,sK53_skl),skolemize(R,sK54_skl)],[f146]) ).
fof(f148,plain,
! [X0,X1,X2] :
( is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1))))
| ~ r5 ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f149,plain,
( ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl))))
| r5 ),
inference(cnf_transformation,[status(thm)],[f147]) ).
fof(f150,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f151,plain,
! [X0,X1] :
( or(X0,X1) = not(and(not(X0),not(X1)))
| ~ op_or ),
inference(cnf_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f153,plain,
! [X0,X1] :
( and(X0,X1) = not(or(not(X0),not(X1)))
| ~ op_and ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f155,plain,
! [X0,X1] :
( implies(X0,X1) = not(and(X0,not(X1)))
| ~ op_implies_and ),
inference(cnf_transformation,[status(thm)],[f154]) ).
fof(f156,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f157,plain,
! [X0,X1] :
( implies(X0,X1) = or(not(X0),X1)
| ~ op_implies_or ),
inference(cnf_transformation,[status(thm)],[f156]) ).
fof(f158,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f159,plain,
! [X0,X1] :
( equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0))
| ~ op_equiv ),
inference(cnf_transformation,[status(thm)],[f158]) ).
fof(f160,plain,
op_or,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f161,plain,
op_implies,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f162,plain,
op_equiv,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f163,plain,
modus_ponens,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f164,plain,
cn1,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f165,plain,
cn2,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f166,plain,
cn3,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f167,plain,
substitution_of_equivalents,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f168,definition,
( sQ0_spl
<=> modus_ponens ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ0_spl
| ~ modus_ponens ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,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(f172,plain,
! [X0,X1] :
( ~ sQ1_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f174,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f168,f171]) ).
fof(f175,definition,
( sQ2_spl
<=> is_a_theorem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ2_spl
| is_a_theorem(sK1_skl) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f179,definition,
( sQ3_spl
<=> is_a_theorem(implies(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ3_spl
| is_a_theorem(implies(sK1_skl,sK0_skl)) ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f183,definition,
( sQ4_spl
<=> is_a_theorem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ4_spl
| ~ is_a_theorem(sK0_skl) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f187,definition,
( sQ5_spl
<=> substitution_of_equivalents ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ5_spl
| ~ substitution_of_equivalents ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
! [X0,X1] :
( sQ6_spl
<=> ( X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1
| ~ is_a_theorem(equiv(X0,X1)) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f51,f187,f190]) ).
fof(f194,definition,
( sQ7_spl
<=> is_a_theorem(equiv(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( ~ sQ7_spl
| is_a_theorem(equiv(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f198,definition,
( sQ8_spl
<=> sK2_skl = sK3_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ8_spl
| sK2_skl != sK3_skl ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f202,definition,
( sQ9_spl
<=> modus_tollens ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ9_spl
| modus_tollens ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( sQ9_spl
| ~ modus_tollens ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
! [X0,X1] :
( sQ10_spl
<=> is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ10_spl
| is_a_theorem(implies(implies(not(X0),not(X1)),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f202,f205]) ).
fof(f209,definition,
( sQ11_spl
<=> is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( ~ sQ11_spl
| is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( sQ11_spl
| ~ is_a_theorem(implies(implies(not(sK5_skl),not(sK4_skl)),implies(sK4_skl,sK5_skl))) ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ sQ11_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f202,f209]) ).
fof(f213,definition,
( sQ12_spl
<=> implies_1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ12_spl
| implies_1 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( sQ12_spl
| ~ implies_1 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
! [X0,X1] :
( sQ13_spl
<=> is_a_theorem(implies(X0,implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f217,plain,
! [X0,X1] :
( ~ sQ13_spl
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f60,f213,f216]) ).
fof(f220,definition,
( sQ14_spl
<=> is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl))) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ14_spl
| is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl))) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ14_spl
| ~ is_a_theorem(implies(sK6_skl,implies(sK7_skl,sK6_skl))) ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( ~ sQ14_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f61,f213,f220]) ).
fof(f224,definition,
( sQ15_spl
<=> implies_2 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ15_spl
| implies_2 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f226,plain,
( sQ15_spl
| ~ implies_2 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,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(f228,plain,
! [X0,X1] :
( ~ sQ16_spl
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f64,f224,f227]) ).
fof(f231,definition,
( sQ17_spl
<=> is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( ~ sQ17_spl
| is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f233,plain,
( sQ17_spl
| ~ is_a_theorem(implies(implies(sK8_skl,implies(sK8_skl,sK9_skl)),implies(sK8_skl,sK9_skl))) ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ17_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f65,f224,f231]) ).
fof(f235,definition,
( sQ18_spl
<=> implies_3 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( ~ sQ18_spl
| implies_3 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( sQ18_spl
| ~ implies_3 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f68,f235,f238]) ).
fof(f242,definition,
( sQ20_spl
<=> is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ20_spl
| is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f244,plain,
( sQ20_spl
| ~ is_a_theorem(implies(implies(sK10_skl,sK11_skl),implies(implies(sK11_skl,sK12_skl),implies(sK10_skl,sK12_skl)))) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,plain,
( ~ sQ20_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f69,f235,f242]) ).
fof(f246,definition,
( sQ21_spl
<=> and_1 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ21_spl
| and_1 ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( sQ21_spl
| ~ and_1 ),
inference(component_clause,[status(thm)],[f246]) ).
fof(f249,definition,
! [X0,X1] :
( sQ22_spl
<=> is_a_theorem(implies(and(X0,X1),X0)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f250,plain,
! [X0,X1] :
( ~ sQ22_spl
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f72,f246,f249]) ).
fof(f253,definition,
( sQ23_spl
<=> is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ23_spl
| is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f255,plain,
( sQ23_spl
| ~ is_a_theorem(implies(and(sK13_skl,sK14_skl),sK13_skl)) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ23_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f73,f246,f253]) ).
fof(f257,definition,
( sQ24_spl
<=> and_2 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ24_spl
| and_2 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f259,plain,
( sQ24_spl
| ~ and_2 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
! [X0,X1] :
( sQ25_spl
<=> is_a_theorem(implies(and(X0,X1),X1)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f261,plain,
! [X0,X1] :
( ~ sQ25_spl
| is_a_theorem(implies(and(X0,X1),X1)) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f76,f257,f260]) ).
fof(f264,definition,
( sQ26_spl
<=> is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ26_spl
| is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( sQ26_spl
| ~ is_a_theorem(implies(and(sK15_skl,sK16_skl),sK16_skl)) ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,plain,
( ~ sQ26_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f77,f257,f264]) ).
fof(f268,definition,
( sQ27_spl
<=> and_3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ27_spl
| and_3 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f270,plain,
( sQ27_spl
| ~ and_3 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f271,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(f272,plain,
! [X0,X1] :
( ~ sQ28_spl
| is_a_theorem(implies(X0,implies(X1,and(X0,X1)))) ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f80,f268,f271]) ).
fof(f275,definition,
( sQ29_spl
<=> is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ29_spl
| is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f277,plain,
( sQ29_spl
| ~ is_a_theorem(implies(sK17_skl,implies(sK18_skl,and(sK17_skl,sK18_skl)))) ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( ~ sQ29_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f81,f268,f275]) ).
fof(f279,definition,
( sQ30_spl
<=> or_1 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ30_spl
| or_1 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f281,plain,
( sQ30_spl
| ~ or_1 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,definition,
! [X0,X1] :
( sQ31_spl
<=> is_a_theorem(implies(X0,or(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f283,plain,
! [X0,X1] :
( ~ sQ31_spl
| is_a_theorem(implies(X0,or(X0,X1))) ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,plain,
( sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f84,f279,f282]) ).
fof(f286,definition,
( sQ32_spl
<=> is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ32_spl
| is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f288,plain,
( sQ32_spl
| ~ is_a_theorem(implies(sK19_skl,or(sK19_skl,sK20_skl))) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ32_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f85,f279,f286]) ).
fof(f290,definition,
( sQ33_spl
<=> or_2 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( ~ sQ33_spl
| or_2 ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f292,plain,
( sQ33_spl
| ~ or_2 ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,definition,
! [X0,X1] :
( sQ34_spl
<=> is_a_theorem(implies(X0,or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f294,plain,
! [X0,X1] :
( ~ sQ34_spl
| is_a_theorem(implies(X0,or(X1,X0))) ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f88,f290,f293]) ).
fof(f297,definition,
( sQ35_spl
<=> is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ35_spl
| is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( sQ35_spl
| ~ is_a_theorem(implies(sK22_skl,or(sK21_skl,sK22_skl))) ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,plain,
( ~ sQ35_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f89,f290,f297]) ).
fof(f301,definition,
( sQ36_spl
<=> or_3 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ36_spl
| or_3 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f303,plain,
( sQ36_spl
| ~ or_3 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,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(f305,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)],[f304]) ).
fof(f307,plain,
( sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f92,f301,f304]) ).
fof(f308,definition,
( sQ38_spl
<=> is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f309,plain,
( ~ sQ38_spl
| is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f310,plain,
( sQ38_spl
| ~ is_a_theorem(implies(implies(sK23_skl,sK25_skl),implies(implies(sK24_skl,sK25_skl),implies(or(sK23_skl,sK24_skl),sK25_skl)))) ),
inference(component_clause,[status(thm)],[f308]) ).
fof(f311,plain,
( ~ sQ38_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f93,f301,f308]) ).
fof(f312,definition,
( sQ39_spl
<=> equivalence_1 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ39_spl
| equivalence_1 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f314,plain,
( sQ39_spl
| ~ equivalence_1 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,definition,
! [X0,X1] :
( sQ40_spl
<=> is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f316,plain,
! [X0,X1] :
( ~ sQ40_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X0,X1))) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f96,f312,f315]) ).
fof(f319,definition,
( sQ41_spl
<=> is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl))) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( ~ sQ41_spl
| is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl))) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f321,plain,
( sQ41_spl
| ~ is_a_theorem(implies(equiv(sK26_skl,sK27_skl),implies(sK26_skl,sK27_skl))) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,plain,
( ~ sQ41_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f97,f312,f319]) ).
fof(f323,definition,
( sQ42_spl
<=> equivalence_2 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ42_spl
| equivalence_2 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f325,plain,
( sQ42_spl
| ~ equivalence_2 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,definition,
! [X0,X1] :
( sQ43_spl
<=> is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f327,plain,
! [X0,X1] :
( ~ sQ43_spl
| is_a_theorem(implies(equiv(X0,X1),implies(X1,X0))) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,plain,
( sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f100,f323,f326]) ).
fof(f330,definition,
( sQ44_spl
<=> is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( ~ sQ44_spl
| is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f332,plain,
( sQ44_spl
| ~ is_a_theorem(implies(equiv(sK28_skl,sK29_skl),implies(sK29_skl,sK28_skl))) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,plain,
( ~ sQ44_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f101,f323,f330]) ).
fof(f334,definition,
( sQ45_spl
<=> equivalence_3 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ45_spl
| equivalence_3 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f336,plain,
( sQ45_spl
| ~ equivalence_3 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
! [X0,X1] :
( sQ46_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f338,plain,
! [X0,X1] :
( ~ sQ46_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(X1,X0),equiv(X0,X1)))) ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( sQ46_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f104,f334,f337]) ).
fof(f341,definition,
( sQ47_spl
<=> is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ47_spl
| is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f343,plain,
( sQ47_spl
| ~ is_a_theorem(implies(implies(sK30_skl,sK31_skl),implies(implies(sK31_skl,sK30_skl),equiv(sK30_skl,sK31_skl)))) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( ~ sQ47_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f105,f334,f341]) ).
fof(f345,definition,
( sQ48_spl
<=> kn1 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( ~ sQ48_spl
| kn1 ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f347,plain,
( sQ48_spl
| ~ kn1 ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,definition,
! [X0] :
( sQ49_spl
<=> is_a_theorem(implies(X0,and(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f349,plain,
! [X0] :
( ~ sQ49_spl
| is_a_theorem(implies(X0,and(X0,X0))) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,plain,
( sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f108,f345,f348]) ).
fof(f352,definition,
( sQ50_spl
<=> is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( ~ sQ50_spl
| is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( sQ50_spl
| ~ is_a_theorem(implies(sK32_skl,and(sK32_skl,sK32_skl))) ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( ~ sQ50_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f109,f345,f352]) ).
fof(f356,definition,
( sQ51_spl
<=> kn2 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ51_spl
| kn2 ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f358,plain,
( sQ51_spl
| ~ kn2 ),
inference(component_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( sQ22_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f112,f356,f249]) ).
fof(f360,definition,
( sQ52_spl
<=> is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ52_spl
| is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ52_spl
| ~ is_a_theorem(implies(and(sK33_skl,sK34_skl),sK33_skl)) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,plain,
( ~ sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f113,f356,f360]) ).
fof(f364,definition,
( sQ53_spl
<=> kn3 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( ~ sQ53_spl
| kn3 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ53_spl
| ~ kn3 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,definition,
! [X0,X1,X2] :
( sQ54_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f368,plain,
! [X0,X1,X2] :
( ~ sQ54_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(and(X1,X2)),not(and(X2,X0))))) ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f116,f364,f367]) ).
fof(f371,definition,
( sQ55_spl
<=> is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl))))) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ55_spl
| is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl))))) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f373,plain,
( sQ55_spl
| ~ is_a_theorem(implies(implies(sK35_skl,sK36_skl),implies(not(and(sK36_skl,sK37_skl)),not(and(sK37_skl,sK35_skl))))) ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,plain,
( ~ sQ55_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f117,f364,f371]) ).
fof(f375,definition,
( sQ56_spl
<=> cn1 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ56_spl
| ~ cn1 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( sQ19_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f120,f375,f238]) ).
fof(f379,definition,
( sQ57_spl
<=> is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( ~ sQ57_spl
| is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f381,plain,
( sQ57_spl
| ~ is_a_theorem(implies(implies(sK38_skl,sK39_skl),implies(implies(sK39_skl,sK40_skl),implies(sK38_skl,sK40_skl)))) ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f383,definition,
( sQ58_spl
<=> cn2 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ58_spl
| ~ cn2 ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,definition,
! [X0,X1] :
( sQ59_spl
<=> is_a_theorem(implies(X0,implies(not(X0),X1))) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f387,plain,
! [X0,X1] :
( ~ sQ59_spl
| is_a_theorem(implies(X0,implies(not(X0),X1))) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,plain,
( sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f124,f383,f386]) ).
fof(f390,definition,
( sQ60_spl
<=> is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ60_spl
| is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f392,plain,
( sQ60_spl
| ~ is_a_theorem(implies(sK41_skl,implies(not(sK41_skl),sK42_skl))) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f394,definition,
( sQ61_spl
<=> cn3 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( sQ61_spl
| ~ cn3 ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f397,definition,
! [X0] :
( sQ62_spl
<=> is_a_theorem(implies(implies(not(X0),X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f398,plain,
! [X0] :
( ~ sQ62_spl
| is_a_theorem(implies(implies(not(X0),X0),X0)) ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,plain,
( sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f128,f394,f397]) ).
fof(f401,definition,
( sQ63_spl
<=> is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( ~ sQ63_spl
| is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)) ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f403,plain,
( sQ63_spl
| ~ is_a_theorem(implies(implies(not(sK43_skl),sK43_skl),sK43_skl)) ),
inference(component_clause,[status(thm)],[f401]) ).
fof(f405,definition,
( sQ64_spl
<=> r1 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f406,plain,
( ~ sQ64_spl
| r1 ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f407,plain,
( sQ64_spl
| ~ r1 ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,definition,
! [X0] :
( sQ65_spl
<=> is_a_theorem(implies(or(X0,X0),X0)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f409,plain,
! [X0] :
( ~ sQ65_spl
| is_a_theorem(implies(or(X0,X0),X0)) ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,plain,
( sQ65_spl
| ~ sQ64_spl ),
inference(split_clause,[status(thm)],[f132,f405,f408]) ).
fof(f412,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(f413,plain,
( ~ sQ66_spl
| is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ66_spl
| ~ is_a_theorem(implies(or(sK44_skl,sK44_skl),sK44_skl)) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,plain,
( ~ sQ66_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f133,f405,f412]) ).
fof(f416,definition,
( sQ67_spl
<=> r2 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ67_spl
| r2 ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f418,plain,
( sQ67_spl
| ~ r2 ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,plain,
( sQ34_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f136,f416,f293]) ).
fof(f420,definition,
( sQ68_spl
<=> is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ68_spl
| is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f422,plain,
( sQ68_spl
| ~ is_a_theorem(implies(sK46_skl,or(sK45_skl,sK46_skl))) ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( ~ sQ68_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f137,f416,f420]) ).
fof(f424,definition,
( sQ69_spl
<=> r3 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( ~ sQ69_spl
| r3 ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f426,plain,
( sQ69_spl
| ~ r3 ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f427,definition,
! [X0,X1] :
( sQ70_spl
<=> is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f428,plain,
! [X0,X1] :
( ~ sQ70_spl
| is_a_theorem(implies(or(X0,X1),or(X1,X0))) ),
inference(component_clause,[status(thm)],[f427]) ).
fof(f430,plain,
( sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f140,f424,f427]) ).
fof(f431,definition,
( sQ71_spl
<=> is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( ~ sQ71_spl
| is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f433,plain,
( sQ71_spl
| ~ is_a_theorem(implies(or(sK47_skl,sK48_skl),or(sK48_skl,sK47_skl))) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,plain,
( ~ sQ71_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f141,f424,f431]) ).
fof(f435,definition,
( sQ72_spl
<=> r4 ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ72_spl
| r4 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f437,plain,
( sQ72_spl
| ~ r4 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
! [X0,X1,X2] :
( sQ73_spl
<=> is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ~ sQ73_spl
| is_a_theorem(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,plain,
( sQ73_spl
| ~ sQ72_spl ),
inference(split_clause,[status(thm)],[f144,f435,f438]) ).
fof(f442,definition,
( sQ74_spl
<=> is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ74_spl
| is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl)))) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f444,plain,
( sQ74_spl
| ~ is_a_theorem(implies(or(sK49_skl,or(sK50_skl,sK51_skl)),or(sK50_skl,or(sK49_skl,sK51_skl)))) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ74_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f145,f435,f442]) ).
fof(f446,definition,
( sQ75_spl
<=> r5 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ75_spl
| r5 ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( sQ75_spl
| ~ r5 ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,definition,
! [X0,X1,X2] :
( sQ76_spl
<=> is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f450,plain,
! [X0,X1,X2] :
( ~ sQ76_spl
| is_a_theorem(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( sQ76_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f148,f446,f449]) ).
fof(f453,definition,
( sQ77_spl
<=> is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ77_spl
| is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f455,plain,
( sQ77_spl
| ~ is_a_theorem(implies(implies(sK53_skl,sK54_skl),implies(or(sK52_skl,sK53_skl),or(sK52_skl,sK54_skl)))) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ77_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f149,f446,f453]) ).
fof(f457,definition,
( sQ78_spl
<=> op_or ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ78_spl
| ~ op_or ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,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(f461,plain,
! [X0,X1] :
( ~ sQ79_spl
| or(X0,X1) = not(and(not(X0),not(X1))) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( sQ79_spl
| ~ sQ78_spl ),
inference(split_clause,[status(thm)],[f151,f457,f460]) ).
fof(f464,definition,
( sQ80_spl
<=> op_and ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ80_spl
| ~ op_and ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
! [X0,X1] :
( sQ81_spl
<=> and(X0,X1) = not(or(not(X0),not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f153,f464,f467]) ).
fof(f471,definition,
( sQ82_spl
<=> op_implies_and ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( sQ82_spl
| ~ op_implies_and ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,definition,
! [X0,X1] :
( sQ83_spl
<=> implies(X0,X1) = not(and(X0,not(X1))) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( sQ83_spl
| ~ sQ82_spl ),
inference(split_clause,[status(thm)],[f155,f471,f474]) ).
fof(f478,definition,
( sQ84_spl
<=> op_implies_or ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ84_spl
| ~ op_implies_or ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f481,definition,
! [X0,X1] :
( sQ85_spl
<=> implies(X0,X1) = or(not(X0),X1) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f157,f478,f481]) ).
fof(f485,definition,
( sQ86_spl
<=> op_equiv ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ86_spl
| ~ op_equiv ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,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(f489,plain,
! [X0,X1] :
( ~ sQ87_spl
| equiv(X0,X1) = and(implies(X0,X1),implies(X1,X0)) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( sQ87_spl
| ~ sQ86_spl ),
inference(split_clause,[status(thm)],[f159,f485,f488]) ).
fof(f492,plain,
( sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f162]) ).
fof(f493,plain,
sQ86_spl,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f494,plain,
( sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f160]) ).
fof(f495,plain,
sQ78_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f496,plain,
( sQ77_spl
| ~ sQ76_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f455,f450]) ).
fof(f497,plain,
( sQ74_spl
| ~ sQ73_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f444,f439]) ).
fof(f498,plain,
( sQ71_spl
| ~ sQ70_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f433,f428]) ).
fof(f499,plain,
( sQ68_spl
| ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f294]) ).
fof(f500,plain,
( sQ68_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f499]) ).
fof(f501,plain,
( sQ66_spl
| ~ sQ65_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f414,f409]) ).
fof(f502,plain,
( sQ63_spl
| ~ sQ62_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f403,f398]) ).
fof(f503,plain,
( sQ60_spl
| ~ sQ59_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f392,f387]) ).
fof(f504,plain,
( sQ57_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f381,f239]) ).
fof(f505,plain,
( sQ57_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f506,plain,
( sQ55_spl
| ~ sQ54_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f373,f368]) ).
fof(f507,plain,
( sQ52_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f250]) ).
fof(f508,plain,
( sQ52_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f509,plain,
( sQ50_spl
| ~ sQ49_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f354,f349]) ).
fof(f510,plain,
( sQ47_spl
| ~ sQ46_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f343,f338]) ).
fof(f511,plain,
( sQ44_spl
| ~ sQ43_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f332,f327]) ).
fof(f512,plain,
( sQ41_spl
| ~ sQ40_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f321,f316]) ).
fof(f513,plain,
( sQ38_spl
| ~ sQ37_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f310,f305]) ).
fof(f514,plain,
( sQ32_spl
| ~ sQ31_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f288,f283]) ).
fof(f515,plain,
( sQ29_spl
| ~ sQ28_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f277,f272]) ).
fof(f516,plain,
( sQ26_spl
| ~ sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f266,f261]) ).
fof(f517,plain,
( sQ17_spl
| ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f233,f228]) ).
fof(f518,plain,
( sQ14_spl
| ~ sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f217]) ).
fof(f519,plain,
( sQ11_spl
| ~ sQ10_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f211,f206]) ).
fof(f520,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f163]) ).
fof(f521,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f522,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f167]) ).
fof(f523,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( sQ77_spl
| ~ sQ76_spl ),
inference(contradiction_clause,[status(thm)],[f496]) ).
fof(f525,plain,
( sQ74_spl
| ~ sQ73_spl ),
inference(contradiction_clause,[status(thm)],[f497]) ).
fof(f526,plain,
( sQ71_spl
| ~ sQ70_spl ),
inference(contradiction_clause,[status(thm)],[f498]) ).
fof(f527,plain,
( sQ66_spl
| ~ sQ65_spl ),
inference(contradiction_clause,[status(thm)],[f501]) ).
fof(f528,plain,
( sQ63_spl
| ~ sQ62_spl ),
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f529,plain,
( sQ60_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f530,plain,
( sQ35_spl
| ~ sQ34_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f299,f294]) ).
fof(f531,plain,
( sQ55_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f532,plain,
( sQ20_spl
| ~ sQ19_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f244,f239]) ).
fof(f533,plain,
( sQ50_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f534,plain,
( sQ47_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f535,plain,
( sQ44_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f511]) ).
fof(f536,plain,
( sQ41_spl
| ~ sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f537,plain,
( sQ38_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f538,plain,
( sQ32_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f539,plain,
( sQ29_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f540,plain,
( sQ26_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f541,plain,
( sQ17_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f542,plain,
( sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f543,plain,
( sQ11_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f544,plain,
( sQ23_spl
| ~ sQ22_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f255,f250]) ).
fof(f545,plain,
( sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f396,f166]) ).
fof(f546,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f545]) ).
fof(f547,plain,
( sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f385,f165]) ).
fof(f548,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f547]) ).
fof(f549,plain,
( sQ35_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f550,plain,
( sQ20_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f551,plain,
( sQ23_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f552,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f164]) ).
fof(f553,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f554,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| or(and(not(X0),not(X1)),X2) = not(and(or(X0,X1),not(X2))) ),
inference(paramodulation,[status(thm)],[f461,f461]) ).
fof(f555,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| or(X0,and(not(X1),not(X2))) = not(and(not(X0),or(X1,X2))) ),
inference(paramodulation,[status(thm)],[f461,f461]) ).
fof(f556,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ62_spl
| is_a_theorem(X0)
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f398,f172]) ).
fof(f557,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))) ),
inference(paramodulation,[status(thm)],[f461,f398]) ).
fof(f558,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f387,f172]) ).
fof(f559,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))) ),
inference(paramodulation,[status(thm)],[f461,f387]) ).
fof(f560,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X1,X2),implies(X0,X2)))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f239,f172]) ).
fof(f565,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ62_spl
| is_a_theorem(and(not(X0),not(X1)))
| ~ is_a_theorem(implies(or(X0,X1),and(not(X0),not(X1)))) ),
inference(paramodulation,[status(thm)],[f461,f556]) ).
fof(f593,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2)) ),
inference(resolution,[status(thm)],[f558,f557]) ).
fof(f594,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(not(implies(implies(not(X0),X0),X0)),X1)) ),
inference(resolution,[status(thm)],[f558,f398]) ).
fof(f595,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3)) ),
inference(resolution,[status(thm)],[f558,f239]) ).
fof(f596,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ1_spl
| is_a_theorem(implies(not(implies(X0,implies(not(X0),X1))),X2)) ),
inference(resolution,[status(thm)],[f558,f387]) ).
fof(f598,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(X1)
| ~ is_a_theorem(not(implies(implies(not(X0),X0),X0))) ),
inference(resolution,[status(thm)],[f594,f172]) ).
fof(f599,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(not(implies(implies(not(X0),X0),X0)),X1)),X2)) ),
inference(resolution,[status(thm)],[f594,f558]) ).
fof(f601,definition,
! [X0] :
( sQ88_spl
<=> ~ is_a_theorem(not(implies(implies(not(X0),X0),X0))) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f602,plain,
! [X0] :
( ~ sQ88_spl
| ~ is_a_theorem(not(implies(implies(not(X0),X0),X0))) ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,definition,
! [X1] :
( sQ89_spl
<=> is_a_theorem(X1) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f605,plain,
! [X0] :
( ~ sQ89_spl
| is_a_theorem(X0) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f607,plain,
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ59_spl
| sQ89_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f598,f601,f604,f386,f397,f171]) ).
fof(f608,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ88_spl
| ~ is_a_theorem(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))) ),
inference(paramodulation,[status(thm)],[f461,f602]) ).
fof(f610,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(X2)
| ~ is_a_theorem(not(implies(X0,implies(not(X0),X1)))) ),
inference(resolution,[status(thm)],[f596,f172]) ).
fof(f611,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(not(implies(not(implies(X0,implies(not(X0),X1))),X2)),X3)) ),
inference(resolution,[status(thm)],[f596,f558]) ).
fof(f612,plain,
! [X0,X1,X2,X3] :
( ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ1_spl
| is_a_theorem(implies(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))),X3)) ),
inference(paramodulation,[status(thm)],[f461,f596]) ).
fof(f613,definition,
! [X0,X1] :
( sQ90_spl
<=> ~ is_a_theorem(not(implies(X0,implies(not(X0),X1)))) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f614,plain,
! [X0,X1] :
( ~ sQ90_spl
| ~ is_a_theorem(not(implies(X0,implies(not(X0),X1)))) ),
inference(component_clause,[status(thm)],[f613]) ).
fof(f616,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| sQ89_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f610,f613,f604,f386,f171]) ).
fof(f617,plain,
! [X0,X1] :
( ~ sQ6_spl
| ~ sQ89_spl
| X0 = X1 ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f605]) ).
fof(f618,plain,
( sQ68_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f422,f605]) ).
fof(f619,plain,
( sQ35_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f299,f605]) ).
fof(f620,plain,
( sQ14_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f222,f605]) ).
fof(f621,plain,
( sQ52_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f362,f605]) ).
fof(f622,plain,
( sQ23_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f255,f605]) ).
fof(f623,plain,
( sQ26_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f266,f605]) ).
fof(f624,plain,
( sQ29_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f277,f605]) ).
fof(f625,plain,
( sQ32_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f288,f605]) ).
fof(f626,plain,
( sQ41_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f321,f605]) ).
fof(f627,plain,
( sQ44_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f332,f605]) ).
fof(f628,plain,
( sQ50_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f354,f605]) ).
fof(f629,plain,
( sQ66_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f414,f605]) ).
fof(f630,plain,
( sQ71_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f433,f605]) ).
fof(f631,plain,
( sQ74_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f444,f605]) ).
fof(f632,plain,
( sQ11_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f211,f605]) ).
fof(f633,plain,
( sQ17_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f233,f605]) ).
fof(f634,plain,
( sQ38_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f310,f605]) ).
fof(f635,plain,
( sQ47_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f343,f605]) ).
fof(f636,plain,
( sQ55_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f373,f605]) ).
fof(f637,plain,
( sQ77_spl
| ~ sQ89_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f455,f605]) ).
fof(f638,plain,
( sQ68_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f647,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ90_spl
| ~ is_a_theorem(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2)))) ),
inference(paramodulation,[status(thm)],[f461,f614]) ).
fof(f671,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(or(X0,X1),X2))
| ~ is_a_theorem(and(not(X0),not(X1))) ),
inference(resolution,[status(thm)],[f559,f172]) ).
fof(f677,plain,
! [X0,X1,X2,X3] :
( ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3))) ),
inference(resolution,[status(thm)],[f560,f559]) ).
fof(f678,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(not(X2),X2),X2)),X1))) ),
inference(resolution,[status(thm)],[f560,f594]) ).
fof(f679,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))) ),
inference(resolution,[status(thm)],[f560,f557]) ).
fof(f680,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))) ),
inference(resolution,[status(thm)],[f560,f398]) ).
fof(f681,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))) ),
inference(resolution,[status(thm)],[f560,f239]) ).
fof(f682,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f560,f387]) ).
fof(f706,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(X2,implies(not(X2),X3))),X1))) ),
inference(resolution,[status(thm)],[f596,f560]) ).
fof(f711,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(implies(implies(not(X0),X0),X1),X2),implies(implies(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f680,f560]) ).
fof(f712,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(X0),X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(resolution,[status(thm)],[f680,f172]) ).
fof(f713,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),X2)) ),
inference(resolution,[status(thm)],[f680,f558]) ).
fof(f728,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(or(X2,X3),and(not(X2),not(X3))),and(not(X2),not(X3)))),X1))) ),
inference(resolution,[status(thm)],[f593,f560]) ).
fof(f729,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(X2)
| ~ is_a_theorem(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))) ),
inference(resolution,[status(thm)],[f593,f172]) ).
fof(f730,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2)),X3)) ),
inference(resolution,[status(thm)],[f593,f558]) ).
fof(f737,definition,
! [X0,X1] :
( sQ91_spl
<=> ~ is_a_theorem(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f738,plain,
! [X0,X1] :
( ~ sQ91_spl
| ~ is_a_theorem(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))) ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f740,plain,
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| sQ89_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f729,f737,f604,f386,f397,f460,f171]) ).
fof(f753,plain,
( sQ14_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f755,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4)))),X1))) ),
inference(resolution,[status(thm)],[f595,f560]) ).
fof(f756,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(X3)
| ~ is_a_theorem(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))) ),
inference(resolution,[status(thm)],[f595,f172]) ).
fof(f757,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3)),X4)) ),
inference(resolution,[status(thm)],[f595,f558]) ).
fof(f758,definition,
! [X0,X1,X2] :
( sQ92_spl
<=> ~ is_a_theorem(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f759,plain,
! [X0,X1,X2] :
( ~ sQ92_spl
| ~ is_a_theorem(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))) ),
inference(component_clause,[status(thm)],[f758]) ).
fof(f761,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| sQ89_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f756,f758,f604,f386,f238,f171]) ).
fof(f762,plain,
( sQ52_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f621]) ).
fof(f768,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(and(not(X0),not(X1)),X2),X3),implies(implies(implies(or(X0,X1),X4),X2),X3))) ),
inference(resolution,[status(thm)],[f677,f560]) ).
fof(f769,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(and(not(X0),not(X1)),X3))
| ~ is_a_theorem(implies(implies(or(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[f677,f172]) ).
fof(f770,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3))),X4)) ),
inference(resolution,[status(thm)],[f677,f558]) ).
fof(f779,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2),X3),implies(implies(and(not(X0),not(X1)),X2),X3))) ),
inference(resolution,[status(thm)],[f679,f560]) ).
fof(f780,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))
| ~ is_a_theorem(implies(and(not(X0),not(X1)),X2)) ),
inference(resolution,[status(thm)],[f679,f172]) ).
fof(f781,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))),X3)) ),
inference(resolution,[status(thm)],[f679,f558]) ).
fof(f801,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(X0,X1),X2),implies(implies(implies(not(X0),X3),X1),X2))) ),
inference(resolution,[status(thm)],[f682,f560]) ).
fof(f802,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(X0,X2))
| ~ is_a_theorem(implies(implies(not(X0),X1),X2)) ),
inference(resolution,[status(thm)],[f682,f172]) ).
fof(f803,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),X3)) ),
inference(resolution,[status(thm)],[f682,f558]) ).
fof(f805,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(and(not(X0),not(X1))),and(not(X0),not(X1))),implies(or(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f712,f559]) ).
fof(f806,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),X2)) ),
inference(resolution,[status(thm)],[f712,f593]) ).
fof(f807,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0))),X1)) ),
inference(resolution,[status(thm)],[f712,f594]) ).
fof(f808,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),X3)) ),
inference(resolution,[status(thm)],[f712,f595]) ).
fof(f809,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(not(implies(X0,implies(not(X0),X1)))),not(implies(X0,implies(not(X0),X1)))),X2)) ),
inference(resolution,[status(thm)],[f712,f596]) ).
fof(f810,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(and(not(X0),not(X1)),X2)),implies(and(not(X0),not(X1)),X2)),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))) ),
inference(resolution,[status(thm)],[f712,f679]) ).
fof(f811,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(not(implies(implies(not(X0),X1),X2)),implies(implies(not(X0),X1),X2)),implies(X0,X2))) ),
inference(resolution,[status(thm)],[f712,f682]) ).
fof(f812,plain,
! [X0,X1,X2,X3] :
( ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(not(implies(implies(or(X0,X1),X2),X3)),implies(implies(or(X0,X1),X2),X3)),implies(and(not(X0),not(X1)),X3))) ),
inference(resolution,[status(thm)],[f712,f677]) ).
fof(f813,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(or(X0,X1),and(not(X0),not(X1)))),implies(or(X0,X1),and(not(X0),not(X1)))),and(not(X0),not(X1)))) ),
inference(resolution,[status(thm)],[f712,f557]) ).
fof(f814,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(not(X0),X0)),implies(not(X0),X0)),X0)) ),
inference(resolution,[status(thm)],[f712,f398]) ).
fof(f815,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(X0,X1)),implies(X0,X1)),implies(implies(not(X0),X0),X1))) ),
inference(resolution,[status(thm)],[f712,f680]) ).
fof(f816,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(not(implies(X0,X1)),implies(X0,X1)),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f712,f239]) ).
fof(f817,plain,
! [X0,X1] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(X0),X0),implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f712,f387]) ).
fof(f818,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),implies(or(X0,X1),X2))) ),
inference(forward_demodulation,[status(thm)],[f461,f805]) ).
fof(f819,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(not(X0),X0)),implies(not(X0),X0)),implies(not(X0),X1))) ),
inference(resolution,[status(thm)],[f817,f712]) ).
fof(f820,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(implies(not(X0),X1),X2),implies(implies(not(X0),X0),X2))) ),
inference(resolution,[status(thm)],[f817,f560]) ).
fof(f821,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(X0),X1))
| ~ is_a_theorem(implies(not(X0),X0)) ),
inference(resolution,[status(thm)],[f817,f172]) ).
fof(f822,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(not(X0),X0),implies(not(X0),X1))),X2)) ),
inference(resolution,[status(thm)],[f817,f558]) ).
fof(f827,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(implies(implies(X0,X1),implies(X2,X1)),X3)),implies(implies(implies(X0,X1),implies(X2,X1)),X3)),implies(implies(X2,X0),X3))) ),
inference(resolution,[status(thm)],[f681,f712]) ).
fof(f828,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(implies(implies(X0,X1),X2),X3),implies(implies(implies(implies(X1,X4),implies(X0,X4)),X2),X3))) ),
inference(resolution,[status(thm)],[f681,f560]) ).
fof(f829,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X2,X0),X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),implies(X2,X1)),X3)) ),
inference(resolution,[status(thm)],[f681,f172]) ).
fof(f830,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))),X4)) ),
inference(resolution,[status(thm)],[f681,f558]) ).
fof(f832,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2)))),not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2)))),X3)) ),
inference(resolution,[status(thm)],[f612,f712]) ).
fof(f833,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(and(not(X2),not(X3)),implies(or(X2,X3),X4))),X1))) ),
inference(resolution,[status(thm)],[f612,f560]) ).
fof(f834,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(X3)
| ~ is_a_theorem(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2)))) ),
inference(resolution,[status(thm)],[f612,f172]) ).
fof(f835,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| is_a_theorem(implies(not(implies(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2))),X3)),X4)) ),
inference(resolution,[status(thm)],[f612,f558]) ).
fof(f840,definition,
! [X0,X1,X2] :
( sQ93_spl
<=> ~ is_a_theorem(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2)))) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f841,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| ~ is_a_theorem(not(implies(and(not(X0),not(X1)),implies(or(X0,X1),X2)))) ),
inference(component_clause,[status(thm)],[f840]) ).
fof(f843,plain,
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ59_spl
| sQ89_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f834,f840,f604,f386,f460,f171]) ).
fof(f848,plain,
( sQ26_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f856,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(and(not(X0),not(X1))),X2))
| ~ is_a_theorem(implies(or(X0,X1),and(not(X0),not(X1)))) ),
inference(paramodulation,[status(thm)],[f461,f821]) ).
fof(f857,plain,
! [X0,X1,X2] :
( ~ sQ79_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(or(X0,X1),X2))
| ~ is_a_theorem(implies(or(X0,X1),and(not(X0),not(X1)))) ),
inference(forward_demodulation,[status(thm)],[f461,f856]) ).
fof(f860,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(not(implies(implies(not(X0),X0),X0)),X1))),not(implies(not(implies(implies(not(X0),X0),X0)),X1))),X2)) ),
inference(resolution,[status(thm)],[f599,f712]) ).
fof(f861,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(not(implies(implies(not(X2),X2),X2)),X3)),X1))) ),
inference(resolution,[status(thm)],[f599,f560]) ).
fof(f862,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(X2)
| ~ is_a_theorem(not(implies(not(implies(implies(not(X0),X0),X0)),X1))) ),
inference(resolution,[status(thm)],[f599,f172]) ).
fof(f863,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(not(implies(not(implies(implies(not(X0),X0),X0)),X1)),X2)),X3)) ),
inference(resolution,[status(thm)],[f599,f558]) ).
fof(f865,definition,
! [X0,X1] :
( sQ94_spl
<=> ~ is_a_theorem(not(implies(not(implies(implies(not(X0),X0),X0)),X1))) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f866,plain,
! [X0,X1] :
( ~ sQ94_spl
| ~ is_a_theorem(not(implies(not(implies(implies(not(X0),X0),X0)),X1))) ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f868,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| sQ89_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f862,f865,f604,f397,f386,f171]) ).
fof(f869,plain,
( sQ29_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f874,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(not(implies(X0,implies(not(X0),X1))),X2))),not(implies(not(implies(X0,implies(not(X0),X1))),X2))),X3)) ),
inference(resolution,[status(thm)],[f611,f712]) ).
fof(f875,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(not(implies(X2,implies(not(X2),X3))),X4)),X1))) ),
inference(resolution,[status(thm)],[f611,f560]) ).
fof(f876,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(X3)
| ~ is_a_theorem(not(implies(not(implies(X0,implies(not(X0),X1))),X2))) ),
inference(resolution,[status(thm)],[f611,f172]) ).
fof(f877,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(not(implies(not(implies(not(implies(X0,implies(not(X0),X1))),X2)),X3)),X4)) ),
inference(resolution,[status(thm)],[f611,f558]) ).
fof(f879,definition,
! [X0,X1,X2] :
( sQ95_spl
<=> ~ is_a_theorem(not(implies(not(implies(X0,implies(not(X0),X1))),X2))) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f880,plain,
! [X0,X1,X2] :
( ~ sQ95_spl
| ~ is_a_theorem(not(implies(not(implies(X0,implies(not(X0),X1))),X2))) ),
inference(component_clause,[status(thm)],[f879]) ).
fof(f882,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| sQ89_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f876,f879,f604,f386,f171]) ).
fof(f883,plain,
( sQ32_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f885,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(not(implies(implies(not(X0),X0),X0)),X1),X2),implies(implies(X3,X1),X2))) ),
inference(resolution,[status(thm)],[f678,f560]) ).
fof(f887,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(X0,X1),implies(not(implies(implies(not(X2),X2),X2)),X1))),X3)) ),
inference(resolution,[status(thm)],[f678,f558]) ).
fof(f890,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(not(implies(X0,implies(not(X0),X1))),X2),X3),implies(implies(X4,X2),X3))) ),
inference(resolution,[status(thm)],[f706,f560]) ).
fof(f892,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(X0,X1),implies(not(implies(X2,implies(not(X2),X3))),X1))),X4)) ),
inference(resolution,[status(thm)],[f706,f558]) ).
fof(f894,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(implies(implies(not(X0),X0),X1),X2)),implies(implies(implies(not(X0),X0),X1),X2)),implies(implies(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f711,f712]) ).
fof(f895,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(implies(implies(X0,X1),X2),X3),implies(implies(implies(implies(not(X0),X0),X1),X2),X3))) ),
inference(resolution,[status(thm)],[f711,f560]) ).
fof(f896,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),X2))
| ~ is_a_theorem(implies(implies(implies(not(X0),X0),X1),X2)) ),
inference(resolution,[status(thm)],[f711,f172]) ).
fof(f897,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(implies(implies(implies(not(X0),X0),X1),X2),implies(implies(X0,X1),X2))),X3)) ),
inference(resolution,[status(thm)],[f711,f558]) ).
fof(f901,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)))),not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)))),X2)) ),
inference(resolution,[status(thm)],[f713,f712]) ).
fof(f902,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(X2,X3),implies(implies(not(X2),X2),X3))),X1))) ),
inference(resolution,[status(thm)],[f713,f560]) ).
fof(f903,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(X2)
| ~ is_a_theorem(not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)))) ),
inference(resolution,[status(thm)],[f713,f172]) ).
fof(f904,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1))),X2)),X3)) ),
inference(resolution,[status(thm)],[f713,f558]) ).
fof(f906,definition,
! [X0,X1] :
( sQ96_spl
<=> ~ is_a_theorem(not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)))) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f907,plain,
! [X0,X1] :
( ~ sQ96_spl
| ~ is_a_theorem(not(implies(implies(X0,X1),implies(implies(not(X0),X0),X1)))) ),
inference(component_clause,[status(thm)],[f906]) ).
fof(f909,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| sQ89_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f903,f906,f604,f238,f397,f386,f171]) ).
fof(f910,plain,
( sQ41_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f912,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2),X3),implies(implies(X4,X2),X3))) ),
inference(resolution,[status(thm)],[f728,f560]) ).
fof(f914,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(implies(X0,X1),implies(not(implies(implies(or(X2,X3),and(not(X2),not(X3))),and(not(X2),not(X3)))),X1))),X4)) ),
inference(resolution,[status(thm)],[f728,f558]) ).
fof(f935,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ79_spl
| is_a_theorem(implies(implies(not(not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2))),not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2))),X3)) ),
inference(resolution,[status(thm)],[f730,f712]) ).
fof(f936,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(not(implies(implies(or(X2,X3),and(not(X2),not(X3))),and(not(X2),not(X3)))),X4)),X1))) ),
inference(resolution,[status(thm)],[f730,f560]) ).
fof(f937,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(X3)
| ~ is_a_theorem(not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2))) ),
inference(resolution,[status(thm)],[f730,f172]) ).
fof(f938,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2)),X3)),X4)) ),
inference(resolution,[status(thm)],[f730,f558]) ).
fof(f945,definition,
! [X0,X1,X2] :
( sQ97_spl
<=> ~ is_a_theorem(not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2))) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f946,plain,
! [X0,X1,X2] :
( ~ sQ97_spl
| ~ is_a_theorem(not(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))),X2))) ),
inference(component_clause,[status(thm)],[f945]) ).
fof(f948,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| sQ89_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f937,f945,f604,f397,f460,f386,f171]) ).
fof(f961,plain,
( sQ44_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f627]) ).
fof(f963,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3),X4),implies(implies(X5,X3),X4))) ),
inference(resolution,[status(thm)],[f755,f560]) ).
fof(f965,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(X0,X1),implies(not(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4)))),X1))),X5)) ),
inference(resolution,[status(thm)],[f755,f558]) ).
fof(f969,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(X0,X0)) ),
inference(resolution,[status(thm)],[f802,f398]) ).
fof(f970,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(implies(X0,implies(not(implies(implies(or(X1,X2),and(not(X1),not(X2))),and(not(X1),not(X2)))),X3))) ),
inference(resolution,[status(thm)],[f802,f728]) ).
fof(f971,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(X0,implies(not(implies(implies(not(X1),X1),X1)),X2))) ),
inference(resolution,[status(thm)],[f802,f678]) ).
fof(f972,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(X0,implies(not(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),X4))) ),
inference(resolution,[status(thm)],[f802,f755]) ).
fof(f973,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(X0,implies(not(implies(X1,implies(not(X1),X2))),X3))) ),
inference(resolution,[status(thm)],[f802,f706]) ).
fof(f974,plain,
! [X0,X1] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(X0,implies(implies(not(not(X0)),not(X0)),X1))) ),
inference(resolution,[status(thm)],[f802,f680]) ).
fof(f975,plain,
! [X0,X1,X2] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ59_spl
| is_a_theorem(implies(X0,implies(implies(X1,X2),implies(not(X0),X2)))) ),
inference(resolution,[status(thm)],[f802,f239]) ).
fof(f976,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(X0,implies(not(implies(not(X0),X1)),X2))) ),
inference(resolution,[status(thm)],[f802,f387]) ).
fof(f982,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(X0,X0)),X1)) ),
inference(resolution,[status(thm)],[f969,f558]) ).
fof(f985,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3))),not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3))),X4)) ),
inference(resolution,[status(thm)],[f757,f712]) ).
fof(f986,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(not(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4)))),X5)),X1))) ),
inference(resolution,[status(thm)],[f757,f560]) ).
fof(f987,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(X4)
| ~ is_a_theorem(not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3))) ),
inference(resolution,[status(thm)],[f757,f172]) ).
fof(f988,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3)),X4)),X5)) ),
inference(resolution,[status(thm)],[f757,f558]) ).
fof(f989,definition,
! [X0,X1,X2,X3] :
( sQ98_spl
<=> ~ is_a_theorem(not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3))) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f990,plain,
! [X0,X1,X2,X3] :
( ~ sQ98_spl
| ~ is_a_theorem(not(implies(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))),X3))) ),
inference(component_clause,[status(thm)],[f989]) ).
fof(f992,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| sQ89_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f987,f989,f604,f238,f386,f171]) ).
fof(f993,plain,
( sQ50_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f994,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(implies(and(not(X0),not(X1)),X2),X3)),implies(implies(and(not(X0),not(X1)),X2),X3)),implies(implies(implies(or(X0,X1),X4),X2),X3))) ),
inference(resolution,[status(thm)],[f768,f712]) ).
fof(f995,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(implies(implies(or(X0,X1),X2),X3),X4),X5),implies(implies(implies(and(not(X0),not(X1)),X3),X4),X5))) ),
inference(resolution,[status(thm)],[f768,f560]) ).
fof(f996,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(or(X0,X1),X4),X2),X3))
| ~ is_a_theorem(implies(implies(and(not(X0),not(X1)),X2),X3)) ),
inference(resolution,[status(thm)],[f768,f172]) ).
fof(f997,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| ~ sQ79_spl
| is_a_theorem(implies(not(implies(implies(implies(and(not(X0),not(X1)),X2),X3),implies(implies(implies(or(X0,X1),X4),X2),X3))),X5)) ),
inference(resolution,[status(thm)],[f768,f558]) ).
fof(f1007,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(and(not(X0),not(X1)),implies(implies(not(or(X0,X1)),or(X0,X1)),X2))) ),
inference(resolution,[status(thm)],[f769,f680]) ).
fof(f1008,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(and(not(X0),not(X1)),implies(implies(X2,X3),implies(or(X0,X1),X3)))) ),
inference(resolution,[status(thm)],[f769,f239]) ).
fof(f1009,plain,
! [X0,X1,X2,X3] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ19_spl
| is_a_theorem(implies(and(not(X0),not(X1)),implies(not(implies(or(X0,X1),X2)),X3))) ),
inference(resolution,[status(thm)],[f769,f387]) ).
fof(f1017,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(X0,X0))),not(implies(X0,X0))),X1)) ),
inference(resolution,[status(thm)],[f982,f712]) ).
fof(f1018,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(X2,X2)),X1))) ),
inference(resolution,[status(thm)],[f982,f560]) ).
fof(f1019,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(X1)
| ~ is_a_theorem(not(implies(X0,X0))) ),
inference(resolution,[status(thm)],[f982,f172]) ).
fof(f1020,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(X0,X0)),X1)),X2)) ),
inference(resolution,[status(thm)],[f982,f558]) ).
fof(f1021,definition,
! [X0] :
( sQ99_spl
<=> ~ is_a_theorem(not(implies(X0,X0))) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1022,plain,
! [X0] :
( ~ sQ99_spl
| ~ is_a_theorem(not(implies(X0,X0))) ),
inference(component_clause,[status(thm)],[f1021]) ).
fof(f1024,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| sQ89_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1019,f1021,f604,f238,f397,f386,f171]) ).
fof(f1025,plain,
( sQ66_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f629]) ).
fof(f1028,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ79_spl
| is_a_theorem(implies(implies(not(not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3)))),not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3)))),X4)) ),
inference(resolution,[status(thm)],[f770,f712]) ).
fof(f1029,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ79_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(implies(or(X2,X3),X4),X5),implies(and(not(X2),not(X3)),X5))),X1))) ),
inference(resolution,[status(thm)],[f770,f560]) ).
fof(f1030,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ19_spl
| is_a_theorem(X4)
| ~ is_a_theorem(not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3)))) ),
inference(resolution,[status(thm)],[f770,f172]) ).
fof(f1031,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3))),X4)),X5)) ),
inference(resolution,[status(thm)],[f770,f558]) ).
fof(f1036,definition,
! [X0,X1,X2,X3] :
( sQ100_spl
<=> ~ is_a_theorem(not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3)))) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1037,plain,
! [X0,X1,X2,X3] :
( ~ sQ100_spl
| ~ is_a_theorem(not(implies(implies(implies(or(X0,X1),X2),X3),implies(and(not(X0),not(X1)),X3)))) ),
inference(component_clause,[status(thm)],[f1036]) ).
fof(f1039,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ19_spl
| sQ89_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1030,f1036,f604,f238,f460,f386,f171]) ).
fof(f1044,plain,
( sQ71_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f630]) ).
fof(f1047,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(and(not(X0),not(X1)),implies(not(implies(not(implies(or(X0,X1),X2)),X3)),X4))) ),
inference(resolution,[status(thm)],[f976,f769]) ).
fof(f1048,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(X0,implies(not(implies(not(implies(not(X0),X1)),X2)),X3))) ),
inference(resolution,[status(thm)],[f976,f802]) ).
fof(f1049,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(X0),X0),implies(not(implies(not(X0),X1)),X2))) ),
inference(resolution,[status(thm)],[f976,f712]) ).
fof(f1050,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(not(implies(not(X0),X1)),X2),X3),implies(X0,X3))) ),
inference(resolution,[status(thm)],[f976,f560]) ).
fof(f1051,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(X0),X1)),X2))
| ~ is_a_theorem(X0) ),
inference(resolution,[status(thm)],[f976,f172]) ).
fof(f1052,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(X0,implies(not(implies(not(X0),X1)),X2))),X3)) ),
inference(resolution,[status(thm)],[f976,f558]) ).
fof(f1054,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ79_spl
| is_a_theorem(implies(implies(not(implies(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2),X3)),implies(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2),X3)),implies(implies(and(not(X0),not(X1)),X2),X3))) ),
inference(resolution,[status(thm)],[f779,f712]) ).
fof(f1055,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(implies(implies(and(not(X0),not(X1)),X2),X3),X4),implies(implies(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2),X3),X4))) ),
inference(resolution,[status(thm)],[f779,f560]) ).
fof(f1056,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(and(not(X0),not(X1)),X2),X3))
| ~ is_a_theorem(implies(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2),X3)) ),
inference(resolution,[status(thm)],[f779,f172]) ).
fof(f1057,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(implies(implies(implies(or(X0,X1),and(not(X0),not(X1))),X2),X3),implies(implies(and(not(X0),not(X1)),X2),X3))),X4)) ),
inference(resolution,[status(thm)],[f779,f558]) ).
fof(f1077,plain,
! [X0,X1,X2,X3] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),implies(not(implies(not(and(not(X0),not(X1))),X2)),X3))) ),
inference(resolution,[status(thm)],[f780,f976]) ).
fof(f1082,plain,
! [X0,X1,X2,X3] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(or(X0,X1),and(not(X0),not(X1))),implies(not(implies(or(X0,X1),X2)),X3))) ),
inference(forward_demodulation,[status(thm)],[f461,f1077]) ).
fof(f1090,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ79_spl
| is_a_theorem(implies(implies(not(not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2)))),not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2)))),X3)) ),
inference(resolution,[status(thm)],[f781,f712]) ).
fof(f1091,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(and(not(X2),not(X3)),X4),implies(implies(or(X2,X3),and(not(X2),not(X3))),X4))),X1))) ),
inference(resolution,[status(thm)],[f781,f560]) ).
fof(f1092,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(X3)
| ~ is_a_theorem(not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2)))) ),
inference(resolution,[status(thm)],[f781,f172]) ).
fof(f1093,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2))),X3)),X4)) ),
inference(resolution,[status(thm)],[f781,f558]) ).
fof(f1100,definition,
! [X0,X1,X2] :
( sQ101_spl
<=> ~ is_a_theorem(not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2)))) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1101,plain,
! [X0,X1,X2] :
( ~ sQ101_spl
| ~ is_a_theorem(not(implies(implies(and(not(X0),not(X1)),X2),implies(implies(or(X0,X1),and(not(X0),not(X1))),X2)))) ),
inference(component_clause,[status(thm)],[f1100]) ).
fof(f1103,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| sQ89_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1092,f1100,f604,f238,f397,f460,f386,f171]) ).
fof(f1116,plain,
( sQ74_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f1117,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(implies(X0,X1),X2)),implies(implies(X0,X1),X2)),implies(implies(implies(not(X0),X3),X1),X2))) ),
inference(resolution,[status(thm)],[f801,f712]) ).
fof(f1118,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(implies(implies(not(X0),X1),X2),X3),X4),implies(implies(implies(X0,X2),X3),X4))) ),
inference(resolution,[status(thm)],[f801,f560]) ).
fof(f1119,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(implies(not(X0),X3),X1),X2))
| ~ is_a_theorem(implies(implies(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f801,f172]) ).
fof(f1120,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(implies(X0,X1),X2),implies(implies(implies(not(X0),X3),X1),X2))),X4)) ),
inference(resolution,[status(thm)],[f801,f558]) ).
fof(f1124,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)))),not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)))),X3)) ),
inference(resolution,[status(thm)],[f803,f712]) ).
fof(f1125,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(implies(not(X2),X3),X4),implies(X2,X4))),X1))) ),
inference(resolution,[status(thm)],[f803,f560]) ).
fof(f1126,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(X3)
| ~ is_a_theorem(not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f803,f172]) ).
fof(f1127,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2))),X3)),X4)) ),
inference(resolution,[status(thm)],[f803,f558]) ).
fof(f1129,definition,
! [X0,X1,X2] :
( sQ102_spl
<=> ~ is_a_theorem(not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)))) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1130,plain,
! [X0,X1,X2] :
( ~ sQ102_spl
| ~ is_a_theorem(not(implies(implies(implies(not(X0),X1),X2),implies(X0,X2)))) ),
inference(component_clause,[status(thm)],[f1129]) ).
fof(f1132,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| sQ89_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f1126,f1129,f604,f238,f386,f171]) ).
fof(f1133,plain,
( sQ11_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f1134,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(not(implies(implies(implies(X0,X1),X2),X3)),implies(implies(implies(X0,X1),X2),X3)),implies(implies(implies(implies(X1,X4),implies(X0,X4)),X2),X3))) ),
inference(resolution,[status(thm)],[f828,f712]) ).
fof(f1135,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),X4),X5),implies(implies(implies(implies(X2,X0),X3),X4),X5))) ),
inference(resolution,[status(thm)],[f828,f560]) ).
fof(f1136,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(implies(implies(X1,X4),implies(X0,X4)),X2),X3))
| ~ is_a_theorem(implies(implies(implies(X0,X1),X2),X3)) ),
inference(resolution,[status(thm)],[f828,f172]) ).
fof(f1137,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(implies(implies(X0,X1),X2),X3),implies(implies(implies(implies(X1,X4),implies(X0,X4)),X2),X3))),X5)) ),
inference(resolution,[status(thm)],[f828,f558]) ).
fof(f1138,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,and(not(X1),not(X2))),implies(implies(implies(or(X1,X2),X3),X4),implies(X0,X4)))) ),
inference(resolution,[status(thm)],[f829,f768]) ).
fof(f1139,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,implies(or(X1,X2),and(not(X1),not(X2)))),implies(implies(and(not(X1),not(X2)),X3),implies(X0,X3)))) ),
inference(resolution,[status(thm)],[f829,f779]) ).
fof(f1140,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,implies(not(X1),X1)),implies(implies(X1,X2),implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f829,f711]) ).
fof(f1141,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(X3,X1),implies(X0,implies(X3,X2))))) ),
inference(resolution,[status(thm)],[f829,f681]) ).
fof(f1142,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,implies(X1,X2)),implies(implies(implies(implies(X2,X3),implies(X1,X3)),X4),implies(X0,X4)))) ),
inference(resolution,[status(thm)],[f829,f828]) ).
fof(f1143,plain,
! [X0,X1,X2] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,not(X1)),implies(X1,implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f829,f682]) ).
fof(f1144,plain,
! [X0,X1,X2,X3] :
( ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,or(X1,X2)),implies(and(not(X1),not(X2)),implies(X0,X3)))) ),
inference(resolution,[status(thm)],[f829,f677]) ).
fof(f1145,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(implies(not(X1),X2),X3),implies(X0,X3)))) ),
inference(resolution,[status(thm)],[f829,f801]) ).
fof(f1146,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(not(implies(X1,X2)),implies(X1,X2)),implies(X0,X2)))) ),
inference(resolution,[status(thm)],[f829,f680]) ).
fof(f1147,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| ~ sQ1_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(implies(X0,X2),X3),implies(implies(X1,X2),X3)))) ),
inference(resolution,[status(thm)],[f829,f239]) ).
fof(f1148,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(not(implies(implies(X1,X2),implies(X0,X2))),X3)),X4))) ),
inference(resolution,[status(thm)],[f829,f976]) ).
fof(f1149,plain,
! [X0,X1,X2,X3] :
( ~ sQ59_spl
| ~ sQ1_spl
| ~ sQ19_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(X1,X2),implies(X0,X2))),X3))) ),
inference(resolution,[status(thm)],[f829,f387]) ).
fof(f1153,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))),not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))),X4)) ),
inference(resolution,[status(thm)],[f830,f712]) ).
fof(f1154,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(implies(implies(implies(X2,X3),implies(X4,X3)),X5),implies(implies(X4,X2),X5))),X1))) ),
inference(resolution,[status(thm)],[f830,f560]) ).
fof(f1155,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(X4)
| ~ is_a_theorem(not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))) ),
inference(resolution,[status(thm)],[f830,f172]) ).
fof(f1156,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3))),X4)),X5)) ),
inference(resolution,[status(thm)],[f830,f558]) ).
fof(f1157,definition,
! [X0,X1,X2,X3] :
( sQ103_spl
<=> ~ is_a_theorem(not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1158,plain,
! [X0,X1,X2,X3] :
( ~ sQ103_spl
| ~ is_a_theorem(not(implies(implies(implies(implies(X0,X1),implies(X2,X1)),X3),implies(implies(X2,X0),X3)))) ),
inference(component_clause,[status(thm)],[f1157]) ).
fof(f1160,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| sQ89_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1155,f1157,f604,f238,f386,f171]) ).
fof(f1161,plain,
( sQ17_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f1165,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(or(X0,X1),and(not(X0),not(X1)))),implies(or(X0,X1),and(not(X0),not(X1)))),implies(or(X0,X1),X2))) ),
inference(resolution,[status(thm)],[f818,f712]) ).
fof(f1166,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(implies(or(X0,X1),X2),X3),implies(implies(or(X0,X1),and(not(X0),not(X1))),X3))) ),
inference(resolution,[status(thm)],[f818,f560]) ).
fof(f1168,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),implies(or(X0,X1),X2))),X3)) ),
inference(resolution,[status(thm)],[f818,f558]) ).
fof(f1188,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))))),implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))))),X2)) ),
inference(resolution,[status(thm)],[f806,f712]) ).
fof(f1189,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(not(not(implies(implies(or(X2,X3),and(not(X2),not(X3))),and(not(X2),not(X3))))),not(implies(implies(or(X2,X3),and(not(X2),not(X3))),and(not(X2),not(X3))))),X1))) ),
inference(resolution,[status(thm)],[f806,f560]) ).
fof(f1190,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))))) ),
inference(resolution,[status(thm)],[f806,f172]) ).
fof(f1191,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),X2)),X3)) ),
inference(resolution,[status(thm)],[f806,f558]) ).
fof(f1204,definition,
! [X0,X1] :
( sQ104_spl
<=> ~ is_a_theorem(implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))))) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1205,plain,
! [X0,X1] :
( ~ sQ104_spl
| ~ is_a_theorem(implies(not(not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1))))),not(implies(implies(or(X0,X1),and(not(X0),not(X1))),and(not(X0),not(X1)))))) ),
inference(component_clause,[status(thm)],[f1204]) ).
fof(f1207,plain,
( ~ sQ1_spl
| ~ sQ79_spl
| ~ sQ62_spl
| ~ sQ59_spl
| ~ sQ19_spl
| sQ89_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f1190,f1204,f604,f238,f386,f397,f460,f171]) ).
fof(f1268,plain,
( sQ38_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f634]) ).
fof(f1273,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(not(implies(not(implies(X0,X0)),X1))),not(implies(not(implies(X0,X0)),X1))),X2)) ),
inference(resolution,[status(thm)],[f1020,f712]) ).
fof(f1274,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(not(implies(not(implies(X2,X2)),X3)),X1))) ),
inference(resolution,[status(thm)],[f1020,f560]) ).
fof(f1275,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(X2)
| ~ is_a_theorem(not(implies(not(implies(X0,X0)),X1))) ),
inference(resolution,[status(thm)],[f1020,f172]) ).
fof(f1276,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(not(implies(not(implies(X0,X0)),X1)),X2)),X3)) ),
inference(resolution,[status(thm)],[f1020,f558]) ).
fof(f1277,definition,
! [X0,X1] :
( sQ105_spl
<=> ~ is_a_theorem(not(implies(not(implies(X0,X0)),X1))) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1278,plain,
! [X0,X1] :
( ~ sQ105_spl
| ~ is_a_theorem(not(implies(not(implies(X0,X0)),X1))) ),
inference(component_clause,[status(thm)],[f1277]) ).
fof(f1280,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| sQ89_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1275,f1277,f604,f238,f397,f386,f171]) ).
fof(f1281,plain,
( sQ47_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f635]) ).
fof(f1285,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0)))),implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0)))),X1)) ),
inference(resolution,[status(thm)],[f807,f712]) ).
fof(f1286,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ62_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(not(not(implies(implies(not(X2),X2),X2))),not(implies(implies(not(X2),X2),X2))),X1))) ),
inference(resolution,[status(thm)],[f807,f560]) ).
fof(f1287,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ59_spl
| ~ sQ19_spl
| is_a_theorem(X1)
| ~ is_a_theorem(implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0)))) ),
inference(resolution,[status(thm)],[f807,f172]) ).
fof(f1288,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0))),X1)),X2)) ),
inference(resolution,[status(thm)],[f807,f558]) ).
fof(f1291,definition,
! [X0] :
( sQ106_spl
<=> ~ is_a_theorem(implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0)))) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1292,plain,
! [X0] :
( ~ sQ106_spl
| ~ is_a_theorem(implies(not(not(implies(implies(not(X0),X0),X0))),not(implies(implies(not(X0),X0),X0)))) ),
inference(component_clause,[status(thm)],[f1291]) ).
fof(f1294,plain,
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ59_spl
| ~ sQ19_spl
| sQ89_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1287,f1291,f604,f238,f386,f397,f171]) ).
fof(f1297,plain,
( sQ55_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f1301,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))),X3)) ),
inference(resolution,[status(thm)],[f808,f712]) ).
fof(f1302,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(not(not(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))))),not(implies(implies(X2,X3),implies(implies(X3,X4),implies(X2,X4))))),X1))) ),
inference(resolution,[status(thm)],[f808,f560]) ).
fof(f1303,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(X3)
| ~ is_a_theorem(implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))) ),
inference(resolution,[status(thm)],[f808,f172]) ).
fof(f1304,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ19_spl
| ~ sQ62_spl
| is_a_theorem(implies(not(implies(implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),X3)),X4)) ),
inference(resolution,[status(thm)],[f808,f558]) ).
fof(f1305,definition,
! [X0,X1,X2] :
( sQ107_spl
<=> ~ is_a_theorem(implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
! [X0,X1,X2] :
( ~ sQ107_spl
| ~ is_a_theorem(implies(not(not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2))))),not(implies(implies(X0,X1),implies(implies(X1,X2),implies(X0,X2)))))) ),
inference(component_clause,[status(thm)],[f1305]) ).
fof(f1308,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| sQ89_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1303,f1305,f604,f397,f386,f238,f171]) ).
fof(f1309,plain,
( sQ77_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f1313,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ62_spl
| ~ sQ19_spl
| ~ sQ59_spl
| is_a_theorem(implies(implies(not(implies(not(not(implies(X0,implies(not(X0),X1)))),not(implies(X0,implies(not(X0),X1))))),implies(not(not(implies(X0,implies(not(X0),X1)))),not(implies(X0,implies(not(X0),X1))))),X2)) ),
inference(resolution,[status(thm)],[f809,f712]) ).
fof(f1314,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ62_spl
| is_a_theorem(implies(implies(X0,X1),implies(implies(not(not(implies(X2,implies(not(X2),X3)))),not(implies(X2,implies(not(X2),X3)))),X1))) ),
inference(resolution,[status(thm)],[f809,f560]) ).
fof(f1315,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(X2)
| ~ is_a_theorem(implies(not(not(implies(X0,implies(not(X0),X1)))),not(implies(X0,implies(not(X0),X1))))) ),
inference(resolution,[status(thm)],[f809,f172]) ).
fof(f1316,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| is_a_theorem(implies(not(implies(implies(not(not(implies(X0,implies(not(X0),X1)))),not(implies(X0,implies(not(X0),X1)))),X2)),X3)) ),
inference(resolution,[status(thm)],[f809,f558]) ).
fof(f1319,definition,
! [X0,X1] :
( sQ108_spl
<=> ~ is_a_theorem(implies(not(not(implies(X0,implies(not(X0),X1)))),not(implies(X0,implies(not(X0),X1))))) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1322,plain,
( ~ sQ1_spl
| ~ sQ59_spl
| ~ sQ62_spl
| ~ sQ19_spl
| sQ89_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1315,f1319,f604,f238,f397,f386,f171]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ5_spl
| sQ6_spl
| sQ9_spl
| sQ10_spl
| sQ11_spl
| sQ12_spl
| sQ13_spl
| sQ14_spl
| sQ15_spl
| sQ16_spl
| sQ17_spl
| sQ18_spl
| sQ19_spl
| sQ20_spl
| sQ21_spl
| sQ22_spl
| sQ23_spl
| sQ24_spl
| sQ25_spl
| sQ26_spl
| sQ27_spl
| sQ28_spl
| sQ29_spl
| sQ30_spl
| sQ31_spl
| sQ32_spl
| sQ33_spl
| sQ34_spl
| sQ35_spl
| sQ36_spl
| sQ37_spl
| sQ38_spl
| sQ39_spl
| sQ40_spl
| sQ41_spl
| sQ42_spl
| sQ43_spl
| sQ44_spl
| sQ45_spl
| sQ46_spl
| sQ47_spl
| sQ48_spl
| sQ49_spl
| sQ50_spl
| sQ51_spl
| sQ52_spl
| sQ53_spl
| sQ54_spl
| sQ55_spl
| sQ56_spl
| sQ57_spl
| sQ58_spl
| sQ59_spl
| sQ60_spl
| sQ61_spl
| sQ62_spl
| sQ63_spl
| sQ64_spl
| sQ65_spl
| sQ66_spl
| sQ67_spl
| sQ68_spl
| sQ69_spl
| sQ70_spl
| sQ71_spl
| sQ72_spl
| sQ73_spl
| sQ74_spl
| sQ75_spl
| sQ76_spl
| sQ77_spl
| sQ78_spl
| sQ79_spl
| ~ sQ80_spl
| ~ sQ82_spl
| ~ sQ84_spl
| sQ86_spl
| sQ87_spl
| sQ89_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL908+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 01:13:51 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.51 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.17/0.51 % SZS output start Saturation for theBenchmark
% See solution above
% 0.17/0.54 % Elapsed time: 0.095958 seconds
% 0.17/0.54 % CPU time: 0.526587 seconds
% 0.17/0.54 % Total memory used: 17.639 MB
% 0.17/0.54 % Net memory used: 16.173 MB
%------------------------------------------------------------------------------