TSTP Solution File: KRS149+1 by Leo-III---1.7.10
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS149+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 : 300s
% DateTime : Tue May 7 07:52:00 EDT 2024
% Result : Theorem 6.43s 2.57s
% Output : Refutation 6.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 242
% Syntax : Number of formulae : 370 ( 25 unt; 116 typ; 0 def)
% Number of atoms : 1047 ( 0 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 2276 ( 265 ~; 0 |; 458 &;1218 @)
% ( 109 <=>; 226 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 117 ( 116 usr; 2 con; 0-2 aty)
% Number of variables : 394 ( 0 ^ 232 !; 162 ?; 394 :)
% Comments :
%------------------------------------------------------------------------------
thf(cowlThing_type,type,
cowlThing: $i > $o ).
thf(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(xsd_string_type,type,
xsd_string: $i > $o ).
thf(xsd_integer_type,type,
xsd_integer: $i > $o ).
thf(cC216_type,type,
cC216: $i > $o ).
thf(iV3102_type,type,
iV3102: $i ).
thf(cC46_type,type,
cC46: $i > $o ).
thf(cC30_type,type,
cC30: $i > $o ).
thf(cC44_type,type,
cC44: $i > $o ).
thf(cC28_type,type,
cC28: $i > $o ).
thf(cC64_type,type,
cC64: $i > $o ).
thf(cC14_type,type,
cC14: $i > $o ).
thf(cC134_type,type,
cC134: $i > $o ).
thf(cC132_type,type,
cC132: $i > $o ).
thf(cC108_type,type,
cC108: $i > $o ).
thf(cC204_type,type,
cC204: $i > $o ).
thf(cC178_type,type,
cC178: $i > $o ).
thf(cC202_type,type,
cC202: $i > $o ).
thf(cC206_type,type,
cC206: $i > $o ).
thf(cC170_type,type,
cC170: $i > $o ).
thf(cC96_type,type,
cC96: $i > $o ).
thf(cC84_type,type,
cC84: $i > $o ).
thf(cC94_type,type,
cC94: $i > $o ).
thf(cC190_type,type,
cC190: $i > $o ).
thf(cC200_type,type,
cC200: $i > $o ).
thf(cC210_type,type,
cC210: $i > $o ).
thf(cC208_type,type,
cC208: $i > $o ).
thf(cC168_type,type,
cC168: $i > $o ).
thf(cC166_type,type,
cC166: $i > $o ).
thf(cC142_type,type,
cC142: $i > $o ).
thf(cC130_type,type,
cC130: $i > $o ).
thf(cC120_type,type,
cC120: $i > $o ).
thf(cC154_type,type,
cC154: $i > $o ).
thf(cC164_type,type,
cC164: $i > $o ).
thf(cC80_type,type,
cC80: $i > $o ).
thf(cC16_type,type,
cC16: $i > $o ).
thf(cC78_type,type,
cC78: $i > $o ).
thf(cC58_type,type,
cC58: $i > $o ).
thf(rR1_type,type,
rR1: $i > $i > $o ).
thf(cC56_type,type,
cC56: $i > $o ).
thf(cC8_type,type,
cC8: $i > $o ).
thf(cC6_type,type,
cC6: $i > $o ).
thf(cC82_type,type,
cC82: $i > $o ).
thf(cC74_type,type,
cC74: $i > $o ).
thf(cC138_type,type,
cC138: $i > $o ).
thf(cC136_type,type,
cC136: $i > $o ).
thf(cC66_type,type,
cC66: $i > $o ).
thf(cC38_type,type,
cC38: $i > $o ).
thf(cC36_type,type,
cC36: $i > $o ).
thf(cC112_type,type,
cC112: $i > $o ).
thf(cC110_type,type,
cC110: $i > $o ).
thf(cC150_type,type,
cC150: $i > $o ).
thf(cC148_type,type,
cC148: $i > $o ).
thf(cC162_type,type,
cC162: $i > $o ).
thf(cC2_type,type,
cC2: $i > $o ).
thf(cC4_type,type,
cC4: $i > $o ).
thf(cC104_type,type,
cC104: $i > $o ).
thf(cC102_type,type,
cC102: $i > $o ).
thf(cC184_type,type,
cC184: $i > $o ).
thf(cC182_type,type,
cC182: $i > $o ).
thf(cC106_type,type,
cC106: $i > $o ).
thf(cC68_type,type,
cC68: $i > $o ).
thf(cC76_type,type,
cC76: $i > $o ).
thf(cC156_type,type,
cC156: $i > $o ).
thf(cC32_type,type,
cC32: $i > $o ).
thf(cC34_type,type,
cC34: $i > $o ).
thf(cC198_type,type,
cC198: $i > $o ).
thf(cC196_type,type,
cC196: $i > $o ).
thf(cC18_type,type,
cC18: $i > $o ).
thf(cC146_type,type,
cC146: $i > $o ).
thf(cC144_type,type,
cC144: $i > $o ).
thf(cC118_type,type,
cC118: $i > $o ).
thf(cC50_type,type,
cC50: $i > $o ).
thf(cC90_type,type,
cC90: $i > $o ).
thf(cC88_type,type,
cC88: $i > $o ).
thf(cC214_type,type,
cC214: $i > $o ).
thf(cC100_type,type,
cC100: $i > $o ).
thf(cC212_type,type,
cC212: $i > $o ).
thf(cC24_type,type,
cC24: $i > $o ).
thf(cC22_type,type,
cC22: $i > $o ).
thf(cC180_type,type,
cC180: $i > $o ).
thf(cC140_type,type,
cC140: $i > $o ).
thf(cC86_type,type,
cC86: $i > $o ).
thf(cC72_type,type,
cC72: $i > $o ).
thf(cC70_type,type,
cC70: $i > $o ).
thf(cC160_type,type,
cC160: $i > $o ).
thf(cC158_type,type,
cC158: $i > $o ).
thf(cC54_type,type,
cC54: $i > $o ).
thf(cC194_type,type,
cC194: $i > $o ).
thf(cC152_type,type,
cC152: $i > $o ).
thf(cC126_type,type,
cC126: $i > $o ).
thf(cC124_type,type,
cC124: $i > $o ).
thf(cC92_type,type,
cC92: $i > $o ).
thf(cC26_type,type,
cC26: $i > $o ).
thf(cC12_type,type,
cC12: $i > $o ).
thf(cC10_type,type,
cC10: $i > $o ).
thf(cC20_type,type,
cC20: $i > $o ).
thf(cC98_type,type,
cC98: $i > $o ).
thf(cC52_type,type,
cC52: $i > $o ).
thf(cC116_type,type,
cC116: $i > $o ).
thf(cC114_type,type,
cC114: $i > $o ).
thf(cC122_type,type,
cC122: $i > $o ).
thf(cC60_type,type,
cC60: $i > $o ).
thf(cC48_type,type,
cC48: $i > $o ).
thf(cC188_type,type,
cC188: $i > $o ).
thf(cC186_type,type,
cC186: $i > $o ).
thf(cC62_type,type,
cC62: $i > $o ).
thf(cC172_type,type,
cC172: $i > $o ).
thf(cC192_type,type,
cC192: $i > $o ).
thf(cC42_type,type,
cC42: $i > $o ).
thf(cC40_type,type,
cC40: $i > $o ).
thf(cC176_type,type,
cC176: $i > $o ).
thf(cC174_type,type,
cC174: $i > $o ).
thf(cC128_type,type,
cC128: $i > $o ).
thf(cTEST_type,type,
cTEST: $i > $o ).
thf(cTOP_type,type,
cTOP: $i > $o ).
thf(117,axiom,
! [A: $i] :
( ( cC28 @ A )
<=> ( ~ ( cC26 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_69) ).
thf(779,plain,
! [A: $i] :
( ( ( cC28 @ A )
=> ( ~ ( cC26 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC26 @ A )
& ~ ( cC16 @ A ) )
=> ( cC28 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(30,axiom,
! [A: $i] :
( ( cC36 @ A )
<=> ( ( cC32 @ A )
& ( cC34 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_72) ).
thf(296,plain,
! [A: $i] :
( ( ( cC36 @ A )
=> ( ( cC32 @ A )
& ( cC34 @ A ) ) )
& ( ( ( cC32 @ A )
& ( cC34 @ A ) )
=> ( cC36 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(106,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC60 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_110) ).
thf(739,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC60 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(127,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC98 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_117) ).
thf(809,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC98 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(111,axiom,
~ ( cC62 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_119) ).
thf(760,plain,
~ ( cC62 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(67,axiom,
! [A: $i] :
( ( cC188 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC186 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(518,plain,
! [A: $i] :
( ( ( cC188 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC186 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC186 @ B ) )
=> ( cC188 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(9,axiom,
! [A: $i] :
( ( cC168 @ A )
<=> ( ~ ( cC166 @ A )
& ~ ( cC142 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(170,plain,
! [A: $i] :
( ( ( cC168 @ A )
=> ( ~ ( cC166 @ A )
& ~ ( cC142 @ A ) ) )
& ( ( ~ ( cC166 @ A )
& ~ ( cC142 @ A ) )
=> ( cC168 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(112,axiom,
~ ( cC100 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_124) ).
thf(762,plain,
~ ( cC100 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(32,axiom,
! [A: $i] :
( ( cC18 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(308,plain,
! [A: $i] :
( ( ( cC18 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC18 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(107,axiom,
! [A: $i] :
( ( cC30 @ A )
<=> ( ( cC14 @ A )
& ( cC28 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_70) ).
thf(741,plain,
! [A: $i] :
( ( ( cC30 @ A )
=> ( ( cC14 @ A )
& ( cC28 @ A ) ) )
& ( ( ( cC14 @ A )
& ( cC28 @ A ) )
=> ( cC30 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(54,axiom,
! [A: $i] :
( ( cC110 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(440,plain,
! [A: $i] :
( ( ( cC110 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC110 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(83,axiom,
! [A: $i] :
( ( cC10 @ A )
<=> ( ~ ( cC8 @ A )
& ~ ( cC2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(614,plain,
! [A: $i] :
( ( ( cC10 @ A )
=> ( ~ ( cC8 @ A )
& ~ ( cC2 @ A ) ) )
& ( ( ~ ( cC8 @ A )
& ~ ( cC2 @ A ) )
=> ( cC10 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(64,axiom,
! [A: $i] :
( ( cC136 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(500,plain,
! [A: $i] :
( ( ( cC136 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC136 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(97,axiom,
! [A: $i] :
( ( cC92 @ A )
<=> ( ~ ( cC90 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_103) ).
thf(698,plain,
! [A: $i] :
( ( ( cC92 @ A )
=> ( ~ ( cC90 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC90 @ A )
& ~ ( cC16 @ A ) )
=> ( cC92 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(108,axiom,
~ ( cC42 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_114) ).
thf(747,plain,
~ ( cC42 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(48,axiom,
! [A: $i] :
( ( cC102 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(404,plain,
! [A: $i] :
( ( ( cC102 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC102 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(34,axiom,
! [A: $i] :
( ( cC120 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC118 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(320,plain,
! [A: $i] :
( ( ( cC120 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC118 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC118 @ B ) )
=> ( cC120 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(118,axiom,
~ ( cC16 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_121) ).
thf(785,plain,
~ ( cC16 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(38,axiom,
! [A: $i] :
( ( cC214 @ A )
<=> ( ( cC100 @ A )
& ~ ( cC212 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(344,plain,
! [A: $i] :
( ( ( cC214 @ A )
=> ( ( cC100 @ A )
& ~ ( cC212 @ A ) ) )
& ( ( ( cC100 @ A )
& ~ ( cC212 @ A ) )
=> ( cC214 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(71,axiom,
! [A: $i] :
( ( cC200 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC198 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(542,plain,
! [A: $i] :
( ( ( cC200 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC198 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC198 @ B ) )
=> ( cC200 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(87,axiom,
! [A: $i] :
( ( cC76 @ A )
<=> ( ( cC74 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_94) ).
thf(638,plain,
! [A: $i] :
( ( ( cC76 @ A )
=> ( ( cC74 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC74 @ A )
& ( cC16 @ A ) )
=> ( cC76 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(50,axiom,
! [A: $i] :
( ( cC152 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC150 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(416,plain,
! [A: $i] :
( ( ( cC152 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC150 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC150 @ B ) )
=> ( cC152 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(6,axiom,
! [A: $i] :
( ( cC96 @ A )
<=> ( ( cC84 @ A )
& ~ ( cC94 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_105) ).
thf(152,plain,
! [A: $i] :
( ( ( cC96 @ A )
=> ( ( cC84 @ A )
& ~ ( cC94 @ A ) ) )
& ( ( ( cC84 @ A )
& ~ ( cC94 @ A ) )
=> ( cC96 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(28,axiom,
! [A: $i] :
( ( cC78 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC76 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_95) ).
thf(284,plain,
! [A: $i] :
( ( ( cC78 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC76 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC76 @ B ) )
=> ( cC78 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(114,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC24 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_113) ).
thf(770,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC24 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(8,axiom,
! [A: $i] :
( ( cC210 @ A )
<=> ( ~ ( cC208 @ A )
& ~ ( cC134 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(164,plain,
! [A: $i] :
( ( ( cC210 @ A )
=> ( ~ ( cC208 @ A )
& ~ ( cC134 @ A ) ) )
& ( ( ~ ( cC208 @ A )
& ~ ( cC134 @ A ) )
=> ( cC210 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(120,axiom,
~ ( cC12 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_115) ).
thf(789,plain,
~ ( cC12 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(81,axiom,
! [A: $i] :
( ( cC178 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC176 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(602,plain,
! [A: $i] :
( ( ( cC178 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC176 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC176 @ A ) )
=> ( cC178 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(96,axiom,
! [A: $i] :
( ( cC40 @ A )
<=> ( ~ ( cC38 @ A )
& ~ ( cC32 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_75) ).
thf(692,plain,
! [A: $i] :
( ( ( cC40 @ A )
=> ( ~ ( cC38 @ A )
& ~ ( cC32 @ A ) ) )
& ( ( ~ ( cC38 @ A )
& ~ ( cC32 @ A ) )
=> ( cC40 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(52,axiom,
! [A: $i] :
( ( cC84 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC82 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_99) ).
thf(428,plain,
! [A: $i] :
( ( ( cC84 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC82 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC82 @ B ) )
=> ( cC84 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(15,axiom,
! [A: $i] :
( ( cC82 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC80 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_98) ).
thf(206,plain,
! [A: $i] :
( ( ( cC82 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC80 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC80 @ B ) )
=> ( cC82 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(56,axiom,
! [A: $i] :
( ( cC148 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC146 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(452,plain,
! [A: $i] :
( ( ( cC148 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC146 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC146 @ B ) )
=> ( cC148 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(22,axiom,
! [A: $i] :
( ( cC164 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC162 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(248,plain,
! [A: $i] :
( ( ( cC164 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC162 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC162 @ B ) )
=> ( cC164 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(44,axiom,
! [A: $i] :
( ( cC88 @ A )
<=> ( ( cC86 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_101) ).
thf(380,plain,
! [A: $i] :
( ( ( cC88 @ A )
=> ( ( cC86 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC86 @ A )
& ( cC16 @ A ) )
=> ( cC88 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(66,axiom,
! [A: $i] :
( ( cC154 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC152 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(512,plain,
! [A: $i] :
( ( ( cC154 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC152 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC152 @ B ) )
=> ( cC154 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(116,axiom,
cowlThing @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_109) ).
thf(778,plain,
cowlThing @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(31,axiom,
! [A: $i] :
( ( cC198 @ A )
<=> ( ~ ( cC196 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(302,plain,
! [A: $i] :
( ( ( cC198 @ A )
=> ( ~ ( cC196 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC196 @ A )
& ~ ( cC16 @ A ) )
=> ( cC198 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [A: $i] :
( ( cC104 @ A )
<=> ( ( cC102 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(260,plain,
! [A: $i] :
( ( ( cC104 @ A )
=> ( ( cC102 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC102 @ A )
& ( cC16 @ A ) )
=> ( cC104 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(46,axiom,
! [A: $i] :
( ( cC160 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC158 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(392,plain,
! [A: $i] :
( ( ( cC160 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC158 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC158 @ B ) )
=> ( cC160 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(103,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC40 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_120) ).
thf(729,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC40 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(75,axiom,
! [A: $i] :
( ( cC186 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC184 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(566,plain,
! [A: $i] :
( ( ( cC186 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC184 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC184 @ A ) )
=> ( cC186 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(99,axiom,
! [A: $i] :
( ( cC158 @ A )
<=> ( ( cC156 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(710,plain,
! [A: $i] :
( ( ( cC158 @ A )
=> ( ( cC156 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC156 @ A )
& ( cC16 @ A ) )
=> ( cC158 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(18,axiom,
! [A: $i] :
( ( cC66 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_89) ).
thf(224,plain,
! [A: $i] :
( ( ( cC66 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC66 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(77,axiom,
! [A: $i] :
( ( cC176 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC174 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(578,plain,
! [A: $i] :
( ( ( cC176 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC174 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC174 @ B ) )
=> ( cC176 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(89,axiom,
! [A: $i] :
( ( cC144 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(650,plain,
! [A: $i] :
( ( ( cC144 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC144 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(12,axiom,
! [A: $i] :
( ( cC80 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC78 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_97) ).
thf(188,plain,
! [A: $i] :
( ( ( cC80 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC78 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC78 @ A ) )
=> ( cC80 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(40,axiom,
! [A: $i] :
( ( cC180 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(356,plain,
! [A: $i] :
( ( ( cC180 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC180 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(62,axiom,
! [A: $i] :
( ( cC98 @ A )
<=> ( ~ ( cC72 @ A )
& ~ ( cC96 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_106) ).
thf(488,plain,
! [A: $i] :
( ( ( cC98 @ A )
=> ( ~ ( cC72 @ A )
& ~ ( cC96 @ A ) ) )
& ( ( ~ ( cC72 @ A )
& ~ ( cC96 @ A ) )
=> ( cC98 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(73,axiom,
! [A: $i] :
( ( cC192 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(554,plain,
! [A: $i] :
( ( ( cC192 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC192 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(79,axiom,
! [A: $i] :
( ( cC182 @ A )
<=> ( ( cC16 @ A )
& ( cC180 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(590,plain,
! [A: $i] :
( ( ( cC182 @ A )
=> ( ( cC16 @ A )
& ( cC180 @ A ) ) )
& ( ( ( cC16 @ A )
& ( cC180 @ A ) )
=> ( cC182 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(16,axiom,
! [A: $i] :
( ( cC74 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_93) ).
thf(212,plain,
! [A: $i] :
( ( ( cC74 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC74 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(95,axiom,
! [A: $i] :
( ( cC20 @ A )
<=> ( ( cC18 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(686,plain,
! [A: $i] :
( ( ( cC20 @ A )
=> ( ( cC18 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC18 @ A )
& ( cC16 @ A ) )
=> ( cC20 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(60,axiom,
! [A: $i] :
( ( cC52 @ A )
<=> ( ( cC50 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_81) ).
thf(476,plain,
! [A: $i] :
( ( ( cC52 @ A )
=> ( ( cC50 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC50 @ A )
& ( cC16 @ A ) )
=> ( cC52 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(3,axiom,
! [A: $i] :
( ( cC134 @ A )
<=> ( ~ ( cC132 @ A )
& ~ ( cC108 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(134,plain,
! [A: $i] :
( ( ( cC134 @ A )
=> ( ~ ( cC132 @ A )
& ~ ( cC108 @ A ) ) )
& ( ( ~ ( cC132 @ A )
& ~ ( cC108 @ A ) )
=> ( cC134 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ( cC216 @ iV3102 )
& ( cC46 @ iV3102 )
& ( cC30 @ iV3102 )
& ( cC44 @ iV3102 )
& ( cC28 @ iV3102 )
& ( cC64 @ iV3102 )
& ( cC14 @ iV3102 )
& ( cowlThing @ iV3102 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ( cC216 @ iV3102 )
& ( cC46 @ iV3102 )
& ( cC30 @ iV3102 )
& ( cC44 @ iV3102 )
& ( cC28 @ iV3102 )
& ( cC64 @ iV3102 )
& ( cC14 @ iV3102 )
& ( cowlThing @ iV3102 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) )
& ( cC216 @ iV3102 )
& ( cC46 @ iV3102 )
& ( cC30 @ iV3102 )
& ( cC44 @ iV3102 )
& ( cC28 @ iV3102 )
& ( cC64 @ iV3102 )
& ( cC14 @ iV3102 )
& ( cowlThing @ iV3102 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(122,axiom,
~ ( cC2 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_122) ).
thf(792,plain,
~ ( cC2 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(25,axiom,
! [A: $i] :
( ( cC184 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC182 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(266,plain,
! [A: $i] :
( ( ( cC184 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC182 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC182 @ B ) )
=> ( cC184 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(47,axiom,
! [A: $i] :
( ( cC56 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC54 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).
thf(398,plain,
! [A: $i] :
( ( ( cC56 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC54 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC54 @ A ) )
=> ( cC56 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(93,axiom,
! [A: $i] :
( ( cC114 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC112 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(674,plain,
! [A: $i] :
( ( ( cC114 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC112 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC112 @ B ) )
=> ( cC114 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(69,axiom,
! [A: $i] :
( ( cC124 @ A )
<=> ( ( cC122 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(530,plain,
! [A: $i] :
( ( ( cC124 @ A )
=> ( ( cC122 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC122 @ A )
& ( cC16 @ A ) )
=> ( cC124 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(123,axiom,
~ ( cC32 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_123) ).
thf(794,plain,
~ ( cC32 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(91,axiom,
! [A: $i] :
( ( cC162 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC160 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(662,plain,
! [A: $i] :
( ( ( cC162 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC160 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC160 @ A ) )
=> ( cC162 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(78,axiom,
! [A: $i] :
( ( cC48 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_79) ).
thf(584,plain,
! [A: $i] :
( ( ( cC48 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC48 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(10,axiom,
! [A: $i] :
( ( cC132 @ A )
<=> ( ~ ( cC130 @ A )
& ( cC120 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(176,plain,
! [A: $i] :
( ( ( cC132 @ A )
=> ( ~ ( cC130 @ A )
& ( cC120 @ A ) ) )
& ( ( ~ ( cC130 @ A )
& ( cC120 @ A ) )
=> ( cC132 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(115,axiom,
! [A: $i] :
( ( cTEST @ A )
<=> ( ( cC216 @ A )
& ( cC46 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_107) ).
thf(772,plain,
! [A: $i] :
( ( ( cTEST @ A )
=> ( ( cC216 @ A )
& ( cC46 @ A ) ) )
& ( ( ( cC216 @ A )
& ( cC46 @ A ) )
=> ( cTEST @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(76,axiom,
! [A: $i] :
( ( cC42 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC40 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_76) ).
thf(572,plain,
! [A: $i] :
( ( ( cC42 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC40 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC40 @ B ) )
=> ( cC42 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(119,axiom,
~ ( cC26 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_116) ).
thf(787,plain,
~ ( cC26 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(20,axiom,
! [A: $i] :
( ( cC112 @ A )
<=> ( ( cC110 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(236,plain,
! [A: $i] :
( ( ( cC112 @ A )
=> ( ( cC110 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC110 @ A )
& ( cC16 @ A ) )
=> ( cC112 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(98,axiom,
! [A: $i] :
( ( cC70 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC68 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_91) ).
thf(704,plain,
! [A: $i] :
( ( ( cC70 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC68 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC68 @ B ) )
=> ( cC70 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(39,axiom,
! [A: $i] :
( ( cC24 @ A )
<=> ( ~ ( cC22 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).
thf(350,plain,
! [A: $i] :
( ( ( cC24 @ A )
=> ( ~ ( cC22 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC22 @ A )
& ~ ( cC16 @ A ) )
=> ( cC24 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(113,axiom,
! [A: $i] :
( ( cC64 @ A )
<=> ( ~ ( cC62 @ A )
& ( cTOP @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_88) ).
thf(764,plain,
! [A: $i] :
( ( ( cC64 @ A )
=> ( ~ ( cC62 @ A )
& ( cTOP @ A ) ) )
& ( ( ~ ( cC62 @ A )
& ( cTOP @ A ) )
=> ( cC64 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(19,axiom,
! [A: $i] :
( ( cC38 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC36 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_73) ).
thf(230,plain,
! [A: $i] :
( ( ( cC38 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC36 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC36 @ B ) )
=> ( cC38 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(41,axiom,
! [A: $i] :
( ( cC140 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC138 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(362,plain,
! [A: $i] :
( ( ( cC140 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC138 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC138 @ B ) )
=> ( cC140 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(105,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC10 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_111) ).
thf(737,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ~ ( cC10 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(53,axiom,
! [A: $i] :
( ( cC94 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC92 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_104) ).
thf(434,plain,
! [A: $i] :
( ( ( cC94 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC92 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC92 @ B ) )
=> ( cC94 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(63,axiom,
! [A: $i] :
( ( cC122 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(494,plain,
! [A: $i] :
( ( ( cC122 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC122 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,axiom,
! [A: $i] :
( ( cC204 @ A )
<=> ( ~ ( cC178 @ A )
& ~ ( cC202 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(140,plain,
! [A: $i] :
( ( ( cC204 @ A )
=> ( ~ ( cC178 @ A )
& ~ ( cC202 @ A ) ) )
& ( ( ~ ( cC178 @ A )
& ~ ( cC202 @ A ) )
=> ( cC204 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(85,axiom,
! [A: $i] :
( ( cC34 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC32 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_71) ).
thf(626,plain,
! [A: $i] :
( ( ( cC34 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC32 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC32 @ B ) )
=> ( cC34 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(92,axiom,
! [A: $i] :
( ( cC190 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC188 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(668,plain,
! [A: $i] :
( ( ( cC190 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC188 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC188 @ B ) )
=> ( cC190 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(27,axiom,
! [A: $i] :
( ( cC68 @ A )
<=> ( ( cC66 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_90) ).
thf(278,plain,
! [A: $i] :
( ( ( cC68 @ A )
=> ( ( cC66 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC66 @ A )
& ( cC16 @ A ) )
=> ( cC68 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(82,axiom,
! [A: $i] :
( ( cC212 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC210 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(608,plain,
! [A: $i] :
( ( ( cC212 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC210 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC210 @ B ) )
=> ( cC212 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(101,axiom,
! [A: $i] :
( ( cC14 @ A )
<=> ( ~ ( cC12 @ A )
& ~ ( cC2 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(722,plain,
! [A: $i] :
( ( ( cC14 @ A )
=> ( ~ ( cC12 @ A )
& ~ ( cC2 @ A ) ) )
& ( ( ~ ( cC12 @ A )
& ~ ( cC2 @ A ) )
=> ( cC14 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(94,axiom,
! [A: $i] :
( ( cC128 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC126 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(680,plain,
! [A: $i] :
( ( ( cC128 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC126 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC126 @ A ) )
=> ( cC128 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(72,axiom,
! [A: $i] :
( ( cC118 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC116 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(548,plain,
! [A: $i] :
( ( ( cC118 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC116 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC116 @ B ) )
=> ( cC118 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(43,axiom,
! [A: $i] :
( ( cC170 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC168 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(374,plain,
! [A: $i] :
( ( ( cC170 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC168 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC168 @ B ) )
=> ( cC170 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(109,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(749,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(110,axiom,
! [A: $i] :
( ( cC216 @ A )
<=> ( ~ ( cC214 @ A )
& ( cC64 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(754,plain,
! [A: $i] :
( ( ( cC216 @ A )
=> ( ~ ( cC214 @ A )
& ( cC64 @ A ) ) )
& ( ( ~ ( cC214 @ A )
& ( cC64 @ A ) )
=> ( cC216 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(57,axiom,
! [A: $i] :
( ( cC12 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC10 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(458,plain,
! [A: $i] :
( ( ( cC12 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC10 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC10 @ B ) )
=> ( cC12 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [A: $i] :
( ( cC58 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC56 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_84) ).
thf(194,plain,
! [A: $i] :
( ( ( cC58 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC56 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC56 @ B ) )
=> ( cC58 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
! [A: $i] :
( ( cC106 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC104 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(338,plain,
! [A: $i] :
( ( ( cC106 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC104 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC104 @ B ) )
=> ( cC106 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(59,axiom,
! [A: $i] :
( ( cC100 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC98 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(470,plain,
! [A: $i] :
( ( ( cC100 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC98 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC98 @ B ) )
=> ( cC100 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(121,axiom,
cTOP @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_112) ).
thf(791,plain,
cTOP @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(11,axiom,
! [A: $i] :
( ( cC166 @ A )
<=> ( ( cC154 @ A )
& ~ ( cC164 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(182,plain,
! [A: $i] :
( ( ( cC166 @ A )
=> ( ( cC154 @ A )
& ~ ( cC164 @ A ) ) )
& ( ( ( cC154 @ A )
& ~ ( cC164 @ A ) )
=> ( cC166 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(90,axiom,
! [A: $i] :
( ( cC54 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC52 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_82) ).
thf(656,plain,
! [A: $i] :
( ( ( cC54 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC52 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC52 @ B ) )
=> ( cC54 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(45,axiom,
! [A: $i] :
( ( cC72 @ A )
<=> ( ~ ( cC70 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_92) ).
thf(386,plain,
! [A: $i] :
( ( ( cC72 @ A )
=> ( ~ ( cC70 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC70 @ A )
& ~ ( cC16 @ A ) )
=> ( cC72 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(33,axiom,
! [A: $i] :
( ( cC146 @ A )
<=> ( ( cC144 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(314,plain,
! [A: $i] :
( ( ( cC146 @ A )
=> ( ( cC144 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC144 @ A )
& ( cC16 @ A ) )
=> ( cC146 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
! [A: $i] :
( ( cC26 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC24 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_68) ).
thf(446,plain,
! [A: $i] :
( ( ( cC26 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC24 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC24 @ B ) )
=> ( cC26 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(61,axiom,
! [A: $i] :
( ( cC116 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC114 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(482,plain,
! [A: $i] :
( ( ( cC116 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC114 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC114 @ A ) )
=> ( cC116 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(68,axiom,
! [A: $i] :
( ( cC62 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC60 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_87) ).
thf(524,plain,
! [A: $i] :
( ( ( cC62 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC60 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC60 @ B ) )
=> ( cC62 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(17,axiom,
! [A: $i] :
( ( cC138 @ A )
<=> ( ( cC136 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(218,plain,
! [A: $i] :
( ( ( cC138 @ A )
=> ( ( cC136 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC136 @ A )
& ( cC16 @ A ) )
=> ( cC138 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(42,axiom,
! [A: $i] :
( ( cC86 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_100) ).
thf(368,plain,
! [A: $i] :
( ( ( cC86 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC86 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(7,axiom,
! [A: $i] :
( ( cC202 @ A )
<=> ( ( cC190 @ A )
& ~ ( cC200 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(158,plain,
! [A: $i] :
( ( ( cC202 @ A )
=> ( ( cC190 @ A )
& ~ ( cC200 @ A ) ) )
& ( ( ( cC190 @ A )
& ~ ( cC200 @ A ) )
=> ( cC202 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
! [A: $i] :
( ( cC130 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC128 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(632,plain,
! [A: $i] :
( ( ( cC130 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC128 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC128 @ B ) )
=> ( cC130 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(104,axiom,
! [A: $i] :
( ( cC44 @ A )
<=> ( ~ ( cC32 @ A )
& ~ ( cC42 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).
thf(731,plain,
! [A: $i] :
( ( ( cC44 @ A )
=> ( ~ ( cC32 @ A )
& ~ ( cC42 @ A ) ) )
& ( ( ~ ( cC32 @ A )
& ~ ( cC42 @ A ) )
=> ( cC44 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(29,axiom,
! [A: $i] :
( ( cC156 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(290,plain,
! [A: $i] :
( ( ( cC156 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC156 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(26,axiom,
! [A: $i] :
( ( cC108 @ A )
<=> ( ~ ( cC106 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(272,plain,
! [A: $i] :
( ( ( cC108 @ A )
=> ( ~ ( cC106 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC106 @ A )
& ~ ( cC16 @ A ) )
=> ( cC108 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(70,axiom,
! [A: $i] :
( ( cC172 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(536,plain,
! [A: $i] :
( ( ( cC172 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC172 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(100,axiom,
! [A: $i] :
( ( cC174 @ A )
<=> ( ( cC172 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(716,plain,
! [A: $i] :
( ( ( cC174 @ A )
=> ( ( cC172 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC172 @ A )
& ( cC16 @ A ) )
=> ( cC174 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(84,axiom,
! [A: $i] :
( ( cC4 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC2 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_74) ).
thf(620,plain,
! [A: $i] :
( ( ( cC4 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC2 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC2 @ B ) )
=> ( cC4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(49,axiom,
! [A: $i] :
( ( cC196 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC194 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(410,plain,
! [A: $i] :
( ( ( cC196 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC194 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC194 @ B ) )
=> ( cC196 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(5,axiom,
! [A: $i] :
( ( cC206 @ A )
<=> ( ( cC170 @ A )
& ( cC204 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(146,plain,
! [A: $i] :
( ( ( cC206 @ A )
=> ( ( cC170 @ A )
& ( cC204 @ A ) ) )
& ( ( ( cC170 @ A )
& ( cC204 @ A ) )
=> ( cC206 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(51,axiom,
! [A: $i] :
( ( cC126 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC124 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(422,plain,
! [A: $i] :
( ( ( cC126 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC124 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC124 @ B ) )
=> ( cC126 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(35,axiom,
! [A: $i] :
( ( cC50 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_80) ).
thf(326,plain,
! [A: $i] :
( ( ( cC50 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ~ ( cC16 @ B ) )
=> ( cC50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(21,axiom,
! [A: $i] :
( ( cC150 @ A )
<=> ( ~ ( cC16 @ A )
& ~ ( cC148 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(242,plain,
! [A: $i] :
( ( ( cC150 @ A )
=> ( ~ ( cC16 @ A )
& ~ ( cC148 @ A ) ) )
& ( ( ~ ( cC16 @ A )
& ~ ( cC148 @ A ) )
=> ( cC150 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(125,axiom,
~ ( cC214 @ iV3102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_118) ).
thf(801,plain,
~ ( cC214 @ iV3102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(65,axiom,
! [A: $i] :
( ( cC60 @ A )
<=> ( ( cC48 @ A )
& ~ ( cC58 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).
thf(506,plain,
! [A: $i] :
( ( ( cC60 @ A )
=> ( ( cC48 @ A )
& ~ ( cC58 @ A ) ) )
& ( ( ( cC48 @ A )
& ~ ( cC58 @ A ) )
=> ( cC60 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(124,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(796,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(102,axiom,
cTEST @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_108) ).
thf(728,plain,
cTEST @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(58,axiom,
! [A: $i] :
( ( cC22 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC20 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).
thf(464,plain,
! [A: $i] :
( ( ( cC22 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC20 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC20 @ B ) )
=> ( cC22 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(36,axiom,
! [A: $i] :
( ( cC90 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC88 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_102) ).
thf(332,plain,
! [A: $i] :
( ( ( cC90 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC88 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC88 @ B ) )
=> ( cC90 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(80,axiom,
! [A: $i] :
( ( cC142 @ A )
<=> ( ~ ( cC140 @ A )
& ~ ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(596,plain,
! [A: $i] :
( ( ( cC142 @ A )
=> ( ~ ( cC140 @ A )
& ~ ( cC16 @ A ) ) )
& ( ( ~ ( cC140 @ A )
& ~ ( cC16 @ A ) )
=> ( cC142 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(88,axiom,
! [A: $i] :
( ( cC208 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC206 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(644,plain,
! [A: $i] :
( ( ( cC208 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC206 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC206 @ B ) )
=> ( cC208 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(14,axiom,
! [A: $i] :
( ( cC8 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC6 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_96) ).
thf(200,plain,
! [A: $i] :
( ( ( cC8 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC6 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC6 @ B ) )
=> ( cC8 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [A: $i] :
( ( cC6 @ A )
<=> ( ( cC2 @ A )
& ( cC4 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).
thf(254,plain,
! [A: $i] :
( ( ( cC6 @ A )
=> ( ( cC2 @ A )
& ( cC4 @ A ) ) )
& ( ( ( cC2 @ A )
& ( cC4 @ A ) )
=> ( cC6 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(126,axiom,
! [A: $i] :
( ( cC46 @ A )
<=> ( ( cC30 @ A )
& ( cC44 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_78) ).
thf(803,plain,
! [A: $i] :
( ( ( cC46 @ A )
=> ( ( cC30 @ A )
& ( cC44 @ A ) ) )
& ( ( ( cC30 @ A )
& ( cC44 @ A ) )
=> ( cC46 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(74,axiom,
! [A: $i] :
( ( cC194 @ A )
<=> ( ( cC192 @ A )
& ( cC16 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).
thf(560,plain,
! [A: $i] :
( ( ( cC194 @ A )
=> ( ( cC192 @ A )
& ( cC16 @ A ) ) )
& ( ( ( cC192 @ A )
& ( cC16 @ A ) )
=> ( cC194 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(811,plain,
$false,
inference(e,[status(thm)],[779,296,739,809,760,518,170,762,308,741,440,614,500,698,747,404,320,785,344,542,638,416,152,284,770,164,789,602,692,428,206,452,248,380,512,778,302,260,392,729,566,710,224,578,650,188,356,488,554,590,212,686,476,134,128,792,266,398,674,530,794,662,584,176,772,572,787,236,704,350,764,230,362,737,434,494,140,626,668,278,608,722,680,548,374,749,754,458,194,338,470,791,182,656,386,314,446,482,524,218,368,158,632,731,290,272,536,716,620,410,146,422,326,242,801,506,796,728,464,332,596,644,200,254,803,560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS149+1 : TPTP v8.1.2. Released v3.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n003.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 6 15:17:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.00/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.41/1.04 % [INFO] Parsing done (176ms).
% 1.41/1.04 % [INFO] Running in sequential loop mode.
% 1.99/1.26 % [INFO] eprover registered as external prover.
% 1.99/1.26 % [INFO] cvc4 registered as external prover.
% 1.99/1.27 % [INFO] Scanning for conjecture ...
% 2.22/1.35 % [INFO] Found a conjecture and 125 axioms. Running axiom selection ...
% 2.37/1.42 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 2.80/1.51 % [INFO] Problem is first-order (TPTP FOF).
% 2.80/1.52 % [INFO] Type checking passed.
% 2.80/1.52 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.17/2.57 % External prover 'e' found a proof!
% 6.17/2.57 % [INFO] Killing All external provers ...
% 6.17/2.57 % Time passed: 2041ms (effective reasoning time: 1518ms)
% 6.17/2.57 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.43/2.57 % Axioms used in derivation (125): axiom_53, axiom_75, axiom_7, axiom_26, axiom_55, axiom_108, axiom_88, axiom_114, axiom_119, axiom_33, axiom_10, axiom_40, axiom_22, axiom_59, axiom_77, axiom_44, axiom_49, axiom_15, axiom_95, axiom_121, axiom_73, axiom_67, axiom_69, axiom_51, axiom_21, axiom_19, axiom_99, axiom_84, axiom_63, axiom_110, axiom_103, axiom_38, axiom_2, axiom_79, axiom_89, axiom_43, axiom_107, axiom_27, axiom_32, axiom_6, axiom_91, axiom_60, axiom_118, axiom_78, axiom_54, axiom_92, axiom_100, axiom_64, axiom_16, axiom_50, axiom_122, axiom_81, axiom_74, axiom_111, axiom_3, axiom_96, axiom_68, axiom_46, axiom_104, axiom_20, axiom_85, axiom_70, axiom_115, axiom_42, axiom_31, axiom_24, axiom_90, axiom_1, axiom_57, axiom_116, axiom_61, axiom_105, axiom_35, axiom_28, axiom_101, axiom_112, axiom_65, axiom_36, axiom_39, axiom_80, axiom_71, axiom_8, axiom_97, axiom_17, axiom_86, axiom_5, axiom_47, axiom_13, axiom_93, axiom_123, axiom_82, axiom_41, axiom_109, axiom_25, axiom_76, axiom_52, axiom_34, axiom_0, axiom_58, axiom_62, axiom_45, axiom_29, axiom_11, axiom_117, axiom_56, axiom_30, axiom_23, axiom_106, axiom_18, axiom_87, axiom_113, axiom_12, axiom_9, axiom_98, axiom_102, axiom_48, axiom_83, axiom_14, axiom_124, axiom_72, axiom_120, axiom_94, axiom_4, axiom_66, axiom_37
% 6.43/2.57 % No. of inferences in proof: 254
% 6.43/2.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2041 ms resp. 1518 ms w/o parsing
% 6.43/2.65 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.43/2.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------