%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL526+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 08:49:27 AM UTC 2026
% Result : Theorem 120.11s 120.47s
% Output : Proof 120.58s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(modus_ponens,axiom,
( modus_ponens
<=> ! [X,Y] :
( ( is_a_theorem(implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('LCL006+0.ax',modus_ponens) ).
fof(substitution_of_equivalents,axiom,
( substitution_of_equivalents
<=> ! [X,Y] :
( is_a_theorem(equiv(X,Y))
=> X = Y ) ),
file('LCL006+0.ax',substitution_of_equivalents) ).
fof(modus_tollens,axiom,
( modus_tollens
<=> ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) ),
file('LCL006+0.ax',modus_tollens) ).
fof(implies_1,axiom,
( implies_1
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,X))) ),
file('LCL006+0.ax',implies_1) ).
fof(implies_2,axiom,
( implies_2
<=> ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) ),
file('LCL006+0.ax',implies_2) ).
fof(implies_3,axiom,
( implies_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) ),
file('LCL006+0.ax',implies_3) ).
fof(and_1,axiom,
( and_1
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),X)) ),
file('LCL006+0.ax',and_1) ).
fof(and_2,axiom,
( and_2
<=> ! [X,Y] : is_a_theorem(implies(and(X,Y),Y)) ),
file('LCL006+0.ax',and_2) ).
fof(and_3,axiom,
( and_3
<=> ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y)))) ),
file('LCL006+0.ax',and_3) ).
fof(or_1,axiom,
( or_1
<=> ! [X,Y] : is_a_theorem(implies(X,or(X,Y))) ),
file('LCL006+0.ax',or_1) ).
fof(or_2,axiom,
( or_2
<=> ! [X,Y] : is_a_theorem(implies(Y,or(X,Y))) ),
file('LCL006+0.ax',or_2) ).
fof(or_3,axiom,
( or_3
<=> ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) ),
file('LCL006+0.ax',or_3) ).
fof(equivalence_1,axiom,
( equivalence_1
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y))) ),
file('LCL006+0.ax',equivalence_1) ).
fof(equivalence_2,axiom,
( equivalence_2
<=> ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X))) ),
file('LCL006+0.ax',equivalence_2) ).
fof(equivalence_3,axiom,
( equivalence_3
<=> ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) ),
file('LCL006+0.ax',equivalence_3) ).
fof(kn1,axiom,
( kn1
<=> ! [P] : is_a_theorem(implies(P,and(P,P))) ),
file('LCL006+0.ax',kn1) ).
fof(kn2,axiom,
( kn2
<=> ! [P,Q] : is_a_theorem(implies(and(P,Q),P)) ),
file('LCL006+0.ax',kn2) ).
fof(kn3,axiom,
( kn3
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) ),
file('LCL006+0.ax',kn3) ).
fof(cn1,axiom,
( cn1
<=> ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) ),
file('LCL006+0.ax',cn1) ).
fof(cn2,axiom,
( cn2
<=> ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q))) ),
file('LCL006+0.ax',cn2) ).
fof(cn3,axiom,
( cn3
<=> ! [P] : is_a_theorem(implies(implies(not(P),P),P)) ),
file('LCL006+0.ax',cn3) ).
fof(r1,axiom,
( r1
<=> ! [P] : is_a_theorem(implies(or(P,P),P)) ),
file('LCL006+0.ax',r1) ).
fof(r2,axiom,
( r2
<=> ! [P,Q] : is_a_theorem(implies(Q,or(P,Q))) ),
file('LCL006+0.ax',r2) ).
fof(r3,axiom,
( r3
<=> ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P))) ),
file('LCL006+0.ax',r3) ).
fof(r4,axiom,
( r4
<=> ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) ),
file('LCL006+0.ax',r4) ).
fof(r5,axiom,
( r5
<=> ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) ),
file('LCL006+0.ax',r5) ).
fof(op_or,axiom,
( op_or
=> ! [X,Y] : or(X,Y) = not(and(not(X),not(Y))) ),
file('LCL006+1.ax',op_or) ).
fof(op_and,axiom,
( op_and
=> ! [X,Y] : and(X,Y) = not(or(not(X),not(Y))) ),
file('LCL006+1.ax',op_and) ).
fof(op_implies_and,axiom,
( op_implies_and
=> ! [X,Y] : implies(X,Y) = not(and(X,not(Y))) ),
file('LCL006+1.ax',op_implies_and) ).
fof(op_implies_or,axiom,
( op_implies_or
=> ! [X,Y] : implies(X,Y) = or(not(X),Y) ),
file('LCL006+1.ax',op_implies_or) ).
fof(op_equiv,axiom,
( op_equiv
=> ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X)) ),
file('LCL006+1.ax',op_equiv) ).
fof(hilbert_op_or,axiom,
op_or,
file('LCL006+2.ax',hilbert_op_or) ).
fof(hilbert_op_implies_and,axiom,
op_implies_and,
file('LCL006+2.ax',hilbert_op_implies_and) ).
fof(hilbert_op_equiv,axiom,
op_equiv,
file('LCL006+2.ax',hilbert_op_equiv) ).
fof(hilbert_modus_ponens,axiom,
modus_ponens,
file('LCL006+2.ax',hilbert_modus_ponens) ).
fof(hilbert_modus_tollens,axiom,
modus_tollens,
file('LCL006+2.ax',hilbert_modus_tollens) ).
fof(hilbert_implies_1,axiom,
implies_1,
file('LCL006+2.ax',hilbert_implies_1) ).
fof(hilbert_implies_2,axiom,
implies_2,
file('LCL006+2.ax',hilbert_implies_2) ).
fof(hilbert_implies_3,axiom,
implies_3,
file('LCL006+2.ax',hilbert_implies_3) ).
fof(hilbert_and_1,axiom,
and_1,
file('LCL006+2.ax',hilbert_and_1) ).
fof(hilbert_and_2,axiom,
and_2,
file('LCL006+2.ax',hilbert_and_2) ).
fof(hilbert_and_3,axiom,
and_3,
file('LCL006+2.ax',hilbert_and_3) ).
fof(hilbert_or_1,axiom,
or_1,
file('LCL006+2.ax',hilbert_or_1) ).
fof(hilbert_or_2,axiom,
or_2,
file('LCL006+2.ax',hilbert_or_2) ).
fof(hilbert_or_3,axiom,
or_3,
file('LCL006+2.ax',hilbert_or_3) ).
fof(hilbert_equivalence_1,axiom,
equivalence_1,
file('LCL006+2.ax',hilbert_equivalence_1) ).
fof(hilbert_equivalence_2,axiom,
equivalence_2,
file('LCL006+2.ax',hilbert_equivalence_2) ).
fof(hilbert_equivalence_3,axiom,
equivalence_3,
file('LCL006+2.ax',hilbert_equivalence_3) ).
fof(use_substitution_of_equivalents,axiom,
substitution_of_equivalents,
file('LCL006+2.ax',use_substitution_of_equivalents) ).
fof(necessitation,axiom,
( necessitation
<=> ! [X] :
( is_a_theorem(X)
=> is_a_theorem(necessarily(X)) ) ),
file('LCL007+0.ax',necessitation) ).
fof(modus_ponens_strict_implies,axiom,
( modus_ponens_strict_implies
<=> ! [X,Y] :
( ( is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) )
=> is_a_theorem(Y) ) ),
file('LCL007+0.ax',modus_ponens_strict_implies) ).
fof(adjunction,axiom,
( adjunction
<=> ! [X,Y] :
( ( is_a_theorem(Y)
& is_a_theorem(X) )
=> is_a_theorem(and(X,Y)) ) ),
file('LCL007+0.ax',adjunction) ).
fof(substitution_strict_equiv,axiom,
( substitution_strict_equiv
<=> ! [X,Y] :
( is_a_theorem(strict_equiv(X,Y))
=> X = Y ) ),
file('LCL007+0.ax',substitution_strict_equiv) ).
fof(axiom_K,axiom,
( axiom_K
<=> ! [X,Y] : is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y)))) ),
file('LCL007+0.ax',axiom_K) ).
fof(axiom_M,axiom,
( axiom_M
<=> ! [X] : is_a_theorem(implies(necessarily(X),X)) ),
file('LCL007+0.ax',axiom_M) ).
fof(axiom_4,axiom,
( axiom_4
<=> ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) ),
file('LCL007+0.ax',axiom_4) ).
fof(axiom_B,axiom,
( axiom_B
<=> ! [X] : is_a_theorem(implies(X,necessarily(possibly(X)))) ),
file('LCL007+0.ax',axiom_B) ).
fof(axiom_5,axiom,
( axiom_5
<=> ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) ),
file('LCL007+0.ax',axiom_5) ).
fof(axiom_s1,axiom,
( axiom_s1
<=> ! [X,Y,Z] : is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z)))) ),
file('LCL007+0.ax',axiom_s1) ).
fof(axiom_s2,axiom,
( axiom_s2
<=> ! [P,Q] : is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q)))) ),
file('LCL007+0.ax',axiom_s2) ).
fof(axiom_s3,axiom,
( axiom_s3
<=> ! [X,Y] : is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X))))) ),
file('LCL007+0.ax',axiom_s3) ).
fof(axiom_s4,axiom,
( axiom_s4
<=> ! [X] : is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X)))) ),
file('LCL007+0.ax',axiom_s4) ).
fof(axiom_m1,axiom,
( axiom_m1
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X))) ),
file('LCL007+0.ax',axiom_m1) ).
fof(axiom_m2,axiom,
( axiom_m2
<=> ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X)) ),
file('LCL007+0.ax',axiom_m2) ).
fof(axiom_m3,axiom,
( axiom_m3
<=> ! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z)))) ),
file('LCL007+0.ax',axiom_m3) ).
fof(axiom_m4,axiom,
( axiom_m4
<=> ! [X] : is_a_theorem(strict_implies(X,and(X,X))) ),
file('LCL007+0.ax',axiom_m4) ).
fof(axiom_m5,axiom,
( axiom_m5
<=> ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) ),
file('LCL007+0.ax',axiom_m5) ).
fof(axiom_m6,axiom,
( axiom_m6
<=> ! [X] : is_a_theorem(strict_implies(X,possibly(X))) ),
file('LCL007+0.ax',axiom_m6) ).
fof(axiom_m7,axiom,
( axiom_m7
<=> ! [P,Q] : is_a_theorem(strict_implies(possibly(and(P,Q)),P)) ),
file('LCL007+0.ax',axiom_m7) ).
fof(axiom_m8,axiom,
( axiom_m8
<=> ! [P,Q] : is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q)))) ),
file('LCL007+0.ax',axiom_m8) ).
fof(axiom_m9,axiom,
( axiom_m9
<=> ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) ),
file('LCL007+0.ax',axiom_m9) ).
fof(axiom_m10,axiom,
( axiom_m10
<=> ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) ),
file('LCL007+0.ax',axiom_m10) ).
fof(op_possibly,axiom,
( op_possibly
=> ! [X] : possibly(X) = not(necessarily(not(X))) ),
file('LCL007+1.ax',op_possibly) ).
fof(op_necessarily,axiom,
( op_necessarily
=> ! [X] : necessarily(X) = not(possibly(not(X))) ),
file('LCL007+1.ax',op_necessarily) ).
fof(op_strict_implies,axiom,
( op_strict_implies
=> ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y)) ),
file('LCL007+1.ax',op_strict_implies) ).
fof(op_strict_equiv,axiom,
( op_strict_equiv
=> ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X)) ),
file('LCL007+1.ax',op_strict_equiv) ).
fof(km5_op_possibly,axiom,
op_possibly,
file('LCL007+2.ax',km5_op_possibly) ).
fof(km5_necessitation,axiom,
necessitation,
file('LCL007+2.ax',km5_necessitation) ).
fof(km5_axiom_K,axiom,
axiom_K,
file('LCL007+2.ax',km5_axiom_K) ).
fof(km5_axiom_M,axiom,
axiom_M,
file('LCL007+2.ax',km5_axiom_M) ).
fof(km5_axiom_5,axiom,
axiom_5,
file('LCL007+2.ax',km5_axiom_5) ).
fof(s1_0_op_possibly,axiom,
op_possibly,
file('theBenchmark.p',s1_0_op_possibly) ).
fof(s1_0_op_or,axiom,
op_or,
file('theBenchmark.p',s1_0_op_or) ).
fof(s1_0_op_implies,axiom,
op_implies,
file('theBenchmark.p',s1_0_op_implies) ).
fof(s1_0_op_strict_implies,axiom,
op_strict_implies,
file('theBenchmark.p',s1_0_op_strict_implies) ).
fof(s1_0_op_equiv,axiom,
op_equiv,
file('theBenchmark.p',s1_0_op_equiv) ).
fof(s1_0_op_strict_equiv,axiom,
op_strict_equiv,
file('theBenchmark.p',s1_0_op_strict_equiv) ).
fof(s1_0_substitution_strict_equiv,conjecture,
substitution_strict_equiv,
file('theBenchmark.p',s1_0_substitution_strict_equiv) ).
fof(f_1_1,plain,
( ( modus_ponens
| ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(implies(X,Y))
& is_a_theorem(X) ) )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens ) ),
inference(fof_nnf,[status(thm)],[modus_ponens]) ).
fof(f_1_2,plain,
( ( modus_ponens
| ? [U_3,U_2] :
( ~ is_a_theorem(U_2)
& is_a_theorem(implies(U_3,U_2))
& is_a_theorem(U_3) ) )
& ( ! [U_1,U_0] :
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1) )
| ~ modus_ponens ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ( modus_ponens
| ? [U_2] :
( ~ is_a_theorem(U_2)
& is_a_theorem(implies(sK1,U_2))
& is_a_theorem(sK1) ) )
& ( ! [U_1,U_0] :
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_2]) ).
fof(f_1_4,plain,
( ( modus_ponens
| ( ~ is_a_theorem(sK2)
& is_a_theorem(implies(sK1,sK2))
& is_a_theorem(sK1) ) )
& ( ! [U_1,U_0] :
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1) )
| ~ modus_ponens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_1_3]) ).
cnf(f_1_5,plain,
( is_a_theorem(U_0)
| ~ is_a_theorem(implies(U_1,U_0))
| ~ is_a_theorem(U_1)
| ~ modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( is_a_theorem(sK1)
| modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_7,plain,
( is_a_theorem(implies(sK1,sK2))
| modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_8,plain,
( ~ is_a_theorem(sK2)
| modus_ponens ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,plain,
( ( substitution_of_equivalents
| ? [X,Y] :
( X != Y
& is_a_theorem(equiv(X,Y)) ) )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(equiv(X,Y)) )
| ~ substitution_of_equivalents ) ),
inference(fof_nnf,[status(thm)],[substitution_of_equivalents]) ).
fof(f_2_2,plain,
( ( substitution_of_equivalents
| ? [U_7,U_6] :
( U_7 != U_6
& is_a_theorem(equiv(U_7,U_6)) ) )
& ( ! [U_5,U_4] :
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4)) )
| ~ substitution_of_equivalents ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ( substitution_of_equivalents
| ? [U_6] :
( sK3 != U_6
& is_a_theorem(equiv(sK3,U_6)) ) )
& ( ! [U_5,U_4] :
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_7,sK3)],[f_2_2]) ).
fof(f_2_4,plain,
( ( substitution_of_equivalents
| ( sK3 != sK4
& is_a_theorem(equiv(sK3,sK4)) ) )
& ( ! [U_5,U_4] :
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4)) )
| ~ substitution_of_equivalents ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_6,sK4)],[f_2_3]) ).
cnf(f_2_5,plain,
( U_5 = U_4
| ~ is_a_theorem(equiv(U_5,U_4))
| ~ substitution_of_equivalents ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( is_a_theorem(equiv(sK3,sK4))
| substitution_of_equivalents ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( sK3 != sK4
| substitution_of_equivalents ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,plain,
( ( modus_tollens
| ? [X,Y] : ~ is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))
| ~ modus_tollens ) ),
inference(fof_nnf,[status(thm)],[modus_tollens]) ).
fof(f_3_2,plain,
( ( modus_tollens
| ? [U_11,U_10] : ~ is_a_theorem(implies(implies(not(U_10),not(U_11)),implies(U_11,U_10))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ( modus_tollens
| ? [U_10] : ~ is_a_theorem(implies(implies(not(U_10),not(sK5)),implies(sK5,U_10))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_11,sK5)],[f_3_2]) ).
fof(f_3_4,plain,
( ( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) )
& ( ! [U_9,U_8] : is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_10,sK6)],[f_3_3]) ).
cnf(f_3_5,plain,
( is_a_theorem(implies(implies(not(U_8),not(U_9)),implies(U_9,U_8)))
| ~ modus_tollens ),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( modus_tollens
| ~ is_a_theorem(implies(implies(not(sK6),not(sK5)),implies(sK5,sK6))) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
( ( implies_1
| ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,X))) )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,X)))
| ~ implies_1 ) ),
inference(fof_nnf,[status(thm)],[implies_1]) ).
fof(f_4_2,plain,
( ( implies_1
| ? [U_15,U_14] : ~ is_a_theorem(implies(U_15,implies(U_14,U_15))) )
& ( ! [U_13,U_12] : is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ( implies_1
| ? [U_14] : ~ is_a_theorem(implies(sK7,implies(U_14,sK7))) )
& ( ! [U_13,U_12] : is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_15,sK7)],[f_4_2]) ).
fof(f_4_4,plain,
( ( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) )
& ( ! [U_13,U_12] : is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_14,sK8)],[f_4_3]) ).
cnf(f_4_5,plain,
( is_a_theorem(implies(U_13,implies(U_12,U_13)))
| ~ implies_1 ),
inference(clausify,[status(thm)],[f_4_4]) ).
cnf(f_4_6,plain,
( implies_1
| ~ is_a_theorem(implies(sK7,implies(sK8,sK7))) ),
inference(clausify,[status(thm)],[f_4_4]) ).
fof(f_5_1,plain,
( ( implies_2
| ? [X,Y] : ~ is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))
| ~ implies_2 ) ),
inference(fof_nnf,[status(thm)],[implies_2]) ).
fof(f_5_2,plain,
( ( implies_2
| ? [U_19,U_18] : ~ is_a_theorem(implies(implies(U_19,implies(U_19,U_18)),implies(U_19,U_18))) )
& ( ! [U_17,U_16] : is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ( implies_2
| ? [U_18] : ~ is_a_theorem(implies(implies(sK9,implies(sK9,U_18)),implies(sK9,U_18))) )
& ( ! [U_17,U_16] : is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_19,sK9)],[f_5_2]) ).
fof(f_5_4,plain,
( ( implies_2
| ~ is_a_theorem(implies(implies(sK9,implies(sK9,sK10)),implies(sK9,sK10))) )
& ( ! [U_17,U_16] : is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_18,sK10)],[f_5_3]) ).
cnf(f_5_5,plain,
( is_a_theorem(implies(implies(U_17,implies(U_17,U_16)),implies(U_17,U_16)))
| ~ implies_2 ),
inference(clausify,[status(thm)],[f_5_4]) ).
cnf(f_5_6,plain,
( implies_2
| ~ is_a_theorem(implies(implies(sK9,implies(sK9,sK10)),implies(sK9,sK10))) ),
inference(clausify,[status(thm)],[f_5_4]) ).
fof(f_6_1,plain,
( ( implies_3
| ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z)))) )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,Z),implies(X,Z))))
| ~ implies_3 ) ),
inference(fof_nnf,[status(thm)],[implies_3]) ).
fof(f_6_2,plain,
( ( implies_3
| ? [U_25,U_24,U_23] : ~ is_a_theorem(implies(implies(U_25,U_24),implies(implies(U_24,U_23),implies(U_25,U_23)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ( implies_3
| ? [U_24,U_23] : ~ is_a_theorem(implies(implies(sK11,U_24),implies(implies(U_24,U_23),implies(sK11,U_23)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_25,sK11)],[f_6_2]) ).
fof(f_6_4,plain,
( ( implies_3
| ? [U_23] : ~ is_a_theorem(implies(implies(sK11,sK12),implies(implies(sK12,U_23),implies(sK11,U_23)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_24,sK12)],[f_6_3]) ).
fof(f_6_5,plain,
( ( implies_3
| ~ is_a_theorem(implies(implies(sK11,sK12),implies(implies(sK12,sK13),implies(sK11,sK13)))) )
& ( ! [U_22,U_21,U_20] : is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_23,sK13)],[f_6_4]) ).
cnf(f_6_6,plain,
( is_a_theorem(implies(implies(U_22,U_21),implies(implies(U_21,U_20),implies(U_22,U_20))))
| ~ implies_3 ),
inference(clausify,[status(thm)],[f_6_5]) ).
cnf(f_6_7,plain,
( implies_3
| ~ is_a_theorem(implies(implies(sK11,sK12),implies(implies(sK12,sK13),implies(sK11,sK13)))) ),
inference(clausify,[status(thm)],[f_6_5]) ).
fof(f_7_1,plain,
( ( and_1
| ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),X)) )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),X))
| ~ and_1 ) ),
inference(fof_nnf,[status(thm)],[and_1]) ).
fof(f_7_2,plain,
( ( and_1
| ? [U_29,U_28] : ~ is_a_theorem(implies(and(U_29,U_28),U_29)) )
& ( ! [U_27,U_26] : is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ( and_1
| ? [U_28] : ~ is_a_theorem(implies(and(sK14,U_28),sK14)) )
& ( ! [U_27,U_26] : is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_29,sK14)],[f_7_2]) ).
fof(f_7_4,plain,
( ( and_1
| ~ is_a_theorem(implies(and(sK14,sK15),sK14)) )
& ( ! [U_27,U_26] : is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_28,sK15)],[f_7_3]) ).
cnf(f_7_5,plain,
( is_a_theorem(implies(and(U_27,U_26),U_27))
| ~ and_1 ),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
( and_1
| ~ is_a_theorem(implies(and(sK14,sK15),sK14)) ),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
( ( and_2
| ? [X,Y] : ~ is_a_theorem(implies(and(X,Y),Y)) )
& ( ! [X,Y] : is_a_theorem(implies(and(X,Y),Y))
| ~ and_2 ) ),
inference(fof_nnf,[status(thm)],[and_2]) ).
fof(f_8_2,plain,
( ( and_2
| ? [U_33,U_32] : ~ is_a_theorem(implies(and(U_33,U_32),U_32)) )
& ( ! [U_31,U_30] : is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ( and_2
| ? [U_32] : ~ is_a_theorem(implies(and(sK16,U_32),U_32)) )
& ( ! [U_31,U_30] : is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_33,sK16)],[f_8_2]) ).
fof(f_8_4,plain,
( ( and_2
| ~ is_a_theorem(implies(and(sK16,sK17),sK17)) )
& ( ! [U_31,U_30] : is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_32,sK17)],[f_8_3]) ).
cnf(f_8_5,plain,
( is_a_theorem(implies(and(U_31,U_30),U_30))
| ~ and_2 ),
inference(clausify,[status(thm)],[f_8_4]) ).
cnf(f_8_6,plain,
( and_2
| ~ is_a_theorem(implies(and(sK16,sK17),sK17)) ),
inference(clausify,[status(thm)],[f_8_4]) ).
fof(f_9_1,plain,
( ( and_3
| ? [X,Y] : ~ is_a_theorem(implies(X,implies(Y,and(X,Y)))) )
& ( ! [X,Y] : is_a_theorem(implies(X,implies(Y,and(X,Y))))
| ~ and_3 ) ),
inference(fof_nnf,[status(thm)],[and_3]) ).
fof(f_9_2,plain,
( ( and_3
| ? [U_37,U_36] : ~ is_a_theorem(implies(U_37,implies(U_36,and(U_37,U_36)))) )
& ( ! [U_35,U_34] : is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ( and_3
| ? [U_36] : ~ is_a_theorem(implies(sK18,implies(U_36,and(sK18,U_36)))) )
& ( ! [U_35,U_34] : is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_37,sK18)],[f_9_2]) ).
fof(f_9_4,plain,
( ( and_3
| ~ is_a_theorem(implies(sK18,implies(sK19,and(sK18,sK19)))) )
& ( ! [U_35,U_34] : is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_36,sK19)],[f_9_3]) ).
cnf(f_9_5,plain,
( is_a_theorem(implies(U_35,implies(U_34,and(U_35,U_34))))
| ~ and_3 ),
inference(clausify,[status(thm)],[f_9_4]) ).
cnf(f_9_6,plain,
( and_3
| ~ is_a_theorem(implies(sK18,implies(sK19,and(sK18,sK19)))) ),
inference(clausify,[status(thm)],[f_9_4]) ).
fof(f_10_1,plain,
( ( or_1
| ? [X,Y] : ~ is_a_theorem(implies(X,or(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(X,or(X,Y)))
| ~ or_1 ) ),
inference(fof_nnf,[status(thm)],[or_1]) ).
fof(f_10_2,plain,
( ( or_1
| ? [U_41,U_40] : ~ is_a_theorem(implies(U_41,or(U_41,U_40))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ( or_1
| ? [U_40] : ~ is_a_theorem(implies(sK20,or(sK20,U_40))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_41,sK20)],[f_10_2]) ).
fof(f_10_4,plain,
( ( or_1
| ~ is_a_theorem(implies(sK20,or(sK20,sK21))) )
& ( ! [U_39,U_38] : is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_40,sK21)],[f_10_3]) ).
cnf(f_10_5,plain,
( is_a_theorem(implies(U_39,or(U_39,U_38)))
| ~ or_1 ),
inference(clausify,[status(thm)],[f_10_4]) ).
cnf(f_10_6,plain,
( or_1
| ~ is_a_theorem(implies(sK20,or(sK20,sK21))) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
( ( or_2
| ? [X,Y] : ~ is_a_theorem(implies(Y,or(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(Y,or(X,Y)))
| ~ or_2 ) ),
inference(fof_nnf,[status(thm)],[or_2]) ).
fof(f_11_2,plain,
( ( or_2
| ? [U_45,U_44] : ~ is_a_theorem(implies(U_44,or(U_45,U_44))) )
& ( ! [U_43,U_42] : is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ( or_2
| ? [U_44] : ~ is_a_theorem(implies(U_44,or(sK22,U_44))) )
& ( ! [U_43,U_42] : is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_45,sK22)],[f_11_2]) ).
fof(f_11_4,plain,
( ( or_2
| ~ is_a_theorem(implies(sK23,or(sK22,sK23))) )
& ( ! [U_43,U_42] : is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_44,sK23)],[f_11_3]) ).
cnf(f_11_5,plain,
( is_a_theorem(implies(U_42,or(U_43,U_42)))
| ~ or_2 ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( or_2
| ~ is_a_theorem(implies(sK23,or(sK22,sK23))) ),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
( ( or_3
| ? [X,Y,Z] : ~ is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z)))) )
& ( ! [X,Y,Z] : is_a_theorem(implies(implies(X,Z),implies(implies(Y,Z),implies(or(X,Y),Z))))
| ~ or_3 ) ),
inference(fof_nnf,[status(thm)],[or_3]) ).
fof(f_12_2,plain,
( ( or_3
| ? [U_51,U_50,U_49] : ~ is_a_theorem(implies(implies(U_51,U_49),implies(implies(U_50,U_49),implies(or(U_51,U_50),U_49)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ( or_3
| ? [U_50,U_49] : ~ is_a_theorem(implies(implies(sK24,U_49),implies(implies(U_50,U_49),implies(or(sK24,U_50),U_49)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_51,sK24)],[f_12_2]) ).
fof(f_12_4,plain,
( ( or_3
| ? [U_49] : ~ is_a_theorem(implies(implies(sK24,U_49),implies(implies(sK25,U_49),implies(or(sK24,sK25),U_49)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_50,sK25)],[f_12_3]) ).
fof(f_12_5,plain,
( ( or_3
| ~ is_a_theorem(implies(implies(sK24,sK26),implies(implies(sK25,sK26),implies(or(sK24,sK25),sK26)))) )
& ( ! [U_48,U_47,U_46] : is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_49,sK26)],[f_12_4]) ).
cnf(f_12_6,plain,
( is_a_theorem(implies(implies(U_48,U_46),implies(implies(U_47,U_46),implies(or(U_48,U_47),U_46))))
| ~ or_3 ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( or_3
| ~ is_a_theorem(implies(implies(sK24,sK26),implies(implies(sK25,sK26),implies(or(sK24,sK25),sK26)))) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
( ( equivalence_1
| ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(X,Y))) )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(X,Y)))
| ~ equivalence_1 ) ),
inference(fof_nnf,[status(thm)],[equivalence_1]) ).
fof(f_13_2,plain,
( ( equivalence_1
| ? [U_55,U_54] : ~ is_a_theorem(implies(equiv(U_55,U_54),implies(U_55,U_54))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ( equivalence_1
| ? [U_54] : ~ is_a_theorem(implies(equiv(sK27,U_54),implies(sK27,U_54))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_55,sK27)],[f_13_2]) ).
fof(f_13_4,plain,
( ( equivalence_1
| ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) )
& ( ! [U_53,U_52] : is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_54,sK28)],[f_13_3]) ).
cnf(f_13_5,plain,
( is_a_theorem(implies(equiv(U_53,U_52),implies(U_53,U_52)))
| ~ equivalence_1 ),
inference(clausify,[status(thm)],[f_13_4]) ).
cnf(f_13_6,plain,
( equivalence_1
| ~ is_a_theorem(implies(equiv(sK27,sK28),implies(sK27,sK28))) ),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
( ( equivalence_2
| ? [X,Y] : ~ is_a_theorem(implies(equiv(X,Y),implies(Y,X))) )
& ( ! [X,Y] : is_a_theorem(implies(equiv(X,Y),implies(Y,X)))
| ~ equivalence_2 ) ),
inference(fof_nnf,[status(thm)],[equivalence_2]) ).
fof(f_14_2,plain,
( ( equivalence_2
| ? [U_59,U_58] : ~ is_a_theorem(implies(equiv(U_59,U_58),implies(U_58,U_59))) )
& ( ! [U_57,U_56] : is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ( equivalence_2
| ? [U_58] : ~ is_a_theorem(implies(equiv(sK29,U_58),implies(U_58,sK29))) )
& ( ! [U_57,U_56] : is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_59,sK29)],[f_14_2]) ).
fof(f_14_4,plain,
( ( equivalence_2
| ~ is_a_theorem(implies(equiv(sK29,sK30),implies(sK30,sK29))) )
& ( ! [U_57,U_56] : is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_58,sK30)],[f_14_3]) ).
cnf(f_14_5,plain,
( is_a_theorem(implies(equiv(U_57,U_56),implies(U_56,U_57)))
| ~ equivalence_2 ),
inference(clausify,[status(thm)],[f_14_4]) ).
cnf(f_14_6,plain,
( equivalence_2
| ~ is_a_theorem(implies(equiv(sK29,sK30),implies(sK30,sK29))) ),
inference(clausify,[status(thm)],[f_14_4]) ).
fof(f_15_1,plain,
( ( equivalence_3
| ? [X,Y] : ~ is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y)))) )
& ( ! [X,Y] : is_a_theorem(implies(implies(X,Y),implies(implies(Y,X),equiv(X,Y))))
| ~ equivalence_3 ) ),
inference(fof_nnf,[status(thm)],[equivalence_3]) ).
fof(f_15_2,plain,
( ( equivalence_3
| ? [U_63,U_62] : ~ is_a_theorem(implies(implies(U_63,U_62),implies(implies(U_62,U_63),equiv(U_63,U_62)))) )
& ( ! [U_61,U_60] : is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ( equivalence_3
| ? [U_62] : ~ is_a_theorem(implies(implies(sK31,U_62),implies(implies(U_62,sK31),equiv(sK31,U_62)))) )
& ( ! [U_61,U_60] : is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_63,sK31)],[f_15_2]) ).
fof(f_15_4,plain,
( ( equivalence_3
| ~ is_a_theorem(implies(implies(sK31,sK32),implies(implies(sK32,sK31),equiv(sK31,sK32)))) )
& ( ! [U_61,U_60] : is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_62,sK32)],[f_15_3]) ).
cnf(f_15_5,plain,
( is_a_theorem(implies(implies(U_61,U_60),implies(implies(U_60,U_61),equiv(U_61,U_60))))
| ~ equivalence_3 ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( equivalence_3
| ~ is_a_theorem(implies(implies(sK31,sK32),implies(implies(sK32,sK31),equiv(sK31,sK32)))) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
( ( kn1
| ? [P] : ~ is_a_theorem(implies(P,and(P,P))) )
& ( ! [P] : is_a_theorem(implies(P,and(P,P)))
| ~ kn1 ) ),
inference(fof_nnf,[status(thm)],[kn1]) ).
fof(f_16_2,plain,
( ( kn1
| ? [U_65] : ~ is_a_theorem(implies(U_65,and(U_65,U_65))) )
& ( ! [U_64] : is_a_theorem(implies(U_64,and(U_64,U_64)))
| ~ kn1 ) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ( kn1
| ~ is_a_theorem(implies(sK33,and(sK33,sK33))) )
& ( ! [U_64] : is_a_theorem(implies(U_64,and(U_64,U_64)))
| ~ kn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_65,sK33)],[f_16_2]) ).
cnf(f_16_4,plain,
( is_a_theorem(implies(U_64,and(U_64,U_64)))
| ~ kn1 ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( kn1
| ~ is_a_theorem(implies(sK33,and(sK33,sK33))) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
( ( kn2
| ? [P,Q] : ~ is_a_theorem(implies(and(P,Q),P)) )
& ( ! [P,Q] : is_a_theorem(implies(and(P,Q),P))
| ~ kn2 ) ),
inference(fof_nnf,[status(thm)],[kn2]) ).
fof(f_17_2,plain,
( ( kn2
| ? [U_69,U_68] : ~ is_a_theorem(implies(and(U_69,U_68),U_69)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ( kn2
| ? [U_68] : ~ is_a_theorem(implies(and(sK34,U_68),sK34)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_69,sK34)],[f_17_2]) ).
fof(f_17_4,plain,
( ( kn2
| ~ is_a_theorem(implies(and(sK34,sK35),sK34)) )
& ( ! [U_67,U_66] : is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_68,sK35)],[f_17_3]) ).
cnf(f_17_5,plain,
( is_a_theorem(implies(and(U_67,U_66),U_67))
| ~ kn2 ),
inference(clausify,[status(thm)],[f_17_4]) ).
cnf(f_17_6,plain,
( kn2
| ~ is_a_theorem(implies(and(sK34,sK35),sK34)) ),
inference(clausify,[status(thm)],[f_17_4]) ).
fof(f_18_1,plain,
( ( kn3
| ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P))))) )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(not(and(Q,R)),not(and(R,P)))))
| ~ kn3 ) ),
inference(fof_nnf,[status(thm)],[kn3]) ).
fof(f_18_2,plain,
( ( kn3
| ? [U_75,U_74,U_73] : ~ is_a_theorem(implies(implies(U_75,U_74),implies(not(and(U_74,U_73)),not(and(U_73,U_75))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ( kn3
| ? [U_74,U_73] : ~ is_a_theorem(implies(implies(sK36,U_74),implies(not(and(U_74,U_73)),not(and(U_73,sK36))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_75,sK36)],[f_18_2]) ).
fof(f_18_4,plain,
( ( kn3
| ? [U_73] : ~ is_a_theorem(implies(implies(sK36,sK37),implies(not(and(sK37,U_73)),not(and(U_73,sK36))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_74,sK37)],[f_18_3]) ).
fof(f_18_5,plain,
( ( kn3
| ~ is_a_theorem(implies(implies(sK36,sK37),implies(not(and(sK37,sK38)),not(and(sK38,sK36))))) )
& ( ! [U_72,U_71,U_70] : is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_73,sK38)],[f_18_4]) ).
cnf(f_18_6,plain,
( is_a_theorem(implies(implies(U_72,U_71),implies(not(and(U_71,U_70)),not(and(U_70,U_72)))))
| ~ kn3 ),
inference(clausify,[status(thm)],[f_18_5]) ).
cnf(f_18_7,plain,
( kn3
| ~ is_a_theorem(implies(implies(sK36,sK37),implies(not(and(sK37,sK38)),not(and(sK38,sK36))))) ),
inference(clausify,[status(thm)],[f_18_5]) ).
fof(f_19_1,plain,
( ( cn1
| ? [P,Q,R] : ~ is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R)))) )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(P,Q),implies(implies(Q,R),implies(P,R))))
| ~ cn1 ) ),
inference(fof_nnf,[status(thm)],[cn1]) ).
fof(f_19_2,plain,
( ( cn1
| ? [U_81,U_80,U_79] : ~ is_a_theorem(implies(implies(U_81,U_80),implies(implies(U_80,U_79),implies(U_81,U_79)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ( cn1
| ? [U_80,U_79] : ~ is_a_theorem(implies(implies(sK39,U_80),implies(implies(U_80,U_79),implies(sK39,U_79)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_81,sK39)],[f_19_2]) ).
fof(f_19_4,plain,
( ( cn1
| ? [U_79] : ~ is_a_theorem(implies(implies(sK39,sK40),implies(implies(sK40,U_79),implies(sK39,U_79)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_80,sK40)],[f_19_3]) ).
fof(f_19_5,plain,
( ( cn1
| ~ is_a_theorem(implies(implies(sK39,sK40),implies(implies(sK40,sK41),implies(sK39,sK41)))) )
& ( ! [U_78,U_77,U_76] : is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_79,sK41)],[f_19_4]) ).
cnf(f_19_6,plain,
( is_a_theorem(implies(implies(U_78,U_77),implies(implies(U_77,U_76),implies(U_78,U_76))))
| ~ cn1 ),
inference(clausify,[status(thm)],[f_19_5]) ).
cnf(f_19_7,plain,
( cn1
| ~ is_a_theorem(implies(implies(sK39,sK40),implies(implies(sK40,sK41),implies(sK39,sK41)))) ),
inference(clausify,[status(thm)],[f_19_5]) ).
fof(f_20_1,plain,
( ( cn2
| ? [P,Q] : ~ is_a_theorem(implies(P,implies(not(P),Q))) )
& ( ! [P,Q] : is_a_theorem(implies(P,implies(not(P),Q)))
| ~ cn2 ) ),
inference(fof_nnf,[status(thm)],[cn2]) ).
fof(f_20_2,plain,
( ( cn2
| ? [U_85,U_84] : ~ is_a_theorem(implies(U_85,implies(not(U_85),U_84))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ( cn2
| ? [U_84] : ~ is_a_theorem(implies(sK42,implies(not(sK42),U_84))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_85,sK42)],[f_20_2]) ).
fof(f_20_4,plain,
( ( cn2
| ~ is_a_theorem(implies(sK42,implies(not(sK42),sK43))) )
& ( ! [U_83,U_82] : is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_84,sK43)],[f_20_3]) ).
cnf(f_20_5,plain,
( is_a_theorem(implies(U_83,implies(not(U_83),U_82)))
| ~ cn2 ),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
( cn2
| ~ is_a_theorem(implies(sK42,implies(not(sK42),sK43))) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
( ( cn3
| ? [P] : ~ is_a_theorem(implies(implies(not(P),P),P)) )
& ( ! [P] : is_a_theorem(implies(implies(not(P),P),P))
| ~ cn3 ) ),
inference(fof_nnf,[status(thm)],[cn3]) ).
fof(f_21_2,plain,
( ( cn3
| ? [U_87] : ~ is_a_theorem(implies(implies(not(U_87),U_87),U_87)) )
& ( ! [U_86] : is_a_theorem(implies(implies(not(U_86),U_86),U_86))
| ~ cn3 ) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ( cn3
| ~ is_a_theorem(implies(implies(not(sK44),sK44),sK44)) )
& ( ! [U_86] : is_a_theorem(implies(implies(not(U_86),U_86),U_86))
| ~ cn3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_87,sK44)],[f_21_2]) ).
cnf(f_21_4,plain,
( is_a_theorem(implies(implies(not(U_86),U_86),U_86))
| ~ cn3 ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( cn3
| ~ is_a_theorem(implies(implies(not(sK44),sK44),sK44)) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
( ( r1
| ? [P] : ~ is_a_theorem(implies(or(P,P),P)) )
& ( ! [P] : is_a_theorem(implies(or(P,P),P))
| ~ r1 ) ),
inference(fof_nnf,[status(thm)],[r1]) ).
fof(f_22_2,plain,
( ( r1
| ? [U_89] : ~ is_a_theorem(implies(or(U_89,U_89),U_89)) )
& ( ! [U_88] : is_a_theorem(implies(or(U_88,U_88),U_88))
| ~ r1 ) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( ( r1
| ~ is_a_theorem(implies(or(sK45,sK45),sK45)) )
& ( ! [U_88] : is_a_theorem(implies(or(U_88,U_88),U_88))
| ~ r1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_89,sK45)],[f_22_2]) ).
cnf(f_22_4,plain,
( is_a_theorem(implies(or(U_88,U_88),U_88))
| ~ r1 ),
inference(clausify,[status(thm)],[f_22_3]) ).
cnf(f_22_5,plain,
( r1
| ~ is_a_theorem(implies(or(sK45,sK45),sK45)) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
( ( r2
| ? [P,Q] : ~ is_a_theorem(implies(Q,or(P,Q))) )
& ( ! [P,Q] : is_a_theorem(implies(Q,or(P,Q)))
| ~ r2 ) ),
inference(fof_nnf,[status(thm)],[r2]) ).
fof(f_23_2,plain,
( ( r2
| ? [U_93,U_92] : ~ is_a_theorem(implies(U_92,or(U_93,U_92))) )
& ( ! [U_91,U_90] : is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( ( r2
| ? [U_92] : ~ is_a_theorem(implies(U_92,or(sK46,U_92))) )
& ( ! [U_91,U_90] : is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_93,sK46)],[f_23_2]) ).
fof(f_23_4,plain,
( ( r2
| ~ is_a_theorem(implies(sK47,or(sK46,sK47))) )
& ( ! [U_91,U_90] : is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_92,sK47)],[f_23_3]) ).
cnf(f_23_5,plain,
( is_a_theorem(implies(U_90,or(U_91,U_90)))
| ~ r2 ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( r2
| ~ is_a_theorem(implies(sK47,or(sK46,sK47))) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
( ( r3
| ? [P,Q] : ~ is_a_theorem(implies(or(P,Q),or(Q,P))) )
& ( ! [P,Q] : is_a_theorem(implies(or(P,Q),or(Q,P)))
| ~ r3 ) ),
inference(fof_nnf,[status(thm)],[r3]) ).
fof(f_24_2,plain,
( ( r3
| ? [U_97,U_96] : ~ is_a_theorem(implies(or(U_97,U_96),or(U_96,U_97))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ( r3
| ? [U_96] : ~ is_a_theorem(implies(or(sK48,U_96),or(U_96,sK48))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_97,sK48)],[f_24_2]) ).
fof(f_24_4,plain,
( ( r3
| ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48))) )
& ( ! [U_95,U_94] : is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_96,sK49)],[f_24_3]) ).
cnf(f_24_5,plain,
( is_a_theorem(implies(or(U_95,U_94),or(U_94,U_95)))
| ~ r3 ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( r3
| ~ is_a_theorem(implies(or(sK48,sK49),or(sK49,sK48))) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
( ( r4
| ? [P,Q,R] : ~ is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R)))) )
& ( ! [P,Q,R] : is_a_theorem(implies(or(P,or(Q,R)),or(Q,or(P,R))))
| ~ r4 ) ),
inference(fof_nnf,[status(thm)],[r4]) ).
fof(f_25_2,plain,
( ( r4
| ? [U_103,U_102,U_101] : ~ is_a_theorem(implies(or(U_103,or(U_102,U_101)),or(U_102,or(U_103,U_101)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ( r4
| ? [U_102,U_101] : ~ is_a_theorem(implies(or(sK50,or(U_102,U_101)),or(U_102,or(sK50,U_101)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_103,sK50)],[f_25_2]) ).
fof(f_25_4,plain,
( ( r4
| ? [U_101] : ~ is_a_theorem(implies(or(sK50,or(sK51,U_101)),or(sK51,or(sK50,U_101)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_102,sK51)],[f_25_3]) ).
fof(f_25_5,plain,
( ( r4
| ~ is_a_theorem(implies(or(sK50,or(sK51,sK52)),or(sK51,or(sK50,sK52)))) )
& ( ! [U_100,U_99,U_98] : is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_101,sK52)],[f_25_4]) ).
cnf(f_25_6,plain,
( is_a_theorem(implies(or(U_100,or(U_99,U_98)),or(U_99,or(U_100,U_98))))
| ~ r4 ),
inference(clausify,[status(thm)],[f_25_5]) ).
cnf(f_25_7,plain,
( r4
| ~ is_a_theorem(implies(or(sK50,or(sK51,sK52)),or(sK51,or(sK50,sK52)))) ),
inference(clausify,[status(thm)],[f_25_5]) ).
fof(f_26_1,plain,
( ( r5
| ? [P,Q,R] : ~ is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R)))) )
& ( ! [P,Q,R] : is_a_theorem(implies(implies(Q,R),implies(or(P,Q),or(P,R))))
| ~ r5 ) ),
inference(fof_nnf,[status(thm)],[r5]) ).
fof(f_26_2,plain,
( ( r5
| ? [U_109,U_108,U_107] : ~ is_a_theorem(implies(implies(U_108,U_107),implies(or(U_109,U_108),or(U_109,U_107)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ( r5
| ? [U_108,U_107] : ~ is_a_theorem(implies(implies(U_108,U_107),implies(or(sK53,U_108),or(sK53,U_107)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_109,sK53)],[f_26_2]) ).
fof(f_26_4,plain,
( ( r5
| ? [U_107] : ~ is_a_theorem(implies(implies(sK54,U_107),implies(or(sK53,sK54),or(sK53,U_107)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_108,sK54)],[f_26_3]) ).
fof(f_26_5,plain,
( ( r5
| ~ is_a_theorem(implies(implies(sK54,sK55),implies(or(sK53,sK54),or(sK53,sK55)))) )
& ( ! [U_106,U_105,U_104] : is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_107,sK55)],[f_26_4]) ).
cnf(f_26_6,plain,
( is_a_theorem(implies(implies(U_105,U_104),implies(or(U_106,U_105),or(U_106,U_104))))
| ~ r5 ),
inference(clausify,[status(thm)],[f_26_5]) ).
cnf(f_26_7,plain,
( r5
| ~ is_a_theorem(implies(implies(sK54,sK55),implies(or(sK53,sK54),or(sK53,sK55)))) ),
inference(clausify,[status(thm)],[f_26_5]) ).
fof(f_27_1,plain,
( ! [X,Y] : or(X,Y) = not(and(not(X),not(Y)))
| ~ op_or ),
inference(fof_nnf,[status(thm)],[op_or]) ).
fof(f_27_2,plain,
( ! [U_111,U_110] : or(U_111,U_110) = not(and(not(U_111),not(U_110)))
| ~ op_or ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( or(U_111,U_110) = not(and(not(U_111),not(U_110)))
| ~ op_or ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
( ! [X,Y] : and(X,Y) = not(or(not(X),not(Y)))
| ~ op_and ),
inference(fof_nnf,[status(thm)],[op_and]) ).
fof(f_28_2,plain,
( ! [U_113,U_112] : and(U_113,U_112) = not(or(not(U_113),not(U_112)))
| ~ op_and ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( and(U_113,U_112) = not(or(not(U_113),not(U_112)))
| ~ op_and ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
( ! [X,Y] : implies(X,Y) = not(and(X,not(Y)))
| ~ op_implies_and ),
inference(fof_nnf,[status(thm)],[op_implies_and]) ).
fof(f_29_2,plain,
( ! [U_115,U_114] : implies(U_115,U_114) = not(and(U_115,not(U_114)))
| ~ op_implies_and ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( implies(U_115,U_114) = not(and(U_115,not(U_114)))
| ~ op_implies_and ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
( ! [X,Y] : implies(X,Y) = or(not(X),Y)
| ~ op_implies_or ),
inference(fof_nnf,[status(thm)],[op_implies_or]) ).
fof(f_30_2,plain,
( ! [U_117,U_116] : implies(U_117,U_116) = or(not(U_117),U_116)
| ~ op_implies_or ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( implies(U_117,U_116) = or(not(U_117),U_116)
| ~ op_implies_or ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
( ! [X,Y] : equiv(X,Y) = and(implies(X,Y),implies(Y,X))
| ~ op_equiv ),
inference(fof_nnf,[status(thm)],[op_equiv]) ).
fof(f_31_2,plain,
( ! [U_119,U_118] : equiv(U_119,U_118) = and(implies(U_119,U_118),implies(U_118,U_119))
| ~ op_equiv ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( equiv(U_119,U_118) = and(implies(U_119,U_118),implies(U_118,U_119))
| ~ op_equiv ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
op_or,
inference(fof_nnf,[status(thm)],[hilbert_op_or]) ).
cnf(f_32_2,plain,
op_or,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
op_implies_and,
inference(fof_nnf,[status(thm)],[hilbert_op_implies_and]) ).
cnf(f_33_2,plain,
op_implies_and,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
op_equiv,
inference(fof_nnf,[status(thm)],[hilbert_op_equiv]) ).
cnf(f_34_2,plain,
op_equiv,
inference(clausify,[status(thm)],[f_34_1]) ).
fof(f_35_1,plain,
modus_ponens,
inference(fof_nnf,[status(thm)],[hilbert_modus_ponens]) ).
cnf(f_35_2,plain,
modus_ponens,
inference(clausify,[status(thm)],[f_35_1]) ).
fof(f_36_1,plain,
modus_tollens,
inference(fof_nnf,[status(thm)],[hilbert_modus_tollens]) ).
cnf(f_36_2,plain,
modus_tollens,
inference(clausify,[status(thm)],[f_36_1]) ).
fof(f_37_1,plain,
implies_1,
inference(fof_nnf,[status(thm)],[hilbert_implies_1]) ).
cnf(f_37_2,plain,
implies_1,
inference(clausify,[status(thm)],[f_37_1]) ).
fof(f_38_1,plain,
implies_2,
inference(fof_nnf,[status(thm)],[hilbert_implies_2]) ).
cnf(f_38_2,plain,
implies_2,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
implies_3,
inference(fof_nnf,[status(thm)],[hilbert_implies_3]) ).
cnf(f_39_2,plain,
implies_3,
inference(clausify,[status(thm)],[f_39_1]) ).
fof(f_40_1,plain,
and_1,
inference(fof_nnf,[status(thm)],[hilbert_and_1]) ).
cnf(f_40_2,plain,
and_1,
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_1,plain,
and_2,
inference(fof_nnf,[status(thm)],[hilbert_and_2]) ).
cnf(f_41_2,plain,
and_2,
inference(clausify,[status(thm)],[f_41_1]) ).
fof(f_42_1,plain,
and_3,
inference(fof_nnf,[status(thm)],[hilbert_and_3]) ).
cnf(f_42_2,plain,
and_3,
inference(clausify,[status(thm)],[f_42_1]) ).
fof(f_43_1,plain,
or_1,
inference(fof_nnf,[status(thm)],[hilbert_or_1]) ).
cnf(f_43_2,plain,
or_1,
inference(clausify,[status(thm)],[f_43_1]) ).
fof(f_44_1,plain,
or_2,
inference(fof_nnf,[status(thm)],[hilbert_or_2]) ).
cnf(f_44_2,plain,
or_2,
inference(clausify,[status(thm)],[f_44_1]) ).
fof(f_45_1,plain,
or_3,
inference(fof_nnf,[status(thm)],[hilbert_or_3]) ).
cnf(f_45_2,plain,
or_3,
inference(clausify,[status(thm)],[f_45_1]) ).
fof(f_46_1,plain,
equivalence_1,
inference(fof_nnf,[status(thm)],[hilbert_equivalence_1]) ).
cnf(f_46_2,plain,
equivalence_1,
inference(clausify,[status(thm)],[f_46_1]) ).
fof(f_47_1,plain,
equivalence_2,
inference(fof_nnf,[status(thm)],[hilbert_equivalence_2]) ).
cnf(f_47_2,plain,
equivalence_2,
inference(clausify,[status(thm)],[f_47_1]) ).
fof(f_48_1,plain,
equivalence_3,
inference(fof_nnf,[status(thm)],[hilbert_equivalence_3]) ).
cnf(f_48_2,plain,
equivalence_3,
inference(clausify,[status(thm)],[f_48_1]) ).
fof(f_49_1,plain,
substitution_of_equivalents,
inference(fof_nnf,[status(thm)],[use_substitution_of_equivalents]) ).
cnf(f_49_2,plain,
substitution_of_equivalents,
inference(clausify,[status(thm)],[f_49_1]) ).
fof(f_50_1,plain,
( ( necessitation
| ? [X] :
( ~ is_a_theorem(necessarily(X))
& is_a_theorem(X) ) )
& ( ! [X] :
( is_a_theorem(necessarily(X))
| ~ is_a_theorem(X) )
| ~ necessitation ) ),
inference(fof_nnf,[status(thm)],[necessitation]) ).
fof(f_50_2,plain,
( ( necessitation
| ? [U_121] :
( ~ is_a_theorem(necessarily(U_121))
& is_a_theorem(U_121) ) )
& ( ! [U_120] :
( is_a_theorem(necessarily(U_120))
| ~ is_a_theorem(U_120) )
| ~ necessitation ) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
( ( necessitation
| ( ~ is_a_theorem(necessarily(sK56))
& is_a_theorem(sK56) ) )
& ( ! [U_120] :
( is_a_theorem(necessarily(U_120))
| ~ is_a_theorem(U_120) )
| ~ necessitation ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_121,sK56)],[f_50_2]) ).
cnf(f_50_4,plain,
( is_a_theorem(necessarily(U_120))
| ~ is_a_theorem(U_120)
| ~ necessitation ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_5,plain,
( is_a_theorem(sK56)
| necessitation ),
inference(clausify,[status(thm)],[f_50_3]) ).
cnf(f_50_6,plain,
( ~ is_a_theorem(necessarily(sK56))
| necessitation ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
( ( modus_ponens_strict_implies
| ? [X,Y] :
( ~ is_a_theorem(Y)
& is_a_theorem(strict_implies(X,Y))
& is_a_theorem(X) ) )
& ( ! [X,Y] :
( is_a_theorem(Y)
| ~ is_a_theorem(strict_implies(X,Y))
| ~ is_a_theorem(X) )
| ~ modus_ponens_strict_implies ) ),
inference(fof_nnf,[status(thm)],[modus_ponens_strict_implies]) ).
fof(f_51_2,plain,
( ( modus_ponens_strict_implies
| ? [U_125,U_124] :
( ~ is_a_theorem(U_124)
& is_a_theorem(strict_implies(U_125,U_124))
& is_a_theorem(U_125) ) )
& ( ! [U_123,U_122] :
( is_a_theorem(U_122)
| ~ is_a_theorem(strict_implies(U_123,U_122))
| ~ is_a_theorem(U_123) )
| ~ modus_ponens_strict_implies ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ( modus_ponens_strict_implies
| ? [U_124] :
( ~ is_a_theorem(U_124)
& is_a_theorem(strict_implies(sK57,U_124))
& is_a_theorem(sK57) ) )
& ( ! [U_123,U_122] :
( is_a_theorem(U_122)
| ~ is_a_theorem(strict_implies(U_123,U_122))
| ~ is_a_theorem(U_123) )
| ~ modus_ponens_strict_implies ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_125,sK57)],[f_51_2]) ).
fof(f_51_4,plain,
( ( modus_ponens_strict_implies
| ( ~ is_a_theorem(sK58)
& is_a_theorem(strict_implies(sK57,sK58))
& is_a_theorem(sK57) ) )
& ( ! [U_123,U_122] :
( is_a_theorem(U_122)
| ~ is_a_theorem(strict_implies(U_123,U_122))
| ~ is_a_theorem(U_123) )
| ~ modus_ponens_strict_implies ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_124,sK58)],[f_51_3]) ).
cnf(f_51_5,plain,
( is_a_theorem(U_122)
| ~ is_a_theorem(strict_implies(U_123,U_122))
| ~ is_a_theorem(U_123)
| ~ modus_ponens_strict_implies ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
( is_a_theorem(sK57)
| modus_ponens_strict_implies ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_7,plain,
( is_a_theorem(strict_implies(sK57,sK58))
| modus_ponens_strict_implies ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_8,plain,
( ~ is_a_theorem(sK58)
| modus_ponens_strict_implies ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
( ( adjunction
| ? [X,Y] :
( ~ is_a_theorem(and(X,Y))
& is_a_theorem(Y)
& is_a_theorem(X) ) )
& ( ! [X,Y] :
( is_a_theorem(and(X,Y))
| ~ is_a_theorem(Y)
| ~ is_a_theorem(X) )
| ~ adjunction ) ),
inference(fof_nnf,[status(thm)],[adjunction]) ).
fof(f_52_2,plain,
( ( adjunction
| ? [U_129,U_128] :
( ~ is_a_theorem(and(U_129,U_128))
& is_a_theorem(U_128)
& is_a_theorem(U_129) ) )
& ( ! [U_127,U_126] :
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127) )
| ~ adjunction ) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ( adjunction
| ? [U_128] :
( ~ is_a_theorem(and(sK59,U_128))
& is_a_theorem(U_128)
& is_a_theorem(sK59) ) )
& ( ! [U_127,U_126] :
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_129,sK59)],[f_52_2]) ).
fof(f_52_4,plain,
( ( adjunction
| ( ~ is_a_theorem(and(sK59,sK60))
& is_a_theorem(sK60)
& is_a_theorem(sK59) ) )
& ( ! [U_127,U_126] :
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127) )
| ~ adjunction ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_128,sK60)],[f_52_3]) ).
cnf(f_52_5,plain,
( is_a_theorem(and(U_127,U_126))
| ~ is_a_theorem(U_126)
| ~ is_a_theorem(U_127)
| ~ adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_6,plain,
( is_a_theorem(sK59)
| adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_7,plain,
( is_a_theorem(sK60)
| adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
cnf(f_52_8,plain,
( ~ is_a_theorem(and(sK59,sK60))
| adjunction ),
inference(clausify,[status(thm)],[f_52_4]) ).
fof(f_53_1,plain,
( ( substitution_strict_equiv
| ? [X,Y] :
( X != Y
& is_a_theorem(strict_equiv(X,Y)) ) )
& ( ! [X,Y] :
( X = Y
| ~ is_a_theorem(strict_equiv(X,Y)) )
| ~ substitution_strict_equiv ) ),
inference(fof_nnf,[status(thm)],[substitution_strict_equiv]) ).
fof(f_53_2,plain,
( ( substitution_strict_equiv
| ? [U_133,U_132] :
( U_133 != U_132
& is_a_theorem(strict_equiv(U_133,U_132)) ) )
& ( ! [U_131,U_130] :
( U_131 = U_130
| ~ is_a_theorem(strict_equiv(U_131,U_130)) )
| ~ substitution_strict_equiv ) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
( ( substitution_strict_equiv
| ? [U_132] :
( sK61 != U_132
& is_a_theorem(strict_equiv(sK61,U_132)) ) )
& ( ! [U_131,U_130] :
( U_131 = U_130
| ~ is_a_theorem(strict_equiv(U_131,U_130)) )
| ~ substitution_strict_equiv ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_133,sK61)],[f_53_2]) ).
fof(f_53_4,plain,
( ( substitution_strict_equiv
| ( sK61 != sK62
& is_a_theorem(strict_equiv(sK61,sK62)) ) )
& ( ! [U_131,U_130] :
( U_131 = U_130
| ~ is_a_theorem(strict_equiv(U_131,U_130)) )
| ~ substitution_strict_equiv ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_132,sK62)],[f_53_3]) ).
cnf(f_53_5,plain,
( U_131 = U_130
| ~ is_a_theorem(strict_equiv(U_131,U_130))
| ~ substitution_strict_equiv ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_6,plain,
( is_a_theorem(strict_equiv(sK61,sK62))
| substitution_strict_equiv ),
inference(clausify,[status(thm)],[f_53_4]) ).
cnf(f_53_7,plain,
( sK61 != sK62
| substitution_strict_equiv ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_1,plain,
( ( axiom_K
| ? [X,Y] : ~ is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y)))) )
& ( ! [X,Y] : is_a_theorem(implies(necessarily(implies(X,Y)),implies(necessarily(X),necessarily(Y))))
| ~ axiom_K ) ),
inference(fof_nnf,[status(thm)],[axiom_K]) ).
fof(f_54_2,plain,
( ( axiom_K
| ? [U_137,U_136] : ~ is_a_theorem(implies(necessarily(implies(U_137,U_136)),implies(necessarily(U_137),necessarily(U_136)))) )
& ( ! [U_135,U_134] : is_a_theorem(implies(necessarily(implies(U_135,U_134)),implies(necessarily(U_135),necessarily(U_134))))
| ~ axiom_K ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ( axiom_K
| ? [U_136] : ~ is_a_theorem(implies(necessarily(implies(sK63,U_136)),implies(necessarily(sK63),necessarily(U_136)))) )
& ( ! [U_135,U_134] : is_a_theorem(implies(necessarily(implies(U_135,U_134)),implies(necessarily(U_135),necessarily(U_134))))
| ~ axiom_K ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_137,sK63)],[f_54_2]) ).
fof(f_54_4,plain,
( ( axiom_K
| ~ is_a_theorem(implies(necessarily(implies(sK63,sK64)),implies(necessarily(sK63),necessarily(sK64)))) )
& ( ! [U_135,U_134] : is_a_theorem(implies(necessarily(implies(U_135,U_134)),implies(necessarily(U_135),necessarily(U_134))))
| ~ axiom_K ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_136,sK64)],[f_54_3]) ).
cnf(f_54_5,plain,
( is_a_theorem(implies(necessarily(implies(U_135,U_134)),implies(necessarily(U_135),necessarily(U_134))))
| ~ axiom_K ),
inference(clausify,[status(thm)],[f_54_4]) ).
cnf(f_54_6,plain,
( axiom_K
| ~ is_a_theorem(implies(necessarily(implies(sK63,sK64)),implies(necessarily(sK63),necessarily(sK64)))) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
( ( axiom_M
| ? [X] : ~ is_a_theorem(implies(necessarily(X),X)) )
& ( ! [X] : is_a_theorem(implies(necessarily(X),X))
| ~ axiom_M ) ),
inference(fof_nnf,[status(thm)],[axiom_M]) ).
fof(f_55_2,plain,
( ( axiom_M
| ? [U_139] : ~ is_a_theorem(implies(necessarily(U_139),U_139)) )
& ( ! [U_138] : is_a_theorem(implies(necessarily(U_138),U_138))
| ~ axiom_M ) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
( ( axiom_M
| ~ is_a_theorem(implies(necessarily(sK65),sK65)) )
& ( ! [U_138] : is_a_theorem(implies(necessarily(U_138),U_138))
| ~ axiom_M ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_139,sK65)],[f_55_2]) ).
cnf(f_55_4,plain,
( is_a_theorem(implies(necessarily(U_138),U_138))
| ~ axiom_M ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_55_5,plain,
( axiom_M
| ~ is_a_theorem(implies(necessarily(sK65),sK65)) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
( ( axiom_4
| ? [X] : ~ is_a_theorem(implies(necessarily(X),necessarily(necessarily(X)))) )
& ( ! [X] : is_a_theorem(implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_4 ) ),
inference(fof_nnf,[status(thm)],[axiom_4]) ).
fof(f_56_2,plain,
( ( axiom_4
| ? [U_141] : ~ is_a_theorem(implies(necessarily(U_141),necessarily(necessarily(U_141)))) )
& ( ! [U_140] : is_a_theorem(implies(necessarily(U_140),necessarily(necessarily(U_140))))
| ~ axiom_4 ) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ( axiom_4
| ~ is_a_theorem(implies(necessarily(sK66),necessarily(necessarily(sK66)))) )
& ( ! [U_140] : is_a_theorem(implies(necessarily(U_140),necessarily(necessarily(U_140))))
| ~ axiom_4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_141,sK66)],[f_56_2]) ).
cnf(f_56_4,plain,
( is_a_theorem(implies(necessarily(U_140),necessarily(necessarily(U_140))))
| ~ axiom_4 ),
inference(clausify,[status(thm)],[f_56_3]) ).
cnf(f_56_5,plain,
( axiom_4
| ~ is_a_theorem(implies(necessarily(sK66),necessarily(necessarily(sK66)))) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_1,plain,
( ( axiom_B
| ? [X] : ~ is_a_theorem(implies(X,necessarily(possibly(X)))) )
& ( ! [X] : is_a_theorem(implies(X,necessarily(possibly(X))))
| ~ axiom_B ) ),
inference(fof_nnf,[status(thm)],[axiom_B]) ).
fof(f_57_2,plain,
( ( axiom_B
| ? [U_143] : ~ is_a_theorem(implies(U_143,necessarily(possibly(U_143)))) )
& ( ! [U_142] : is_a_theorem(implies(U_142,necessarily(possibly(U_142))))
| ~ axiom_B ) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
( ( axiom_B
| ~ is_a_theorem(implies(sK67,necessarily(possibly(sK67)))) )
& ( ! [U_142] : is_a_theorem(implies(U_142,necessarily(possibly(U_142))))
| ~ axiom_B ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_143,sK67)],[f_57_2]) ).
cnf(f_57_4,plain,
( is_a_theorem(implies(U_142,necessarily(possibly(U_142))))
| ~ axiom_B ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_57_5,plain,
( axiom_B
| ~ is_a_theorem(implies(sK67,necessarily(possibly(sK67)))) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
( ( axiom_5
| ? [X] : ~ is_a_theorem(implies(possibly(X),necessarily(possibly(X)))) )
& ( ! [X] : is_a_theorem(implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_5 ) ),
inference(fof_nnf,[status(thm)],[axiom_5]) ).
fof(f_58_2,plain,
( ( axiom_5
| ? [U_145] : ~ is_a_theorem(implies(possibly(U_145),necessarily(possibly(U_145)))) )
& ( ! [U_144] : is_a_theorem(implies(possibly(U_144),necessarily(possibly(U_144))))
| ~ axiom_5 ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ( axiom_5
| ~ is_a_theorem(implies(possibly(sK68),necessarily(possibly(sK68)))) )
& ( ! [U_144] : is_a_theorem(implies(possibly(U_144),necessarily(possibly(U_144))))
| ~ axiom_5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_145,sK68)],[f_58_2]) ).
cnf(f_58_4,plain,
( is_a_theorem(implies(possibly(U_144),necessarily(possibly(U_144))))
| ~ axiom_5 ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( axiom_5
| ~ is_a_theorem(implies(possibly(sK68),necessarily(possibly(sK68)))) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
( ( axiom_s1
| ? [X,Y,Z] : ~ is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z)))) )
& ( ! [X,Y,Z] : is_a_theorem(implies(and(necessarily(implies(X,Y)),necessarily(implies(Y,Z))),necessarily(implies(X,Z))))
| ~ axiom_s1 ) ),
inference(fof_nnf,[status(thm)],[axiom_s1]) ).
fof(f_59_2,plain,
( ( axiom_s1
| ? [U_151,U_150,U_149] : ~ is_a_theorem(implies(and(necessarily(implies(U_151,U_150)),necessarily(implies(U_150,U_149))),necessarily(implies(U_151,U_149)))) )
& ( ! [U_148,U_147,U_146] : is_a_theorem(implies(and(necessarily(implies(U_148,U_147)),necessarily(implies(U_147,U_146))),necessarily(implies(U_148,U_146))))
| ~ axiom_s1 ) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ( axiom_s1
| ? [U_150,U_149] : ~ is_a_theorem(implies(and(necessarily(implies(sK69,U_150)),necessarily(implies(U_150,U_149))),necessarily(implies(sK69,U_149)))) )
& ( ! [U_148,U_147,U_146] : is_a_theorem(implies(and(necessarily(implies(U_148,U_147)),necessarily(implies(U_147,U_146))),necessarily(implies(U_148,U_146))))
| ~ axiom_s1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_151,sK69)],[f_59_2]) ).
fof(f_59_4,plain,
( ( axiom_s1
| ? [U_149] : ~ is_a_theorem(implies(and(necessarily(implies(sK69,sK70)),necessarily(implies(sK70,U_149))),necessarily(implies(sK69,U_149)))) )
& ( ! [U_148,U_147,U_146] : is_a_theorem(implies(and(necessarily(implies(U_148,U_147)),necessarily(implies(U_147,U_146))),necessarily(implies(U_148,U_146))))
| ~ axiom_s1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_150,sK70)],[f_59_3]) ).
fof(f_59_5,plain,
( ( axiom_s1
| ~ is_a_theorem(implies(and(necessarily(implies(sK69,sK70)),necessarily(implies(sK70,sK71))),necessarily(implies(sK69,sK71)))) )
& ( ! [U_148,U_147,U_146] : is_a_theorem(implies(and(necessarily(implies(U_148,U_147)),necessarily(implies(U_147,U_146))),necessarily(implies(U_148,U_146))))
| ~ axiom_s1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_149,sK71)],[f_59_4]) ).
cnf(f_59_6,plain,
( is_a_theorem(implies(and(necessarily(implies(U_148,U_147)),necessarily(implies(U_147,U_146))),necessarily(implies(U_148,U_146))))
| ~ axiom_s1 ),
inference(clausify,[status(thm)],[f_59_5]) ).
cnf(f_59_7,plain,
( axiom_s1
| ~ is_a_theorem(implies(and(necessarily(implies(sK69,sK70)),necessarily(implies(sK70,sK71))),necessarily(implies(sK69,sK71)))) ),
inference(clausify,[status(thm)],[f_59_5]) ).
fof(f_60_1,plain,
( ( axiom_s2
| ? [P,Q] : ~ is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q)))) )
& ( ! [P,Q] : is_a_theorem(strict_implies(possibly(and(P,Q)),and(possibly(P),possibly(Q))))
| ~ axiom_s2 ) ),
inference(fof_nnf,[status(thm)],[axiom_s2]) ).
fof(f_60_2,plain,
( ( axiom_s2
| ? [U_155,U_154] : ~ is_a_theorem(strict_implies(possibly(and(U_155,U_154)),and(possibly(U_155),possibly(U_154)))) )
& ( ! [U_153,U_152] : is_a_theorem(strict_implies(possibly(and(U_153,U_152)),and(possibly(U_153),possibly(U_152))))
| ~ axiom_s2 ) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
( ( axiom_s2
| ? [U_154] : ~ is_a_theorem(strict_implies(possibly(and(sK72,U_154)),and(possibly(sK72),possibly(U_154)))) )
& ( ! [U_153,U_152] : is_a_theorem(strict_implies(possibly(and(U_153,U_152)),and(possibly(U_153),possibly(U_152))))
| ~ axiom_s2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_155,sK72)],[f_60_2]) ).
fof(f_60_4,plain,
( ( axiom_s2
| ~ is_a_theorem(strict_implies(possibly(and(sK72,sK73)),and(possibly(sK72),possibly(sK73)))) )
& ( ! [U_153,U_152] : is_a_theorem(strict_implies(possibly(and(U_153,U_152)),and(possibly(U_153),possibly(U_152))))
| ~ axiom_s2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_154,sK73)],[f_60_3]) ).
cnf(f_60_5,plain,
( is_a_theorem(strict_implies(possibly(and(U_153,U_152)),and(possibly(U_153),possibly(U_152))))
| ~ axiom_s2 ),
inference(clausify,[status(thm)],[f_60_4]) ).
cnf(f_60_6,plain,
( axiom_s2
| ~ is_a_theorem(strict_implies(possibly(and(sK72,sK73)),and(possibly(sK72),possibly(sK73)))) ),
inference(clausify,[status(thm)],[f_60_4]) ).
fof(f_61_1,plain,
( ( axiom_s3
| ? [X,Y] : ~ is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X))))) )
& ( ! [X,Y] : is_a_theorem(strict_implies(strict_implies(X,Y),strict_implies(not(possibly(Y)),not(possibly(X)))))
| ~ axiom_s3 ) ),
inference(fof_nnf,[status(thm)],[axiom_s3]) ).
fof(f_61_2,plain,
( ( axiom_s3
| ? [U_159,U_158] : ~ is_a_theorem(strict_implies(strict_implies(U_159,U_158),strict_implies(not(possibly(U_158)),not(possibly(U_159))))) )
& ( ! [U_157,U_156] : is_a_theorem(strict_implies(strict_implies(U_157,U_156),strict_implies(not(possibly(U_156)),not(possibly(U_157)))))
| ~ axiom_s3 ) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
( ( axiom_s3
| ? [U_158] : ~ is_a_theorem(strict_implies(strict_implies(sK74,U_158),strict_implies(not(possibly(U_158)),not(possibly(sK74))))) )
& ( ! [U_157,U_156] : is_a_theorem(strict_implies(strict_implies(U_157,U_156),strict_implies(not(possibly(U_156)),not(possibly(U_157)))))
| ~ axiom_s3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_159,sK74)],[f_61_2]) ).
fof(f_61_4,plain,
( ( axiom_s3
| ~ is_a_theorem(strict_implies(strict_implies(sK74,sK75),strict_implies(not(possibly(sK75)),not(possibly(sK74))))) )
& ( ! [U_157,U_156] : is_a_theorem(strict_implies(strict_implies(U_157,U_156),strict_implies(not(possibly(U_156)),not(possibly(U_157)))))
| ~ axiom_s3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_158,sK75)],[f_61_3]) ).
cnf(f_61_5,plain,
( is_a_theorem(strict_implies(strict_implies(U_157,U_156),strict_implies(not(possibly(U_156)),not(possibly(U_157)))))
| ~ axiom_s3 ),
inference(clausify,[status(thm)],[f_61_4]) ).
cnf(f_61_6,plain,
( axiom_s3
| ~ is_a_theorem(strict_implies(strict_implies(sK74,sK75),strict_implies(not(possibly(sK75)),not(possibly(sK74))))) ),
inference(clausify,[status(thm)],[f_61_4]) ).
fof(f_62_1,plain,
( ( axiom_s4
| ? [X] : ~ is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X)))) )
& ( ! [X] : is_a_theorem(strict_implies(necessarily(X),necessarily(necessarily(X))))
| ~ axiom_s4 ) ),
inference(fof_nnf,[status(thm)],[axiom_s4]) ).
fof(f_62_2,plain,
( ( axiom_s4
| ? [U_161] : ~ is_a_theorem(strict_implies(necessarily(U_161),necessarily(necessarily(U_161)))) )
& ( ! [U_160] : is_a_theorem(strict_implies(necessarily(U_160),necessarily(necessarily(U_160))))
| ~ axiom_s4 ) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
( ( axiom_s4
| ~ is_a_theorem(strict_implies(necessarily(sK76),necessarily(necessarily(sK76)))) )
& ( ! [U_160] : is_a_theorem(strict_implies(necessarily(U_160),necessarily(necessarily(U_160))))
| ~ axiom_s4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_161,sK76)],[f_62_2]) ).
cnf(f_62_4,plain,
( is_a_theorem(strict_implies(necessarily(U_160),necessarily(necessarily(U_160))))
| ~ axiom_s4 ),
inference(clausify,[status(thm)],[f_62_3]) ).
cnf(f_62_5,plain,
( axiom_s4
| ~ is_a_theorem(strict_implies(necessarily(sK76),necessarily(necessarily(sK76)))) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
( ( axiom_m1
| ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),and(Y,X))) )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),and(Y,X)))
| ~ axiom_m1 ) ),
inference(fof_nnf,[status(thm)],[axiom_m1]) ).
fof(f_63_2,plain,
( ( axiom_m1
| ? [U_165,U_164] : ~ is_a_theorem(strict_implies(and(U_165,U_164),and(U_164,U_165))) )
& ( ! [U_163,U_162] : is_a_theorem(strict_implies(and(U_163,U_162),and(U_162,U_163)))
| ~ axiom_m1 ) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
( ( axiom_m1
| ? [U_164] : ~ is_a_theorem(strict_implies(and(sK77,U_164),and(U_164,sK77))) )
& ( ! [U_163,U_162] : is_a_theorem(strict_implies(and(U_163,U_162),and(U_162,U_163)))
| ~ axiom_m1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_165,sK77)],[f_63_2]) ).
fof(f_63_4,plain,
( ( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK77,sK78),and(sK78,sK77))) )
& ( ! [U_163,U_162] : is_a_theorem(strict_implies(and(U_163,U_162),and(U_162,U_163)))
| ~ axiom_m1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_164,sK78)],[f_63_3]) ).
cnf(f_63_5,plain,
( is_a_theorem(strict_implies(and(U_163,U_162),and(U_162,U_163)))
| ~ axiom_m1 ),
inference(clausify,[status(thm)],[f_63_4]) ).
cnf(f_63_6,plain,
( axiom_m1
| ~ is_a_theorem(strict_implies(and(sK77,sK78),and(sK78,sK77))) ),
inference(clausify,[status(thm)],[f_63_4]) ).
fof(f_64_1,plain,
( ( axiom_m2
| ? [X,Y] : ~ is_a_theorem(strict_implies(and(X,Y),X)) )
& ( ! [X,Y] : is_a_theorem(strict_implies(and(X,Y),X))
| ~ axiom_m2 ) ),
inference(fof_nnf,[status(thm)],[axiom_m2]) ).
fof(f_64_2,plain,
( ( axiom_m2
| ? [U_169,U_168] : ~ is_a_theorem(strict_implies(and(U_169,U_168),U_169)) )
& ( ! [U_167,U_166] : is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ( axiom_m2
| ? [U_168] : ~ is_a_theorem(strict_implies(and(sK79,U_168),sK79)) )
& ( ! [U_167,U_166] : is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_169,sK79)],[f_64_2]) ).
fof(f_64_4,plain,
( ( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK79,sK80),sK79)) )
& ( ! [U_167,U_166] : is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_168,sK80)],[f_64_3]) ).
cnf(f_64_5,plain,
( is_a_theorem(strict_implies(and(U_167,U_166),U_167))
| ~ axiom_m2 ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_6,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK79,sK80),sK79)) ),
inference(clausify,[status(thm)],[f_64_4]) ).
fof(f_65_1,plain,
( ( axiom_m3
| ? [X,Y,Z] : ~ is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z)))) )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(and(X,Y),Z),and(X,and(Y,Z))))
| ~ axiom_m3 ) ),
inference(fof_nnf,[status(thm)],[axiom_m3]) ).
fof(f_65_2,plain,
( ( axiom_m3
| ? [U_175,U_174,U_173] : ~ is_a_theorem(strict_implies(and(and(U_175,U_174),U_173),and(U_175,and(U_174,U_173)))) )
& ( ! [U_172,U_171,U_170] : is_a_theorem(strict_implies(and(and(U_172,U_171),U_170),and(U_172,and(U_171,U_170))))
| ~ axiom_m3 ) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
( ( axiom_m3
| ? [U_174,U_173] : ~ is_a_theorem(strict_implies(and(and(sK81,U_174),U_173),and(sK81,and(U_174,U_173)))) )
& ( ! [U_172,U_171,U_170] : is_a_theorem(strict_implies(and(and(U_172,U_171),U_170),and(U_172,and(U_171,U_170))))
| ~ axiom_m3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_175,sK81)],[f_65_2]) ).
fof(f_65_4,plain,
( ( axiom_m3
| ? [U_173] : ~ is_a_theorem(strict_implies(and(and(sK81,sK82),U_173),and(sK81,and(sK82,U_173)))) )
& ( ! [U_172,U_171,U_170] : is_a_theorem(strict_implies(and(and(U_172,U_171),U_170),and(U_172,and(U_171,U_170))))
| ~ axiom_m3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_174,sK82)],[f_65_3]) ).
fof(f_65_5,plain,
( ( axiom_m3
| ~ is_a_theorem(strict_implies(and(and(sK81,sK82),sK83),and(sK81,and(sK82,sK83)))) )
& ( ! [U_172,U_171,U_170] : is_a_theorem(strict_implies(and(and(U_172,U_171),U_170),and(U_172,and(U_171,U_170))))
| ~ axiom_m3 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_173,sK83)],[f_65_4]) ).
cnf(f_65_6,plain,
( is_a_theorem(strict_implies(and(and(U_172,U_171),U_170),and(U_172,and(U_171,U_170))))
| ~ axiom_m3 ),
inference(clausify,[status(thm)],[f_65_5]) ).
cnf(f_65_7,plain,
( axiom_m3
| ~ is_a_theorem(strict_implies(and(and(sK81,sK82),sK83),and(sK81,and(sK82,sK83)))) ),
inference(clausify,[status(thm)],[f_65_5]) ).
fof(f_66_1,plain,
( ( axiom_m4
| ? [X] : ~ is_a_theorem(strict_implies(X,and(X,X))) )
& ( ! [X] : is_a_theorem(strict_implies(X,and(X,X)))
| ~ axiom_m4 ) ),
inference(fof_nnf,[status(thm)],[axiom_m4]) ).
fof(f_66_2,plain,
( ( axiom_m4
| ? [U_177] : ~ is_a_theorem(strict_implies(U_177,and(U_177,U_177))) )
& ( ! [U_176] : is_a_theorem(strict_implies(U_176,and(U_176,U_176)))
| ~ axiom_m4 ) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
( ( axiom_m4
| ~ is_a_theorem(strict_implies(sK84,and(sK84,sK84))) )
& ( ! [U_176] : is_a_theorem(strict_implies(U_176,and(U_176,U_176)))
| ~ axiom_m4 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_177,sK84)],[f_66_2]) ).
cnf(f_66_4,plain,
( is_a_theorem(strict_implies(U_176,and(U_176,U_176)))
| ~ axiom_m4 ),
inference(clausify,[status(thm)],[f_66_3]) ).
cnf(f_66_5,plain,
( axiom_m4
| ~ is_a_theorem(strict_implies(sK84,and(sK84,sK84))) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
( ( axiom_m5
| ? [X,Y,Z] : ~ is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z))) )
& ( ! [X,Y,Z] : is_a_theorem(strict_implies(and(strict_implies(X,Y),strict_implies(Y,Z)),strict_implies(X,Z)))
| ~ axiom_m5 ) ),
inference(fof_nnf,[status(thm)],[axiom_m5]) ).
fof(f_67_2,plain,
( ( axiom_m5
| ? [U_183,U_182,U_181] : ~ is_a_theorem(strict_implies(and(strict_implies(U_183,U_182),strict_implies(U_182,U_181)),strict_implies(U_183,U_181))) )
& ( ! [U_180,U_179,U_178] : is_a_theorem(strict_implies(and(strict_implies(U_180,U_179),strict_implies(U_179,U_178)),strict_implies(U_180,U_178)))
| ~ axiom_m5 ) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ( axiom_m5
| ? [U_182,U_181] : ~ is_a_theorem(strict_implies(and(strict_implies(sK85,U_182),strict_implies(U_182,U_181)),strict_implies(sK85,U_181))) )
& ( ! [U_180,U_179,U_178] : is_a_theorem(strict_implies(and(strict_implies(U_180,U_179),strict_implies(U_179,U_178)),strict_implies(U_180,U_178)))
| ~ axiom_m5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_183,sK85)],[f_67_2]) ).
fof(f_67_4,plain,
( ( axiom_m5
| ? [U_181] : ~ is_a_theorem(strict_implies(and(strict_implies(sK85,sK86),strict_implies(sK86,U_181)),strict_implies(sK85,U_181))) )
& ( ! [U_180,U_179,U_178] : is_a_theorem(strict_implies(and(strict_implies(U_180,U_179),strict_implies(U_179,U_178)),strict_implies(U_180,U_178)))
| ~ axiom_m5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_182,sK86)],[f_67_3]) ).
fof(f_67_5,plain,
( ( axiom_m5
| ~ is_a_theorem(strict_implies(and(strict_implies(sK85,sK86),strict_implies(sK86,sK87)),strict_implies(sK85,sK87))) )
& ( ! [U_180,U_179,U_178] : is_a_theorem(strict_implies(and(strict_implies(U_180,U_179),strict_implies(U_179,U_178)),strict_implies(U_180,U_178)))
| ~ axiom_m5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_181,sK87)],[f_67_4]) ).
cnf(f_67_6,plain,
( is_a_theorem(strict_implies(and(strict_implies(U_180,U_179),strict_implies(U_179,U_178)),strict_implies(U_180,U_178)))
| ~ axiom_m5 ),
inference(clausify,[status(thm)],[f_67_5]) ).
cnf(f_67_7,plain,
( axiom_m5
| ~ is_a_theorem(strict_implies(and(strict_implies(sK85,sK86),strict_implies(sK86,sK87)),strict_implies(sK85,sK87))) ),
inference(clausify,[status(thm)],[f_67_5]) ).
fof(f_68_1,plain,
( ( axiom_m6
| ? [X] : ~ is_a_theorem(strict_implies(X,possibly(X))) )
& ( ! [X] : is_a_theorem(strict_implies(X,possibly(X)))
| ~ axiom_m6 ) ),
inference(fof_nnf,[status(thm)],[axiom_m6]) ).
fof(f_68_2,plain,
( ( axiom_m6
| ? [U_185] : ~ is_a_theorem(strict_implies(U_185,possibly(U_185))) )
& ( ! [U_184] : is_a_theorem(strict_implies(U_184,possibly(U_184)))
| ~ axiom_m6 ) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
( ( axiom_m6
| ~ is_a_theorem(strict_implies(sK88,possibly(sK88))) )
& ( ! [U_184] : is_a_theorem(strict_implies(U_184,possibly(U_184)))
| ~ axiom_m6 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_185,sK88)],[f_68_2]) ).
cnf(f_68_4,plain,
( is_a_theorem(strict_implies(U_184,possibly(U_184)))
| ~ axiom_m6 ),
inference(clausify,[status(thm)],[f_68_3]) ).
cnf(f_68_5,plain,
( axiom_m6
| ~ is_a_theorem(strict_implies(sK88,possibly(sK88))) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_1,plain,
( ( axiom_m7
| ? [P,Q] : ~ is_a_theorem(strict_implies(possibly(and(P,Q)),P)) )
& ( ! [P,Q] : is_a_theorem(strict_implies(possibly(and(P,Q)),P))
| ~ axiom_m7 ) ),
inference(fof_nnf,[status(thm)],[axiom_m7]) ).
fof(f_69_2,plain,
( ( axiom_m7
| ? [U_189,U_188] : ~ is_a_theorem(strict_implies(possibly(and(U_189,U_188)),U_189)) )
& ( ! [U_187,U_186] : is_a_theorem(strict_implies(possibly(and(U_187,U_186)),U_187))
| ~ axiom_m7 ) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
( ( axiom_m7
| ? [U_188] : ~ is_a_theorem(strict_implies(possibly(and(sK89,U_188)),sK89)) )
& ( ! [U_187,U_186] : is_a_theorem(strict_implies(possibly(and(U_187,U_186)),U_187))
| ~ axiom_m7 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_189,sK89)],[f_69_2]) ).
fof(f_69_4,plain,
( ( axiom_m7
| ~ is_a_theorem(strict_implies(possibly(and(sK89,sK90)),sK89)) )
& ( ! [U_187,U_186] : is_a_theorem(strict_implies(possibly(and(U_187,U_186)),U_187))
| ~ axiom_m7 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_188,sK90)],[f_69_3]) ).
cnf(f_69_5,plain,
( is_a_theorem(strict_implies(possibly(and(U_187,U_186)),U_187))
| ~ axiom_m7 ),
inference(clausify,[status(thm)],[f_69_4]) ).
cnf(f_69_6,plain,
( axiom_m7
| ~ is_a_theorem(strict_implies(possibly(and(sK89,sK90)),sK89)) ),
inference(clausify,[status(thm)],[f_69_4]) ).
fof(f_70_1,plain,
( ( axiom_m8
| ? [P,Q] : ~ is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q)))) )
& ( ! [P,Q] : is_a_theorem(strict_implies(strict_implies(P,Q),strict_implies(possibly(P),possibly(Q))))
| ~ axiom_m8 ) ),
inference(fof_nnf,[status(thm)],[axiom_m8]) ).
fof(f_70_2,plain,
( ( axiom_m8
| ? [U_193,U_192] : ~ is_a_theorem(strict_implies(strict_implies(U_193,U_192),strict_implies(possibly(U_193),possibly(U_192)))) )
& ( ! [U_191,U_190] : is_a_theorem(strict_implies(strict_implies(U_191,U_190),strict_implies(possibly(U_191),possibly(U_190))))
| ~ axiom_m8 ) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
( ( axiom_m8
| ? [U_192] : ~ is_a_theorem(strict_implies(strict_implies(sK91,U_192),strict_implies(possibly(sK91),possibly(U_192)))) )
& ( ! [U_191,U_190] : is_a_theorem(strict_implies(strict_implies(U_191,U_190),strict_implies(possibly(U_191),possibly(U_190))))
| ~ axiom_m8 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_193,sK91)],[f_70_2]) ).
fof(f_70_4,plain,
( ( axiom_m8
| ~ is_a_theorem(strict_implies(strict_implies(sK91,sK92),strict_implies(possibly(sK91),possibly(sK92)))) )
& ( ! [U_191,U_190] : is_a_theorem(strict_implies(strict_implies(U_191,U_190),strict_implies(possibly(U_191),possibly(U_190))))
| ~ axiom_m8 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_192,sK92)],[f_70_3]) ).
cnf(f_70_5,plain,
( is_a_theorem(strict_implies(strict_implies(U_191,U_190),strict_implies(possibly(U_191),possibly(U_190))))
| ~ axiom_m8 ),
inference(clausify,[status(thm)],[f_70_4]) ).
cnf(f_70_6,plain,
( axiom_m8
| ~ is_a_theorem(strict_implies(strict_implies(sK91,sK92),strict_implies(possibly(sK91),possibly(sK92)))) ),
inference(clausify,[status(thm)],[f_70_4]) ).
fof(f_71_1,plain,
( ( axiom_m9
| ? [X] : ~ is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X))) )
& ( ! [X] : is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))
| ~ axiom_m9 ) ),
inference(fof_nnf,[status(thm)],[axiom_m9]) ).
fof(f_71_2,plain,
( ( axiom_m9
| ? [U_195] : ~ is_a_theorem(strict_implies(possibly(possibly(U_195)),possibly(U_195))) )
& ( ! [U_194] : is_a_theorem(strict_implies(possibly(possibly(U_194)),possibly(U_194)))
| ~ axiom_m9 ) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
( ( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK93)),possibly(sK93))) )
& ( ! [U_194] : is_a_theorem(strict_implies(possibly(possibly(U_194)),possibly(U_194)))
| ~ axiom_m9 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_195,sK93)],[f_71_2]) ).
cnf(f_71_4,plain,
( is_a_theorem(strict_implies(possibly(possibly(U_194)),possibly(U_194)))
| ~ axiom_m9 ),
inference(clausify,[status(thm)],[f_71_3]) ).
cnf(f_71_5,plain,
( axiom_m9
| ~ is_a_theorem(strict_implies(possibly(possibly(sK93)),possibly(sK93))) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
( ( axiom_m10
| ? [X] : ~ is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X)))) )
& ( ! [X] : is_a_theorem(strict_implies(possibly(X),necessarily(possibly(X))))
| ~ axiom_m10 ) ),
inference(fof_nnf,[status(thm)],[axiom_m10]) ).
fof(f_72_2,plain,
( ( axiom_m10
| ? [U_197] : ~ is_a_theorem(strict_implies(possibly(U_197),necessarily(possibly(U_197)))) )
& ( ! [U_196] : is_a_theorem(strict_implies(possibly(U_196),necessarily(possibly(U_196))))
| ~ axiom_m10 ) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK94),necessarily(possibly(sK94)))) )
& ( ! [U_196] : is_a_theorem(strict_implies(possibly(U_196),necessarily(possibly(U_196))))
| ~ axiom_m10 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_197,sK94)],[f_72_2]) ).
cnf(f_72_4,plain,
( is_a_theorem(strict_implies(possibly(U_196),necessarily(possibly(U_196))))
| ~ axiom_m10 ),
inference(clausify,[status(thm)],[f_72_3]) ).
cnf(f_72_5,plain,
( axiom_m10
| ~ is_a_theorem(strict_implies(possibly(sK94),necessarily(possibly(sK94)))) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_1,plain,
( ! [X] : possibly(X) = not(necessarily(not(X)))
| ~ op_possibly ),
inference(fof_nnf,[status(thm)],[op_possibly]) ).
fof(f_73_2,plain,
( ! [U_198] : possibly(U_198) = not(necessarily(not(U_198)))
| ~ op_possibly ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
cnf(f_73_3,plain,
( possibly(U_198) = not(necessarily(not(U_198)))
| ~ op_possibly ),
inference(clausify,[status(thm)],[f_73_2]) ).
fof(f_74_1,plain,
( ! [X] : necessarily(X) = not(possibly(not(X)))
| ~ op_necessarily ),
inference(fof_nnf,[status(thm)],[op_necessarily]) ).
fof(f_74_2,plain,
( ! [U_199] : necessarily(U_199) = not(possibly(not(U_199)))
| ~ op_necessarily ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
cnf(f_74_3,plain,
( necessarily(U_199) = not(possibly(not(U_199)))
| ~ op_necessarily ),
inference(clausify,[status(thm)],[f_74_2]) ).
fof(f_75_1,plain,
( ! [X,Y] : strict_implies(X,Y) = necessarily(implies(X,Y))
| ~ op_strict_implies ),
inference(fof_nnf,[status(thm)],[op_strict_implies]) ).
fof(f_75_2,plain,
( ! [U_201,U_200] : strict_implies(U_201,U_200) = necessarily(implies(U_201,U_200))
| ~ op_strict_implies ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
cnf(f_75_3,plain,
( strict_implies(U_201,U_200) = necessarily(implies(U_201,U_200))
| ~ op_strict_implies ),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_1,plain,
( ! [X,Y] : strict_equiv(X,Y) = and(strict_implies(X,Y),strict_implies(Y,X))
| ~ op_strict_equiv ),
inference(fof_nnf,[status(thm)],[op_strict_equiv]) ).
fof(f_76_2,plain,
( ! [U_203,U_202] : strict_equiv(U_203,U_202) = and(strict_implies(U_203,U_202),strict_implies(U_202,U_203))
| ~ op_strict_equiv ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
cnf(f_76_3,plain,
( strict_equiv(U_203,U_202) = and(strict_implies(U_203,U_202),strict_implies(U_202,U_203))
| ~ op_strict_equiv ),
inference(clausify,[status(thm)],[f_76_2]) ).
fof(f_77_1,plain,
op_possibly,
inference(fof_nnf,[status(thm)],[km5_op_possibly]) ).
cnf(f_77_2,plain,
op_possibly,
inference(clausify,[status(thm)],[f_77_1]) ).
fof(f_78_1,plain,
necessitation,
inference(fof_nnf,[status(thm)],[km5_necessitation]) ).
cnf(f_78_2,plain,
necessitation,
inference(clausify,[status(thm)],[f_78_1]) ).
fof(f_79_1,plain,
axiom_K,
inference(fof_nnf,[status(thm)],[km5_axiom_K]) ).
cnf(f_79_2,plain,
axiom_K,
inference(clausify,[status(thm)],[f_79_1]) ).
fof(f_80_1,plain,
axiom_M,
inference(fof_nnf,[status(thm)],[km5_axiom_M]) ).
cnf(f_80_2,plain,
axiom_M,
inference(clausify,[status(thm)],[f_80_1]) ).
fof(f_81_1,plain,
axiom_5,
inference(fof_nnf,[status(thm)],[km5_axiom_5]) ).
cnf(f_81_2,plain,
axiom_5,
inference(clausify,[status(thm)],[f_81_1]) ).
fof(f_82_1,plain,
op_possibly,
inference(fof_nnf,[status(thm)],[s1_0_op_possibly]) ).
cnf(f_82_2,plain,
op_possibly,
inference(clausify,[status(thm)],[f_82_1]) ).
fof(f_83_1,plain,
op_or,
inference(fof_nnf,[status(thm)],[s1_0_op_or]) ).
cnf(f_83_2,plain,
op_or,
inference(clausify,[status(thm)],[f_83_1]) ).
fof(f_84_1,plain,
op_implies,
inference(fof_nnf,[status(thm)],[s1_0_op_implies]) ).
cnf(f_84_2,plain,
op_implies,
inference(clausify,[status(thm)],[f_84_1]) ).
fof(f_85_1,plain,
op_strict_implies,
inference(fof_nnf,[status(thm)],[s1_0_op_strict_implies]) ).
cnf(f_85_2,plain,
op_strict_implies,
inference(clausify,[status(thm)],[f_85_1]) ).
fof(f_86_1,plain,
op_equiv,
inference(fof_nnf,[status(thm)],[s1_0_op_equiv]) ).
cnf(f_86_2,plain,
op_equiv,
inference(clausify,[status(thm)],[f_86_1]) ).
fof(f_87_1,plain,
op_strict_equiv,
inference(fof_nnf,[status(thm)],[s1_0_op_strict_equiv]) ).
cnf(f_87_2,plain,
op_strict_equiv,
inference(clausify,[status(thm)],[f_87_1]) ).
fof(f_88_1,negated_conjecture,
~ substitution_strict_equiv,
inference(negate,[status(cth)],[s1_0_substitution_strict_equiv]) ).
fof(f_88_2,negated_conjecture,
~ substitution_strict_equiv,
inference(definitional_conversion,[status(esa)],[f_88_1]) ).
cnf(f_88_3,negated_conjecture,
~ substitution_strict_equiv,
inference(clausify,[status(thm)],[f_88_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( implies(Eq_x_0,Eq_x_1) = implies(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( equiv(Eq_x_0,Eq_x_1) = equiv(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( not(Eq_x_0) = not(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( and(Eq_x_0,Eq_x_1) = and(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( or(Eq_x_0,Eq_x_1) = or(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( necessarily(Eq_x_0) = necessarily(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( strict_implies(Eq_x_0,Eq_x_1) = strict_implies(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( strict_equiv(Eq_x_0,Eq_x_1) = strict_equiv(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( possibly(Eq_x_0) = possibly(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( is_a_theorem(Eq_y_0)
| ~ is_a_theorem(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL526+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 15:10:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 120.11/120.47 % SZS status Theorem for theBenchmark
% 120.11/120.47 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------