TSTP Solution File: LCL452+1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : LCL452+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 12:23:26 EDT 2022
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 148
% Syntax : Number of formulae : 660 ( 330 unt; 95 typ; 0 def)
% Number of atoms : 2828 ( 793 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 5823 ( 763 ~; 681 |; 64 &;4245 @)
% ( 52 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 98 ( 95 usr; 91 con; 0-2 aty)
% Number of variables : 767 ( 0 ^ 767 !; 0 ?; 767 :)
% Comments :
%------------------------------------------------------------------------------
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_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_tollens,type,
modus_tollens: $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_or,type,
op_or: $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_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_sK10_SY72,type,
sK10_SY72: $i ).
thf(tp_sK11_P,type,
sK11_P: $i ).
thf(tp_sK12_P,type,
sK12_P: $i ).
thf(tp_sK13_P,type,
sK13_P: $i ).
thf(tp_sK14_SY73,type,
sK14_SY73: $i ).
thf(tp_sK15_P,type,
sK15_P: $i ).
thf(tp_sK16_SY74,type,
sK16_SY74: $i ).
thf(tp_sK17_SY76,type,
sK17_SY76: $i ).
thf(tp_sK18_P,type,
sK18_P: $i ).
thf(tp_sK19_SY77,type,
sK19_SY77: $i ).
thf(tp_sK1_P,type,
sK1_P: $i ).
thf(tp_sK20_SY79,type,
sK20_SY79: $i ).
thf(tp_sK21_P,type,
sK21_P: $i ).
thf(tp_sK22_SY80,type,
sK22_SY80: $i ).
thf(tp_sK23_P,type,
sK23_P: $i ).
thf(tp_sK24_X,type,
sK24_X: $i ).
thf(tp_sK25_SY81,type,
sK25_SY81: $i ).
thf(tp_sK26_X,type,
sK26_X: $i ).
thf(tp_sK27_SY82,type,
sK27_SY82: $i ).
thf(tp_sK28_X,type,
sK28_X: $i ).
thf(tp_sK29_SY83,type,
sK29_SY83: $i ).
thf(tp_sK2_SY65,type,
sK2_SY65: $i ).
thf(tp_sK30_X,type,
sK30_X: $i ).
thf(tp_sK31_SY84,type,
sK31_SY84: $i ).
thf(tp_sK32_SY86,type,
sK32_SY86: $i ).
thf(tp_sK33_X,type,
sK33_X: $i ).
thf(tp_sK34_SY87,type,
sK34_SY87: $i ).
thf(tp_sK35_X,type,
sK35_X: $i ).
thf(tp_sK36_SY88,type,
sK36_SY88: $i ).
thf(tp_sK37_X,type,
sK37_X: $i ).
thf(tp_sK38_SY89,type,
sK38_SY89: $i ).
thf(tp_sK39_X,type,
sK39_X: $i ).
thf(tp_sK3_SY67,type,
sK3_SY67: $i ).
thf(tp_sK40_SY90,type,
sK40_SY90: $i ).
thf(tp_sK41_X,type,
sK41_X: $i ).
thf(tp_sK42_SY91,type,
sK42_SY91: $i ).
thf(tp_sK43_X,type,
sK43_X: $i ).
thf(tp_sK44_SY92,type,
sK44_SY92: $i ).
thf(tp_sK45_SY94,type,
sK45_SY94: $i ).
thf(tp_sK46_X,type,
sK46_X: $i ).
thf(tp_sK47_SY95,type,
sK47_SY95: $i ).
thf(tp_sK48_X,type,
sK48_X: $i ).
thf(tp_sK49_SY96,type,
sK49_SY96: $i ).
thf(tp_sK4_P,type,
sK4_P: $i ).
thf(tp_sK50_X,type,
sK50_X: $i ).
thf(tp_sK51_SY97,type,
sK51_SY97: $i ).
thf(tp_sK52_X,type,
sK52_X: $i ).
thf(tp_sK53_SY98,type,
sK53_SY98: $i ).
thf(tp_sK54_REN,type,
sK54_REN: $o ).
thf(tp_sK55_X,type,
sK55_X: $i ).
thf(tp_sK56_SY99,type,
sK56_SY99: $i ).
thf(tp_sK57_REN,type,
sK57_REN: $o ).
thf(tp_sK5_SY68,type,
sK5_SY68: $i ).
thf(tp_sK6_SY70,type,
sK6_SY70: $i ).
thf(tp_sK7_P,type,
sK7_P: $i ).
thf(tp_sK8_SY71,type,
sK8_SY71: $i ).
thf(tp_sK9_P,type,
sK9_P: $i ).
thf(tp_substitution_of_equivalents,type,
substitution_of_equivalents: $o ).
thf(1,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_equiv) ).
thf(2,axiom,
op_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_implies) ).
thf(3,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_op_or) ).
thf(4,axiom,
substitution_of_equivalents,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',substitution_of_equivalents) ).
thf(5,axiom,
equivalence_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_3) ).
thf(6,axiom,
equivalence_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_2) ).
thf(7,axiom,
equivalence_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_equivalence_1) ).
thf(8,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_3) ).
thf(9,axiom,
or_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_2) ).
thf(10,axiom,
or_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_or_1) ).
thf(11,axiom,
and_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_3) ).
thf(12,axiom,
and_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_2) ).
thf(13,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_and_1) ).
thf(14,axiom,
implies_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_3) ).
thf(15,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_2) ).
thf(16,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_implies_1) ).
thf(17,axiom,
modus_tollens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_tollens) ).
thf(18,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_modus_ponens) ).
thf(19,axiom,
op_equiv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_equiv) ).
thf(20,axiom,
op_implies_and,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_implies_and) ).
thf(21,axiom,
op_or,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hilbert_op_or) ).
thf(22,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(23,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(24,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(25,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(26,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(27,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(28,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(29,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(30,axiom,
( r2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2) ).
thf(31,axiom,
( r1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r1) ).
thf(32,axiom,
( cn3
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn3) ).
thf(33,axiom,
( cn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn2) ).
thf(34,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(35,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(36,axiom,
( kn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn2) ).
thf(37,axiom,
( kn1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kn1) ).
thf(38,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(39,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(40,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(41,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(42,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(43,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(44,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(45,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(46,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(47,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(48,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(49,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(50,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(51,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(52,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(53,conjecture,
cn2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',luka_cn2) ).
thf(54,negated_conjecture,
cn2 = $false,
inference(negate_conjecture,[status(cth)],[53]) ).
thf(55,plain,
cn2 = $false,
inference(unfold_def,[status(thm)],[54]) ).
thf(56,plain,
op_equiv = $true,
inference(unfold_def,[status(thm)],[1]) ).
thf(57,plain,
op_implies = $true,
inference(unfold_def,[status(thm)],[2]) ).
thf(58,plain,
op_or = $true,
inference(unfold_def,[status(thm)],[3]) ).
thf(59,plain,
substitution_of_equivalents = $true,
inference(unfold_def,[status(thm)],[4]) ).
thf(60,plain,
equivalence_3 = $true,
inference(unfold_def,[status(thm)],[5]) ).
thf(61,plain,
equivalence_2 = $true,
inference(unfold_def,[status(thm)],[6]) ).
thf(62,plain,
equivalence_1 = $true,
inference(unfold_def,[status(thm)],[7]) ).
thf(63,plain,
or_3 = $true,
inference(unfold_def,[status(thm)],[8]) ).
thf(64,plain,
or_2 = $true,
inference(unfold_def,[status(thm)],[9]) ).
thf(65,plain,
or_1 = $true,
inference(unfold_def,[status(thm)],[10]) ).
thf(66,plain,
and_3 = $true,
inference(unfold_def,[status(thm)],[11]) ).
thf(67,plain,
and_2 = $true,
inference(unfold_def,[status(thm)],[12]) ).
thf(68,plain,
and_1 = $true,
inference(unfold_def,[status(thm)],[13]) ).
thf(69,plain,
implies_3 = $true,
inference(unfold_def,[status(thm)],[14]) ).
thf(70,plain,
implies_2 = $true,
inference(unfold_def,[status(thm)],[15]) ).
thf(71,plain,
implies_1 = $true,
inference(unfold_def,[status(thm)],[16]) ).
thf(72,plain,
modus_tollens = $true,
inference(unfold_def,[status(thm)],[17]) ).
thf(73,plain,
modus_ponens = $true,
inference(unfold_def,[status(thm)],[18]) ).
thf(74,plain,
op_equiv = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(75,plain,
op_implies_and = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(76,plain,
op_or = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(77,plain,
( ( op_equiv
=> ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(78,plain,
( ( op_implies_or
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(79,plain,
( ( op_implies_and
=> ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(80,plain,
( ( op_and
=> ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(81,plain,
( ( op_or
=> ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(82,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)],[27]) ).
thf(83,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)],[28]) ).
thf(84,plain,
( ( r3
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(85,plain,
( ( r2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(86,plain,
( ( r1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(87,plain,
( ( cn3
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(88,plain,
( ( cn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(89,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)],[34]) ).
thf(90,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)],[35]) ).
thf(91,plain,
( ( kn2
<=> ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(92,plain,
( ( kn1
<=> ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(93,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)],[38]) ).
thf(94,plain,
( ( equivalence_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(95,plain,
( ( equivalence_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(96,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)],[41]) ).
thf(97,plain,
( ( or_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(98,plain,
( ( or_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(99,plain,
( ( and_3
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(100,plain,
( ( and_2
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(101,plain,
( ( and_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(102,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)],[47]) ).
thf(103,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)],[48]) ).
thf(104,plain,
( ( implies_1
<=> ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(105,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)],[50]) ).
thf(106,plain,
( ( substitution_of_equivalents
<=> ! [X: $i,Y: $i] :
( ( is_a_theorem @ ( equiv @ X @ Y ) )
=> ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(107,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)],[52]) ).
thf(108,plain,
( ( ~ cn2 )
= $true ),
inference(polarity_switch,[status(thm)],[55]) ).
thf(109,plain,
( ( ~ op_equiv
| ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(110,plain,
( ( ~ op_implies_or
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(111,plain,
( ( ~ op_implies_and
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(112,plain,
( ( ~ op_and
| ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(113,plain,
( ( ~ op_or
| ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(114,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
| 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)],[82]) ).
thf(115,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
| 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)],[83]) ).
thf(116,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
| r3 )
& ( ~ r3
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(117,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
| r2 )
& ( ~ r2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(118,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
| r1 )
& ( ~ r1
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(119,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
| cn3 )
& ( ~ cn3
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(120,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
| cn2 )
& ( ~ cn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(121,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
| 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)],[89]) ).
thf(122,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_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)],[90]) ).
thf(123,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
| kn2 )
& ( ~ kn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[91]) ).
thf(124,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
| kn1 )
& ( ~ kn1
| ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(125,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
| 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)],[93]) ).
thf(126,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_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)],[94]) ).
thf(127,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
| equivalence_1 )
& ( ~ equivalence_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(128,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
| 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)],[96]) ).
thf(129,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
| or_2 )
& ( ~ or_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(130,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
| or_1 )
& ( ~ or_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[98]) ).
thf(131,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
| and_3 )
& ( ~ and_3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(132,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
| and_2 )
& ( ~ and_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(133,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
| and_1 )
& ( ~ and_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(134,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
| 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)],[102]) ).
thf(135,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
| 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)],[103]) ).
thf(136,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
| implies_1 )
& ( ~ implies_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(137,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
| 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)],[105]) ).
thf(138,plain,
( ( ( sK54_REN
| substitution_of_equivalents )
& ( sK54_REN
=> ( ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
& ( sK52_X != sK53_SY98 ) ) )
& ( ~ substitution_of_equivalents
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equiv @ X @ Y ) )
| ( X = Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(139,plain,
( ( ( sK57_REN
| modus_ponens )
& ( sK57_REN
=> ( ( is_a_theorem @ sK55_X )
& ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) )
& ~ ( is_a_theorem @ sK56_SY99 ) ) )
& ( ~ 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)],[107]) ).
thf(140,plain,
( ( ( sK57_REN
| modus_ponens )
& ( sK57_REN
=> ( ( is_a_theorem @ sK55_X )
& ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) )
& ~ ( is_a_theorem @ sK56_SY99 ) ) )
& ( ~ 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)],[139]) ).
thf(141,plain,
( ( ( sK54_REN
| substitution_of_equivalents )
& ( sK54_REN
=> ( ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
& ( sK52_X != sK53_SY98 ) ) )
& ( ~ substitution_of_equivalents
| ! [X: $i,Y: $i] :
( ~ ( is_a_theorem @ ( equiv @ X @ Y ) )
| ( X = Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(142,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
| 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)],[137]) ).
thf(143,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
| implies_1 )
& ( ~ implies_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(144,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
| 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)],[135]) ).
thf(145,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
| 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)],[134]) ).
thf(146,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
| and_1 )
& ( ~ and_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(147,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
| and_2 )
& ( ~ and_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(148,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
| and_3 )
& ( ~ and_3
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(149,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
| or_1 )
& ( ~ or_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(150,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
| or_2 )
& ( ~ or_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(151,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
| 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)],[128]) ).
thf(152,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
| equivalence_1 )
& ( ~ equivalence_1
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(153,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_X ) ) )
| equivalence_2 )
& ( ~ equivalence_2
| ! [X: $i,Y: $i] : ( is_a_theorem @ ( implies @ ( equiv @ X @ Y ) @ ( implies @ Y @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(154,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
| 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)],[125]) ).
thf(155,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
| kn1 )
& ( ~ kn1
| ! [P: $i] : ( is_a_theorem @ ( implies @ P @ ( and @ P @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(156,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
| kn2 )
& ( ~ kn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( and @ P @ Q ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(157,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_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)],[122]) ).
thf(158,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
| 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)],[121]) ).
thf(159,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
| cn2 )
& ( ~ cn2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ P @ ( implies @ ( not @ P ) @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(160,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
| cn3 )
& ( ~ cn3
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(161,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
| r1 )
& ( ~ r1
| ! [P: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ P ) @ P ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(162,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
| r2 )
& ( ~ r2
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ Q @ ( or @ P @ Q ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(163,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
| r3 )
& ( ~ r3
| ! [P: $i,Q: $i] : ( is_a_theorem @ ( implies @ ( or @ P @ Q ) @ ( or @ Q @ P ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(164,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
| 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)],[115]) ).
thf(165,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
| 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)],[114]) ).
thf(166,plain,
( ( ~ op_or
| ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(167,plain,
( ( ~ op_and
| ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(168,plain,
( ( ~ op_implies_and
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(169,plain,
( ( ~ op_implies_or
| ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(170,plain,
( ( ~ op_equiv
| ! [X: $i,Y: $i] :
( ( equiv @ X @ Y )
= ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(171,plain,
op_or = $true,
inference(copy,[status(thm)],[76]) ).
thf(172,plain,
op_implies_and = $true,
inference(copy,[status(thm)],[75]) ).
thf(173,plain,
op_equiv = $true,
inference(copy,[status(thm)],[74]) ).
thf(174,plain,
modus_ponens = $true,
inference(copy,[status(thm)],[73]) ).
thf(175,plain,
modus_tollens = $true,
inference(copy,[status(thm)],[72]) ).
thf(176,plain,
implies_1 = $true,
inference(copy,[status(thm)],[71]) ).
thf(177,plain,
implies_2 = $true,
inference(copy,[status(thm)],[70]) ).
thf(178,plain,
implies_3 = $true,
inference(copy,[status(thm)],[69]) ).
thf(179,plain,
and_1 = $true,
inference(copy,[status(thm)],[68]) ).
thf(180,plain,
and_2 = $true,
inference(copy,[status(thm)],[67]) ).
thf(181,plain,
and_3 = $true,
inference(copy,[status(thm)],[66]) ).
thf(182,plain,
or_1 = $true,
inference(copy,[status(thm)],[65]) ).
thf(183,plain,
or_2 = $true,
inference(copy,[status(thm)],[64]) ).
thf(184,plain,
or_3 = $true,
inference(copy,[status(thm)],[63]) ).
thf(185,plain,
equivalence_1 = $true,
inference(copy,[status(thm)],[62]) ).
thf(186,plain,
equivalence_2 = $true,
inference(copy,[status(thm)],[61]) ).
thf(187,plain,
equivalence_3 = $true,
inference(copy,[status(thm)],[60]) ).
thf(188,plain,
substitution_of_equivalents = $true,
inference(copy,[status(thm)],[59]) ).
thf(189,plain,
op_or = $true,
inference(copy,[status(thm)],[58]) ).
thf(190,plain,
op_implies = $true,
inference(copy,[status(thm)],[57]) ).
thf(191,plain,
op_equiv = $true,
inference(copy,[status(thm)],[56]) ).
thf(192,plain,
( ( ~ cn2 )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(193,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
| or_1 )
| ~ ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[149]) ).
thf(194,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
| r3 )
| ~ ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[163]) ).
thf(195,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
| and_2 )
| ~ ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[147]) ).
thf(196,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
| 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)],[158]) ).
thf(197,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
| 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)],[151]) ).
thf(198,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
| 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)],[154]) ).
thf(199,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
| kn1 )
| ~ ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(200,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
| 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)],[165]) ).
thf(201,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
| and_1 )
| ~ ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[146]) ).
thf(202,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
| kn2 )
| ~ ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[156]) ).
thf(203,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
| 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)],[164]) ).
thf(204,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_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)],[153]) ).
thf(205,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
| r2 )
| ~ ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(206,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
| and_3 )
| ~ ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[148]) ).
thf(207,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_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)],[157]) ).
thf(208,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
| 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)],[144]) ).
thf(209,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
| 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)],[142]) ).
thf(210,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
| r1 )
| ~ ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[161]) ).
thf(211,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
| or_2 )
| ~ ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[150]) ).
thf(212,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
| implies_1 )
| ~ ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[143]) ).
thf(213,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
| cn2 )
| ~ ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[159]) ).
thf(214,plain,
( ( ~ ( ~ ~ ( ~ ( sK57_REN
| modus_ponens )
| ~ ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) ) )
| ~ ( ~ 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)],[140]) ).
thf(215,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
| cn3 )
| ~ ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(216,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
| equivalence_1 )
| ~ ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[152]) ).
thf(217,plain,
( ( ~ ( ~ ~ ( ~ ( sK54_REN
| substitution_of_equivalents )
| ~ ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) ) )
| ~ ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[141]) ).
thf(218,plain,
( ( ~ ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
| 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)],[145]) ).
thf(219,plain,
( ( ( ~ op_or )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[166]) ).
thf(220,plain,
( ( ( ~ op_and )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(221,plain,
( ( ( ~ op_implies_and )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(222,plain,
( ( ( ~ op_implies_or )
= $true )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(223,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)],[170]) ).
thf(224,plain,
cn2 = $false,
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(225,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
| or_1 )
| ~ ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(226,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
| r3 )
| ~ ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(227,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
| and_2 )
| ~ ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(228,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
| 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)],[196]) ).
thf(229,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
| 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)],[197]) ).
thf(230,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
| 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)],[198]) ).
thf(231,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
| kn1 )
| ~ ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(232,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
| 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)],[200]) ).
thf(233,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
| and_1 )
| ~ ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(234,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
| kn2 )
| ~ ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(235,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
| 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)],[203]) ).
thf(236,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_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)],[204]) ).
thf(237,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
| r2 )
| ~ ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(238,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
| 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)],[206]) ).
thf(239,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_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)],[207]) ).
thf(240,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
| 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)],[208]) ).
thf(241,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
| 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)],[209]) ).
thf(242,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
| r1 )
| ~ ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(243,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
| or_2 )
| ~ ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(244,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
| implies_1 )
| ~ ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(245,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
| cn2 )
| ~ ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(246,plain,
( ( ~ ~ ( ~ ( sK57_REN
| modus_ponens )
| ~ ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) ) )
| ~ ( ~ 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)],[214]) ).
thf(247,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
| cn3 )
| ~ ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(248,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
| 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)],[216]) ).
thf(249,plain,
( ( ~ ~ ( ~ ( sK54_REN
| substitution_of_equivalents )
| ~ ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) ) )
| ~ ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(250,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
| 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)],[218]) ).
thf(251,plain,
( ( op_or = $false )
| ( ( ! [X: $i,Y: $i] :
( ( or @ X @ Y )
= ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(252,plain,
( ( op_and = $false )
| ( ( ! [X: $i,Y: $i] :
( ( and @ X @ Y )
= ( not @ ( or @ ( not @ X ) @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(253,plain,
( ( op_implies_and = $false )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( not @ ( and @ X @ ( not @ Y ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(254,plain,
( ( op_implies_or = $false )
| ( ( ! [X: $i,Y: $i] :
( ( implies @ X @ Y )
= ( or @ ( not @ X ) @ Y ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(255,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)],[223]) ).
thf(256,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
| or_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(257,plain,
( ( ~ ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[225]) ).
thf(258,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
| r3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(259,plain,
( ( ~ ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(260,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
| and_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(261,plain,
( ( ~ ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[227]) ).
thf(262,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
| cn1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[228]) ).
thf(263,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)],[228]) ).
thf(264,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
| or_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[229]) ).
thf(265,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)],[229]) ).
thf(266,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
| equivalence_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[230]) ).
thf(267,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)],[230]) ).
thf(268,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
| kn1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(269,plain,
( ( ~ ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[231]) ).
thf(270,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
| r5 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[232]) ).
thf(271,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)],[232]) ).
thf(272,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
| and_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(273,plain,
( ( ~ ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[233]) ).
thf(274,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
| kn2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(275,plain,
( ( ~ ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(276,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
| r4 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[235]) ).
thf(277,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)],[235]) ).
thf(278,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_X ) ) )
| equivalence_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(279,plain,
( ( ~ ( ~ equivalence_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[236]) ).
thf(280,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
| r2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(281,plain,
( ( ~ ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[237]) ).
thf(282,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
| and_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(283,plain,
( ( ~ ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[238]) ).
thf(284,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_P ) ) ) ) )
| kn3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[239]) ).
thf(285,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)],[239]) ).
thf(286,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
| implies_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[240]) ).
thf(287,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)],[240]) ).
thf(288,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
| modus_tollens ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[241]) ).
thf(289,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)],[241]) ).
thf(290,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
| r1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(291,plain,
( ( ~ ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[242]) ).
thf(292,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
| or_2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(293,plain,
( ( ~ ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[243]) ).
thf(294,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
| implies_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(295,plain,
( ( ~ ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[244]) ).
thf(296,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
| cn2 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(297,plain,
( ( ~ ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[245]) ).
thf(298,plain,
( ( ~ ~ ( ~ ( sK57_REN
| modus_ponens )
| ~ ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[246]) ).
thf(299,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)],[246]) ).
thf(300,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
| cn3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(301,plain,
( ( ~ ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[247]) ).
thf(302,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
| equivalence_1 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(303,plain,
( ( ~ ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[248]) ).
thf(304,plain,
( ( ~ ~ ( ~ ( sK54_REN
| substitution_of_equivalents )
| ~ ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(305,plain,
( ( ~ ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[249]) ).
thf(306,plain,
( ( ~ ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
| implies_3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[250]) ).
thf(307,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)],[250]) ).
thf(308,plain,
! [SV1: $i] :
( ( ( ! [SY100: $i] :
( ( or @ SV1 @ SY100 )
= ( not @ ( and @ ( not @ SV1 ) @ ( not @ SY100 ) ) ) ) )
= $true )
| ( op_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(309,plain,
! [SV2: $i] :
( ( ( ! [SY101: $i] :
( ( and @ SV2 @ SY101 )
= ( not @ ( or @ ( not @ SV2 ) @ ( not @ SY101 ) ) ) ) )
= $true )
| ( op_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(310,plain,
! [SV3: $i] :
( ( ( ! [SY102: $i] :
( ( implies @ SV3 @ SY102 )
= ( not @ ( and @ SV3 @ ( not @ SY102 ) ) ) ) )
= $true )
| ( op_implies_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(311,plain,
! [SV4: $i] :
( ( ( ! [SY103: $i] :
( ( implies @ SV4 @ SY103 )
= ( or @ ( not @ SV4 ) @ SY103 ) ) )
= $true )
| ( op_implies_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(312,plain,
! [SV5: $i] :
( ( ( ! [SY104: $i] :
( ( equiv @ SV5 @ SY104 )
= ( and @ ( implies @ SV5 @ SY104 ) @ ( implies @ SY104 @ SV5 ) ) ) )
= $true )
| ( op_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(313,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
| or_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[256]) ).
thf(314,plain,
( ( ~ or_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[257]) ).
thf(315,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
| r3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[258]) ).
thf(316,plain,
( ( ~ r3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[259]) ).
thf(317,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
| and_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[260]) ).
thf(318,plain,
( ( ~ and_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[261]) ).
thf(319,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
| cn1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[262]) ).
thf(320,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)],[263]) ).
thf(321,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
| or_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[264]) ).
thf(322,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)],[265]) ).
thf(323,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
| equivalence_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[266]) ).
thf(324,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)],[267]) ).
thf(325,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
| kn1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[268]) ).
thf(326,plain,
( ( ~ kn1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[269]) ).
thf(327,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
| r5 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[270]) ).
thf(328,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)],[271]) ).
thf(329,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
| and_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[272]) ).
thf(330,plain,
( ( ~ and_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[273]) ).
thf(331,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
| kn2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[274]) ).
thf(332,plain,
( ( ~ kn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[275]) ).
thf(333,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
| r4 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[276]) ).
thf(334,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)],[277]) ).
thf(335,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_X ) ) )
| equivalence_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[278]) ).
thf(336,plain,
( ( ~ equivalence_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[279]) ).
thf(337,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
| r2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[280]) ).
thf(338,plain,
( ( ~ r2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[281]) ).
thf(339,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
| and_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[282]) ).
thf(340,plain,
( ( ~ and_3
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ ( and @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[283]) ).
thf(341,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_P ) ) ) ) )
| kn3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[284]) ).
thf(342,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)],[285]) ).
thf(343,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
| implies_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[286]) ).
thf(344,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)],[287]) ).
thf(345,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
| modus_tollens )
= $true ),
inference(extcnf_not_neg,[status(thm)],[288]) ).
thf(346,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)],[289]) ).
thf(347,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
| r1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[290]) ).
thf(348,plain,
( ( ~ r1
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[291]) ).
thf(349,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
| or_2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[292]) ).
thf(350,plain,
( ( ~ or_2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[293]) ).
thf(351,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
| implies_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[294]) ).
thf(352,plain,
( ( ~ implies_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[295]) ).
thf(353,plain,
( ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
| cn2 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[296]) ).
thf(354,plain,
( ( ~ cn2
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[297]) ).
thf(355,plain,
( ( ~ ( ~ ( sK57_REN
| modus_ponens )
| ~ ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[298]) ).
thf(356,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)],[299]) ).
thf(357,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
| cn3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[300]) ).
thf(358,plain,
( ( ~ cn3
| ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[301]) ).
thf(359,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
| equivalence_1 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[302]) ).
thf(360,plain,
( ( ~ equivalence_1
| ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SX0 @ SX1 ) @ ( implies @ SX0 @ SX1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[303]) ).
thf(361,plain,
( ( ~ ( ~ ( sK54_REN
| substitution_of_equivalents )
| ~ ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[304]) ).
thf(362,plain,
( ( ~ substitution_of_equivalents
| ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[305]) ).
thf(363,plain,
( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
| implies_3 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[306]) ).
thf(364,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)],[307]) ).
thf(365,plain,
! [SV6: $i,SV1: $i] :
( ( ( ( or @ SV1 @ SV6 )
= ( not @ ( and @ ( not @ SV1 ) @ ( not @ SV6 ) ) ) )
= $true )
| ( op_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(366,plain,
! [SV7: $i,SV2: $i] :
( ( ( ( and @ SV2 @ SV7 )
= ( not @ ( or @ ( not @ SV2 ) @ ( not @ SV7 ) ) ) )
= $true )
| ( op_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(367,plain,
! [SV8: $i,SV3: $i] :
( ( ( ( implies @ SV3 @ SV8 )
= ( not @ ( and @ SV3 @ ( not @ SV8 ) ) ) )
= $true )
| ( op_implies_and = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(368,plain,
! [SV9: $i,SV4: $i] :
( ( ( ( implies @ SV4 @ SV9 )
= ( or @ ( not @ SV4 ) @ SV9 ) )
= $true )
| ( op_implies_or = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(369,plain,
! [SV10: $i,SV5: $i] :
( ( ( ( equiv @ SV5 @ SV10 )
= ( and @ ( implies @ SV5 @ SV10 ) @ ( implies @ SV10 @ SV5 ) ) )
= $true )
| ( op_equiv = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(370,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) ) )
= $true )
| ( or_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(371,plain,
( ( ( ~ or_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(372,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) ) )
= $true )
| ( r3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(373,plain,
( ( ( ~ r3 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(374,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) ) )
= $true )
| ( and_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(375,plain,
( ( ( ~ and_2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(376,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) ) )
= $true )
| ( cn1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(377,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)],[320]) ).
thf(378,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) ) )
= $true )
| ( or_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(379,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)],[322]) ).
thf(380,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) ) )
= $true )
| ( equivalence_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(381,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)],[324]) ).
thf(382,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) ) )
= $true )
| ( kn1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(383,plain,
( ( ( ~ kn1 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(384,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) ) )
= $true )
| ( r5 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(385,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)],[328]) ).
thf(386,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) ) )
= $true )
| ( and_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[329]) ).
thf(387,plain,
( ( ( ~ and_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(388,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) ) )
= $true )
| ( kn2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(389,plain,
( ( ( ~ kn2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(390,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) ) )
= $true )
| ( r4 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(391,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)],[334]) ).
thf(392,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_X ) ) ) )
= $true )
| ( equivalence_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(393,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)],[336]) ).
thf(394,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) ) )
= $true )
| ( r2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(395,plain,
( ( ( ~ r2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(396,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) ) )
= $true )
| ( and_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(397,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)],[340]) ).
thf(398,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_P ) ) ) ) ) )
= $true )
| ( kn3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(399,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)],[342]) ).
thf(400,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) ) )
= $true )
| ( implies_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(401,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)],[344]) ).
thf(402,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) ) )
= $true )
| ( modus_tollens = $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(403,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)],[346]) ).
thf(404,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) ) )
= $true )
| ( r1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(405,plain,
( ( ( ~ r1 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(406,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) ) )
= $true )
| ( or_2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(407,plain,
( ( ( ~ or_2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(408,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) ) )
= $true )
| ( implies_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[351]) ).
thf(409,plain,
( ( ( ~ implies_1 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(410,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) ) )
= $true )
| ( cn2 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[353]) ).
thf(411,plain,
( ( ( ~ cn2 )
= $true )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(412,plain,
( ( ~ ( sK57_REN
| modus_ponens )
| ~ ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(413,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)],[356]) ).
thf(414,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) ) )
= $true )
| ( cn3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[357]) ).
thf(415,plain,
( ( ( ~ cn3 )
= $true )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[358]) ).
thf(416,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) ) )
= $true )
| ( equivalence_1 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[359]) ).
thf(417,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)],[360]) ).
thf(418,plain,
( ( ~ ( sK54_REN
| substitution_of_equivalents )
| ~ ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(419,plain,
( ( ( ~ substitution_of_equivalents )
= $true )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(420,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) ) )
= $true )
| ( implies_3 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(421,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)],[364]) ).
thf(422,plain,
( ( ( is_a_theorem @ ( implies @ sK35_X @ ( or @ sK35_X @ sK36_SY88 ) ) )
= $false )
| ( or_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(423,plain,
( ( or_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(424,plain,
( ( ( is_a_theorem @ ( implies @ ( or @ sK7_P @ sK8_SY71 ) @ ( or @ sK8_SY71 @ sK7_P ) ) )
= $false )
| ( r3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(425,plain,
( ( r3 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX1 ) @ ( or @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(426,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ sK39_X @ sK40_SY90 ) @ sK40_SY90 ) )
= $false )
| ( and_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(427,plain,
( ( and_2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(428,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK15_P @ sK16_SY74 ) @ ( implies @ ( implies @ sK16_SY74 @ sK17_SY76 ) @ ( implies @ sK15_P @ sK17_SY76 ) ) ) )
= $false )
| ( cn1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(429,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)],[377]) ).
thf(430,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK30_X @ sK32_SY86 ) @ ( implies @ ( implies @ sK31_SY84 @ sK32_SY86 ) @ ( implies @ ( or @ sK30_X @ sK31_SY84 ) @ sK32_SY86 ) ) ) )
= $false )
| ( or_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[378]) ).
thf(431,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)],[379]) ).
thf(432,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK24_X @ sK25_SY81 ) @ ( implies @ ( implies @ sK25_SY81 @ sK24_X ) @ ( equiv @ sK24_X @ sK25_SY81 ) ) ) )
= $false )
| ( equivalence_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(433,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)],[381]) ).
thf(434,plain,
( ( ( is_a_theorem @ ( implies @ sK23_P @ ( and @ sK23_P @ sK23_P ) ) )
= $false )
| ( kn1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(435,plain,
( ( kn1 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( and @ SX0 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(436,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK2_SY65 @ sK3_SY67 ) @ ( implies @ ( or @ sK1_P @ sK2_SY65 ) @ ( or @ sK1_P @ sK3_SY67 ) ) ) )
= $false )
| ( r5 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(437,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)],[385]) ).
thf(438,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ sK41_X @ sK42_SY91 ) @ sK41_X ) )
= $false )
| ( and_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(439,plain,
( ( and_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(440,plain,
( ( ( is_a_theorem @ ( implies @ ( and @ sK21_P @ sK22_SY80 ) @ sK21_P ) )
= $false )
| ( kn2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(441,plain,
( ( kn2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ ( and @ SX0 @ SX1 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(442,plain,
( ( ( is_a_theorem @ ( implies @ ( or @ sK4_P @ ( or @ sK5_SY68 @ sK6_SY70 ) ) @ ( or @ sK5_SY68 @ ( or @ sK4_P @ sK6_SY70 ) ) ) )
= $false )
| ( r4 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(443,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)],[391]) ).
thf(444,plain,
( ( ( is_a_theorem @ ( implies @ ( equiv @ sK26_X @ sK27_SY82 ) @ ( implies @ sK27_SY82 @ sK26_X ) ) )
= $false )
| ( equivalence_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(445,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)],[393]) ).
thf(446,plain,
( ( ( is_a_theorem @ ( implies @ sK10_SY72 @ ( or @ sK9_P @ sK10_SY72 ) ) )
= $false )
| ( r2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[394]) ).
thf(447,plain,
( ( r2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(448,plain,
( ( ( is_a_theorem @ ( implies @ sK37_X @ ( implies @ sK38_SY89 @ ( and @ sK37_X @ sK38_SY89 ) ) ) )
= $false )
| ( and_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[396]) ).
thf(449,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)],[397]) ).
thf(450,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK18_P @ sK19_SY77 ) @ ( implies @ ( not @ ( and @ sK19_SY77 @ sK20_SY79 ) ) @ ( not @ ( and @ sK20_SY79 @ sK18_P ) ) ) ) )
= $false )
| ( kn3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(451,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)],[399]) ).
thf(452,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK46_X @ ( implies @ sK46_X @ sK47_SY95 ) ) @ ( implies @ sK46_X @ sK47_SY95 ) ) )
= $false )
| ( implies_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(453,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)],[401]) ).
thf(454,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK51_SY97 ) @ ( not @ sK50_X ) ) @ ( implies @ sK50_X @ sK51_SY97 ) ) )
= $false )
| ( modus_tollens = $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(455,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)],[403]) ).
thf(456,plain,
( ( ( is_a_theorem @ ( implies @ ( or @ sK11_P @ sK11_P ) @ sK11_P ) )
= $false )
| ( r1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(457,plain,
( ( r1 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( or @ SX0 @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(458,plain,
( ( ( is_a_theorem @ ( implies @ sK34_SY87 @ ( or @ sK33_X @ sK34_SY87 ) ) )
= $false )
| ( or_2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(459,plain,
( ( or_2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX1 @ ( or @ SX0 @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(460,plain,
( ( ( is_a_theorem @ ( implies @ sK48_X @ ( implies @ sK49_SY96 @ sK48_X ) ) )
= $false )
| ( implies_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(461,plain,
( ( implies_1 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ SX1 @ SX0 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(462,plain,
( ( ( is_a_theorem @ ( implies @ sK13_P @ ( implies @ ( not @ sK13_P ) @ sK14_SY73 ) ) )
= $false )
| ( cn2 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(463,plain,
( ( cn2 = $false )
| ( ( ! [SX0: $i,SX1: $i] : ( is_a_theorem @ ( implies @ SX0 @ ( implies @ ( not @ SX0 ) @ SX1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(464,plain,
( ( ~ ( sK57_REN
| modus_ponens ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(465,plain,
( ( ~ ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[412]) ).
thf(466,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)],[413]) ).
thf(467,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ sK12_P ) @ sK12_P ) @ sK12_P ) )
= $false )
| ( cn3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(468,plain,
( ( cn3 = $false )
| ( ( ! [SX0: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SX0 ) @ SX0 ) @ SX0 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(469,plain,
( ( ( is_a_theorem @ ( implies @ ( equiv @ sK28_X @ sK29_SY83 ) @ ( implies @ sK28_X @ sK29_SY83 ) ) )
= $false )
| ( equivalence_1 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(470,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)],[417]) ).
thf(471,plain,
( ( ~ ( sK54_REN
| substitution_of_equivalents ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(472,plain,
( ( ~ ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[418]) ).
thf(473,plain,
( ( substitution_of_equivalents = $false )
| ( ( ! [SX0: $i,SX1: $i] :
( ~ ( is_a_theorem @ ( equiv @ SX0 @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[419]) ).
thf(474,plain,
( ( ( is_a_theorem @ ( implies @ ( implies @ sK43_X @ sK44_SY92 ) @ ( implies @ ( implies @ sK44_SY92 @ sK45_SY94 ) @ ( implies @ sK43_X @ sK45_SY94 ) ) ) )
= $false )
| ( implies_3 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[420]) ).
thf(475,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)],[421]) ).
thf(476,plain,
! [SV11: $i] :
( ( ( ! [SY105: $i] : ( is_a_theorem @ ( implies @ SV11 @ ( or @ SV11 @ SY105 ) ) ) )
= $true )
| ( or_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(477,plain,
! [SV12: $i] :
( ( ( ! [SY106: $i] : ( is_a_theorem @ ( implies @ ( or @ SV12 @ SY106 ) @ ( or @ SY106 @ SV12 ) ) ) )
= $true )
| ( r3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(478,plain,
! [SV13: $i] :
( ( ( ! [SY107: $i] : ( is_a_theorem @ ( implies @ ( and @ SV13 @ SY107 ) @ SY107 ) ) )
= $true )
| ( and_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(479,plain,
! [SV14: $i] :
( ( ( ! [SY108: $i,SY109: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV14 @ SY108 ) @ ( implies @ ( implies @ SY108 @ SY109 ) @ ( implies @ SV14 @ SY109 ) ) ) ) )
= $true )
| ( cn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(480,plain,
! [SV15: $i] :
( ( ( ! [SY110: $i,SY111: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV15 @ SY111 ) @ ( implies @ ( implies @ SY110 @ SY111 ) @ ( implies @ ( or @ SV15 @ SY110 ) @ SY111 ) ) ) ) )
= $true )
| ( or_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(481,plain,
! [SV16: $i] :
( ( ( ! [SY112: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV16 @ SY112 ) @ ( implies @ ( implies @ SY112 @ SV16 ) @ ( equiv @ SV16 @ SY112 ) ) ) ) )
= $true )
| ( equivalence_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(482,plain,
! [SV17: $i] :
( ( ( is_a_theorem @ ( implies @ SV17 @ ( and @ SV17 @ SV17 ) ) )
= $true )
| ( kn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(483,plain,
! [SV18: $i] :
( ( ( ! [SY113: $i,SY114: $i] : ( is_a_theorem @ ( implies @ ( implies @ SY113 @ SY114 ) @ ( implies @ ( or @ SV18 @ SY113 ) @ ( or @ SV18 @ SY114 ) ) ) ) )
= $true )
| ( r5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(484,plain,
! [SV19: $i] :
( ( ( ! [SY115: $i] : ( is_a_theorem @ ( implies @ ( and @ SV19 @ SY115 ) @ SV19 ) ) )
= $true )
| ( and_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(485,plain,
! [SV20: $i] :
( ( ( ! [SY116: $i] : ( is_a_theorem @ ( implies @ ( and @ SV20 @ SY116 ) @ SV20 ) ) )
= $true )
| ( kn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(486,plain,
! [SV21: $i] :
( ( ( ! [SY117: $i,SY118: $i] : ( is_a_theorem @ ( implies @ ( or @ SV21 @ ( or @ SY117 @ SY118 ) ) @ ( or @ SY117 @ ( or @ SV21 @ SY118 ) ) ) ) )
= $true )
| ( r4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(487,plain,
! [SV22: $i] :
( ( ( ! [SY119: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SV22 @ SY119 ) @ ( implies @ SY119 @ SV22 ) ) ) )
= $true )
| ( equivalence_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(488,plain,
! [SV23: $i] :
( ( ( ! [SY120: $i] : ( is_a_theorem @ ( implies @ SY120 @ ( or @ SV23 @ SY120 ) ) ) )
= $true )
| ( r2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(489,plain,
! [SV24: $i] :
( ( ( ! [SY121: $i] : ( is_a_theorem @ ( implies @ SV24 @ ( implies @ SY121 @ ( and @ SV24 @ SY121 ) ) ) ) )
= $true )
| ( and_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(490,plain,
! [SV25: $i] :
( ( ( ! [SY122: $i,SY123: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV25 @ SY122 ) @ ( implies @ ( not @ ( and @ SY122 @ SY123 ) ) @ ( not @ ( and @ SY123 @ SV25 ) ) ) ) ) )
= $true )
| ( kn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(491,plain,
! [SV26: $i] :
( ( ( ! [SY124: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV26 @ ( implies @ SV26 @ SY124 ) ) @ ( implies @ SV26 @ SY124 ) ) ) )
= $true )
| ( implies_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(492,plain,
! [SV27: $i] :
( ( ( ! [SY125: $i] : ( is_a_theorem @ ( implies @ ( implies @ ( not @ SY125 ) @ ( not @ SV27 ) ) @ ( implies @ SV27 @ SY125 ) ) ) )
= $true )
| ( modus_tollens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(493,plain,
! [SV28: $i] :
( ( ( is_a_theorem @ ( implies @ ( or @ SV28 @ SV28 ) @ SV28 ) )
= $true )
| ( r1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(494,plain,
! [SV29: $i] :
( ( ( ! [SY126: $i] : ( is_a_theorem @ ( implies @ SY126 @ ( or @ SV29 @ SY126 ) ) ) )
= $true )
| ( or_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(495,plain,
! [SV30: $i] :
( ( ( ! [SY127: $i] : ( is_a_theorem @ ( implies @ SV30 @ ( implies @ SY127 @ SV30 ) ) ) )
= $true )
| ( implies_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(496,plain,
! [SV31: $i] :
( ( ( ! [SY128: $i] : ( is_a_theorem @ ( implies @ SV31 @ ( implies @ ( not @ SV31 ) @ SY128 ) ) ) )
= $true )
| ( cn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(497,plain,
( ( sK57_REN
| modus_ponens )
= $true ),
inference(extcnf_not_neg,[status(thm)],[464]) ).
thf(498,plain,
( ( ~ sK57_REN
| ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[465]) ).
thf(499,plain,
! [SV32: $i] :
( ( ( ! [SY129: $i] :
( ~ ( is_a_theorem @ SV32 )
| ~ ( is_a_theorem @ ( implies @ SV32 @ SY129 ) )
| ( is_a_theorem @ SY129 ) ) )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(500,plain,
! [SV33: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV33 ) @ SV33 ) @ SV33 ) )
= $true )
| ( cn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(501,plain,
! [SV34: $i] :
( ( ( ! [SY130: $i] : ( is_a_theorem @ ( implies @ ( equiv @ SV34 @ SY130 ) @ ( implies @ SV34 @ SY130 ) ) ) )
= $true )
| ( equivalence_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(502,plain,
( ( sK54_REN
| substitution_of_equivalents )
= $true ),
inference(extcnf_not_neg,[status(thm)],[471]) ).
thf(503,plain,
( ( ~ sK54_REN
| ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[472]) ).
thf(504,plain,
! [SV35: $i] :
( ( ( ! [SY131: $i] :
( ~ ( is_a_theorem @ ( equiv @ SV35 @ SY131 ) )
| ( SV35 = SY131 ) ) )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(505,plain,
! [SV36: $i] :
( ( ( ! [SY132: $i,SY133: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV36 @ SY132 ) @ ( implies @ ( implies @ SY132 @ SY133 ) @ ( implies @ SV36 @ SY133 ) ) ) ) )
= $true )
| ( implies_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(506,plain,
! [SV37: $i,SV11: $i] :
( ( ( is_a_theorem @ ( implies @ SV11 @ ( or @ SV11 @ SV37 ) ) )
= $true )
| ( or_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(507,plain,
! [SV38: $i,SV12: $i] :
( ( ( is_a_theorem @ ( implies @ ( or @ SV12 @ SV38 ) @ ( or @ SV38 @ SV12 ) ) )
= $true )
| ( r3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(508,plain,
! [SV39: $i,SV13: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ SV13 @ SV39 ) @ SV39 ) )
= $true )
| ( and_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(509,plain,
! [SV40: $i,SV14: $i] :
( ( ( ! [SY134: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV14 @ SV40 ) @ ( implies @ ( implies @ SV40 @ SY134 ) @ ( implies @ SV14 @ SY134 ) ) ) ) )
= $true )
| ( cn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(510,plain,
! [SV41: $i,SV15: $i] :
( ( ( ! [SY135: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV15 @ SY135 ) @ ( implies @ ( implies @ SV41 @ SY135 ) @ ( implies @ ( or @ SV15 @ SV41 ) @ SY135 ) ) ) ) )
= $true )
| ( or_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(511,plain,
! [SV42: $i,SV16: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV16 @ SV42 ) @ ( implies @ ( implies @ SV42 @ SV16 ) @ ( equiv @ SV16 @ SV42 ) ) ) )
= $true )
| ( equivalence_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(512,plain,
! [SV18: $i,SV43: $i] :
( ( ( ! [SY136: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV43 @ SY136 ) @ ( implies @ ( or @ SV18 @ SV43 ) @ ( or @ SV18 @ SY136 ) ) ) ) )
= $true )
| ( r5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(513,plain,
! [SV44: $i,SV19: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ SV19 @ SV44 ) @ SV19 ) )
= $true )
| ( and_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(514,plain,
! [SV45: $i,SV20: $i] :
( ( ( is_a_theorem @ ( implies @ ( and @ SV20 @ SV45 ) @ SV20 ) )
= $true )
| ( kn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(515,plain,
! [SV46: $i,SV21: $i] :
( ( ( ! [SY137: $i] : ( is_a_theorem @ ( implies @ ( or @ SV21 @ ( or @ SV46 @ SY137 ) ) @ ( or @ SV46 @ ( or @ SV21 @ SY137 ) ) ) ) )
= $true )
| ( r4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(516,plain,
! [SV47: $i,SV22: $i] :
( ( ( is_a_theorem @ ( implies @ ( equiv @ SV22 @ SV47 ) @ ( implies @ SV47 @ SV22 ) ) )
= $true )
| ( equivalence_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(517,plain,
! [SV23: $i,SV48: $i] :
( ( ( is_a_theorem @ ( implies @ SV48 @ ( or @ SV23 @ SV48 ) ) )
= $true )
| ( r2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(518,plain,
! [SV49: $i,SV24: $i] :
( ( ( is_a_theorem @ ( implies @ SV24 @ ( implies @ SV49 @ ( and @ SV24 @ SV49 ) ) ) )
= $true )
| ( and_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(519,plain,
! [SV50: $i,SV25: $i] :
( ( ( ! [SY138: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV25 @ SV50 ) @ ( implies @ ( not @ ( and @ SV50 @ SY138 ) ) @ ( not @ ( and @ SY138 @ SV25 ) ) ) ) ) )
= $true )
| ( kn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(520,plain,
! [SV51: $i,SV26: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV26 @ ( implies @ SV26 @ SV51 ) ) @ ( implies @ SV26 @ SV51 ) ) )
= $true )
| ( implies_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(521,plain,
! [SV27: $i,SV52: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ ( not @ SV52 ) @ ( not @ SV27 ) ) @ ( implies @ SV27 @ SV52 ) ) )
= $true )
| ( modus_tollens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(522,plain,
! [SV29: $i,SV53: $i] :
( ( ( is_a_theorem @ ( implies @ SV53 @ ( or @ SV29 @ SV53 ) ) )
= $true )
| ( or_2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(523,plain,
! [SV54: $i,SV30: $i] :
( ( ( is_a_theorem @ ( implies @ SV30 @ ( implies @ SV54 @ SV30 ) ) )
= $true )
| ( implies_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(524,plain,
! [SV55: $i,SV31: $i] :
( ( ( is_a_theorem @ ( implies @ SV31 @ ( implies @ ( not @ SV31 ) @ SV55 ) ) )
= $true )
| ( cn2 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(525,plain,
( ( sK57_REN = $true )
| ( modus_ponens = $true ) ),
inference(extcnf_or_pos,[status(thm)],[497]) ).
thf(526,plain,
( ( ( ~ sK57_REN )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(527,plain,
! [SV56: $i,SV32: $i] :
( ( ( ~ ( is_a_theorem @ SV32 )
| ~ ( is_a_theorem @ ( implies @ SV32 @ SV56 ) )
| ( is_a_theorem @ SV56 ) )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(528,plain,
! [SV57: $i,SV34: $i] :
( ( ( is_a_theorem @ ( implies @ ( equiv @ SV34 @ SV57 ) @ ( implies @ SV34 @ SV57 ) ) )
= $true )
| ( equivalence_1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(529,plain,
( ( sK54_REN = $true )
| ( substitution_of_equivalents = $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(530,plain,
( ( ( ~ sK54_REN )
= $true )
| ( ( ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(531,plain,
! [SV58: $i,SV35: $i] :
( ( ( ~ ( is_a_theorem @ ( equiv @ SV35 @ SV58 ) )
| ( SV35 = SV58 ) )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(532,plain,
! [SV59: $i,SV36: $i] :
( ( ( ! [SY139: $i] : ( is_a_theorem @ ( implies @ ( implies @ SV36 @ SV59 ) @ ( implies @ ( implies @ SV59 @ SY139 ) @ ( implies @ SV36 @ SY139 ) ) ) ) )
= $true )
| ( implies_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(533,plain,
! [SV60: $i,SV40: $i,SV14: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV14 @ SV40 ) @ ( implies @ ( implies @ SV40 @ SV60 ) @ ( implies @ SV14 @ SV60 ) ) ) )
= $true )
| ( cn1 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(534,plain,
! [SV41: $i,SV61: $i,SV15: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV15 @ SV61 ) @ ( implies @ ( implies @ SV41 @ SV61 ) @ ( implies @ ( or @ SV15 @ SV41 ) @ SV61 ) ) ) )
= $true )
| ( or_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(535,plain,
! [SV18: $i,SV62: $i,SV43: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV43 @ SV62 ) @ ( implies @ ( or @ SV18 @ SV43 ) @ ( or @ SV18 @ SV62 ) ) ) )
= $true )
| ( r5 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(536,plain,
! [SV63: $i,SV46: $i,SV21: $i] :
( ( ( is_a_theorem @ ( implies @ ( or @ SV21 @ ( or @ SV46 @ SV63 ) ) @ ( or @ SV46 @ ( or @ SV21 @ SV63 ) ) ) )
= $true )
| ( r4 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(537,plain,
! [SV64: $i,SV50: $i,SV25: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV25 @ SV50 ) @ ( implies @ ( not @ ( and @ SV50 @ SV64 ) ) @ ( not @ ( and @ SV64 @ SV25 ) ) ) ) )
= $true )
| ( kn3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(538,plain,
( ( sK57_REN = $false )
| ( ( ~ ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(539,plain,
! [SV56: $i,SV32: $i] :
( ( ( ~ ( is_a_theorem @ SV32 )
| ~ ( is_a_theorem @ ( implies @ SV32 @ SV56 ) ) )
= $true )
| ( ( is_a_theorem @ SV56 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(540,plain,
( ( sK54_REN = $false )
| ( ( ~ ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(541,plain,
! [SV58: $i,SV35: $i] :
( ( ( ~ ( is_a_theorem @ ( equiv @ SV35 @ SV58 ) ) )
= $true )
| ( ( SV35 = SV58 )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(542,plain,
! [SV65: $i,SV59: $i,SV36: $i] :
( ( ( is_a_theorem @ ( implies @ ( implies @ SV36 @ SV59 ) @ ( implies @ ( implies @ SV59 @ SV65 ) @ ( implies @ SV36 @ SV65 ) ) ) )
= $true )
| ( implies_3 = $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(543,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
| ~ ~ ( is_a_theorem @ sK56_SY99 ) )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(544,plain,
! [SV56: $i,SV32: $i] :
( ( ( ~ ( is_a_theorem @ SV32 ) )
= $true )
| ( ( ~ ( is_a_theorem @ ( implies @ SV32 @ SV56 ) ) )
= $true )
| ( ( is_a_theorem @ SV56 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(545,plain,
( ( ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
| ~ ( ( sK52_X != sK53_SY98 ) ) )
= $false )
| ( sK54_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(546,plain,
! [SV58: $i,SV35: $i] :
( ( ( is_a_theorem @ ( equiv @ SV35 @ SV58 ) )
= $false )
| ( ( SV35 = SV58 )
= $true )
| ( substitution_of_equivalents = $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(547,plain,
( ( ( ~ ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) ) )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(548,plain,
( ( ( ~ ~ ( is_a_theorem @ sK56_SY99 ) )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[543]) ).
thf(549,plain,
! [SV56: $i,SV32: $i] :
( ( ( is_a_theorem @ SV32 )
= $false )
| ( ( ~ ( is_a_theorem @ ( implies @ SV32 @ SV56 ) ) )
= $true )
| ( ( is_a_theorem @ SV56 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(550,plain,
( ( ( ~ ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) ) )
= $false )
| ( sK54_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(551,plain,
( ( ( ~ ( ( sK52_X != sK53_SY98 ) ) )
= $false )
| ( sK54_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[545]) ).
thf(552,plain,
( ( ( ~ ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) ) )
= $true )
| ( sK57_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[547]) ).
thf(553,plain,
( ( ( ~ ( is_a_theorem @ sK56_SY99 ) )
= $true )
| ( sK57_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[548]) ).
thf(554,plain,
! [SV56: $i,SV32: $i] :
( ( ( is_a_theorem @ ( implies @ SV32 @ SV56 ) )
= $false )
| ( ( is_a_theorem @ SV32 )
= $false )
| ( ( is_a_theorem @ SV56 )
= $true )
| ( modus_ponens = $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(555,plain,
( ( ( is_a_theorem @ ( equiv @ sK52_X @ sK53_SY98 ) )
= $true )
| ( sK54_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[550]) ).
thf(556,plain,
( ( ( ( sK52_X != sK53_SY98 ) )
= $true )
| ( sK54_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[551]) ).
thf(557,plain,
( ( ( ~ ( is_a_theorem @ sK55_X )
| ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(558,plain,
( ( ( is_a_theorem @ sK56_SY99 )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(559,plain,
( ( ( sK52_X = sK53_SY98 )
= $false )
| ( sK54_REN = $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(560,plain,
( ( ( ~ ( is_a_theorem @ sK55_X ) )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(561,plain,
( ( ( ~ ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) ) )
= $false )
| ( sK57_REN = $false ) ),
inference(extcnf_or_neg,[status(thm)],[557]) ).
thf(562,plain,
( ( ( is_a_theorem @ sK55_X )
= $true )
| ( sK57_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[560]) ).
thf(563,plain,
( ( ( is_a_theorem @ ( implies @ sK55_X @ sK56_SY99 ) )
= $true )
| ( sK57_REN = $false ) ),
inference(extcnf_not_neg,[status(thm)],[561]) ).
thf(564,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[171,563,562,559,558,555,554,546,542,537,536,535,534,533,529,528,525,524,523,522,521,520,518,517,516,514,513,511,508,507,506,500,493,482,474,469,467,462,460,458,456,454,452,450,448,446,444,442,440,438,436,434,432,430,428,426,424,422,369,368,367,366,365,224,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172]) ).
thf(565,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[564]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : LCL452+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n027.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jul 4 23:52:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.36
% 0.12/0.36 No.of.Axioms: 52
% 0.12/0.36
% 0.12/0.36 Length.of.Defs: 0
% 0.12/0.36
% 0.12/0.36 Contains.Choice.Funs: false
% 0.12/0.36 .
% 0.12/0.37 (rf:0,axioms:52,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:54,loop_count:0,foatp_calls:0,translation:fof_full)............................
% 0.19/0.57
% 0.19/0.57 ********************************
% 0.19/0.57 * All subproblems solved! *
% 0.19/0.57 ********************************
% 0.19/0.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:52,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:564,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.46/0.64
% 0.46/0.64 %**** Beginning of derivation protocol ****
% 0.46/0.64 % SZS output start CNFRefutation
% See solution above
% 0.46/0.65
% 0.46/0.65 %**** End of derivation protocol ****
% 0.46/0.65 %**** no. of clauses in derivation: 565 ****
% 0.46/0.65 %**** clause counter: 564 ****
% 0.46/0.65
% 0.46/0.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:52,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:564,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------