%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS149+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:44:45 AM UTC 2026
% Result : Theorem 13.59s 5.42s
% Output : Refutation 14.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 126
% Syntax : Number of formulae : 254 ( 25 unt; 0 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 : 0 ( 0 >; 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_decl,type,
cowlThing: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(xsd_string_decl,type,
xsd_string: $i > $o ).
thf(xsd_integer_decl,type,
xsd_integer: $i > $o ).
thf(cC216_decl,type,
cC216: $i > $o ).
thf(iV3102_decl,type,
iV3102: $i ).
thf(cC46_decl,type,
cC46: $i > $o ).
thf(cC30_decl,type,
cC30: $i > $o ).
thf(cC44_decl,type,
cC44: $i > $o ).
thf(cC28_decl,type,
cC28: $i > $o ).
thf(cC64_decl,type,
cC64: $i > $o ).
thf(cC14_decl,type,
cC14: $i > $o ).
thf(cC134_decl,type,
cC134: $i > $o ).
thf(cC132_decl,type,
cC132: $i > $o ).
thf(cC108_decl,type,
cC108: $i > $o ).
thf(cC204_decl,type,
cC204: $i > $o ).
thf(cC178_decl,type,
cC178: $i > $o ).
thf(cC202_decl,type,
cC202: $i > $o ).
thf(cC206_decl,type,
cC206: $i > $o ).
thf(cC170_decl,type,
cC170: $i > $o ).
thf(cC96_decl,type,
cC96: $i > $o ).
thf(cC84_decl,type,
cC84: $i > $o ).
thf(cC94_decl,type,
cC94: $i > $o ).
thf(cC190_decl,type,
cC190: $i > $o ).
thf(cC200_decl,type,
cC200: $i > $o ).
thf(cC210_decl,type,
cC210: $i > $o ).
thf(cC208_decl,type,
cC208: $i > $o ).
thf(cC168_decl,type,
cC168: $i > $o ).
thf(cC166_decl,type,
cC166: $i > $o ).
thf(cC142_decl,type,
cC142: $i > $o ).
thf(cC130_decl,type,
cC130: $i > $o ).
thf(cC120_decl,type,
cC120: $i > $o ).
thf(cC154_decl,type,
cC154: $i > $o ).
thf(cC164_decl,type,
cC164: $i > $o ).
thf(cC80_decl,type,
cC80: $i > $o ).
thf(cC16_decl,type,
cC16: $i > $o ).
thf(cC78_decl,type,
cC78: $i > $o ).
thf(cC58_decl,type,
cC58: $i > $o ).
thf(rR1_decl,type,
rR1: $i > $i > $o ).
thf(cC56_decl,type,
cC56: $i > $o ).
thf(cC8_decl,type,
cC8: $i > $o ).
thf(cC6_decl,type,
cC6: $i > $o ).
thf(cC82_decl,type,
cC82: $i > $o ).
thf(cC74_decl,type,
cC74: $i > $o ).
thf(cC138_decl,type,
cC138: $i > $o ).
thf(cC136_decl,type,
cC136: $i > $o ).
thf(cC66_decl,type,
cC66: $i > $o ).
thf(cC38_decl,type,
cC38: $i > $o ).
thf(cC36_decl,type,
cC36: $i > $o ).
thf(cC112_decl,type,
cC112: $i > $o ).
thf(cC110_decl,type,
cC110: $i > $o ).
thf(cC150_decl,type,
cC150: $i > $o ).
thf(cC148_decl,type,
cC148: $i > $o ).
thf(cC162_decl,type,
cC162: $i > $o ).
thf(cC2_decl,type,
cC2: $i > $o ).
thf(cC4_decl,type,
cC4: $i > $o ).
thf(cC104_decl,type,
cC104: $i > $o ).
thf(cC102_decl,type,
cC102: $i > $o ).
thf(cC184_decl,type,
cC184: $i > $o ).
thf(cC182_decl,type,
cC182: $i > $o ).
thf(cC106_decl,type,
cC106: $i > $o ).
thf(cC68_decl,type,
cC68: $i > $o ).
thf(cC76_decl,type,
cC76: $i > $o ).
thf(cC156_decl,type,
cC156: $i > $o ).
thf(cC32_decl,type,
cC32: $i > $o ).
thf(cC34_decl,type,
cC34: $i > $o ).
thf(cC198_decl,type,
cC198: $i > $o ).
thf(cC196_decl,type,
cC196: $i > $o ).
thf(cC18_decl,type,
cC18: $i > $o ).
thf(cC146_decl,type,
cC146: $i > $o ).
thf(cC144_decl,type,
cC144: $i > $o ).
thf(cC118_decl,type,
cC118: $i > $o ).
thf(cC50_decl,type,
cC50: $i > $o ).
thf(cC90_decl,type,
cC90: $i > $o ).
thf(cC88_decl,type,
cC88: $i > $o ).
thf(cC214_decl,type,
cC214: $i > $o ).
thf(cC100_decl,type,
cC100: $i > $o ).
thf(cC212_decl,type,
cC212: $i > $o ).
thf(cC24_decl,type,
cC24: $i > $o ).
thf(cC22_decl,type,
cC22: $i > $o ).
thf(cC180_decl,type,
cC180: $i > $o ).
thf(cC140_decl,type,
cC140: $i > $o ).
thf(cC86_decl,type,
cC86: $i > $o ).
thf(cC72_decl,type,
cC72: $i > $o ).
thf(cC70_decl,type,
cC70: $i > $o ).
thf(cC160_decl,type,
cC160: $i > $o ).
thf(cC158_decl,type,
cC158: $i > $o ).
thf(cC54_decl,type,
cC54: $i > $o ).
thf(cC194_decl,type,
cC194: $i > $o ).
thf(cC152_decl,type,
cC152: $i > $o ).
thf(cC126_decl,type,
cC126: $i > $o ).
thf(cC124_decl,type,
cC124: $i > $o ).
thf(cC92_decl,type,
cC92: $i > $o ).
thf(cC26_decl,type,
cC26: $i > $o ).
thf(cC12_decl,type,
cC12: $i > $o ).
thf(cC10_decl,type,
cC10: $i > $o ).
thf(cC20_decl,type,
cC20: $i > $o ).
thf(cC98_decl,type,
cC98: $i > $o ).
thf(cC52_decl,type,
cC52: $i > $o ).
thf(cC116_decl,type,
cC116: $i > $o ).
thf(cC114_decl,type,
cC114: $i > $o ).
thf(cC122_decl,type,
cC122: $i > $o ).
thf(cC60_decl,type,
cC60: $i > $o ).
thf(cC48_decl,type,
cC48: $i > $o ).
thf(cC188_decl,type,
cC188: $i > $o ).
thf(cC186_decl,type,
cC186: $i > $o ).
thf(cC62_decl,type,
cC62: $i > $o ).
thf(cC172_decl,type,
cC172: $i > $o ).
thf(cC192_decl,type,
cC192: $i > $o ).
thf(cC42_decl,type,
cC42: $i > $o ).
thf(cC40_decl,type,
cC40: $i > $o ).
thf(cC176_decl,type,
cC176: $i > $o ).
thf(cC174_decl,type,
cC174: $i > $o ).
thf(cC128_decl,type,
cC128: $i > $o ).
thf(cTEST_decl,type,
cTEST: $i > $o ).
thf(cTOP_decl,type,
cTOP: $i > $o ).
thf(71,axiom,
! [A: $i] :
( ( A @ cC200 )
<=> ? [B: $i] :
( ( B @ cC198 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(611,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC198 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC200 ) )
& ( ( A @ cC200 )
=> ? [B: $i] :
( ( B @ cC198 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ( ~ ( A @ cC96 )
& ~ ( A @ cC72 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_106) ).
thf(548,plain,
! [A: $i] :
( ( ( ~ ( A @ cC96 )
& ~ ( A @ cC72 ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ( ~ ( A @ cC96 )
& ~ ( A @ cC72 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(118,axiom,
~ ( iV3102 @ cC16 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_121) ).
thf(892,plain,
~ ( iV3102 @ cC16 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(125,axiom,
~ ( iV3102 @ cC214 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_118) ).
thf(909,plain,
~ ( iV3102 @ cC214 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ cC122 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(555,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC122 ) )
& ( ( A @ cC122 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ cC120 )
<=> ? [B: $i] :
( ( B @ cC118 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(352,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC118 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC120 ) )
& ( ( A @ cC120 )
=> ? [B: $i] :
( ( B @ cC118 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(88,axiom,
! [A: $i] :
( ( A @ cC208 )
<=> ? [B: $i] :
( ( B @ cC206 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(730,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC206 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC208 ) )
& ( ( A @ cC208 )
=> ? [B: $i] :
( ( B @ cC206 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cC38 )
<=> ? [B: $i] :
( ( B @ cC36 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_73) ).
thf(247,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC36 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC38 ) )
& ( ( A @ cC38 )
=> ? [B: $i] :
( ( B @ cC36 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ cC124 )
<=> ( ( A @ cC16 )
& ( A @ cC122 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(597,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC122 ) )
=> ( A @ cC124 ) )
& ( ( A @ cC124 )
=> ( ( A @ cC16 )
& ( A @ cC122 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_100) ).
thf(408,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cC210 )
<=> ( ~ ( A @ cC134 )
& ~ ( A @ cC208 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(170,plain,
! [A: $i] :
( ( ( ~ ( A @ cC134 )
& ~ ( A @ cC208 ) )
=> ( A @ cC210 ) )
& ( ( A @ cC210 )
=> ( ~ ( A @ cC134 )
& ~ ( A @ cC208 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cC204 )
<=> ( ~ ( A @ cC202 )
& ~ ( A @ cC178 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(142,plain,
! [A: $i] :
( ( ( ~ ( A @ cC202 )
& ~ ( A @ cC178 ) )
=> ( A @ cC204 ) )
& ( ( A @ cC204 )
=> ( ~ ( A @ cC202 )
& ~ ( A @ cC178 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ cC174 )
<=> ( ( A @ cC16 )
& ( A @ cC172 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(814,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC172 ) )
=> ( A @ cC174 ) )
& ( ( A @ cC174 )
=> ( ( A @ cC16 )
& ( A @ cC172 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC40 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_120) ).
thf(829,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC40 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(121,axiom,
iV3102 @ cTOP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_112) ).
thf(898,plain,
iV3102 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ cC34 )
<=> ? [B: $i] :
( ~ ( B @ cC32 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_71) ).
thf(709,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC32 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC34 ) )
& ( ( A @ cC34 )
=> ? [B: $i] :
( ~ ( B @ cC32 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ cC28 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC26 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_69) ).
thf(885,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC26 ) )
=> ( A @ cC28 ) )
& ( ( A @ cC28 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC26 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cC160 )
<=> ? [B: $i] :
( ( B @ cC158 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(436,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC158 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC160 ) )
& ( ( A @ cC160 )
=> ? [B: $i] :
( ( B @ cC158 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cC132 )
<=> ( ( A @ cC120 )
& ~ ( A @ cC130 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(184,plain,
! [A: $i] :
( ( ( ( A @ cC120 )
& ~ ( A @ cC130 ) )
=> ( A @ cC132 ) )
& ( ( A @ cC132 )
=> ( ( A @ cC120 )
& ~ ( A @ cC130 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_111) ).
thf(838,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC10 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ cC4 )
<=> ? [B: $i] :
( ~ ( B @ cC2 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_74) ).
thf(702,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC2 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC4 ) )
& ( ( A @ cC4 )
=> ? [B: $i] :
( ~ ( B @ cC2 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ cC162 )
<=> ( ~ ( A @ cC160 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(751,plain,
! [A: $i] :
( ( ( ~ ( A @ cC160 )
& ~ ( A @ cC16 ) )
=> ( A @ cC162 ) )
& ( ( A @ cC162 )
=> ( ~ ( A @ cC160 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cC184 )
<=> ? [B: $i] :
( ( B @ cC182 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(289,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC182 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC184 ) )
& ( ( A @ cC184 )
=> ? [B: $i] :
( ( B @ cC182 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cC150 )
<=> ( ~ ( A @ cC148 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(261,plain,
! [A: $i] :
( ( ( ~ ( A @ cC148 )
& ~ ( A @ cC16 ) )
=> ( A @ cC150 ) )
& ( ( A @ cC150 )
=> ( ~ ( A @ cC148 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cC110 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(492,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC110 ) )
& ( ( A @ cC110 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ cC56 )
<=> ( ~ ( A @ cC54 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).
thf(443,plain,
! [A: $i] :
( ( ( ~ ( A @ cC54 )
& ~ ( A @ cC16 ) )
=> ( A @ cC56 ) )
& ( ( A @ cC56 )
=> ( ~ ( A @ cC54 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ cC42 )
<=> ? [B: $i] :
( ( B @ cC40 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_76) ).
thf(646,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC40 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC42 ) )
& ( ( A @ cC42 )
=> ? [B: $i] :
( ( B @ cC40 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cC94 )
<=> ? [B: $i] :
( ( B @ cC92 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_104) ).
thf(485,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC92 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC94 ) )
& ( ( A @ cC94 )
=> ? [B: $i] :
( ( B @ cC92 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ cC14 )
<=> ( ~ ( A @ cC2 )
& ~ ( A @ cC12 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(821,plain,
! [A: $i] :
( ( ( ~ ( A @ cC2 )
& ~ ( A @ cC12 ) )
=> ( A @ cC14 ) )
& ( ( A @ cC14 )
=> ( ~ ( A @ cC2 )
& ~ ( A @ cC12 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(115,axiom,
! [A: $i] :
( ( A @ cTEST )
<=> ( ( A @ cC46 )
& ( A @ cC216 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_107) ).
thf(877,plain,
! [A: $i] :
( ( ( ( A @ cC46 )
& ( A @ cC216 ) )
=> ( A @ cTEST ) )
& ( ( A @ cTEST )
=> ( ( A @ cC46 )
& ( A @ cC216 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(112,axiom,
~ ( iV3102 @ cC100 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_124) ).
thf(866,plain,
~ ( iV3102 @ cC100 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ cC48 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_79) ).
thf(660,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC48 ) )
& ( ( A @ cC48 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(108,axiom,
~ ( iV3102 @ cC42 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_114) ).
thf(849,plain,
~ ( iV3102 @ cC42 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ? [B: $i] :
( ~ ( B @ cC98 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(527,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC98 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC100 ) )
& ( ( A @ cC100 )
=> ? [B: $i] :
( ~ ( B @ cC98 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cC138 )
<=> ( ( A @ cC16 )
& ( A @ cC136 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(233,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC136 ) )
=> ( A @ cC138 ) )
& ( ( A @ cC138 )
=> ( ( A @ cC16 )
& ( A @ cC136 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cC214 )
<=> ( ~ ( A @ cC212 )
& ( A @ cC100 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(380,plain,
! [A: $i] :
( ( ( ~ ( A @ cC212 )
& ( A @ cC100 ) )
=> ( A @ cC214 ) )
& ( ( A @ cC214 )
=> ( ~ ( A @ cC212 )
& ( A @ cC100 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ cC92 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC90 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_103) ).
thf(793,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC90 ) )
=> ( A @ cC92 ) )
& ( ( A @ cC92 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC90 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cC90 )
<=> ? [B: $i] :
( ( B @ cC88 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_102) ).
thf(366,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC88 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC90 ) )
& ( ( A @ cC90 )
=> ? [B: $i] :
( ( B @ cC88 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ cC52 )
<=> ( ( A @ cC16 )
& ( A @ cC50 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_81) ).
thf(534,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC50 ) )
=> ( A @ cC52 ) )
& ( ( A @ cC52 )
=> ( ( A @ cC16 )
& ( A @ cC50 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(119,axiom,
~ ( iV3102 @ cC26 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_116) ).
thf(894,plain,
~ ( iV3102 @ cC26 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cC72 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC70 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_92) ).
thf(429,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC70 ) )
=> ( A @ cC72 ) )
& ( ( A @ cC72 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC70 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cC6 )
<=> ( ( A @ cC4 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).
thf(275,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC2 ) )
=> ( A @ cC6 ) )
& ( ( A @ cC6 )
=> ( ( A @ cC4 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ cC192 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(625,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC192 ) )
& ( ( A @ cC192 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ cC188 )
<=> ? [B: $i] :
( ( B @ cC186 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(583,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC186 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC188 ) )
& ( ( A @ cC188 )
=> ? [B: $i] :
( ( B @ cC186 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(107,axiom,
! [A: $i] :
( ( A @ cC30 )
<=> ( ( A @ cC28 )
& ( A @ cC14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_70) ).
thf(842,plain,
! [A: $i] :
( ( ( ( A @ cC28 )
& ( A @ cC14 ) )
=> ( A @ cC30 ) )
& ( ( A @ cC30 )
=> ( ( A @ cC28 )
& ( A @ cC14 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cC36 )
<=> ( ( A @ cC34 )
& ( A @ cC32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_72) ).
thf(324,plain,
! [A: $i] :
( ( ( ( A @ cC34 )
& ( A @ cC32 ) )
=> ( A @ cC36 ) )
& ( ( A @ cC36 )
=> ( ( A @ cC34 )
& ( A @ cC32 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cC156 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(317,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC156 ) )
& ( ( A @ cC156 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cC96 )
<=> ( ~ ( A @ cC94 )
& ( A @ cC84 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_105) ).
thf(156,plain,
! [A: $i] :
( ( ( ~ ( A @ cC94 )
& ( A @ cC84 ) )
=> ( A @ cC96 ) )
& ( ( A @ cC96 )
=> ( ~ ( A @ cC94 )
& ( A @ cC84 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ cC26 )
<=> ? [B: $i] :
( ( B @ cC24 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_68) ).
thf(499,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC24 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC26 ) )
& ( ( A @ cC26 )
=> ? [B: $i] :
( ( B @ cC24 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(110,axiom,
! [A: $i] :
( ( A @ cC216 )
<=> ( ( A @ cC64 )
& ~ ( A @ cC214 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(857,plain,
! [A: $i] :
( ( ( ( A @ cC64 )
& ~ ( A @ cC214 ) )
=> ( A @ cC216 ) )
& ( ( A @ cC216 )
=> ( ( A @ cC64 )
& ~ ( A @ cC214 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ cC126 )
<=> ? [B: $i] :
( ( B @ cC124 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(471,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC124 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC126 ) )
& ( ( A @ cC126 )
=> ? [B: $i] :
( ( B @ cC124 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(116,axiom,
iV3102 @ cowlThing,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_109) ).
thf(884,plain,
iV3102 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(123,axiom,
~ ( iV3102 @ cC32 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_123) ).
thf(901,plain,
~ ( iV3102 @ cC32 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ cC62 )
<=> ? [B: $i] :
( ( B @ cC60 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_87) ).
thf(590,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC60 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC62 ) )
& ( ( A @ cC62 )
=> ? [B: $i] :
( ( B @ cC60 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cC8 )
<=> ? [B: $i] :
( ( B @ cC6 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_96) ).
thf(212,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC6 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC8 ) )
& ( ( A @ cC8 )
=> ? [B: $i] :
( ( B @ cC6 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cC196 )
<=> ? [B: $i] :
( ( B @ cC194 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(457,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC194 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC196 ) )
& ( ( A @ cC196 )
=> ? [B: $i] :
( ( B @ cC194 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ cC46 )
<=> ( ( A @ cC44 )
& ( A @ cC30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_78) ).
thf(911,plain,
! [A: $i] :
( ( ( ( A @ cC44 )
& ( A @ cC30 ) )
=> ( A @ cC46 ) )
& ( ( A @ cC46 )
=> ( ( A @ cC44 )
& ( A @ cC30 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ cC60 )
<=> ( ~ ( A @ cC58 )
& ( A @ cC48 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).
thf(569,plain,
! [A: $i] :
( ( ( ~ ( A @ cC58 )
& ( A @ cC48 ) )
=> ( A @ cC60 ) )
& ( ( A @ cC60 )
=> ( ~ ( A @ cC58 )
& ( A @ cC48 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ cC20 )
<=> ( ( A @ cC16 )
& ( A @ cC18 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(779,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC18 ) )
=> ( A @ cC20 ) )
& ( ( A @ cC20 )
=> ( ( A @ cC16 )
& ( A @ cC18 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(1,conjecture,
( ( iV3102 @ cowlThing )
& ( iV3102 @ cC14 )
& ( iV3102 @ cC64 )
& ( iV3102 @ cC28 )
& ( iV3102 @ cC44 )
& ( iV3102 @ cC30 )
& ( iV3102 @ cC46 )
& ( iV3102 @ cC216 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ( iV3102 @ cowlThing )
& ( iV3102 @ cC14 )
& ( iV3102 @ cC64 )
& ( iV3102 @ cC28 )
& ( iV3102 @ cC44 )
& ( iV3102 @ cC30 )
& ( iV3102 @ cC46 )
& ( iV3102 @ cC216 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(128,plain,
~ ( ( iV3102 @ cowlThing )
& ( iV3102 @ cC14 )
& ( iV3102 @ cC64 )
& ( iV3102 @ cC28 )
& ( iV3102 @ cC44 )
& ( iV3102 @ cC30 )
& ( iV3102 @ cC46 )
& ( iV3102 @ cC216 )
& ! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ? [B: $i] :
( ( B @ cC56 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_84) ).
thf(205,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC56 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC58 ) )
& ( ( A @ cC58 )
=> ? [B: $i] :
( ( B @ cC56 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ cC116 )
<=> ( ~ ( A @ cC114 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(541,plain,
! [A: $i] :
( ( ( ~ ( A @ cC114 )
& ~ ( A @ cC16 ) )
=> ( A @ cC116 ) )
& ( ( A @ cC116 )
=> ( ~ ( A @ cC114 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(93,axiom,
! [A: $i] :
( ( A @ cC114 )
<=> ? [B: $i] :
( ( B @ cC112 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(765,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC112 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC114 ) )
& ( ( A @ cC114 )
=> ? [B: $i] :
( ( B @ cC112 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ cC142 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC140 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(674,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC140 ) )
=> ( A @ cC142 ) )
& ( ( A @ cC142 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC140 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ cC118 )
<=> ? [B: $i] :
( ( B @ cC116 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(618,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC116 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC118 ) )
& ( ( A @ cC118 )
=> ? [B: $i] :
( ( B @ cC116 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ cC12 )
<=> ? [B: $i] :
( ( B @ cC10 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(513,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC10 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC12 ) )
& ( ( A @ cC12 )
=> ? [B: $i] :
( ( B @ cC10 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cC108 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC106 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(296,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC106 ) )
=> ( A @ cC108 ) )
& ( ( A @ cC108 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC106 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cC206 )
<=> ( ( A @ cC204 )
& ( A @ cC170 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(149,plain,
! [A: $i] :
( ( ( ( A @ cC204 )
& ( A @ cC170 ) )
=> ( A @ cC206 ) )
& ( ( A @ cC206 )
=> ( ( A @ cC204 )
& ( A @ cC170 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ cC136 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(562,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC136 ) )
& ( ( A @ cC136 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cC166 )
<=> ( ~ ( A @ cC164 )
& ( A @ cC154 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(191,plain,
! [A: $i] :
( ( ( ~ ( A @ cC164 )
& ( A @ cC154 ) )
=> ( A @ cC166 ) )
& ( ( A @ cC166 )
=> ( ~ ( A @ cC164 )
& ( A @ cC154 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ cC128 )
<=> ( ~ ( A @ cC126 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(772,plain,
! [A: $i] :
( ( ( ~ ( A @ cC126 )
& ~ ( A @ cC16 ) )
=> ( A @ cC128 ) )
& ( ( A @ cC128 )
=> ( ~ ( A @ cC126 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(114,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC24 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_113) ).
thf(875,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC24 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ cC172 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(604,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC172 ) )
& ( ( A @ cC172 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ cC44 )
<=> ( ~ ( A @ cC42 )
& ~ ( A @ cC32 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).
thf(831,plain,
! [A: $i] :
( ( ( ~ ( A @ cC42 )
& ~ ( A @ cC32 ) )
=> ( A @ cC44 ) )
& ( ( A @ cC44 )
=> ( ~ ( A @ cC42 )
& ~ ( A @ cC32 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ cC178 )
<=> ( ~ ( A @ cC176 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(681,plain,
! [A: $i] :
( ( ( ~ ( A @ cC176 )
& ~ ( A @ cC16 ) )
=> ( A @ cC178 ) )
& ( ( A @ cC178 )
=> ( ~ ( A @ cC176 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cC82 )
<=> ? [B: $i] :
( ( B @ cC80 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_98) ).
thf(219,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC80 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC82 ) )
& ( ( A @ cC82 )
=> ? [B: $i] :
( ( B @ cC80 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ cC144 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(737,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC144 ) )
& ( ( A @ cC144 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cC68 )
<=> ( ( A @ cC16 )
& ( A @ cC66 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_90) ).
thf(303,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC66 ) )
=> ( A @ cC68 ) )
& ( ( A @ cC68 )
=> ( ( A @ cC16 )
& ( A @ cC66 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cC24 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC22 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).
thf(387,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC22 ) )
=> ( A @ cC24 ) )
& ( ( A @ cC24 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC22 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(92,axiom,
! [A: $i] :
( ( A @ cC190 )
<=> ? [B: $i] :
( ( B @ cC188 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(758,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC188 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC190 ) )
& ( ( A @ cC190 )
=> ? [B: $i] :
( ( B @ cC188 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cC146 )
<=> ( ( A @ cC16 )
& ( A @ cC144 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(345,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC144 ) )
=> ( A @ cC146 ) )
& ( ( A @ cC146 )
=> ( ( A @ cC16 )
& ( A @ cC144 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ cC22 )
<=> ? [B: $i] :
( ( B @ cC20 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).
thf(520,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC20 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC22 ) )
& ( ( A @ cC22 )
=> ? [B: $i] :
( ( B @ cC20 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ cC66 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_89) ).
thf(240,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC66 ) )
& ( ( A @ cC66 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cC80 )
<=> ( ~ ( A @ cC78 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_97) ).
thf(198,plain,
! [A: $i] :
( ( ( ~ ( A @ cC78 )
& ~ ( A @ cC16 ) )
=> ( A @ cC80 ) )
& ( ( A @ cC80 )
=> ( ~ ( A @ cC78 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ cC10 )
<=> ( ~ ( A @ cC2 )
& ~ ( A @ cC8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(695,plain,
! [A: $i] :
( ( ( ~ ( A @ cC2 )
& ~ ( A @ cC8 ) )
=> ( A @ cC10 ) )
& ( ( A @ cC10 )
=> ( ~ ( A @ cC2 )
& ~ ( A @ cC8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ cC64 )
<=> ( ( A @ cTOP )
& ~ ( A @ cC62 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_88) ).
thf(868,plain,
! [A: $i] :
( ( ( ( A @ cTOP )
& ~ ( A @ cC62 ) )
=> ( A @ cC64 ) )
& ( ( A @ cC64 )
=> ( ( A @ cTOP )
& ~ ( A @ cC62 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cC180 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(394,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC180 ) )
& ( ( A @ cC180 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cC134 )
<=> ( ~ ( A @ cC108 )
& ~ ( A @ cC132 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(135,plain,
! [A: $i] :
( ( ( ~ ( A @ cC108 )
& ~ ( A @ cC132 ) )
=> ( A @ cC134 ) )
& ( ( A @ cC134 )
=> ( ~ ( A @ cC108 )
& ~ ( A @ cC132 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ cC74 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_93) ).
thf(226,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC74 ) )
& ( ( A @ cC74 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(851,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ cC176 )
<=> ? [B: $i] :
( ( B @ cC174 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(653,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC174 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC176 ) )
& ( ( A @ cC176 )
=> ? [B: $i] :
( ( B @ cC174 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cC104 )
<=> ( ( A @ cC16 )
& ( A @ cC102 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(282,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC102 ) )
=> ( A @ cC104 ) )
& ( ( A @ cC104 )
=> ( ( A @ cC16 )
& ( A @ cC102 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ cC78 )
<=> ? [B: $i] :
( ( B @ cC76 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_95) ).
thf(310,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC76 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC78 ) )
& ( ( A @ cC78 )
=> ? [B: $i] :
( ( B @ cC76 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cC168 )
<=> ( ~ ( A @ cC142 )
& ~ ( A @ cC166 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(177,plain,
! [A: $i] :
( ( ( ~ ( A @ cC142 )
& ~ ( A @ cC166 ) )
=> ( A @ cC168 ) )
& ( ( A @ cC168 )
=> ( ~ ( A @ cC142 )
& ~ ( A @ cC166 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cC198 )
<=> ( ~ ( A @ cC16 )
& ~ ( A @ cC196 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(331,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ~ ( A @ cC196 ) )
=> ( A @ cC198 ) )
& ( ( A @ cC198 )
=> ( ~ ( A @ cC16 )
& ~ ( A @ cC196 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC60 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_110) ).
thf(840,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ~ ( A @ cC60 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cC18 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(338,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC18 ) )
& ( ( A @ cC18 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ cC154 )
<=> ? [B: $i] :
( ( B @ cC152 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(576,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC152 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC154 ) )
& ( ( A @ cC154 )
=> ? [B: $i] :
( ( B @ cC152 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cC50 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_80) ).
thf(359,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC50 ) )
& ( ( A @ cC50 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ cC54 )
<=> ? [B: $i] :
( ( B @ cC52 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_82) ).
thf(744,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC52 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC54 ) )
& ( ( A @ cC54 )
=> ? [B: $i] :
( ( B @ cC52 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(111,axiom,
~ ( iV3102 @ cC62 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_119) ).
thf(864,plain,
~ ( iV3102 @ cC62 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cC102 )
<=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(450,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC102 ) )
& ( ( A @ cC102 )
=> ? [B: $i] :
( ~ ( B @ cC16 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ cC212 )
<=> ? [B: $i] :
( ( B @ cC210 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(688,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC210 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC212 ) )
& ( ( A @ cC212 )
=> ? [B: $i] :
( ( B @ cC210 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(124,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(903,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(120,axiom,
~ ( iV3102 @ cC12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_115) ).
thf(896,plain,
~ ( iV3102 @ cC12 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ cC194 )
<=> ( ( A @ cC16 )
& ( A @ cC192 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_53) ).
thf(632,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC192 ) )
=> ( A @ cC194 ) )
& ( ( A @ cC194 )
=> ( ( A @ cC16 )
& ( A @ cC192 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ cC140 )
<=> ? [B: $i] :
( ( B @ cC138 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(401,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC138 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC140 ) )
& ( ( A @ cC140 )
=> ? [B: $i] :
( ( B @ cC138 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ( ~ ( A @ cC32 )
& ~ ( A @ cC38 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_75) ).
thf(786,plain,
! [A: $i] :
( ( ( ~ ( A @ cC32 )
& ~ ( A @ cC38 ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ( ~ ( A @ cC32 )
& ~ ( A @ cC38 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ cC182 )
<=> ( ( A @ cC180 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(667,plain,
! [A: $i] :
( ( ( ( A @ cC180 )
& ( A @ cC16 ) )
=> ( A @ cC182 ) )
& ( ( A @ cC182 )
=> ( ( A @ cC180 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cC84 )
<=> ? [B: $i] :
( ( B @ cC82 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_99) ).
thf(478,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC82 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC84 ) )
& ( ( A @ cC84 )
=> ? [B: $i] :
( ( B @ cC82 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(122,axiom,
~ ( iV3102 @ cC2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_122) ).
thf(899,plain,
~ ( iV3102 @ cC2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ cC130 )
<=> ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(716,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC130 ) )
& ( ( A @ cC130 )
=> ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ cC70 )
<=> ? [B: $i] :
( ( B @ cC68 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_91) ).
thf(800,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC68 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC70 ) )
& ( ( A @ cC70 )
=> ? [B: $i] :
( ( B @ cC68 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cC88 )
<=> ( ( A @ cC16 )
& ( A @ cC86 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_101) ).
thf(422,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC86 ) )
=> ( A @ cC88 ) )
& ( ( A @ cC88 )
=> ( ( A @ cC16 )
& ( A @ cC86 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cC106 )
<=> ? [B: $i] :
( ( B @ cC104 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(373,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC104 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC106 ) )
& ( ( A @ cC106 )
=> ? [B: $i] :
( ( B @ cC104 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(127,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_117) ).
thf(918,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC98 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ cC158 )
<=> ( ( A @ cC16 )
& ( A @ cC156 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(807,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC156 ) )
=> ( A @ cC158 ) )
& ( ( A @ cC158 )
=> ( ( A @ cC16 )
& ( A @ cC156 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(102,axiom,
iV3102 @ cTEST,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_108) ).
thf(828,plain,
iV3102 @ cTEST,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cC170 )
<=> ? [B: $i] :
( ~ ( B @ cC168 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(415,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC168 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC170 ) )
& ( ( A @ cC170 )
=> ? [B: $i] :
( ~ ( B @ cC168 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ cC148 )
<=> ? [B: $i] :
( ( B @ cC146 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(506,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC146 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC148 ) )
& ( ( A @ cC148 )
=> ? [B: $i] :
( ( B @ cC146 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cC164 )
<=> ? [B: $i] :
( ( B @ cC162 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(268,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC162 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC164 ) )
& ( ( A @ cC164 )
=> ? [B: $i] :
( ( B @ cC162 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cC152 )
<=> ? [B: $i] :
( ( B @ cC150 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(464,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC150 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC152 ) )
& ( ( A @ cC152 )
=> ? [B: $i] :
( ( B @ cC150 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ cC76 )
<=> ( ( A @ cC16 )
& ( A @ cC74 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_94) ).
thf(723,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC74 ) )
=> ( A @ cC76 ) )
& ( ( A @ cC76 )
=> ( ( A @ cC16 )
& ( A @ cC74 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cC202 )
<=> ( ~ ( A @ cC200 )
& ( A @ cC190 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(163,plain,
! [A: $i] :
( ( ( ~ ( A @ cC200 )
& ( A @ cC190 ) )
=> ( A @ cC202 ) )
& ( ( A @ cC202 )
=> ( ~ ( A @ cC200 )
& ( A @ cC190 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ( ( A @ cC16 )
& ( A @ cC110 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(254,plain,
! [A: $i] :
( ( ( ( A @ cC16 )
& ( A @ cC110 ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ( ( A @ cC16 )
& ( A @ cC110 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ cC186 )
<=> ( ~ ( A @ cC184 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(639,plain,
! [A: $i] :
( ( ( ~ ( A @ cC184 )
& ~ ( A @ cC16 ) )
=> ( A @ cC186 ) )
& ( ( A @ cC186 )
=> ( ~ ( A @ cC184 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(930,plain,
$false,
inference(e,[status(thm)],[611,548,892,909,555,352,730,247,597,408,170,142,814,829,898,709,885,436,184,838,702,751,289,261,492,443,646,485,821,877,866,660,849,527,233,380,793,366,534,894,429,275,625,583,842,324,317,156,499,857,471,884,901,590,212,457,911,569,779,128,205,541,765,674,618,513,296,149,562,191,772,875,604,831,681,219,737,303,387,758,345,520,240,198,695,868,394,135,226,851,653,282,310,177,331,840,338,576,359,744,864,450,688,903,896,632,401,786,667,478,899,716,800,422,373,918,807,828,415,506,268,464,723,163,254,639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS149+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.11 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.21/0.47 % Computer : n026.cluster.edu
% 0.21/0.47 % Model : x86_64 x86_64
% 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.47 % Memory : 8046.5625MB
% 0.21/0.47 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Fri Sep 25 19:44:10 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.26/1.27 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.06/1.67 % [INFO] Parsing done (390ms).
% 2.06/1.69 % [INFO] Running in sequential loop mode.
% 3.24/2.27 % [INFO] eprover registered as external prover.
% 3.24/2.29 % [INFO] Scanning for conjecture ...
% 3.63/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 125 axioms. Running axiom selection ...
% 4.02/2.63 % [INFO] Axiom selection finished. Selected 125 axioms (removed 0 axioms).
% 4.55/2.81 % [INFO] Problem is first-order (TPTP FOF).
% 4.55/2.84 % [INFO] Type checking passed.
% 4.55/2.84 % [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 ...
% 13.59/5.42 % External prover 'e' found a proof!
% 13.59/5.42 % [INFO] Killing All external provers ...
% 13.59/5.42 % Time passed: 4777ms (effective reasoning time: 3720ms)
% 13.59/5.42 % 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)>
% 13.59/5.42 % 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
% 13.59/5.42 % No. of inferences in proof: 254
% 13.59/5.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4777 ms resp. 3720 ms w/o parsing
% 14.27/5.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.27/5.68 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------