TSTP Solution File: LCL538+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 12:24:01 EDT 2022
% Result : Theorem 0.53s 0.80s
% Output : CNFRefutation 0.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 258
% Syntax : Number of formulae : 1222 ( 596 unt; 169 typ; 0 def)
% Number of atoms : 5516 (1517 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 11064 (1657 ~;1411 |; 134 &;7722 @)
% ( 98 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 172 ( 169 usr; 161 con; 0-2 aty)
% Number of variables : 1302 ( 0 ^1302 !; 0 ?;1302 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_adjunction,type,
adjunction: $o ).
thf(tp_and,type,
and: $i > $i > $i ).
thf(tp_and_1,type,
and_1: $o ).
thf(tp_and_2,type,
and_2: $o ).
thf(tp_and_3,type,
and_3: $o ).
thf(tp_axiom_4,type,
axiom_4: $o ).
thf(tp_axiom_5,type,
axiom_5: $o ).
thf(tp_axiom_B,type,
axiom_B: $o ).
thf(tp_axiom_K,type,
axiom_K: $o ).
thf(tp_axiom_M,type,
axiom_M: $o ).
thf(tp_axiom_m1,type,
axiom_m1: $o ).
thf(tp_axiom_m10,type,
axiom_m10: $o ).
thf(tp_axiom_m2,type,
axiom_m2: $o ).
thf(tp_axiom_m3,type,
axiom_m3: $o ).
thf(tp_axiom_m4,type,
axiom_m4: $o ).
thf(tp_axiom_m5,type,
axiom_m5: $o ).
thf(tp_axiom_m6,type,
axiom_m6: $o ).
thf(tp_axiom_m7,type,
axiom_m7: $o ).
thf(tp_axiom_m8,type,
axiom_m8: $o ).
thf(tp_axiom_m9,type,
axiom_m9: $o ).
thf(tp_axiom_s1,type,
axiom_s1: $o ).
thf(tp_axiom_s2,type,
axiom_s2: $o ).
thf(tp_axiom_s3,type,
axiom_s3: $o ).
thf(tp_axiom_s4,type,
axiom_s4: $o ).
thf(tp_cn1,type,
cn1: $o ).
thf(tp_cn2,type,
cn2: $o ).
thf(tp_cn3,type,
cn3: $o ).
thf(tp_equiv,type,
equiv: $i > $i > $i ).
thf(tp_equivalence_1,type,
equivalence_1: $o ).
thf(tp_equivalence_2,type,
equivalence_2: $o ).
thf(tp_equivalence_3,type,
equivalence_3: $o ).
thf(tp_implies,type,
implies: $i > $i > $i ).
thf(tp_implies_1,type,
implies_1: $o ).
thf(tp_implies_2,type,
implies_2: $o ).
thf(tp_implies_3,type,
implies_3: $o ).
thf(tp_is_a_theorem,type,
is_a_theorem: $i > $o ).
thf(tp_kn1,type,
kn1: $o ).
thf(tp_kn2,type,
kn2: $o ).
thf(tp_kn3,type,
kn3: $o ).
thf(tp_modus_ponens,type,
modus_ponens: $o ).
thf(tp_modus_ponens_strict_implies,type,
modus_ponens_strict_implies: $o ).
thf(tp_modus_tollens,type,
modus_tollens: $o ).
thf(tp_necessarily,type,
necessarily: $i > $i ).
thf(tp_necessitation,type,
necessitation: $o ).
thf(tp_not,type,
not: $i > $i ).
thf(tp_op_and,type,
op_and: $o ).
thf(tp_op_equiv,type,
op_equiv: $o ).
thf(tp_op_implies,type,
op_implies: $o ).
thf(tp_op_implies_and,type,
op_implies_and: $o ).
thf(tp_op_implies_or,type,
op_implies_or: $o ).
thf(tp_op_necessarily,type,
op_necessarily: $o ).
thf(tp_op_or,type,
op_or: $o ).
thf(tp_op_possibly,type,
op_possibly: $o ).
thf(tp_op_strict_equiv,type,
op_strict_equiv: $o ).
thf(tp_op_strict_implies,type,
op_strict_implies: $o ).
thf(tp_or,type,
or: $i > $i > $i ).
thf(tp_or_1,type,
or_1: $o ).
thf(tp_or_2,type,
or_2: $o ).
thf(tp_or_3,type,
or_3: $o ).
thf(tp_possibly,type,
possibly: $i > $i ).
thf(tp_r1,type,
r1: $o ).
thf(tp_r2,type,
r2: $o ).
thf(tp_r3,type,
r3: $o ).
thf(tp_r4,type,
r4: $o ).
thf(tp_r5,type,
r5: $o ).
thf(tp_sK100_REN,type,
sK100_REN: $o ).
thf(tp_sK10_SY114,type,
sK10_SY114: $i ).
thf(tp_sK11_X,type,
sK11_X: $i ).
thf(tp_sK12_X,type,
sK12_X: $i ).
thf(tp_sK13_SY115,type,
sK13_SY115: $i ).
thf(tp_sK14_SY117,type,
sK14_SY117: $i ).
thf(tp_sK15_X,type,
sK15_X: $i ).
thf(tp_sK16_SY118,type,
sK16_SY118: $i ).
thf(tp_sK17_X,type,
sK17_X: $i ).
thf(tp_sK18_SY119,type,
sK18_SY119: $i ).
thf(tp_sK19_X,type,
sK19_X: $i ).
thf(tp_sK1_X,type,
sK1_X: $i ).
thf(tp_sK20_X,type,
sK20_X: $i ).
thf(tp_sK21_SY120,type,
sK21_SY120: $i ).
thf(tp_sK22_P,type,
sK22_P: $i ).
thf(tp_sK23_SY121,type,
sK23_SY121: $i ).
thf(tp_sK24_X,type,
sK24_X: $i ).
thf(tp_sK25_SY122,type,
sK25_SY122: $i ).
thf(tp_sK26_SY124,type,
sK26_SY124: $i ).
thf(tp_sK27_X,type,
sK27_X: $i ).
thf(tp_sK28_X,type,
sK28_X: $i ).
thf(tp_sK29_X,type,
sK29_X: $i ).
thf(tp_sK2_X,type,
sK2_X: $i ).
thf(tp_sK30_X,type,
sK30_X: $i ).
thf(tp_sK31_X,type,
sK31_X: $i ).
thf(tp_sK32_SY125,type,
sK32_SY125: $i ).
thf(tp_sK33_X,type,
sK33_X: $i ).
thf(tp_sK34_SY126,type,
sK34_SY126: $i ).
thf(tp_sK35_REN,type,
sK35_REN: $o ).
thf(tp_sK36_X,type,
sK36_X: $i ).
thf(tp_sK37_SY127,type,
sK37_SY127: $i ).
thf(tp_sK38_REN,type,
sK38_REN: $o ).
thf(tp_sK39_X,type,
sK39_X: $i ).
thf(tp_sK3_P,type,
sK3_P: $i ).
thf(tp_sK40_SY128,type,
sK40_SY128: $i ).
thf(tp_sK41_REN,type,
sK41_REN: $o ).
thf(tp_sK42_X,type,
sK42_X: $i ).
thf(tp_sK43_REN,type,
sK43_REN: $o ).
thf(tp_sK44_P,type,
sK44_P: $i ).
thf(tp_sK45_SY129,type,
sK45_SY129: $i ).
thf(tp_sK46_SY131,type,
sK46_SY131: $i ).
thf(tp_sK47_P,type,
sK47_P: $i ).
thf(tp_sK48_SY132,type,
sK48_SY132: $i ).
thf(tp_sK49_SY134,type,
sK49_SY134: $i ).
thf(tp_sK4_SY110,type,
sK4_SY110: $i ).
thf(tp_sK50_P,type,
sK50_P: $i ).
thf(tp_sK51_SY135,type,
sK51_SY135: $i ).
thf(tp_sK52_P,type,
sK52_P: $i ).
thf(tp_sK53_SY136,type,
sK53_SY136: $i ).
thf(tp_sK54_P,type,
sK54_P: $i ).
thf(tp_sK55_P,type,
sK55_P: $i ).
thf(tp_sK56_P,type,
sK56_P: $i ).
thf(tp_sK57_SY137,type,
sK57_SY137: $i ).
thf(tp_sK58_P,type,
sK58_P: $i ).
thf(tp_sK59_SY138,type,
sK59_SY138: $i ).
thf(tp_sK5_P,type,
sK5_P: $i ).
thf(tp_sK60_SY140,type,
sK60_SY140: $i ).
thf(tp_sK61_P,type,
sK61_P: $i ).
thf(tp_sK62_SY141,type,
sK62_SY141: $i ).
thf(tp_sK63_SY143,type,
sK63_SY143: $i ).
thf(tp_sK64_P,type,
sK64_P: $i ).
thf(tp_sK65_SY144,type,
sK65_SY144: $i ).
thf(tp_sK66_P,type,
sK66_P: $i ).
thf(tp_sK67_X,type,
sK67_X: $i ).
thf(tp_sK68_SY145,type,
sK68_SY145: $i ).
thf(tp_sK69_X,type,
sK69_X: $i ).
thf(tp_sK6_SY111,type,
sK6_SY111: $i ).
thf(tp_sK70_SY146,type,
sK70_SY146: $i ).
thf(tp_sK71_X,type,
sK71_X: $i ).
thf(tp_sK72_SY147,type,
sK72_SY147: $i ).
thf(tp_sK73_X,type,
sK73_X: $i ).
thf(tp_sK74_SY148,type,
sK74_SY148: $i ).
thf(tp_sK75_SY150,type,
sK75_SY150: $i ).
thf(tp_sK76_X,type,
sK76_X: $i ).
thf(tp_sK77_SY151,type,
sK77_SY151: $i ).
thf(tp_sK78_X,type,
sK78_X: $i ).
thf(tp_sK79_SY152,type,
sK79_SY152: $i ).
thf(tp_sK7_X,type,
sK7_X: $i ).
thf(tp_sK80_X,type,
sK80_X: $i ).
thf(tp_sK81_SY153,type,
sK81_SY153: $i ).
thf(tp_sK82_X,type,
sK82_X: $i ).
thf(tp_sK83_SY154,type,
sK83_SY154: $i ).
thf(tp_sK84_X,type,
sK84_X: $i ).
thf(tp_sK85_SY155,type,
sK85_SY155: $i ).
thf(tp_sK86_X,type,
sK86_X: $i ).
thf(tp_sK87_SY156,type,
sK87_SY156: $i ).
thf(tp_sK88_SY158,type,
sK88_SY158: $i ).
thf(tp_sK89_X,type,
sK89_X: $i ).
thf(tp_sK8_X,type,
sK8_X: $i ).
thf(tp_sK90_SY159,type,
sK90_SY159: $i ).
thf(tp_sK91_X,type,
sK91_X: $i ).
thf(tp_sK92_SY160,type,
sK92_SY160: $i ).
thf(tp_sK93_X,type,
sK93_X: $i ).
thf(tp_sK94_SY161,type,
sK94_SY161: $i ).
thf(tp_sK95_X,type,
sK95_X: $i ).
thf(tp_sK96_SY162,type,
sK96_SY162: $i ).
thf(tp_sK97_REN,type,
sK97_REN: $o ).
thf(tp_sK98_X,type,
sK98_X: $i ).
thf(tp_sK99_SY163,type,
sK99_SY163: $i ).
thf(tp_sK9_SY112,type,
sK9_SY112: $i ).
thf(tp_strict_equiv,type,
strict_equiv: $i > $i > $i ).
thf(tp_strict_implies,type,
strict_implies: $i > $i > $i ).
thf(tp_substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
thf(tp_substitution_strict_equiv,type,
substitution_strict_equiv: $o ).
thf(1,axiom,
op_strict_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_equiv) ).
thf(2,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_equiv) ).
thf(3,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
thf(4,axiom,
op_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_implies) ).
thf(5,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_or) ).
thf(6,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_possibly) ).
thf(7,axiom,
axiom_B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_B) ).
thf(8,axiom,
axiom_4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_4) ).
thf(9,axiom,
axiom_M,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_M) ).
thf(10,axiom,
axiom_K,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_axiom_K) ).
thf(11,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_necessitation) ).
thf(12,axiom,
op_possibly,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',km4b_op_possibly) ).
thf(13,axiom,
( op_strict_equiv
=> ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_equiv) ).
thf(14,axiom,
( op_strict_implies
=> ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_strict_implies) ).
thf(15,axiom,
( op_necessarily
=> ! [X: $i] :
( ( necessarily @ X )
= ( not @ ( possibly @ ( not @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_necessarily) ).
thf(16,axiom,
( op_possibly
=> ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_possibly) ).
thf(17,axiom,
( axiom_m10
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m10) ).
thf(18,axiom,
( axiom_m9
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X ) ) @ ( possibly @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m9) ).
thf(19,axiom,
( axiom_m8
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ P @ Q ) @ ( strict_implies @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m8) ).
thf(20,axiom,
( axiom_m7
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m7) ).
thf(21,axiom,
( axiom_m6
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( possibly @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m6) ).
thf(22,axiom,
( axiom_m5
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ Z ) ) @ ( strict_implies @ X @ Z ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m5) ).
thf(23,axiom,
( axiom_m4
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( and @ X @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m4) ).
thf(24,axiom,
( axiom_m3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ X @ Y ) @ Z ) @ ( and @ X @ ( and @ Y @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m3) ).
thf(25,axiom,
( axiom_m2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m2) ).
thf(26,axiom,
( axiom_m1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ ( and @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_m1) ).
thf(27,axiom,
( axiom_s4
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s4) ).
thf(28,axiom,
( axiom_s3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ X @ Y ) @ ( strict_implies @ ( not @ ( possibly @ Y ) ) @ ( not @ ( possibly @ X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s3) ).
thf(29,axiom,
( axiom_s2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ ( and @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s2) ).
thf(30,axiom,
( axiom_s1
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ X @ Y ) ) @ ( necessarily @ ( implies @ Y @ Z ) ) ) @ ( necessarily @ ( implies @ X @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_s1) ).
thf(31,axiom,
( axiom_5
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(32,axiom,
( axiom_B
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ X @ ( necessarily @ ( possibly @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_B) ).
thf(33,axiom,
( axiom_4
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(34,axiom,
( axiom_M
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_M) ).
thf(35,axiom,
( axiom_K
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ X @ Y ) ) @ ( implies @ ( necessarily @ X ) @ ( necessarily @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_K) ).
thf(36,axiom,
( substitution_strict_equiv
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( strict_equiv @ X @ Y ) )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_strict_equiv) ).
thf(37,axiom,
( adjunction
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ Y ) )
=> ( is_a_theorem @ ( and @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adjunction) ).
thf(38,axiom,
( modus_ponens_strict_implies
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ ( strict_implies @ X @ Y ) ) )
=> ( is_a_theorem @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens_strict_implies) ).
thf(39,axiom,
( necessitation
<=> ! [X: $i] :
( ( is_a_theorem @ X )
=> ( is_a_theorem @ ( necessarily @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',necessitation) ).
thf(40,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(41,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
thf(42,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(43,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
thf(44,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
thf(45,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(46,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(47,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(48,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
thf(49,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(50,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
thf(51,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
thf(52,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
thf(53,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
thf(54,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
thf(55,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(56,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(57,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(58,axiom,
( op_equiv
=> ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_equiv) ).
thf(59,axiom,
( op_implies_or
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_or) ).
thf(60,axiom,
( op_implies_and
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_implies_and) ).
thf(61,axiom,
( op_and
=> ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_and) ).
thf(62,axiom,
( op_or
=> ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',op_or) ).
thf(63,axiom,
( r5
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(64,axiom,
( r4
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(65,axiom,
( r3
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3) ).
thf(66,axiom,
( r2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(67,axiom,
( r1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(68,axiom,
( cn3
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(69,axiom,
( cn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(70,axiom,
( cn1
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn1) ).
thf(71,axiom,
( kn3
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn3) ).
thf(72,axiom,
( kn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(73,axiom,
( kn1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(74,axiom,
( equivalence_3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_3) ).
thf(75,axiom,
( equivalence_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_2) ).
thf(76,axiom,
( equivalence_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalence_1) ).
thf(77,axiom,
( or_3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_3) ).
thf(78,axiom,
( or_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_2) ).
thf(79,axiom,
( or_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_1) ).
thf(80,axiom,
( and_3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_3) ).
thf(81,axiom,
( and_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_2) ).
thf(82,axiom,
( and_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_1) ).
thf(83,axiom,
( implies_3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_3) ).
thf(84,axiom,
( implies_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_2) ).
thf(85,axiom,
( implies_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_1) ).
thf(86,axiom,
( modus_tollens
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_tollens) ).
thf(87,axiom,
( substitution_of_equivalents
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( equiv @ X @ Y ) )
=> ( X = Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(88,axiom,
( modus_ponens
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ ( implies @ X @ Y ) ) )
=> ( is_a_theorem @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modus_ponens) ).
thf(89,conjecture,
modus_ponens_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_modus_ponens_strict_implies) ).
thf(90,negated_conjecture,
modus_ponens_strict_implies = $false,
inference(negate_conjecture,[status(cth)],[89]) ).
thf(91,plain,
modus_ponens_strict_implies = $false,
inference(unfold_def,[status(thm)],[90]) ).
thf(92,plain,
op_strict_equiv = $true,
inference(unfold_def,[status(thm)],[1]) ).
thf(93,plain,
op_equiv = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(94,plain,
op_strict_implies = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(95,plain,
op_implies = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(96,plain,
op_or = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(97,plain,
op_possibly = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(98,plain,
axiom_B = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(99,plain,
axiom_4 = $true,
inference(unfold_def,[status(thm)],[8]) ).
thf(100,plain,
axiom_M = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(101,plain,
axiom_K = $true,
inference(unfold_def,[status(thm)],[10]) ).
thf(102,plain,
necessitation = $true,
inference(unfold_def,[status(thm)],[11]) ).
thf(103,plain,
op_possibly = $true,
inference(unfold_def,[status(thm)],[12]) ).
thf(104,plain,
( ( op_strict_equiv
=> ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(105,plain,
( ( op_strict_implies
=> ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(106,plain,
( ( op_necessarily
=> ! [X: $i] :
( ( necessarily @ X )
= ( not @ ( possibly @ ( not @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(107,plain,
( ( op_possibly
=> ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(108,plain,
( ( axiom_m10
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(109,plain,
( ( axiom_m9
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X ) ) @ ( possibly @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(110,plain,
( ( axiom_m8
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ P @ Q ) @ ( strict_implies @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(111,plain,
( ( axiom_m7
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(112,plain,
( ( axiom_m6
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( possibly @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(113,plain,
( ( axiom_m5
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ Z ) ) @ ( strict_implies @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(114,plain,
( ( axiom_m4
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( and @ X @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(115,plain,
( ( axiom_m3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ X @ Y ) @ Z ) @ ( and @ X @ ( and @ Y @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(116,plain,
( ( axiom_m2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(117,plain,
( ( axiom_m1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ ( and @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(118,plain,
( ( axiom_s4
<=> ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(119,plain,
( ( axiom_s3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ X @ Y ) @ ( strict_implies @ ( not @ ( possibly @ Y ) ) @ ( not @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(120,plain,
( ( axiom_s2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ ( and @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(121,plain,
( ( axiom_s1
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ X @ Y ) ) @ ( necessarily @ ( implies @ Y @ Z ) ) ) @ ( necessarily @ ( implies @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(122,plain,
( ( axiom_5
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(123,plain,
( ( axiom_B
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ X @ ( necessarily @ ( possibly @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(124,plain,
( ( axiom_4
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(125,plain,
( ( axiom_M
<=> ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(126,plain,
( ( axiom_K
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ X @ Y ) ) @ ( implies @ ( necessarily @ X ) @ ( necessarily @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(127,plain,
( ( substitution_strict_equiv
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( strict_equiv @ X @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(128,plain,
( ( adjunction
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ Y ) )
=> ( is_a_theorem @ ( and @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(129,plain,
( ( modus_ponens_strict_implies
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ ( strict_implies @ X @ Y ) ) )
=> ( is_a_theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(130,plain,
( ( necessitation
<=> ! [X: $i] :
( ( is_a_theorem @ X )
=> ( is_a_theorem @ ( necessarily @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(131,plain,
substitution_of_equivalents = $true,
inference(unfold_def,[status(thm)],[40]) ).
thf(132,plain,
equivalence_3 = $true,
inference(unfold_def,[status(thm)],[41]) ).
thf(133,plain,
equivalence_2 = $true,
inference(unfold_def,[status(thm)],[42]) ).
thf(134,plain,
equivalence_1 = $true,
inference(unfold_def,[status(thm)],[43]) ).
thf(135,plain,
or_3 = $true,
inference(unfold_def,[status(thm)],[44]) ).
thf(136,plain,
or_2 = $true,
inference(unfold_def,[status(thm)],[45]) ).
thf(137,plain,
or_1 = $true,
inference(unfold_def,[status(thm)],[46]) ).
thf(138,plain,
and_3 = $true,
inference(unfold_def,[status(thm)],[47]) ).
thf(139,plain,
and_2 = $true,
inference(unfold_def,[status(thm)],[48]) ).
thf(140,plain,
and_1 = $true,
inference(unfold_def,[status(thm)],[49]) ).
thf(141,plain,
implies_3 = $true,
inference(unfold_def,[status(thm)],[50]) ).
thf(142,plain,
implies_2 = $true,
inference(unfold_def,[status(thm)],[51]) ).
thf(143,plain,
implies_1 = $true,
inference(unfold_def,[status(thm)],[52]) ).
thf(144,plain,
modus_tollens = $true,
inference(unfold_def,[status(thm)],[53]) ).
thf(145,plain,
modus_ponens = $true,
inference(unfold_def,[status(thm)],[54]) ).
thf(146,plain,
op_equiv = $true,
inference(unfold_def,[status(thm)],[55]) ).
thf(147,plain,
op_implies_and = $true,
inference(unfold_def,[status(thm)],[56]) ).
thf(148,plain,
op_or = $true,
inference(unfold_def,[status(thm)],[57]) ).
thf(149,plain,
( ( op_equiv
=> ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(150,plain,
( ( op_implies_or
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(151,plain,
( ( op_implies_and
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(152,plain,
( ( op_and
=> ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(153,plain,
( ( op_or
=> ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(154,plain,
( ( r5
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(155,plain,
( ( r4
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(156,plain,
( ( r3
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(157,plain,
( ( r2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(158,plain,
( ( r1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(159,plain,
( ( cn3
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(160,plain,
( ( cn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(161,plain,
( ( cn1
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(162,plain,
( ( kn3
<=> ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(163,plain,
( ( kn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(164,plain,
( ( kn1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(165,plain,
( ( equivalence_3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(166,plain,
( ( equivalence_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(167,plain,
( ( equivalence_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(168,plain,
( ( or_3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(169,plain,
( ( or_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(170,plain,
( ( or_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(171,plain,
( ( and_3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(172,plain,
( ( and_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(173,plain,
( ( and_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(174,plain,
( ( implies_3
<=> ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(175,plain,
( ( implies_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(176,plain,
( ( implies_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(177,plain,
( ( modus_tollens
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(178,plain,
( ( substitution_of_equivalents
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( equiv @ X @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(179,plain,
( ( modus_ponens
<=> ! [X: $i,Y: $i] :
( ( ( is_a_theorem @ X )
& ( is_a_theorem @ ( implies @ X @ Y ) ) )
=> ( is_a_theorem @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(180,plain,
( ( ~ modus_ponens_strict_implies )
= $true ),
inference(polarity_switch,[status(thm)],[91]) ).
thf(181,plain,
( ( ~ op_strict_equiv
| ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(182,plain,
( ( ~ op_strict_implies
| ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(183,plain,
( ( ~ op_necessarily
| ! [X: $i] :
( ( necessarily @ X )
= ( not @ ( possibly @ ( not @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(184,plain,
( ( ~ op_possibly
| ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(185,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
| axiom_m10 )
& ( ~ axiom_m10
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(186,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
| axiom_m9 )
& ( ~ axiom_m9
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X ) ) @ ( possibly @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(187,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
| axiom_m8 )
& ( ~ axiom_m8
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ P @ Q ) @ ( strict_implies @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(188,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
| axiom_m7 )
& ( ~ axiom_m7
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(189,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
| axiom_m6 )
& ( ~ axiom_m6
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( possibly @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(190,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
| axiom_m5 )
& ( ~ axiom_m5
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ Z ) ) @ ( strict_implies @ X @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(191,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
| axiom_m4 )
& ( ~ axiom_m4
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( and @ X @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(192,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
| axiom_m3 )
& ( ~ axiom_m3
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ X @ Y ) @ Z ) @ ( and @ X @ ( and @ Y @ Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(193,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
| axiom_m2 )
& ( ~ axiom_m2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(194,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
| axiom_m1 )
& ( ~ axiom_m1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ ( and @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[117]) ).
thf(195,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
| axiom_s4 )
& ( ~ axiom_s4
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(196,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
| axiom_s3 )
& ( ~ axiom_s3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ X @ Y ) @ ( strict_implies @ ( not @ ( possibly @ Y ) ) @ ( not @ ( possibly @ X ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(197,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
| axiom_s2 )
& ( ~ axiom_s2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ ( and @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[120]) ).
thf(198,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
| axiom_s1 )
& ( ~ axiom_s1
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ X @ Y ) ) @ ( necessarily @ ( implies @ Y @ Z ) ) ) @ ( necessarily @ ( implies @ X @ Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(199,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
| axiom_5 )
& ( ~ axiom_5
| ! [X: $i] : ( is_a_theorem @ ( implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(200,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
| axiom_B )
& ( ~ axiom_B
| ! [X: $i] : ( is_a_theorem @ ( implies @ X @ ( necessarily @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(201,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
| axiom_4 )
& ( ~ axiom_4
| ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(202,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
| axiom_M )
& ( ~ axiom_M
| ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(203,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
| axiom_K )
& ( ~ axiom_K
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ X @ Y ) ) @ ( implies @ ( necessarily @ X ) @ ( necessarily @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(204,plain,
( ( ( sK35_REN
| substitution_strict_equiv )
& ( sK35_REN
=> ( ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
& ( sK33_X != sK34_SY126 ) ) )
& ( ~ substitution_strict_equiv
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X @ Y ) )
| ( X = Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(205,plain,
( ( ( sK38_REN
| adjunction )
& ( sK38_REN
=> ( ( is_a_theorem @ sK36_X )
& ( is_a_theorem @ sK37_SY127 )
& ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) )
& ( ~ adjunction
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ X )
| ~ ( is_a_theorem @ Y )
| ( is_a_theorem @ ( and @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(206,plain,
( ( ( sK41_REN
| modus_ponens_strict_implies )
& ( sK41_REN
=> ( ( is_a_theorem @ sK39_X )
& ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) )
& ~ ( is_a_theorem @ sK40_SY128 ) ) )
& ( ~ modus_ponens_strict_implies
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ X )
| ~ ( is_a_theorem @ ( strict_implies @ X @ Y ) )
| ( is_a_theorem @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(207,plain,
( ( ( sK43_REN
| necessitation )
& ( sK43_REN
=> ( ( is_a_theorem @ sK42_X )
& ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) )
& ( ~ necessitation
| ! [X: $i] :
( ~ ( is_a_theorem @ X )
| ( is_a_theorem @ ( necessarily @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(208,plain,
( ( ~ op_equiv
| ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(209,plain,
( ( ~ op_implies_or
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(210,plain,
( ( ~ op_implies_and
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(211,plain,
( ( ~ op_and
| ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(212,plain,
( ( ~ op_or
| ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(213,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
| r5 )
& ( ~ r5
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(214,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
| r4 )
& ( ~ r4
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(215,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
| r3 )
& ( ~ r3
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(216,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
| r2 )
& ( ~ r2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(217,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
| r1 )
& ( ~ r1
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(218,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
| cn3 )
& ( ~ cn3
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(219,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
| cn2 )
& ( ~ cn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(220,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
| cn1 )
& ( ~ cn1
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(221,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
| kn3 )
& ( ~ kn3
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(222,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
| kn2 )
& ( ~ kn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(223,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
| kn1 )
& ( ~ kn1
| ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(224,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
| equivalence_3 )
& ( ~ equivalence_3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[165]) ).
thf(225,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
| equivalence_2 )
& ( ~ equivalence_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(226,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
| equivalence_1 )
& ( ~ equivalence_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[167]) ).
thf(227,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
| or_3 )
& ( ~ or_3
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(228,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
| or_2 )
& ( ~ or_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(229,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
| or_1 )
& ( ~ or_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[170]) ).
thf(230,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
| and_3 )
& ( ~ and_3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(231,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
| and_2 )
& ( ~ and_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(232,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
| and_1 )
& ( ~ and_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(233,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
| implies_3 )
& ( ~ implies_3
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(234,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
| implies_2 )
& ( ~ implies_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[175]) ).
thf(235,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
| implies_1 )
& ( ~ implies_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(236,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
| modus_tollens )
& ( ~ modus_tollens
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[177]) ).
thf(237,plain,
( ( ( sK97_REN
| substitution_of_equivalents )
& ( sK97_REN
=> ( ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
& ( sK95_X != sK96_SY162 ) ) )
& ( ~ substitution_of_equivalents
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equiv @ X @ Y ) )
| ( X = Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[178]) ).
thf(238,plain,
( ( ( sK100_REN
| modus_ponens )
& ( sK100_REN
=> ( ( is_a_theorem @ sK98_X )
& ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) )
& ~ ( is_a_theorem @ sK99_SY163 ) ) )
& ( ~ modus_ponens
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ X )
| ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ( is_a_theorem @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(239,plain,
( ( ( sK100_REN
| modus_ponens )
& ( sK100_REN
=> ( ( is_a_theorem @ sK98_X )
& ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) )
& ~ ( is_a_theorem @ sK99_SY163 ) ) )
& ( ~ modus_ponens
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ X )
| ~ ( is_a_theorem @ ( implies @ X @ Y ) )
| ( is_a_theorem @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(240,plain,
( ( ( sK97_REN
| substitution_of_equivalents )
& ( sK97_REN
=> ( ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
& ( sK95_X != sK96_SY162 ) ) )
& ( ~ substitution_of_equivalents
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equiv @ X @ Y ) )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(241,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
| modus_tollens )
& ( ~ modus_tollens
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(242,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
| implies_1 )
& ( ~ implies_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(243,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
| implies_2 )
& ( ~ implies_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(244,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
| implies_3 )
& ( ~ implies_3
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(245,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
| and_1 )
& ( ~ and_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(246,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
| and_2 )
& ( ~ and_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(247,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
| and_3 )
& ( ~ and_3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(248,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
| or_1 )
& ( ~ or_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(249,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
| or_2 )
& ( ~ or_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(250,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
| or_3 )
& ( ~ or_3
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Z ) @ ( implies @ ( implies @ Y @ Z ) @ ( implies @ ( or @ X @ Y ) @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(251,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
| equivalence_1 )
& ( ~ equivalence_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(252,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
| equivalence_2 )
& ( ~ equivalence_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(253,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
| equivalence_3 )
& ( ~ equivalence_3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( implies @ X @ Y ) @ ( implies @ ( implies @ Y @ X ) @ ( equiv @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(254,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
| kn1 )
& ( ~ kn1
| ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(255,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
| kn2 )
& ( ~ kn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(256,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
| kn3 )
& ( ~ kn3
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( not @ ( and @ Q @ R ) ) @ ( not @ ( and @ R @ P ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(257,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
| cn1 )
& ( ~ cn1
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ P @ Q ) @ ( implies @ ( implies @ Q @ R ) @ ( implies @ P @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(258,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
| cn2 )
& ( ~ cn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(259,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
| cn3 )
& ( ~ cn3
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(260,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
| r1 )
& ( ~ r1
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(261,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
| r2 )
& ( ~ r2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(262,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
| r3 )
& ( ~ r3
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(263,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
| r4 )
& ( ~ r4
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ ( or @ Q @ R ) ) @ ( or @ Q @ ( or @ P @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(264,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
| r5 )
& ( ~ r5
| ! [P: $i,Q: $i,R: $i] : ( is_a_theorem @ ( implies @ ( implies @ Q @ R ) @ ( implies @ ( or @ P @ Q ) @ ( or @ P @ R ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(265,plain,
( ( ~ op_or
| ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(266,plain,
( ( ~ op_and
| ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(267,plain,
( ( ~ op_implies_and
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(268,plain,
( ( ~ op_implies_or
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(269,plain,
( ( ~ op_equiv
| ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(270,plain,
op_or = $true,
inference(copy,[status(thm)],[148]) ).
thf(271,plain,
op_implies_and = $true,
inference(copy,[status(thm)],[147]) ).
thf(272,plain,
op_equiv = $true,
inference(copy,[status(thm)],[146]) ).
thf(273,plain,
modus_ponens = $true,
inference(copy,[status(thm)],[145]) ).
thf(274,plain,
modus_tollens = $true,
inference(copy,[status(thm)],[144]) ).
thf(275,plain,
implies_1 = $true,
inference(copy,[status(thm)],[143]) ).
thf(276,plain,
implies_2 = $true,
inference(copy,[status(thm)],[142]) ).
thf(277,plain,
implies_3 = $true,
inference(copy,[status(thm)],[141]) ).
thf(278,plain,
and_1 = $true,
inference(copy,[status(thm)],[140]) ).
thf(279,plain,
and_2 = $true,
inference(copy,[status(thm)],[139]) ).
thf(280,plain,
and_3 = $true,
inference(copy,[status(thm)],[138]) ).
thf(281,plain,
or_1 = $true,
inference(copy,[status(thm)],[137]) ).
thf(282,plain,
or_2 = $true,
inference(copy,[status(thm)],[136]) ).
thf(283,plain,
or_3 = $true,
inference(copy,[status(thm)],[135]) ).
thf(284,plain,
equivalence_1 = $true,
inference(copy,[status(thm)],[134]) ).
thf(285,plain,
equivalence_2 = $true,
inference(copy,[status(thm)],[133]) ).
thf(286,plain,
equivalence_3 = $true,
inference(copy,[status(thm)],[132]) ).
thf(287,plain,
substitution_of_equivalents = $true,
inference(copy,[status(thm)],[131]) ).
thf(288,plain,
( ( ( sK43_REN
| necessitation )
& ( sK43_REN
=> ( ( is_a_theorem @ sK42_X )
& ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) )
& ( ~ necessitation
| ! [X: $i] :
( ~ ( is_a_theorem @ X )
| ( is_a_theorem @ ( necessarily @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(289,plain,
( ( ( sK41_REN
| modus_ponens_strict_implies )
& ( sK41_REN
=> ( ( is_a_theorem @ sK39_X )
& ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) )
& ~ ( is_a_theorem @ sK40_SY128 ) ) )
& ( ~ modus_ponens_strict_implies
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ X )
| ~ ( is_a_theorem @ ( strict_implies @ X @ Y ) )
| ( is_a_theorem @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(290,plain,
( ( ( sK38_REN
| adjunction )
& ( sK38_REN
=> ( ( is_a_theorem @ sK36_X )
& ( is_a_theorem @ sK37_SY127 )
& ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) )
& ( ~ adjunction
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ X )
| ~ ( is_a_theorem @ Y )
| ( is_a_theorem @ ( and @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(291,plain,
( ( ( sK35_REN
| substitution_strict_equiv )
& ( sK35_REN
=> ( ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
& ( sK33_X != sK34_SY126 ) ) )
& ( ~ substitution_strict_equiv
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ X @ Y ) )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(292,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
| axiom_K )
& ( ~ axiom_K
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ X @ Y ) ) @ ( implies @ ( necessarily @ X ) @ ( necessarily @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(293,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
| axiom_M )
& ( ~ axiom_M
| ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(294,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
| axiom_4 )
& ( ~ axiom_4
| ! [X: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(295,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
| axiom_B )
& ( ~ axiom_B
| ! [X: $i] : ( is_a_theorem @ ( implies @ X @ ( necessarily @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(296,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
| axiom_5 )
& ( ~ axiom_5
| ! [X: $i] : ( is_a_theorem @ ( implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(297,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
| axiom_s1 )
& ( ~ axiom_s1
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ X @ Y ) ) @ ( necessarily @ ( implies @ Y @ Z ) ) ) @ ( necessarily @ ( implies @ X @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(298,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
| axiom_s2 )
& ( ~ axiom_s2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ ( and @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(299,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
| axiom_s3 )
& ( ~ axiom_s3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ X @ Y ) @ ( strict_implies @ ( not @ ( possibly @ Y ) ) @ ( not @ ( possibly @ X ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(300,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
| axiom_s4 )
& ( ~ axiom_s4
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(301,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
| axiom_m1 )
& ( ~ axiom_m1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ ( and @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(302,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
| axiom_m2 )
& ( ~ axiom_m2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ X @ Y ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(303,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
| axiom_m3 )
& ( ~ axiom_m3
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ X @ Y ) @ Z ) @ ( and @ X @ ( and @ Y @ Z ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(304,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
| axiom_m4 )
& ( ~ axiom_m4
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( and @ X @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(305,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
| axiom_m5 )
& ( ~ axiom_m5
| ! [X: $i,Y: $i,Z: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ Z ) ) @ ( strict_implies @ X @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(306,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
| axiom_m6 )
& ( ~ axiom_m6
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ X @ ( possibly @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(307,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
| axiom_m7 )
& ( ~ axiom_m7
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ P @ Q ) ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(308,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
| axiom_m8 )
& ( ~ axiom_m8
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ P @ Q ) @ ( strict_implies @ ( possibly @ P ) @ ( possibly @ Q ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(309,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
| axiom_m9 )
& ( ~ axiom_m9
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ X ) ) @ ( possibly @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(310,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
| axiom_m10 )
& ( ~ axiom_m10
| ! [X: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(311,plain,
( ( ~ op_possibly
| ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(312,plain,
( ( ~ op_necessarily
| ! [X: $i] :
( ( necessarily @ X )
= ( not @ ( possibly @ ( not @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(313,plain,
( ( ~ op_strict_implies
| ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(314,plain,
( ( ~ op_strict_equiv
| ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(315,plain,
op_possibly = $true,
inference(copy,[status(thm)],[103]) ).
thf(316,plain,
necessitation = $true,
inference(copy,[status(thm)],[102]) ).
thf(317,plain,
axiom_K = $true,
inference(copy,[status(thm)],[101]) ).
thf(318,plain,
axiom_M = $true,
inference(copy,[status(thm)],[100]) ).
thf(319,plain,
axiom_4 = $true,
inference(copy,[status(thm)],[99]) ).
thf(320,plain,
axiom_B = $true,
inference(copy,[status(thm)],[98]) ).
thf(321,plain,
op_possibly = $true,
inference(copy,[status(thm)],[97]) ).
thf(322,plain,
op_or = $true,
inference(copy,[status(thm)],[96]) ).
thf(323,plain,
op_implies = $true,
inference(copy,[status(thm)],[95]) ).
thf(324,plain,
op_strict_implies = $true,
inference(copy,[status(thm)],[94]) ).
thf(325,plain,
op_equiv = $true,
inference(copy,[status(thm)],[93]) ).
thf(326,plain,
op_strict_equiv = $true,
inference(copy,[status(thm)],[92]) ).
thf(327,plain,
( ( ~ modus_ponens_strict_implies )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(328,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
| r4 )
| ~ ( ~ r4
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ ( or @ SX1 @ SX2 ) ) @ ( or @ SX1 @ ( or @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263]) ).
thf(329,plain,
( ( ~ ( ~ ~ ( ~ ( sK38_REN
| adjunction )
| ~ ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) ) )
| ~ ( ~ adjunction
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ SX1 )
| ( is_a_theorem @ ( and @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290]) ).
thf(330,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
| or_1 )
| ~ ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248]) ).
thf(331,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
| r1 )
| ~ ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[260]) ).
thf(332,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
| kn2 )
| ~ ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255]) ).
thf(333,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
| axiom_s4 )
| ~ ( ~ axiom_s4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300]) ).
thf(334,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
| axiom_m4 )
| ~ ( ~ axiom_m4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304]) ).
thf(335,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
| axiom_s3 )
| ~ ( ~ axiom_s3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( not @ ( possibly @ SX1 ) ) @ ( not @ ( possibly @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299]) ).
thf(336,plain,
( ( ~ ( ~ ~ ( ~ ( sK43_REN
| necessitation )
| ~ ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) ) )
| ~ ( ~ necessitation
| ! [SX0: $i] :
( ~ ( is_a_theorem @ SX0 )
| ( is_a_theorem @ ( necessarily @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288]) ).
thf(337,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
| kn1 )
| ~ ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254]) ).
thf(338,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
| axiom_m9 )
| ~ ( ~ axiom_m9
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SX0 ) ) @ ( possibly @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309]) ).
thf(339,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
| r2 )
| ~ ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261]) ).
thf(340,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
| axiom_s2 )
| ~ ( ~ axiom_s2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ ( and @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[298]) ).
thf(341,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
| implies_2 )
| ~ ( ~ implies_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243]) ).
thf(342,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
| implies_3 )
| ~ ( ~ implies_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244]) ).
thf(343,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
| cn3 )
| ~ ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259]) ).
thf(344,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
| axiom_m7 )
| ~ ( ~ axiom_m7
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307]) ).
thf(345,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
| axiom_5 )
| ~ ( ~ axiom_5
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[296]) ).
thf(346,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
| axiom_m6 )
| ~ ( ~ axiom_m6
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( possibly @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306]) ).
thf(347,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
| cn2 )
| ~ ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258]) ).
thf(348,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
| axiom_m1 )
| ~ ( ~ axiom_m1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ ( and @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301]) ).
thf(349,plain,
( ( ~ ( ~ ~ ( ~ ( sK100_REN
| modus_ponens )
| ~ ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) ) )
| ~ ( ~ modus_ponens
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239]) ).
thf(350,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
| equivalence_3 )
| ~ ( ~ equivalence_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX0 ) @ ( equiv @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253]) ).
thf(351,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
| equivalence_2 )
| ~ ( ~ equivalence_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252]) ).
thf(352,plain,
( ( ~ ( ~ ~ ( ~ ( sK97_REN
| substitution_of_equivalents )
| ~ ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) ) )
| ~ ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240]) ).
thf(353,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
| axiom_M )
| ~ ( ~ axiom_M
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293]) ).
thf(354,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
| kn3 )
| ~ ( ~ kn3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( not @ ( and @ SX1 @ SX2 ) ) @ ( not @ ( and @ SX2 @ SX0 ) ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256]) ).
thf(355,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
| axiom_m8 )
| ~ ( ~ axiom_m8
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308]) ).
thf(356,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
| or_2 )
| ~ ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249]) ).
thf(357,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
| cn1 )
| ~ ( ~ cn1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[257]) ).
thf(358,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
| and_1 )
| ~ ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245]) ).
thf(359,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
| axiom_m3 )
| ~ ( ~ axiom_m3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SX0 @ SX1 ) @ SX2 ) @ ( and @ SX0 @ ( and @ SX1 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303]) ).
thf(360,plain,
( ( ~ ( ~ ~ ( ~ ( sK35_REN
| substitution_strict_equiv )
| ~ ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) ) )
| ~ ( ~ substitution_strict_equiv
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291]) ).
thf(361,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
| or_3 )
| ~ ( ~ or_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX2 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250]) ).
thf(362,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
| axiom_m10 )
| ~ ( ~ axiom_m10
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310]) ).
thf(363,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
| axiom_4 )
| ~ ( ~ axiom_4
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294]) ).
thf(364,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
| axiom_K )
| ~ ( ~ axiom_K
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292]) ).
thf(365,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
| equivalence_1 )
| ~ ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[251]) ).
thf(366,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
| modus_tollens )
| ~ ( ~ modus_tollens
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX1 ) @ ( not @ SX0 ) ) @ ( implies @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241]) ).
thf(367,plain,
( ( ~ ( ~ ~ ( ~ ( sK41_REN
| modus_ponens_strict_implies )
| ~ ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) ) )
| ~ ( ~ modus_ponens_strict_implies
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( strict_implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289]) ).
thf(368,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
| r3 )
| ~ ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[262]) ).
thf(369,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
| axiom_B )
| ~ ( ~ axiom_B
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295]) ).
thf(370,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
| r5 )
| ~ ( ~ r5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[264]) ).
thf(371,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
| axiom_s1 )
| ~ ( ~ axiom_s1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( necessarily @ ( implies @ SX1 @ SX2 ) ) ) @ ( necessarily @ ( implies @ SX0 @ SX2 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297]) ).
thf(372,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
| and_3 )
| ~ ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247]) ).
thf(373,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
| implies_1 )
| ~ ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242]) ).
thf(374,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
| axiom_m5 )
| ~ ( ~ axiom_m5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ SX1 @ SX2 ) ) @ ( strict_implies @ SX0 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305]) ).
thf(375,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
| and_2 )
| ~ ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246]) ).
thf(376,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
| axiom_m2 )
| ~ ( ~ axiom_m2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302]) ).
thf(377,plain,
( ( ( ~ op_or )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(378,plain,
( ( ( ~ op_and )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(379,plain,
( ( ( ~ op_implies_and )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[267]) ).
thf(380,plain,
( ( ( ~ op_implies_or )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(381,plain,
( ( ( ~ op_equiv )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(382,plain,
( ( ( ~ op_possibly )
= $true )
| ( ( ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(383,plain,
( ( ( ~ op_necessarily )
= $true )
| ( ( ! [X: $i] :
( ( necessarily @ X )
= ( not @ ( possibly @ ( not @ X ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(384,plain,
( ( ( ~ op_strict_implies )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(385,plain,
( ( ( ~ op_strict_equiv )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(386,plain,
modus_ponens_strict_implies = $false,
inference(extcnf_not_pos,[status(thm)],[327]) ).
thf(387,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
| r4 )
| ~ ( ~ r4
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ ( or @ SX1 @ SX2 ) ) @ ( or @ SX1 @ ( or @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(388,plain,
( ( ~ ~ ( ~ ( sK38_REN
| adjunction )
| ~ ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) ) )
| ~ ( ~ adjunction
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ SX1 )
| ( is_a_theorem @ ( and @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[329]) ).
thf(389,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
| or_1 )
| ~ ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(390,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
| r1 )
| ~ ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(391,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
| kn2 )
| ~ ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(392,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
| axiom_s4 )
| ~ ( ~ axiom_s4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(393,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
| axiom_m4 )
| ~ ( ~ axiom_m4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(394,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
| axiom_s3 )
| ~ ( ~ axiom_s3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( not @ ( possibly @ SX1 ) ) @ ( not @ ( possibly @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(395,plain,
( ( ~ ~ ( ~ ( sK43_REN
| necessitation )
| ~ ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) ) )
| ~ ( ~ necessitation
| ! [SX0: $i] :
( ~ ( is_a_theorem @ SX0 )
| ( is_a_theorem @ ( necessarily @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(396,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
| kn1 )
| ~ ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(397,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
| axiom_m9 )
| ~ ( ~ axiom_m9
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SX0 ) ) @ ( possibly @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(398,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
| r2 )
| ~ ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(399,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
| axiom_s2 )
| ~ ( ~ axiom_s2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ ( and @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[340]) ).
thf(400,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
| implies_2 )
| ~ ( ~ implies_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[341]) ).
thf(401,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
| implies_3 )
| ~ ( ~ implies_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(402,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
| cn3 )
| ~ ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(403,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
| axiom_m7 )
| ~ ( ~ axiom_m7
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(404,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
| axiom_5 )
| ~ ( ~ axiom_5
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(405,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
| axiom_m6 )
| ~ ( ~ axiom_m6
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( possibly @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(406,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
| cn2 )
| ~ ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[347]) ).
thf(407,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
| axiom_m1 )
| ~ ( ~ axiom_m1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ ( and @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(408,plain,
( ( ~ ~ ( ~ ( sK100_REN
| modus_ponens )
| ~ ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) ) )
| ~ ( ~ modus_ponens
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(409,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
| equivalence_3 )
| ~ ( ~ equivalence_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX0 ) @ ( equiv @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(410,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
| equivalence_2 )
| ~ ( ~ equivalence_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(411,plain,
( ( ~ ~ ( ~ ( sK97_REN
| substitution_of_equivalents )
| ~ ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) ) )
| ~ ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(412,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
| axiom_M )
| ~ ( ~ axiom_M
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(413,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
| kn3 )
| ~ ( ~ kn3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( not @ ( and @ SX1 @ SX2 ) ) @ ( not @ ( and @ SX2 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(414,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
| axiom_m8 )
| ~ ( ~ axiom_m8
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(415,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
| or_2 )
| ~ ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(416,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
| cn1 )
| ~ ( ~ cn1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(417,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
| and_1 )
| ~ ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(418,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
| axiom_m3 )
| ~ ( ~ axiom_m3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SX0 @ SX1 ) @ SX2 ) @ ( and @ SX0 @ ( and @ SX1 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(419,plain,
( ( ~ ~ ( ~ ( sK35_REN
| substitution_strict_equiv )
| ~ ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) ) )
| ~ ( ~ substitution_strict_equiv
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(420,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
| or_3 )
| ~ ( ~ or_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX2 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(421,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
| axiom_m10 )
| ~ ( ~ axiom_m10
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(422,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
| axiom_4 )
| ~ ( ~ axiom_4
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[363]) ).
thf(423,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
| axiom_K )
| ~ ( ~ axiom_K
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[364]) ).
thf(424,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
| equivalence_1 )
| ~ ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[365]) ).
thf(425,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
| modus_tollens )
| ~ ( ~ modus_tollens
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX1 ) @ ( not @ SX0 ) ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(426,plain,
( ( ~ ~ ( ~ ( sK41_REN
| modus_ponens_strict_implies )
| ~ ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) ) )
| ~ ( ~ modus_ponens_strict_implies
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( strict_implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(427,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
| r3 )
| ~ ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(428,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
| axiom_B )
| ~ ( ~ axiom_B
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(429,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
| r5 )
| ~ ( ~ r5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(430,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
| axiom_s1 )
| ~ ( ~ axiom_s1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( necessarily @ ( implies @ SX1 @ SX2 ) ) ) @ ( necessarily @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(431,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
| and_3 )
| ~ ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(432,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
| implies_1 )
| ~ ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(433,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
| axiom_m5 )
| ~ ( ~ axiom_m5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ SX1 @ SX2 ) ) @ ( strict_implies @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(434,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
| and_2 )
| ~ ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(435,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
| axiom_m2 )
| ~ ( ~ axiom_m2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(436,plain,
( ( op_or = $false )
| ( ( ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(437,plain,
( ( op_and = $false )
| ( ( ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(438,plain,
( ( op_implies_and = $false )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(439,plain,
( ( op_implies_or = $false )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(440,plain,
( ( op_equiv = $false )
| ( ( ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(441,plain,
( ( op_possibly = $false )
| ( ( ! [X: $i] :
( ( possibly @ X )
= ( not @ ( necessarily @ ( not @ X ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(442,plain,
( ( op_necessarily = $false )
| ( ( ! [X: $i] :
( ( necessarily @ X )
= ( not @ ( possibly @ ( not @ X ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(443,plain,
( ( op_strict_implies = $false )
| ( ( ! [X: $i,Y: $i] :
( ( strict_implies @ X @ Y )
= ( necessarily @ ( implies @ X @ Y ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(444,plain,
( ( op_strict_equiv = $false )
| ( ( ! [X: $i,Y: $i] :
( ( strict_equiv @ X @ Y )
= ( and @ ( strict_implies @ X @ Y ) @ ( strict_implies @ Y @ X ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(445,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
| r4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(446,plain,
( ( ~ ( ~ r4
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ ( or @ SX1 @ SX2 ) ) @ ( or @ SX1 @ ( or @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[387]) ).
thf(447,plain,
( ( ~ ~ ( ~ ( sK38_REN
| adjunction )
| ~ ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(448,plain,
( ( ~ ( ~ adjunction
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ SX1 )
| ( is_a_theorem @ ( and @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[388]) ).
thf(449,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
| or_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(450,plain,
( ( ~ ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[389]) ).
thf(451,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
| r1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(452,plain,
( ( ~ ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[390]) ).
thf(453,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
| kn2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(454,plain,
( ( ~ ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[391]) ).
thf(455,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
| axiom_s4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(456,plain,
( ( ~ ( ~ axiom_s4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[392]) ).
thf(457,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
| axiom_m4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(458,plain,
( ( ~ ( ~ axiom_m4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[393]) ).
thf(459,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
| axiom_s3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(460,plain,
( ( ~ ( ~ axiom_s3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( not @ ( possibly @ SX1 ) ) @ ( not @ ( possibly @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[394]) ).
thf(461,plain,
( ( ~ ~ ( ~ ( sK43_REN
| necessitation )
| ~ ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(462,plain,
( ( ~ ( ~ necessitation
| ! [SX0: $i] :
( ~ ( is_a_theorem @ SX0 )
| ( is_a_theorem @ ( necessarily @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[395]) ).
thf(463,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
| kn1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(464,plain,
( ( ~ ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[396]) ).
thf(465,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
| axiom_m9 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(466,plain,
( ( ~ ( ~ axiom_m9
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SX0 ) ) @ ( possibly @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[397]) ).
thf(467,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
| r2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(468,plain,
( ( ~ ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[398]) ).
thf(469,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
| axiom_s2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(470,plain,
( ( ~ ( ~ axiom_s2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ ( and @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[399]) ).
thf(471,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
| implies_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(472,plain,
( ( ~ ( ~ implies_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[400]) ).
thf(473,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
| implies_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(474,plain,
( ( ~ ( ~ implies_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[401]) ).
thf(475,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
| cn3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(476,plain,
( ( ~ ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[402]) ).
thf(477,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
| axiom_m7 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(478,plain,
( ( ~ ( ~ axiom_m7
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[403]) ).
thf(479,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
| axiom_5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(480,plain,
( ( ~ ( ~ axiom_5
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[404]) ).
thf(481,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
| axiom_m6 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(482,plain,
( ( ~ ( ~ axiom_m6
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( possibly @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[405]) ).
thf(483,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
| cn2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(484,plain,
( ( ~ ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[406]) ).
thf(485,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
| axiom_m1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(486,plain,
( ( ~ ( ~ axiom_m1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ ( and @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[407]) ).
thf(487,plain,
( ( ~ ~ ( ~ ( sK100_REN
| modus_ponens )
| ~ ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(488,plain,
( ( ~ ( ~ modus_ponens
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[408]) ).
thf(489,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
| equivalence_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(490,plain,
( ( ~ ( ~ equivalence_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX0 ) @ ( equiv @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[409]) ).
thf(491,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
| equivalence_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(492,plain,
( ( ~ ( ~ equivalence_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[410]) ).
thf(493,plain,
( ( ~ ~ ( ~ ( sK97_REN
| substitution_of_equivalents )
| ~ ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(494,plain,
( ( ~ ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[411]) ).
thf(495,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
| axiom_M ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(496,plain,
( ( ~ ( ~ axiom_M
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(497,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
| kn3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(498,plain,
( ( ~ ( ~ kn3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( not @ ( and @ SX1 @ SX2 ) ) @ ( not @ ( and @ SX2 @ SX0 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[413]) ).
thf(499,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
| axiom_m8 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(500,plain,
( ( ~ ( ~ axiom_m8
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[414]) ).
thf(501,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
| or_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(502,plain,
( ( ~ ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[415]) ).
thf(503,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
| cn1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(504,plain,
( ( ~ ( ~ cn1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[416]) ).
thf(505,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
| and_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(506,plain,
( ( ~ ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[417]) ).
thf(507,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
| axiom_m3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(508,plain,
( ( ~ ( ~ axiom_m3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SX0 @ SX1 ) @ SX2 ) @ ( and @ SX0 @ ( and @ SX1 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(509,plain,
( ( ~ ~ ( ~ ( sK35_REN
| substitution_strict_equiv )
| ~ ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(510,plain,
( ( ~ ( ~ substitution_strict_equiv
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[419]) ).
thf(511,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
| or_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(512,plain,
( ( ~ ( ~ or_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX2 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[420]) ).
thf(513,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
| axiom_m10 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(514,plain,
( ( ~ ( ~ axiom_m10
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[421]) ).
thf(515,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
| axiom_4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(516,plain,
( ( ~ ( ~ axiom_4
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[422]) ).
thf(517,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
| axiom_K ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(518,plain,
( ( ~ ( ~ axiom_K
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[423]) ).
thf(519,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
| equivalence_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(520,plain,
( ( ~ ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[424]) ).
thf(521,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
| modus_tollens ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(522,plain,
( ( ~ ( ~ modus_tollens
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX1 ) @ ( not @ SX0 ) ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[425]) ).
thf(523,plain,
( ( ~ ~ ( ~ ( sK41_REN
| modus_ponens_strict_implies )
| ~ ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(524,plain,
( ( ~ ( ~ modus_ponens_strict_implies
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( strict_implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[426]) ).
thf(525,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
| r3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(526,plain,
( ( ~ ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[427]) ).
thf(527,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
| axiom_B ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(528,plain,
( ( ~ ( ~ axiom_B
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( necessarily @ ( possibly @ SX0 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[428]) ).
thf(529,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
| r5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(530,plain,
( ( ~ ( ~ r5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[429]) ).
thf(531,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
| axiom_s1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(532,plain,
( ( ~ ( ~ axiom_s1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( necessarily @ ( implies @ SX1 @ SX2 ) ) ) @ ( necessarily @ ( implies @ SX0 @ SX2 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[430]) ).
thf(533,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
| and_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(534,plain,
( ( ~ ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[431]) ).
thf(535,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
| implies_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(536,plain,
( ( ~ ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[432]) ).
thf(537,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
| axiom_m5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(538,plain,
( ( ~ ( ~ axiom_m5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ SX1 @ SX2 ) ) @ ( strict_implies @ SX0 @ SX2 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[433]) ).
thf(539,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
| and_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(540,plain,
( ( ~ ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[434]) ).
thf(541,plain,
( ( ~ ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
| axiom_m2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(542,plain,
( ( ~ ( ~ axiom_m2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[435]) ).
thf(543,plain,
! [SV1: $i] :
( ( ( ! [SY164: $i] :
( ( or @ SV1 @ SY164 )
= ( not @ ( and @ ( not @ SV1 ) @ ( not @ SY164 ) ) ) ) )
= $true )
| ( op_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(544,plain,
! [SV2: $i] :
( ( ( ! [SY165: $i] :
( ( and @ SV2 @ SY165 )
= ( not @ ( or @ ( not @ SV2 ) @ ( not @ SY165 ) ) ) ) )
= $true )
| ( op_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(545,plain,
! [SV3: $i] :
( ( ( ! [SY166: $i] :
( ( implies @ SV3 @ SY166 )
= ( not @ ( and @ SV3 @ ( not @ SY166 ) ) ) ) )
= $true )
| ( op_implies_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(546,plain,
! [SV4: $i] :
( ( ( ! [SY167: $i] :
( ( implies @ SV4 @ SY167 )
= ( or @ ( not @ SV4 ) @ SY167 ) ) )
= $true )
| ( op_implies_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(547,plain,
! [SV5: $i] :
( ( ( ! [SY168: $i] :
( ( equiv @ SV5 @ SY168 )
= ( and @ ( implies @ SV5 @ SY168 ) @ ( implies @ SY168 @ SV5 ) ) ) )
= $true )
| ( op_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(548,plain,
! [SV6: $i] :
( ( ( ( possibly @ SV6 )
= ( not @ ( necessarily @ ( not @ SV6 ) ) ) )
= $true )
| ( op_possibly = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(549,plain,
! [SV7: $i] :
( ( ( ( necessarily @ SV7 )
= ( not @ ( possibly @ ( not @ SV7 ) ) ) )
= $true )
| ( op_necessarily = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(550,plain,
! [SV8: $i] :
( ( ( ! [SY169: $i] :
( ( strict_implies @ SV8 @ SY169 )
= ( necessarily @ ( implies @ SV8 @ SY169 ) ) ) )
= $true )
| ( op_strict_implies = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(551,plain,
! [SV9: $i] :
( ( ( ! [SY170: $i] :
( ( strict_equiv @ SV9 @ SY170 )
= ( and @ ( strict_implies @ SV9 @ SY170 ) @ ( strict_implies @ SY170 @ SV9 ) ) ) )
= $true )
| ( op_strict_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(552,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
| r4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[445]) ).
thf(553,plain,
( ( ~ r4
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ ( or @ SX1 @ SX2 ) ) @ ( or @ SX1 @ ( or @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[446]) ).
thf(554,plain,
( ( ~ ( ~ ( sK38_REN
| adjunction )
| ~ ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[447]) ).
thf(555,plain,
( ( ~ adjunction
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ SX1 )
| ( is_a_theorem @ ( and @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[448]) ).
thf(556,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
| or_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[449]) ).
thf(557,plain,
( ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[450]) ).
thf(558,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
| r1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[451]) ).
thf(559,plain,
( ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[452]) ).
thf(560,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
| kn2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[453]) ).
thf(561,plain,
( ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[454]) ).
thf(562,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
| axiom_s4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[455]) ).
thf(563,plain,
( ( ~ axiom_s4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[456]) ).
thf(564,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
| axiom_m4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[457]) ).
thf(565,plain,
( ( ~ axiom_m4
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[458]) ).
thf(566,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
| axiom_s3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[459]) ).
thf(567,plain,
( ( ~ axiom_s3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( not @ ( possibly @ SX1 ) ) @ ( not @ ( possibly @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[460]) ).
thf(568,plain,
( ( ~ ( ~ ( sK43_REN
| necessitation )
| ~ ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[461]) ).
thf(569,plain,
( ( ~ necessitation
| ! [SX0: $i] :
( ~ ( is_a_theorem @ SX0 )
| ( is_a_theorem @ ( necessarily @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[462]) ).
thf(570,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
| kn1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[463]) ).
thf(571,plain,
( ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(572,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
| axiom_m9 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(573,plain,
( ( ~ axiom_m9
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SX0 ) ) @ ( possibly @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[466]) ).
thf(574,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
| r2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[467]) ).
thf(575,plain,
( ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[468]) ).
thf(576,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
| axiom_s2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[469]) ).
thf(577,plain,
( ( ~ axiom_s2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ ( and @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[470]) ).
thf(578,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
| implies_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(579,plain,
( ( ~ implies_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(580,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
| implies_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[473]) ).
thf(581,plain,
( ( ~ implies_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[474]) ).
thf(582,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
| cn3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[475]) ).
thf(583,plain,
( ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[476]) ).
thf(584,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
| axiom_m7 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[477]) ).
thf(585,plain,
( ( ~ axiom_m7
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[478]) ).
thf(586,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
| axiom_5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[479]) ).
thf(587,plain,
( ( ~ axiom_5
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[480]) ).
thf(588,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
| axiom_m6 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[481]) ).
thf(589,plain,
( ( ~ axiom_m6
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( possibly @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[482]) ).
thf(590,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
| cn2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[483]) ).
thf(591,plain,
( ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[484]) ).
thf(592,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
| axiom_m1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[485]) ).
thf(593,plain,
( ( ~ axiom_m1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ ( and @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[486]) ).
thf(594,plain,
( ( ~ ( ~ ( sK100_REN
| modus_ponens )
| ~ ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[487]) ).
thf(595,plain,
( ( ~ modus_ponens
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[488]) ).
thf(596,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
| equivalence_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[489]) ).
thf(597,plain,
( ( ~ equivalence_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX0 ) @ ( equiv @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[490]) ).
thf(598,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
| equivalence_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[491]) ).
thf(599,plain,
( ( ~ equivalence_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[492]) ).
thf(600,plain,
( ( ~ ( ~ ( sK97_REN
| substitution_of_equivalents )
| ~ ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[493]) ).
thf(601,plain,
( ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[494]) ).
thf(602,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
| axiom_M )
= $true ),
inference(extcnf_not_neg,[status(thm)],[495]) ).
thf(603,plain,
( ( ~ axiom_M
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[496]) ).
thf(604,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
| kn3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[497]) ).
thf(605,plain,
( ( ~ kn3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( not @ ( and @ SX1 @ SX2 ) ) @ ( not @ ( and @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[498]) ).
thf(606,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
| axiom_m8 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[499]) ).
thf(607,plain,
( ( ~ axiom_m8
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[500]) ).
thf(608,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
| or_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[501]) ).
thf(609,plain,
( ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[502]) ).
thf(610,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
| cn1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[503]) ).
thf(611,plain,
( ( ~ cn1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[504]) ).
thf(612,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
| and_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[505]) ).
thf(613,plain,
( ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[506]) ).
thf(614,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
| axiom_m3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[507]) ).
thf(615,plain,
( ( ~ axiom_m3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SX0 @ SX1 ) @ SX2 ) @ ( and @ SX0 @ ( and @ SX1 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[508]) ).
thf(616,plain,
( ( ~ ( ~ ( sK35_REN
| substitution_strict_equiv )
| ~ ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[509]) ).
thf(617,plain,
( ( ~ substitution_strict_equiv
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[510]) ).
thf(618,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
| or_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[511]) ).
thf(619,plain,
( ( ~ or_3
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX2 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[512]) ).
thf(620,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
| axiom_m10 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[513]) ).
thf(621,plain,
( ( ~ axiom_m10
| ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[514]) ).
thf(622,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
| axiom_4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[515]) ).
thf(623,plain,
( ( ~ axiom_4
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[516]) ).
thf(624,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
| axiom_K )
= $true ),
inference(extcnf_not_neg,[status(thm)],[517]) ).
thf(625,plain,
( ( ~ axiom_K
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[518]) ).
thf(626,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
| equivalence_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[519]) ).
thf(627,plain,
( ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[520]) ).
thf(628,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
| modus_tollens )
= $true ),
inference(extcnf_not_neg,[status(thm)],[521]) ).
thf(629,plain,
( ( ~ modus_tollens
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX1 ) @ ( not @ SX0 ) ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[522]) ).
thf(630,plain,
( ( ~ ( ~ ( sK41_REN
| modus_ponens_strict_implies )
| ~ ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[523]) ).
thf(631,plain,
( ( ~ modus_ponens_strict_implies
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( strict_implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[524]) ).
thf(632,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
| r3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[525]) ).
thf(633,plain,
( ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[526]) ).
thf(634,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
| axiom_B )
= $true ),
inference(extcnf_not_neg,[status(thm)],[527]) ).
thf(635,plain,
( ( ~ axiom_B
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[528]) ).
thf(636,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
| r5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[529]) ).
thf(637,plain,
( ( ~ r5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[530]) ).
thf(638,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
| axiom_s1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[531]) ).
thf(639,plain,
( ( ~ axiom_s1
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( necessarily @ ( implies @ SX1 @ SX2 ) ) ) @ ( necessarily @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[532]) ).
thf(640,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
| and_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[533]) ).
thf(641,plain,
( ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[534]) ).
thf(642,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
| implies_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[535]) ).
thf(643,plain,
( ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[536]) ).
thf(644,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
| axiom_m5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[537]) ).
thf(645,plain,
( ( ~ axiom_m5
| ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ SX1 @ SX2 ) ) @ ( strict_implies @ SX0 @ SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[538]) ).
thf(646,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
| and_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[539]) ).
thf(647,plain,
( ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[540]) ).
thf(648,plain,
( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
| axiom_m2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[541]) ).
thf(649,plain,
( ( ~ axiom_m2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[542]) ).
thf(650,plain,
! [SV10: $i,SV1: $i] :
( ( ( ( or @ SV1 @ SV10 )
= ( not @ ( and @ ( not @ SV1 ) @ ( not @ SV10 ) ) ) )
= $true )
| ( op_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(651,plain,
! [SV11: $i,SV2: $i] :
( ( ( ( and @ SV2 @ SV11 )
= ( not @ ( or @ ( not @ SV2 ) @ ( not @ SV11 ) ) ) )
= $true )
| ( op_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(652,plain,
! [SV12: $i,SV3: $i] :
( ( ( ( implies @ SV3 @ SV12 )
= ( not @ ( and @ SV3 @ ( not @ SV12 ) ) ) )
= $true )
| ( op_implies_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(653,plain,
! [SV13: $i,SV4: $i] :
( ( ( ( implies @ SV4 @ SV13 )
= ( or @ ( not @ SV4 ) @ SV13 ) )
= $true )
| ( op_implies_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(654,plain,
! [SV14: $i,SV5: $i] :
( ( ( ( equiv @ SV5 @ SV14 )
= ( and @ ( implies @ SV5 @ SV14 ) @ ( implies @ SV14 @ SV5 ) ) )
= $true )
| ( op_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(655,plain,
! [SV15: $i,SV8: $i] :
( ( ( ( strict_implies @ SV8 @ SV15 )
= ( necessarily @ ( implies @ SV8 @ SV15 ) ) )
= $true )
| ( op_strict_implies = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(656,plain,
! [SV16: $i,SV9: $i] :
( ( ( ( strict_equiv @ SV9 @ SV16 )
= ( and @ ( strict_implies @ SV9 @ SV16 ) @ ( strict_implies @ SV16 @ SV9 ) ) )
= $true )
| ( op_strict_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(657,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) ) )
= $true )
| ( r4 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(658,plain,
( ( ( ~ r4 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ ( or @ SX1 @ SX2 ) ) @ ( or @ SX1 @ ( or @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(659,plain,
( ( ~ ( sK38_REN
| adjunction )
| ~ ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(660,plain,
( ( ( ~ adjunction )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ SX1 )
| ( is_a_theorem @ ( and @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(661,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) ) )
= $true )
| ( or_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(662,plain,
( ( ( ~ or_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(663,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) ) )
= $true )
| ( r1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(664,plain,
( ( ( ~ r1 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(665,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) ) )
= $true )
| ( kn2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(666,plain,
( ( ( ~ kn2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(667,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) ) )
= $true )
| ( axiom_s4 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(668,plain,
( ( ( ~ axiom_s4 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(669,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) ) )
= $true )
| ( axiom_m4 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(670,plain,
( ( ( ~ axiom_m4 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(671,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) ) )
= $true )
| ( axiom_s3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(672,plain,
( ( ( ~ axiom_s3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( not @ ( possibly @ SX1 ) ) @ ( not @ ( possibly @ SX0 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(673,plain,
( ( ~ ( sK43_REN
| necessitation )
| ~ ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(674,plain,
( ( ( ~ necessitation )
= $true )
| ( ( ! [SX0: $i] :
( ~ ( is_a_theorem @ SX0 )
| ( is_a_theorem @ ( necessarily @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(675,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) ) )
= $true )
| ( kn1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(676,plain,
( ( ( ~ kn1 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(677,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) ) )
= $true )
| ( axiom_m9 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(678,plain,
( ( ( ~ axiom_m9 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SX0 ) ) @ ( possibly @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(679,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) ) )
= $true )
| ( r2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(680,plain,
( ( ( ~ r2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(681,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) ) )
= $true )
| ( axiom_s2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(682,plain,
( ( ( ~ axiom_s2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ ( and @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(683,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) ) )
= $true )
| ( implies_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(684,plain,
( ( ( ~ implies_2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(685,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) ) )
= $true )
| ( implies_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(686,plain,
( ( ( ~ implies_3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(687,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) ) )
= $true )
| ( cn3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[582]) ).
thf(688,plain,
( ( ( ~ cn3 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(689,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) ) )
= $true )
| ( axiom_m7 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(690,plain,
( ( ( ~ axiom_m7 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[585]) ).
thf(691,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) ) )
= $true )
| ( axiom_5 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(692,plain,
( ( ( ~ axiom_5 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(693,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) ) )
= $true )
| ( axiom_m6 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(694,plain,
( ( ( ~ axiom_m6 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( possibly @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(695,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) ) )
= $true )
| ( cn2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(696,plain,
( ( ( ~ cn2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(697,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) ) )
= $true )
| ( axiom_m1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(698,plain,
( ( ( ~ axiom_m1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ ( and @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(699,plain,
( ( ~ ( sK100_REN
| modus_ponens )
| ~ ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(700,plain,
( ( ( ~ modus_ponens )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(701,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) ) )
= $true )
| ( equivalence_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(702,plain,
( ( ( ~ equivalence_3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX0 ) @ ( equiv @ SX0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(703,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) ) )
= $true )
| ( equivalence_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[598]) ).
thf(704,plain,
( ( ( ~ equivalence_2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[599]) ).
thf(705,plain,
( ( ~ ( sK97_REN
| substitution_of_equivalents )
| ~ ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(706,plain,
( ( ( ~ substitution_of_equivalents )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(707,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) ) )
= $true )
| ( axiom_M = $true ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(708,plain,
( ( ( ~ axiom_M )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(709,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) ) )
= $true )
| ( kn3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(710,plain,
( ( ( ~ kn3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( not @ ( and @ SX1 @ SX2 ) ) @ ( not @ ( and @ SX2 @ SX0 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(711,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) ) )
= $true )
| ( axiom_m8 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(712,plain,
( ( ( ~ axiom_m8 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(713,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) ) )
= $true )
| ( or_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(714,plain,
( ( ( ~ or_2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(715,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) ) )
= $true )
| ( cn1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(716,plain,
( ( ( ~ cn1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[611]) ).
thf(717,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) ) )
= $true )
| ( and_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(718,plain,
( ( ( ~ and_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(719,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) ) )
= $true )
| ( axiom_m3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[614]) ).
thf(720,plain,
( ( ( ~ axiom_m3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SX0 @ SX1 ) @ SX2 ) @ ( and @ SX0 @ ( and @ SX1 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(721,plain,
( ( ~ ( sK35_REN
| substitution_strict_equiv )
| ~ ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[616]) ).
thf(722,plain,
( ( ( ~ substitution_strict_equiv )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(723,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) ) )
= $true )
| ( or_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(724,plain,
( ( ( ~ or_3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX2 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(725,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) ) )
= $true )
| ( axiom_m10 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(726,plain,
( ( ( ~ axiom_m10 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(727,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) ) )
= $true )
| ( axiom_4 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(728,plain,
( ( ( ~ axiom_4 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(729,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) ) )
= $true )
| ( axiom_K = $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(730,plain,
( ( ( ~ axiom_K )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(731,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) ) )
= $true )
| ( equivalence_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(732,plain,
( ( ( ~ equivalence_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(733,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) ) )
= $true )
| ( modus_tollens = $true ) ),
inference(extcnf_or_pos,[status(thm)],[628]) ).
thf(734,plain,
( ( ( ~ modus_tollens )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX1 ) @ ( not @ SX0 ) ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[629]) ).
thf(735,plain,
( ( ~ ( sK41_REN
| modus_ponens_strict_implies )
| ~ ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(736,plain,
( ( ( ~ modus_ponens_strict_implies )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( strict_implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(737,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) ) )
= $true )
| ( r3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(738,plain,
( ( ( ~ r3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(739,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) ) )
= $true )
| ( axiom_B = $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(740,plain,
( ( ( ~ axiom_B )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(741,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) ) )
= $true )
| ( r5 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[636]) ).
thf(742,plain,
( ( ( ~ r5 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(743,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) ) )
= $true )
| ( axiom_s1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(744,plain,
( ( ( ~ axiom_s1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( necessarily @ ( implies @ SX1 @ SX2 ) ) ) @ ( necessarily @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(745,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) ) )
= $true )
| ( and_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(746,plain,
( ( ( ~ and_3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[641]) ).
thf(747,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) ) )
= $true )
| ( implies_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(748,plain,
( ( ( ~ implies_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(749,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) ) )
= $true )
| ( axiom_m5 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(750,plain,
( ( ( ~ axiom_m5 )
= $true )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ SX1 @ SX2 ) ) @ ( strict_implies @ SX0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(751,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) ) )
= $true )
| ( and_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(752,plain,
( ( ( ~ and_2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(753,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) ) )
= $true )
| ( axiom_m2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(754,plain,
( ( ( ~ axiom_m2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(755,plain,
( ( ( is_a_theorem @ ( implies @ ( or @ sK47_P @ ( or @ sK48_SY132 @ sK49_SY134 ) ) @ ( or @ sK48_SY132 @ ( or @ sK47_P @ sK49_SY134 ) ) ) )
= $false )
| ( r4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(756,plain,
( ( r4 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ ( or @ SX1 @ SX2 ) ) @ ( or @ SX1 @ ( or @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(757,plain,
( ( ~ ( sK38_REN
| adjunction ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(758,plain,
( ( ~ ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[659]) ).
thf(759,plain,
( ( adjunction = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ SX1 )
| ( is_a_theorem @ ( and @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(760,plain,
( ( ( is_a_theorem @ ( implies @ sK78_X @ ( or @ sK78_X @ sK79_SY152 ) ) )
= $false )
| ( or_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[661]) ).
thf(761,plain,
( ( or_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(762,plain,
( ( ( is_a_theorem @ ( implies @ ( or @ sK54_P @ sK54_P ) @ sK54_P ) )
= $false )
| ( r1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[663]) ).
thf(763,plain,
( ( r1 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[664]) ).
thf(764,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ sK64_P @ sK65_SY144 ) @ sK64_P ) )
= $false )
| ( kn2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(765,plain,
( ( kn2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[666]) ).
thf(766,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( necessarily @ sK19_X ) @ ( necessarily @ ( necessarily @ sK19_X ) ) ) )
= $false )
| ( axiom_s4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(767,plain,
( ( axiom_s4 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(768,plain,
( ( ( is_a_theorem @ ( strict_implies @ sK11_X @ ( and @ sK11_X @ sK11_X ) ) )
= $false )
| ( axiom_m4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(769,plain,
( ( axiom_m4 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(770,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK20_X @ sK21_SY120 ) @ ( strict_implies @ ( not @ ( possibly @ sK21_SY120 ) ) @ ( not @ ( possibly @ sK20_X ) ) ) ) )
= $false )
| ( axiom_s3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(771,plain,
( ( axiom_s3 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( not @ ( possibly @ SX1 ) ) @ ( not @ ( possibly @ SX0 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(772,plain,
( ( ~ ( sK43_REN
| necessitation ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(773,plain,
( ( ~ ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[673]) ).
thf(774,plain,
( ( necessitation = $false )
| ( ( ! [SX0: $i] :
( ~ ( is_a_theorem @ SX0 )
| ( is_a_theorem @ ( necessarily @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[674]) ).
thf(775,plain,
( ( ( is_a_theorem @ ( implies @ sK66_P @ ( and @ sK66_P @ sK66_P ) ) )
= $false )
| ( kn1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(776,plain,
( ( kn1 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(777,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ sK2_X ) ) @ ( possibly @ sK2_X ) ) )
= $false )
| ( axiom_m9 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(778,plain,
( ( axiom_m9 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SX0 ) ) @ ( possibly @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(779,plain,
( ( ( is_a_theorem @ ( implies @ sK53_SY136 @ ( or @ sK52_P @ sK53_SY136 ) ) )
= $false )
| ( r2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[679]) ).
thf(780,plain,
( ( r2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(781,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK22_P @ sK23_SY121 ) ) @ ( and @ ( possibly @ sK22_P ) @ ( possibly @ sK23_SY121 ) ) ) )
= $false )
| ( axiom_s2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[681]) ).
thf(782,plain,
( ( axiom_s2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ ( and @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(783,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK89_X @ ( implies @ sK89_X @ sK90_SY159 ) ) @ ( implies @ sK89_X @ sK90_SY159 ) ) )
= $false )
| ( implies_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(784,plain,
( ( implies_2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(785,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK86_X @ sK87_SY156 ) @ ( implies @ ( implies @ sK87_SY156 @ sK88_SY158 ) @ ( implies @ sK86_X @ sK88_SY158 ) ) ) )
= $false )
| ( implies_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[685]) ).
thf(786,plain,
( ( implies_3 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(787,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK55_P ) @ sK55_P ) @ sK55_P ) )
= $false )
| ( cn3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[687]) ).
thf(788,plain,
( ( cn3 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(789,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ sK5_P @ sK6_SY111 ) ) @ sK5_P ) )
= $false )
| ( axiom_m7 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(790,plain,
( ( axiom_m7 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SX0 @ SX1 ) ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(791,plain,
( ( ( is_a_theorem @ ( implies @ ( possibly @ sK27_X ) @ ( necessarily @ ( possibly @ sK27_X ) ) ) )
= $false )
| ( axiom_5 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[691]) ).
thf(792,plain,
( ( axiom_5 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(793,plain,
( ( ( is_a_theorem @ ( strict_implies @ sK7_X @ ( possibly @ sK7_X ) ) )
= $false )
| ( axiom_m6 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(794,plain,
( ( axiom_m6 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ SX0 @ ( possibly @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[694]) ).
thf(795,plain,
( ( ( is_a_theorem @ ( implies @ sK56_P @ ( implies @ ( not @ sK56_P ) @ sK57_SY137 ) ) )
= $false )
| ( cn2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(796,plain,
( ( cn2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(797,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( and @ sK17_X @ sK18_SY119 ) @ ( and @ sK18_SY119 @ sK17_X ) ) )
= $false )
| ( axiom_m1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(798,plain,
( ( axiom_m1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ ( and @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(799,plain,
( ( ~ ( sK100_REN
| modus_ponens ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(800,plain,
( ( ~ ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[699]) ).
thf(801,plain,
( ( modus_ponens = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(802,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK67_X @ sK68_SY145 ) @ ( implies @ ( implies @ sK68_SY145 @ sK67_X ) @ ( equiv @ sK67_X @ sK68_SY145 ) ) ) )
= $false )
| ( equivalence_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(803,plain,
( ( equivalence_3 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX0 ) @ ( equiv @ SX0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(804,plain,
( ( ( is_a_theorem @ ( implies @ ( equiv @ sK69_X @ sK70_SY146 ) @ ( implies @ sK70_SY146 @ sK69_X ) ) )
= $false )
| ( equivalence_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(805,plain,
( ( equivalence_2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(806,plain,
( ( ~ ( sK97_REN
| substitution_of_equivalents ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(807,plain,
( ( ~ ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[705]) ).
thf(808,plain,
( ( substitution_of_equivalents = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(809,plain,
( ( ( is_a_theorem @ ( implies @ ( necessarily @ sK30_X ) @ sK30_X ) )
= $false )
| ( axiom_M = $true ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(810,plain,
( ( axiom_M = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(811,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK61_P @ sK62_SY141 ) @ ( implies @ ( not @ ( and @ sK62_SY141 @ sK63_SY143 ) ) @ ( not @ ( and @ sK63_SY143 @ sK61_P ) ) ) ) )
= $false )
| ( kn3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(812,plain,
( ( kn3 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( not @ ( and @ SX1 @ SX2 ) ) @ ( not @ ( and @ SX2 @ SX0 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[710]) ).
thf(813,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( strict_implies @ sK3_P @ sK4_SY110 ) @ ( strict_implies @ ( possibly @ sK3_P ) @ ( possibly @ sK4_SY110 ) ) ) )
= $false )
| ( axiom_m8 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[711]) ).
thf(814,plain,
( ( axiom_m8 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ ( possibly @ SX0 ) @ ( possibly @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[712]) ).
thf(815,plain,
( ( ( is_a_theorem @ ( implies @ sK77_SY151 @ ( or @ sK76_X @ sK77_SY151 ) ) )
= $false )
| ( or_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(816,plain,
( ( or_2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(817,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK58_P @ sK59_SY138 ) @ ( implies @ ( implies @ sK59_SY138 @ sK60_SY140 ) @ ( implies @ sK58_P @ sK60_SY140 ) ) ) )
= $false )
| ( cn1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(818,plain,
( ( cn1 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX1 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(819,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ sK84_X @ sK85_SY155 ) @ sK84_X ) )
= $false )
| ( and_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(820,plain,
( ( and_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(821,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ sK12_X @ sK13_SY115 ) @ sK14_SY117 ) @ ( and @ sK12_X @ ( and @ sK13_SY115 @ sK14_SY117 ) ) ) )
= $false )
| ( axiom_m3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(822,plain,
( ( axiom_m3 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SX0 @ SX1 ) @ SX2 ) @ ( and @ SX0 @ ( and @ SX1 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(823,plain,
( ( ~ ( sK35_REN
| substitution_strict_equiv ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(824,plain,
( ( ~ ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[721]) ).
thf(825,plain,
( ( substitution_strict_equiv = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(826,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK73_X @ sK75_SY150 ) @ ( implies @ ( implies @ sK74_SY148 @ sK75_SY150 ) @ ( implies @ ( or @ sK73_X @ sK74_SY148 ) @ sK75_SY150 ) ) ) )
= $false )
| ( or_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(827,plain,
( ( or_3 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX0 @ SX2 ) @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(828,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ sK1_X ) @ ( necessarily @ ( possibly @ sK1_X ) ) ) )
= $false )
| ( axiom_m10 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(829,plain,
( ( axiom_m10 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ SX0 ) @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(830,plain,
( ( ( is_a_theorem @ ( implies @ ( necessarily @ sK29_X ) @ ( necessarily @ ( necessarily @ sK29_X ) ) ) )
= $false )
| ( axiom_4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(831,plain,
( ( axiom_4 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ ( necessarily @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(832,plain,
( ( ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ sK31_X @ sK32_SY125 ) ) @ ( implies @ ( necessarily @ sK31_X ) @ ( necessarily @ sK32_SY125 ) ) ) )
= $false )
| ( axiom_K = $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(833,plain,
( ( axiom_K = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( implies @ ( necessarily @ SX0 ) @ ( necessarily @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(834,plain,
( ( ( is_a_theorem @ ( implies @ ( equiv @ sK71_X @ sK72_SY147 ) @ ( implies @ sK71_X @ sK72_SY147 ) ) )
= $false )
| ( equivalence_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(835,plain,
( ( equivalence_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(836,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK94_SY161 ) @ ( not @ sK93_X ) ) @ ( implies @ sK93_X @ sK94_SY161 ) ) )
= $false )
| ( modus_tollens = $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(837,plain,
( ( modus_tollens = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX1 ) @ ( not @ SX0 ) ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(838,plain,
( ( ~ ( sK41_REN
| modus_ponens_strict_implies ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(839,plain,
( ( ~ ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[735]) ).
thf(840,plain,
( ( modus_ponens_strict_implies = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ SX0 )
| ~ ( is_a_theorem @ ( strict_implies @ SX0 @ SX1 ) )
| ( is_a_theorem @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[736]) ).
thf(841,plain,
( ( ( is_a_theorem @ ( implies @ ( or @ sK50_P @ sK51_SY135 ) @ ( or @ sK51_SY135 @ sK50_P ) ) )
= $false )
| ( r3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(842,plain,
( ( r3 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(843,plain,
( ( ( is_a_theorem @ ( implies @ sK28_X @ ( necessarily @ ( possibly @ sK28_X ) ) ) )
= $false )
| ( axiom_B = $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(844,plain,
( ( axiom_B = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( necessarily @ ( possibly @ SX0 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[740]) ).
thf(845,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK45_SY129 @ sK46_SY131 ) @ ( implies @ ( or @ sK44_P @ sK45_SY129 ) @ ( or @ sK44_P @ sK46_SY131 ) ) ) )
= $false )
| ( r5 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(846,plain,
( ( r5 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( implies @ SX1 @ SX2 ) @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(847,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ sK24_X @ sK25_SY122 ) ) @ ( necessarily @ ( implies @ sK25_SY122 @ sK26_SY124 ) ) ) @ ( necessarily @ ( implies @ sK24_X @ sK26_SY124 ) ) ) )
= $false )
| ( axiom_s1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(848,plain,
( ( axiom_s1 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SX0 @ SX1 ) ) @ ( necessarily @ ( implies @ SX1 @ SX2 ) ) ) @ ( necessarily @ ( implies @ SX0 @ SX2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(849,plain,
( ( ( is_a_theorem @ ( implies @ sK80_X @ ( implies @ sK81_SY153 @ ( and @ sK80_X @ sK81_SY153 ) ) ) )
= $false )
| ( and_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(850,plain,
( ( and_3 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[746]) ).
thf(851,plain,
( ( ( is_a_theorem @ ( implies @ sK91_X @ ( implies @ sK92_SY160 @ sK91_X ) ) )
= $false )
| ( implies_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[747]) ).
thf(852,plain,
( ( implies_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(853,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ sK8_X @ sK9_SY112 ) @ ( strict_implies @ sK9_SY112 @ sK10_SY114 ) ) @ ( strict_implies @ sK8_X @ sK10_SY114 ) ) )
= $false )
| ( axiom_m5 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(854,plain,
( ( axiom_m5 = $false )
| ( ( ! [SX0: $i,SX1: $i,SX2: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SX0 @ SX1 ) @ ( strict_implies @ SX1 @ SX2 ) ) @ ( strict_implies @ SX0 @ SX2 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[750]) ).
thf(855,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ sK82_X @ sK83_SY154 ) @ sK83_SY154 ) )
= $false )
| ( and_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[751]) ).
thf(856,plain,
( ( and_2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(857,plain,
( ( ( is_a_theorem @ ( strict_implies @ ( and @ sK15_X @ sK16_SY118 ) @ sK15_X ) )
= $false )
| ( axiom_m2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(858,plain,
( ( axiom_m2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(859,plain,
! [SV17: $i] :
( ( ( ! [SY171: $i,SY172: $i] : ( is_a_theorem @ ( implies @ ( or @ SV17 @ ( or @ SY171 @ SY172 ) ) @ ( or @ SY171 @ ( or @ SV17 @ SY172 ) ) ) ) )
= $true )
| ( r4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(860,plain,
( ( sK38_REN
| adjunction )
= $true ),
inference(extcnf_not_neg,[status(thm)],[757]) ).
thf(861,plain,
( ( ~ sK38_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[758]) ).
thf(862,plain,
! [SV18: $i] :
( ( ( ! [SY173: $i] :
( ~ ( is_a_theorem @ SV18 )
| ~ ( is_a_theorem @ SY173 )
| ( is_a_theorem @ ( and @ SV18 @ SY173 ) ) ) )
= $true )
| ( adjunction = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(863,plain,
! [SV19: $i] :
( ( ( ! [SY174: $i] : ( is_a_theorem @ ( implies @ SV19 @ ( or @ SV19 @ SY174 ) ) ) )
= $true )
| ( or_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[761]) ).
thf(864,plain,
! [SV20: $i] :
( ( ( is_a_theorem @ ( implies @ ( or @ SV20 @ SV20 ) @ SV20 ) )
= $true )
| ( r1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(865,plain,
! [SV21: $i] :
( ( ( ! [SY175: $i] : ( is_a_theorem @ ( implies @ ( and @ SV21 @ SY175 ) @ SV21 ) ) )
= $true )
| ( kn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(866,plain,
! [SV22: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( necessarily @ SV22 ) @ ( necessarily @ ( necessarily @ SV22 ) ) ) )
= $true )
| ( axiom_s4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(867,plain,
! [SV23: $i] :
( ( ( is_a_theorem @ ( strict_implies @ SV23 @ ( and @ SV23 @ SV23 ) ) )
= $true )
| ( axiom_m4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(868,plain,
! [SV24: $i] :
( ( ( ! [SY176: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SV24 @ SY176 ) @ ( strict_implies @ ( not @ ( possibly @ SY176 ) ) @ ( not @ ( possibly @ SV24 ) ) ) ) ) )
= $true )
| ( axiom_s3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(869,plain,
( ( sK43_REN
| necessitation )
= $true ),
inference(extcnf_not_neg,[status(thm)],[772]) ).
thf(870,plain,
( ( ~ sK43_REN
| ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[773]) ).
thf(871,plain,
! [SV25: $i] :
( ( ( ~ ( is_a_theorem @ SV25 )
| ( is_a_theorem @ ( necessarily @ SV25 ) ) )
= $true )
| ( necessitation = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(872,plain,
! [SV26: $i] :
( ( ( is_a_theorem @ ( implies @ SV26 @ ( and @ SV26 @ SV26 ) ) )
= $true )
| ( kn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(873,plain,
! [SV27: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( possibly @ SV27 ) ) @ ( possibly @ SV27 ) ) )
= $true )
| ( axiom_m9 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(874,plain,
! [SV28: $i] :
( ( ( ! [SY177: $i] : ( is_a_theorem @ ( implies @ SY177 @ ( or @ SV28 @ SY177 ) ) ) )
= $true )
| ( r2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(875,plain,
! [SV29: $i] :
( ( ( ! [SY178: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SV29 @ SY178 ) ) @ ( and @ ( possibly @ SV29 ) @ ( possibly @ SY178 ) ) ) ) )
= $true )
| ( axiom_s2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(876,plain,
! [SV30: $i] :
( ( ( ! [SY179: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV30 @ ( implies @ SV30 @ SY179 ) ) @ ( implies @ SV30 @ SY179 ) ) ) )
= $true )
| ( implies_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(877,plain,
! [SV31: $i] :
( ( ( ! [SY180: $i,SY181: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV31 @ SY180 ) @ ( implies @ ( implies @ SY180 @ SY181 ) @ ( implies @ SV31 @ SY181 ) ) ) ) )
= $true )
| ( implies_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(878,plain,
! [SV32: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV32 ) @ SV32 ) @ SV32 ) )
= $true )
| ( cn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(879,plain,
! [SV33: $i] :
( ( ( ! [SY182: $i] : ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SV33 @ SY182 ) ) @ SV33 ) ) )
= $true )
| ( axiom_m7 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(880,plain,
! [SV34: $i] :
( ( ( is_a_theorem @ ( implies @ ( possibly @ SV34 ) @ ( necessarily @ ( possibly @ SV34 ) ) ) )
= $true )
| ( axiom_5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(881,plain,
! [SV35: $i] :
( ( ( is_a_theorem @ ( strict_implies @ SV35 @ ( possibly @ SV35 ) ) )
= $true )
| ( axiom_m6 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(882,plain,
! [SV36: $i] :
( ( ( ! [SY183: $i] : ( is_a_theorem @ ( implies @ SV36 @ ( implies @ ( not @ SV36 ) @ SY183 ) ) ) )
= $true )
| ( cn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(883,plain,
! [SV37: $i] :
( ( ( ! [SY184: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SV37 @ SY184 ) @ ( and @ SY184 @ SV37 ) ) ) )
= $true )
| ( axiom_m1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(884,plain,
( ( sK100_REN
| modus_ponens )
= $true ),
inference(extcnf_not_neg,[status(thm)],[799]) ).
thf(885,plain,
( ( ~ sK100_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[800]) ).
thf(886,plain,
! [SV38: $i] :
( ( ( ! [SY185: $i] :
( ~ ( is_a_theorem @ SV38 )
| ~ ( is_a_theorem @ ( implies @ SV38 @ SY185 ) )
| ( is_a_theorem @ SY185 ) ) )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(887,plain,
! [SV39: $i] :
( ( ( ! [SY186: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV39 @ SY186 ) @ ( implies @ ( implies @ SY186 @ SV39 ) @ ( equiv @ SV39 @ SY186 ) ) ) ) )
= $true )
| ( equivalence_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(888,plain,
! [SV40: $i] :
( ( ( ! [SY187: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SV40 @ SY187 ) @ ( implies @ SY187 @ SV40 ) ) ) )
= $true )
| ( equivalence_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(889,plain,
( ( sK97_REN
| substitution_of_equivalents )
= $true ),
inference(extcnf_not_neg,[status(thm)],[806]) ).
thf(890,plain,
( ( ~ sK97_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[807]) ).
thf(891,plain,
! [SV41: $i] :
( ( ( ! [SY188: $i] :
( ~ ( is_a_theorem @ ( equiv @ SV41 @ SY188 ) )
| ( SV41 = SY188 ) ) )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(892,plain,
! [SV42: $i] :
( ( ( is_a_theorem @ ( implies @ ( necessarily @ SV42 ) @ SV42 ) )
= $true )
| ( axiom_M = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(893,plain,
! [SV43: $i] :
( ( ( ! [SY189: $i,SY190: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV43 @ SY189 ) @ ( implies @ ( not @ ( and @ SY189 @ SY190 ) ) @ ( not @ ( and @ SY190 @ SV43 ) ) ) ) ) )
= $true )
| ( kn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(894,plain,
! [SV44: $i] :
( ( ( ! [SY191: $i] : ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SV44 @ SY191 ) @ ( strict_implies @ ( possibly @ SV44 ) @ ( possibly @ SY191 ) ) ) ) )
= $true )
| ( axiom_m8 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(895,plain,
! [SV45: $i] :
( ( ( ! [SY192: $i] : ( is_a_theorem @ ( implies @ SY192 @ ( or @ SV45 @ SY192 ) ) ) )
= $true )
| ( or_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(896,plain,
! [SV46: $i] :
( ( ( ! [SY193: $i,SY194: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV46 @ SY193 ) @ ( implies @ ( implies @ SY193 @ SY194 ) @ ( implies @ SV46 @ SY194 ) ) ) ) )
= $true )
| ( cn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(897,plain,
! [SV47: $i] :
( ( ( ! [SY195: $i] : ( is_a_theorem @ ( implies @ ( and @ SV47 @ SY195 ) @ SV47 ) ) )
= $true )
| ( and_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(898,plain,
! [SV48: $i] :
( ( ( ! [SY196: $i,SY197: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SV48 @ SY196 ) @ SY197 ) @ ( and @ SV48 @ ( and @ SY196 @ SY197 ) ) ) ) )
= $true )
| ( axiom_m3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(899,plain,
( ( sK35_REN
| substitution_strict_equiv )
= $true ),
inference(extcnf_not_neg,[status(thm)],[823]) ).
thf(900,plain,
( ( ~ sK35_REN
| ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[824]) ).
thf(901,plain,
! [SV49: $i] :
( ( ( ! [SY198: $i] :
( ~ ( is_a_theorem @ ( strict_equiv @ SV49 @ SY198 ) )
| ( SV49 = SY198 ) ) )
= $true )
| ( substitution_strict_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(902,plain,
! [SV50: $i] :
( ( ( ! [SY199: $i,SY200: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV50 @ SY200 ) @ ( implies @ ( implies @ SY199 @ SY200 ) @ ( implies @ ( or @ SV50 @ SY199 ) @ SY200 ) ) ) ) )
= $true )
| ( or_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(903,plain,
! [SV51: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ SV51 ) @ ( necessarily @ ( possibly @ SV51 ) ) ) )
= $true )
| ( axiom_m10 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(904,plain,
! [SV52: $i] :
( ( ( is_a_theorem @ ( implies @ ( necessarily @ SV52 ) @ ( necessarily @ ( necessarily @ SV52 ) ) ) )
= $true )
| ( axiom_4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(905,plain,
! [SV53: $i] :
( ( ( ! [SY201: $i] : ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SV53 @ SY201 ) ) @ ( implies @ ( necessarily @ SV53 ) @ ( necessarily @ SY201 ) ) ) ) )
= $true )
| ( axiom_K = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(906,plain,
! [SV54: $i] :
( ( ( ! [SY202: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SV54 @ SY202 ) @ ( implies @ SV54 @ SY202 ) ) ) )
= $true )
| ( equivalence_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(907,plain,
! [SV55: $i] :
( ( ( ! [SY203: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SY203 ) @ ( not @ SV55 ) ) @ ( implies @ SV55 @ SY203 ) ) ) )
= $true )
| ( modus_tollens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(908,plain,
( ( sK41_REN
| modus_ponens_strict_implies )
= $true ),
inference(extcnf_not_neg,[status(thm)],[838]) ).
thf(909,plain,
( ( ~ sK41_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[839]) ).
thf(910,plain,
! [SV56: $i] :
( ( ( ! [SY204: $i] :
( ~ ( is_a_theorem @ SV56 )
| ~ ( is_a_theorem @ ( strict_implies @ SV56 @ SY204 ) )
| ( is_a_theorem @ SY204 ) ) )
= $true )
| ( modus_ponens_strict_implies = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(911,plain,
! [SV57: $i] :
( ( ( ! [SY205: $i] : ( is_a_theorem @ ( implies @ ( or @ SV57 @ SY205 ) @ ( or @ SY205 @ SV57 ) ) ) )
= $true )
| ( r3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[842]) ).
thf(912,plain,
! [SV58: $i] :
( ( ( is_a_theorem @ ( implies @ SV58 @ ( necessarily @ ( possibly @ SV58 ) ) ) )
= $true )
| ( axiom_B = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(913,plain,
! [SV59: $i] :
( ( ( ! [SY206: $i,SY207: $i] : ( is_a_theorem @ ( implies @ ( implies @ SY206 @ SY207 ) @ ( implies @ ( or @ SV59 @ SY206 ) @ ( or @ SV59 @ SY207 ) ) ) ) )
= $true )
| ( r5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(914,plain,
! [SV60: $i] :
( ( ( ! [SY208: $i,SY209: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SV60 @ SY208 ) ) @ ( necessarily @ ( implies @ SY208 @ SY209 ) ) ) @ ( necessarily @ ( implies @ SV60 @ SY209 ) ) ) ) )
= $true )
| ( axiom_s1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[848]) ).
thf(915,plain,
! [SV61: $i] :
( ( ( ! [SY210: $i] : ( is_a_theorem @ ( implies @ SV61 @ ( implies @ SY210 @ ( and @ SV61 @ SY210 ) ) ) ) )
= $true )
| ( and_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(916,plain,
! [SV62: $i] :
( ( ( ! [SY211: $i] : ( is_a_theorem @ ( implies @ SV62 @ ( implies @ SY211 @ SV62 ) ) ) )
= $true )
| ( implies_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(917,plain,
! [SV63: $i] :
( ( ( ! [SY212: $i,SY213: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SV63 @ SY212 ) @ ( strict_implies @ SY212 @ SY213 ) ) @ ( strict_implies @ SV63 @ SY213 ) ) ) )
= $true )
| ( axiom_m5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(918,plain,
! [SV64: $i] :
( ( ( ! [SY214: $i] : ( is_a_theorem @ ( implies @ ( and @ SV64 @ SY214 ) @ SY214 ) ) )
= $true )
| ( and_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[856]) ).
thf(919,plain,
! [SV65: $i] :
( ( ( ! [SY215: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ SV65 @ SY215 ) @ SV65 ) ) )
= $true )
| ( axiom_m2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[858]) ).
thf(920,plain,
! [SV66: $i,SV17: $i] :
( ( ( ! [SY216: $i] : ( is_a_theorem @ ( implies @ ( or @ SV17 @ ( or @ SV66 @ SY216 ) ) @ ( or @ SV66 @ ( or @ SV17 @ SY216 ) ) ) ) )
= $true )
| ( r4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(921,plain,
( ( sK38_REN = $true )
| ( adjunction = $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(922,plain,
( ( ( ~ sK38_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(923,plain,
! [SV67: $i,SV18: $i] :
( ( ( ~ ( is_a_theorem @ SV18 )
| ~ ( is_a_theorem @ SV67 )
| ( is_a_theorem @ ( and @ SV18 @ SV67 ) ) )
= $true )
| ( adjunction = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(924,plain,
! [SV68: $i,SV19: $i] :
( ( ( is_a_theorem @ ( implies @ SV19 @ ( or @ SV19 @ SV68 ) ) )
= $true )
| ( or_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[863]) ).
thf(925,plain,
! [SV69: $i,SV21: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ SV21 @ SV69 ) @ SV21 ) )
= $true )
| ( kn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(926,plain,
! [SV70: $i,SV24: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SV24 @ SV70 ) @ ( strict_implies @ ( not @ ( possibly @ SV70 ) ) @ ( not @ ( possibly @ SV24 ) ) ) ) )
= $true )
| ( axiom_s3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(927,plain,
( ( sK43_REN = $true )
| ( necessitation = $true ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(928,plain,
( ( ( ~ sK43_REN )
= $true )
| ( ( ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(929,plain,
! [SV25: $i] :
( ( ( ~ ( is_a_theorem @ SV25 ) )
= $true )
| ( ( is_a_theorem @ ( necessarily @ SV25 ) )
= $true )
| ( necessitation = $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(930,plain,
! [SV28: $i,SV71: $i] :
( ( ( is_a_theorem @ ( implies @ SV71 @ ( or @ SV28 @ SV71 ) ) )
= $true )
| ( r2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(931,plain,
! [SV72: $i,SV29: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SV29 @ SV72 ) ) @ ( and @ ( possibly @ SV29 ) @ ( possibly @ SV72 ) ) ) )
= $true )
| ( axiom_s2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(932,plain,
! [SV73: $i,SV30: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV30 @ ( implies @ SV30 @ SV73 ) ) @ ( implies @ SV30 @ SV73 ) ) )
= $true )
| ( implies_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(933,plain,
! [SV74: $i,SV31: $i] :
( ( ( ! [SY217: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV31 @ SV74 ) @ ( implies @ ( implies @ SV74 @ SY217 ) @ ( implies @ SV31 @ SY217 ) ) ) ) )
= $true )
| ( implies_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(934,plain,
! [SV75: $i,SV33: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( possibly @ ( and @ SV33 @ SV75 ) ) @ SV33 ) )
= $true )
| ( axiom_m7 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(935,plain,
! [SV76: $i,SV36: $i] :
( ( ( is_a_theorem @ ( implies @ SV36 @ ( implies @ ( not @ SV36 ) @ SV76 ) ) )
= $true )
| ( cn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(936,plain,
! [SV77: $i,SV37: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( and @ SV37 @ SV77 ) @ ( and @ SV77 @ SV37 ) ) )
= $true )
| ( axiom_m1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[883]) ).
thf(937,plain,
( ( sK100_REN = $true )
| ( modus_ponens = $true ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(938,plain,
( ( ( ~ sK100_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(939,plain,
! [SV78: $i,SV38: $i] :
( ( ( ~ ( is_a_theorem @ SV38 )
| ~ ( is_a_theorem @ ( implies @ SV38 @ SV78 ) )
| ( is_a_theorem @ SV78 ) )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(940,plain,
! [SV79: $i,SV39: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV39 @ SV79 ) @ ( implies @ ( implies @ SV79 @ SV39 ) @ ( equiv @ SV39 @ SV79 ) ) ) )
= $true )
| ( equivalence_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[887]) ).
thf(941,plain,
! [SV80: $i,SV40: $i] :
( ( ( is_a_theorem @ ( implies @ ( equiv @ SV40 @ SV80 ) @ ( implies @ SV80 @ SV40 ) ) )
= $true )
| ( equivalence_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[888]) ).
thf(942,plain,
( ( sK97_REN = $true )
| ( substitution_of_equivalents = $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(943,plain,
( ( ( ~ sK97_REN )
= $true )
| ( ( ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(944,plain,
! [SV81: $i,SV41: $i] :
( ( ( ~ ( is_a_theorem @ ( equiv @ SV41 @ SV81 ) )
| ( SV41 = SV81 ) )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(945,plain,
! [SV82: $i,SV43: $i] :
( ( ( ! [SY218: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV43 @ SV82 ) @ ( implies @ ( not @ ( and @ SV82 @ SY218 ) ) @ ( not @ ( and @ SY218 @ SV43 ) ) ) ) ) )
= $true )
| ( kn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(946,plain,
! [SV83: $i,SV44: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( strict_implies @ SV44 @ SV83 ) @ ( strict_implies @ ( possibly @ SV44 ) @ ( possibly @ SV83 ) ) ) )
= $true )
| ( axiom_m8 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(947,plain,
! [SV45: $i,SV84: $i] :
( ( ( is_a_theorem @ ( implies @ SV84 @ ( or @ SV45 @ SV84 ) ) )
= $true )
| ( or_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[895]) ).
thf(948,plain,
! [SV85: $i,SV46: $i] :
( ( ( ! [SY219: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV46 @ SV85 ) @ ( implies @ ( implies @ SV85 @ SY219 ) @ ( implies @ SV46 @ SY219 ) ) ) ) )
= $true )
| ( cn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[896]) ).
thf(949,plain,
! [SV86: $i,SV47: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ SV47 @ SV86 ) @ SV47 ) )
= $true )
| ( and_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[897]) ).
thf(950,plain,
! [SV87: $i,SV48: $i] :
( ( ( ! [SY220: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SV48 @ SV87 ) @ SY220 ) @ ( and @ SV48 @ ( and @ SV87 @ SY220 ) ) ) ) )
= $true )
| ( axiom_m3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[898]) ).
thf(951,plain,
( ( sK35_REN = $true )
| ( substitution_strict_equiv = $true ) ),
inference(extcnf_or_pos,[status(thm)],[899]) ).
thf(952,plain,
( ( ( ~ sK35_REN )
= $true )
| ( ( ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[900]) ).
thf(953,plain,
! [SV88: $i,SV49: $i] :
( ( ( ~ ( is_a_theorem @ ( strict_equiv @ SV49 @ SV88 ) )
| ( SV49 = SV88 ) )
= $true )
| ( substitution_strict_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[901]) ).
thf(954,plain,
! [SV89: $i,SV50: $i] :
( ( ( ! [SY221: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV50 @ SY221 ) @ ( implies @ ( implies @ SV89 @ SY221 ) @ ( implies @ ( or @ SV50 @ SV89 ) @ SY221 ) ) ) ) )
= $true )
| ( or_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(955,plain,
! [SV90: $i,SV53: $i] :
( ( ( is_a_theorem @ ( implies @ ( necessarily @ ( implies @ SV53 @ SV90 ) ) @ ( implies @ ( necessarily @ SV53 ) @ ( necessarily @ SV90 ) ) ) )
= $true )
| ( axiom_K = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[905]) ).
thf(956,plain,
! [SV91: $i,SV54: $i] :
( ( ( is_a_theorem @ ( implies @ ( equiv @ SV54 @ SV91 ) @ ( implies @ SV54 @ SV91 ) ) )
= $true )
| ( equivalence_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[906]) ).
thf(957,plain,
! [SV55: $i,SV92: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV92 ) @ ( not @ SV55 ) ) @ ( implies @ SV55 @ SV92 ) ) )
= $true )
| ( modus_tollens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(958,plain,
( ( sK41_REN = $true )
| ( modus_ponens_strict_implies = $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(959,plain,
( ( ( ~ sK41_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[909]) ).
thf(960,plain,
! [SV93: $i,SV56: $i] :
( ( ( ~ ( is_a_theorem @ SV56 )
| ~ ( is_a_theorem @ ( strict_implies @ SV56 @ SV93 ) )
| ( is_a_theorem @ SV93 ) )
= $true )
| ( modus_ponens_strict_implies = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[910]) ).
thf(961,plain,
! [SV94: $i,SV57: $i] :
( ( ( is_a_theorem @ ( implies @ ( or @ SV57 @ SV94 ) @ ( or @ SV94 @ SV57 ) ) )
= $true )
| ( r3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(962,plain,
! [SV59: $i,SV95: $i] :
( ( ( ! [SY222: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV95 @ SY222 ) @ ( implies @ ( or @ SV59 @ SV95 ) @ ( or @ SV59 @ SY222 ) ) ) ) )
= $true )
| ( r5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[913]) ).
thf(963,plain,
! [SV96: $i,SV60: $i] :
( ( ( ! [SY223: $i] : ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SV60 @ SV96 ) ) @ ( necessarily @ ( implies @ SV96 @ SY223 ) ) ) @ ( necessarily @ ( implies @ SV60 @ SY223 ) ) ) ) )
= $true )
| ( axiom_s1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(964,plain,
! [SV97: $i,SV61: $i] :
( ( ( is_a_theorem @ ( implies @ SV61 @ ( implies @ SV97 @ ( and @ SV61 @ SV97 ) ) ) )
= $true )
| ( and_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(965,plain,
! [SV98: $i,SV62: $i] :
( ( ( is_a_theorem @ ( implies @ SV62 @ ( implies @ SV98 @ SV62 ) ) )
= $true )
| ( implies_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(966,plain,
! [SV99: $i,SV63: $i] :
( ( ( ! [SY224: $i] : ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SV63 @ SV99 ) @ ( strict_implies @ SV99 @ SY224 ) ) @ ( strict_implies @ SV63 @ SY224 ) ) ) )
= $true )
| ( axiom_m5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[917]) ).
thf(967,plain,
! [SV100: $i,SV64: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ SV64 @ SV100 ) @ SV100 ) )
= $true )
| ( and_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(968,plain,
! [SV101: $i,SV65: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( and @ SV65 @ SV101 ) @ SV65 ) )
= $true )
| ( axiom_m2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(969,plain,
! [SV102: $i,SV66: $i,SV17: $i] :
( ( ( is_a_theorem @ ( implies @ ( or @ SV17 @ ( or @ SV66 @ SV102 ) ) @ ( or @ SV66 @ ( or @ SV17 @ SV102 ) ) ) )
= $true )
| ( r4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[920]) ).
thf(970,plain,
( ( sK38_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(971,plain,
! [SV67: $i,SV18: $i] :
( ( ( ~ ( is_a_theorem @ SV18 )
| ~ ( is_a_theorem @ SV67 ) )
= $true )
| ( ( is_a_theorem @ ( and @ SV18 @ SV67 ) )
= $true )
| ( adjunction = $false ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(972,plain,
( ( sK43_REN = $false )
| ( ( ~ ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[928]) ).
thf(973,plain,
! [SV25: $i] :
( ( ( is_a_theorem @ SV25 )
= $false )
| ( ( is_a_theorem @ ( necessarily @ SV25 ) )
= $true )
| ( necessitation = $false ) ),
inference(extcnf_not_pos,[status(thm)],[929]) ).
thf(974,plain,
! [SV103: $i,SV74: $i,SV31: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV31 @ SV74 ) @ ( implies @ ( implies @ SV74 @ SV103 ) @ ( implies @ SV31 @ SV103 ) ) ) )
= $true )
| ( implies_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(975,plain,
( ( sK100_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[938]) ).
thf(976,plain,
! [SV78: $i,SV38: $i] :
( ( ( ~ ( is_a_theorem @ SV38 )
| ~ ( is_a_theorem @ ( implies @ SV38 @ SV78 ) ) )
= $true )
| ( ( is_a_theorem @ SV78 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(977,plain,
( ( sK97_REN = $false )
| ( ( ~ ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(978,plain,
! [SV81: $i,SV41: $i] :
( ( ( ~ ( is_a_theorem @ ( equiv @ SV41 @ SV81 ) ) )
= $true )
| ( ( SV41 = SV81 )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(979,plain,
! [SV104: $i,SV82: $i,SV43: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV43 @ SV82 ) @ ( implies @ ( not @ ( and @ SV82 @ SV104 ) ) @ ( not @ ( and @ SV104 @ SV43 ) ) ) ) )
= $true )
| ( kn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[945]) ).
thf(980,plain,
! [SV105: $i,SV85: $i,SV46: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV46 @ SV85 ) @ ( implies @ ( implies @ SV85 @ SV105 ) @ ( implies @ SV46 @ SV105 ) ) ) )
= $true )
| ( cn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(981,plain,
! [SV106: $i,SV87: $i,SV48: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( and @ ( and @ SV48 @ SV87 ) @ SV106 ) @ ( and @ SV48 @ ( and @ SV87 @ SV106 ) ) ) )
= $true )
| ( axiom_m3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[950]) ).
thf(982,plain,
( ( sK35_REN = $false )
| ( ( ~ ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[952]) ).
thf(983,plain,
! [SV88: $i,SV49: $i] :
( ( ( ~ ( is_a_theorem @ ( strict_equiv @ SV49 @ SV88 ) ) )
= $true )
| ( ( SV49 = SV88 )
= $true )
| ( substitution_strict_equiv = $false ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(984,plain,
! [SV89: $i,SV107: $i,SV50: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV50 @ SV107 ) @ ( implies @ ( implies @ SV89 @ SV107 ) @ ( implies @ ( or @ SV50 @ SV89 ) @ SV107 ) ) ) )
= $true )
| ( or_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(985,plain,
( ( sK41_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(986,plain,
! [SV93: $i,SV56: $i] :
( ( ( ~ ( is_a_theorem @ SV56 )
| ~ ( is_a_theorem @ ( strict_implies @ SV56 @ SV93 ) ) )
= $true )
| ( ( is_a_theorem @ SV93 )
= $true )
| ( modus_ponens_strict_implies = $false ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(987,plain,
! [SV59: $i,SV108: $i,SV95: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV95 @ SV108 ) @ ( implies @ ( or @ SV59 @ SV95 ) @ ( or @ SV59 @ SV108 ) ) ) )
= $true )
| ( r5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(988,plain,
! [SV109: $i,SV96: $i,SV60: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ ( necessarily @ ( implies @ SV60 @ SV96 ) ) @ ( necessarily @ ( implies @ SV96 @ SV109 ) ) ) @ ( necessarily @ ( implies @ SV60 @ SV109 ) ) ) )
= $true )
| ( axiom_s1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[963]) ).
thf(989,plain,
! [SV110: $i,SV99: $i,SV63: $i] :
( ( ( is_a_theorem @ ( strict_implies @ ( and @ ( strict_implies @ SV63 @ SV99 ) @ ( strict_implies @ SV99 @ SV110 ) ) @ ( strict_implies @ SV63 @ SV110 ) ) )
= $true )
| ( axiom_m5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(990,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
| ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(991,plain,
! [SV67: $i,SV18: $i] :
( ( ( ~ ( is_a_theorem @ SV18 ) )
= $true )
| ( ( ~ ( is_a_theorem @ SV67 ) )
= $true )
| ( ( is_a_theorem @ ( and @ SV18 @ SV67 ) )
= $true )
| ( adjunction = $false ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(992,plain,
( ( ( ~ ( is_a_theorem @ sK42_X )
| ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) )
= $false )
| ( sK43_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(993,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
| ~ ~ ( is_a_theorem @ sK99_SY163 ) )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[975]) ).
thf(994,plain,
! [SV78: $i,SV38: $i] :
( ( ( ~ ( is_a_theorem @ SV38 ) )
= $true )
| ( ( ~ ( is_a_theorem @ ( implies @ SV38 @ SV78 ) ) )
= $true )
| ( ( is_a_theorem @ SV78 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_or_pos,[status(thm)],[976]) ).
thf(995,plain,
( ( ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
| ~ ( ( sK95_X != sK96_SY162 ) ) )
= $false )
| ( sK97_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(996,plain,
! [SV81: $i,SV41: $i] :
( ( ( is_a_theorem @ ( equiv @ SV41 @ SV81 ) )
= $false )
| ( ( SV41 = SV81 )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_not_pos,[status(thm)],[978]) ).
thf(997,plain,
( ( ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
| ~ ( ( sK33_X != sK34_SY126 ) ) )
= $false )
| ( sK35_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(998,plain,
! [SV88: $i,SV49: $i] :
( ( ( is_a_theorem @ ( strict_equiv @ SV49 @ SV88 ) )
= $false )
| ( ( SV49 = SV88 )
= $true )
| ( substitution_strict_equiv = $false ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(999,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
| ~ ~ ( is_a_theorem @ sK40_SY128 ) )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1000,plain,
! [SV93: $i,SV56: $i] :
( ( ( ~ ( is_a_theorem @ SV56 ) )
= $true )
| ( ( ~ ( is_a_theorem @ ( strict_implies @ SV56 @ SV93 ) ) )
= $true )
| ( ( is_a_theorem @ SV93 )
= $true )
| ( modus_ponens_strict_implies = $false ) ),
inference(extcnf_or_pos,[status(thm)],[986]) ).
thf(1001,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1002,plain,
( ( ( ~ ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[990]) ).
thf(1003,plain,
! [SV67: $i,SV18: $i] :
( ( ( is_a_theorem @ SV18 )
= $false )
| ( ( ~ ( is_a_theorem @ SV67 ) )
= $true )
| ( ( is_a_theorem @ ( and @ SV18 @ SV67 ) )
= $true )
| ( adjunction = $false ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1004,plain,
( ( ( ~ ( is_a_theorem @ sK42_X ) )
= $false )
| ( sK43_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1005,plain,
( ( ( ~ ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) )
= $false )
| ( sK43_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[992]) ).
thf(1006,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) ) )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1007,plain,
( ( ( ~ ~ ( is_a_theorem @ sK99_SY163 ) )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[993]) ).
thf(1008,plain,
! [SV78: $i,SV38: $i] :
( ( ( is_a_theorem @ SV38 )
= $false )
| ( ( ~ ( is_a_theorem @ ( implies @ SV38 @ SV78 ) ) )
= $true )
| ( ( is_a_theorem @ SV78 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1009,plain,
( ( ( ~ ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) ) )
= $false )
| ( sK97_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1010,plain,
( ( ( ~ ( ( sK95_X != sK96_SY162 ) ) )
= $false )
| ( sK97_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[995]) ).
thf(1011,plain,
( ( ( ~ ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) ) )
= $false )
| ( sK35_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1012,plain,
( ( ( ~ ( ( sK33_X != sK34_SY126 ) ) )
= $false )
| ( sK35_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[997]) ).
thf(1013,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) ) )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1014,plain,
( ( ( ~ ~ ( is_a_theorem @ sK40_SY128 ) )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[999]) ).
thf(1015,plain,
! [SV93: $i,SV56: $i] :
( ( ( is_a_theorem @ SV56 )
= $false )
| ( ( ~ ( is_a_theorem @ ( strict_implies @ SV56 @ SV93 ) ) )
= $true )
| ( ( is_a_theorem @ SV93 )
= $true )
| ( modus_ponens_strict_implies = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1016,plain,
( ( ( ~ ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) ) )
= $true )
| ( sK38_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1001]) ).
thf(1017,plain,
( ( ( ~ ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) ) )
= $true )
| ( sK38_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1002]) ).
thf(1018,plain,
! [SV18: $i,SV67: $i] :
( ( ( is_a_theorem @ SV67 )
= $false )
| ( ( is_a_theorem @ SV18 )
= $false )
| ( ( is_a_theorem @ ( and @ SV18 @ SV67 ) )
= $true )
| ( adjunction = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1019,plain,
( ( ( is_a_theorem @ sK42_X )
= $true )
| ( sK43_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1004]) ).
thf(1020,plain,
( ( ( ~ ( is_a_theorem @ ( necessarily @ sK42_X ) ) )
= $true )
| ( sK43_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1005]) ).
thf(1021,plain,
( ( ( ~ ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) ) )
= $true )
| ( sK100_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1006]) ).
thf(1022,plain,
( ( ( ~ ( is_a_theorem @ sK99_SY163 ) )
= $true )
| ( sK100_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1007]) ).
thf(1023,plain,
! [SV78: $i,SV38: $i] :
( ( ( is_a_theorem @ ( implies @ SV38 @ SV78 ) )
= $false )
| ( ( is_a_theorem @ SV38 )
= $false )
| ( ( is_a_theorem @ SV78 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1024,plain,
( ( ( is_a_theorem @ ( equiv @ sK95_X @ sK96_SY162 ) )
= $true )
| ( sK97_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1009]) ).
thf(1025,plain,
( ( ( ( sK95_X != sK96_SY162 ) )
= $true )
| ( sK97_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1010]) ).
thf(1026,plain,
( ( ( is_a_theorem @ ( strict_equiv @ sK33_X @ sK34_SY126 ) )
= $true )
| ( sK35_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1011]) ).
thf(1027,plain,
( ( ( ( sK33_X != sK34_SY126 ) )
= $true )
| ( sK35_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1012]) ).
thf(1028,plain,
( ( ( ~ ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) ) )
= $true )
| ( sK41_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1013]) ).
thf(1029,plain,
( ( ( ~ ( is_a_theorem @ sK40_SY128 ) )
= $true )
| ( sK41_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1014]) ).
thf(1030,plain,
! [SV93: $i,SV56: $i] :
( ( ( is_a_theorem @ ( strict_implies @ SV56 @ SV93 ) )
= $false )
| ( ( is_a_theorem @ SV56 )
= $false )
| ( ( is_a_theorem @ SV93 )
= $true )
| ( modus_ponens_strict_implies = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1031,plain,
( ( ( ~ ( is_a_theorem @ sK36_X )
| ~ ( is_a_theorem @ sK37_SY127 ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1032,plain,
( ( ( is_a_theorem @ ( and @ sK36_X @ sK37_SY127 ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1033,plain,
( ( ( is_a_theorem @ ( necessarily @ sK42_X ) )
= $false )
| ( sK43_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1034,plain,
( ( ( ~ ( is_a_theorem @ sK98_X )
| ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1035,plain,
( ( ( is_a_theorem @ sK99_SY163 )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1036,plain,
( ( ( sK95_X = sK96_SY162 )
= $false )
| ( sK97_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1025]) ).
thf(1037,plain,
( ( ( sK33_X = sK34_SY126 )
= $false )
| ( sK35_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1027]) ).
thf(1038,plain,
( ( ( ~ ( is_a_theorem @ sK39_X )
| ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1039,plain,
( ( ( is_a_theorem @ sK40_SY128 )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[1029]) ).
thf(1040,plain,
( ( ( ~ ( is_a_theorem @ sK36_X ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1041,plain,
( ( ( ~ ( is_a_theorem @ sK37_SY127 ) )
= $false )
| ( sK38_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1031]) ).
thf(1042,plain,
( ( ( ~ ( is_a_theorem @ sK98_X ) )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1043,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) ) )
= $false )
| ( sK100_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1034]) ).
thf(1044,plain,
( ( ( ~ ( is_a_theorem @ sK39_X ) )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1045,plain,
( ( ( ~ ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) ) )
= $false )
| ( sK41_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[1038]) ).
thf(1046,plain,
( ( ( is_a_theorem @ sK36_X )
= $true )
| ( sK38_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1040]) ).
thf(1047,plain,
( ( ( is_a_theorem @ sK37_SY127 )
= $true )
| ( sK38_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1041]) ).
thf(1048,plain,
( ( ( is_a_theorem @ sK98_X )
= $true )
| ( sK100_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1042]) ).
thf(1049,plain,
( ( ( is_a_theorem @ ( implies @ sK98_X @ sK99_SY163 ) )
= $true )
| ( sK100_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1043]) ).
thf(1050,plain,
( ( ( is_a_theorem @ sK39_X )
= $true )
| ( sK41_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1044]) ).
thf(1051,plain,
( ( ( is_a_theorem @ ( strict_implies @ sK39_X @ sK40_SY128 ) )
= $true )
| ( sK41_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[1045]) ).
thf(1052,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[270,1051,1050,1049,1048,1047,1046,1039,1037,1036,1035,1033,1032,1030,1026,1024,1023,1019,1018,998,996,989,988,987,984,981,980,979,974,973,969,968,967,965,964,961,958,957,956,955,951,949,947,946,942,941,940,937,936,935,934,932,931,930,927,926,925,924,921,912,904,903,892,881,880,878,873,872,867,866,864,857,855,853,851,849,847,845,843,841,836,834,832,830,828,826,821,819,817,815,813,811,809,804,802,797,795,793,791,789,787,785,783,781,779,777,775,770,768,766,764,762,760,755,656,655,654,653,652,651,650,549,548,386,326,325,324,323,322,321,320,319,318,317,316,315,287,286,285,284,283,282,281,280,279,278,277,276,275,274,273,272,271]) ).
thf(1053,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1052]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL538+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.34 % Computer : n027.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Mon Jul 4 21:02:11 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.37 .
% 0.14/0.38
% 0.14/0.38 No.of.Axioms: 88
% 0.14/0.38
% 0.14/0.38 Length.of.Defs: 0
% 0.14/0.38
% 0.14/0.38 Contains.Choice.Funs: false
% 0.14/0.40 ..
% 0.20/0.42 (rf:0,axioms:88,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:90,loop_count:0,foatp_calls:0,translation:fof_full).................................................
% 0.53/0.80
% 0.53/0.80 ********************************
% 0.53/0.80 * All subproblems solved! *
% 0.53/0.80 ********************************
% 0.53/0.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:88,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1052,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.86/1.06
% 0.86/1.06 %**** Beginning of derivation protocol ****
% 0.86/1.06 % SZS output start CNFRefutation
% See solution above
% 0.86/1.06
% 0.86/1.06 %**** End of derivation protocol ****
% 0.86/1.06 %**** no. of clauses in derivation: 1053 ****
% 0.86/1.06 %**** clause counter: 1052 ****
% 0.86/1.06
% 0.86/1.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:88,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:1052,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------