%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS154+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 07:44:46 AM UTC 2026
% Result : Theorem 11.33s 4.12s
% Output : Refutation 12.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 113
% Syntax : Number of formulae : 228 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 761 ( 0 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1547 ( 83 ~; 0 |; 259 &; 931 @)
% ( 90 <=>; 184 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 108 ( 107 usr; 2 con; 0-2 aty)
% Number of variables : 355 ( 0 ^; 190 !; 165 ?; 355 :)
% 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(cC58_decl,type,
cC58: $i > $o ).
thf(iV822576_decl,type,
iV822576: $i ).
thf(cC116_decl,type,
cC116: $i > $o ).
thf(cC114_decl,type,
cC114: $i > $o ).
thf(cC94_decl,type,
cC94: $i > $o ).
thf(cC80_decl,type,
cC80: $i > $o ).
thf(cC110_decl,type,
cC110: $i > $o ).
thf(cC136_decl,type,
cC136: $i > $o ).
thf(cC56_decl,type,
cC56: $i > $o ).
thf(cC98_decl,type,
cC98: $i > $o ).
thf(ra_Px63_decl,type,
ra_Px63: $i > $i > $o ).
thf(cC36_decl,type,
cC36: $i > $o ).
thf(cC34xcomp_decl,type,
cC34xcomp: $i > $o ).
thf(cC4_decl,type,
cC4: $i > $o ).
thf(cC90_decl,type,
cC90: $i > $o ).
thf(ra_Px52_decl,type,
ra_Px52: $i > $i > $o ).
thf(ra_Px9_decl,type,
ra_Px9: $i > $i > $o ).
thf(cC82_decl,type,
cC82: $i > $o ).
thf(ra_Px65_decl,type,
ra_Px65: $i > $i > $o ).
thf(cC126_decl,type,
cC126: $i > $o ).
thf(cC124_decl,type,
cC124: $i > $o ).
thf(cC2xcomp_decl,type,
cC2xcomp: $i > $o ).
thf(ra_Px22_decl,type,
ra_Px22: $i > $i > $o ).
thf(rR1_decl,type,
rR1: $i > $i > $o ).
thf(cC88_decl,type,
cC88: $i > $o ).
thf(cC86_decl,type,
cC86: $i > $o ).
thf(ra_Px28_decl,type,
ra_Px28: $i > $i > $o ).
thf(cC64_decl,type,
cC64: $i > $o ).
thf(cC62_decl,type,
cC62: $i > $o ).
thf(cC76_decl,type,
cC76: $i > $o ).
thf(ra_Px24_decl,type,
ra_Px24: $i > $i > $o ).
thf(cC18_decl,type,
cC18: $i > $o ).
thf(ra_Px56_decl,type,
ra_Px56: $i > $i > $o ).
thf(cC100_decl,type,
cC100: $i > $o ).
thf(ra_Px49_decl,type,
ra_Px49: $i > $i > $o ).
thf(cC130_decl,type,
cC130: $i > $o ).
thf(cC128_decl,type,
cC128: $i > $o ).
thf(cC122_decl,type,
cC122: $i > $o ).
thf(cC112_decl,type,
cC112: $i > $o ).
thf(ra_Px39_decl,type,
ra_Px39: $i > $i > $o ).
thf(cC84_decl,type,
cC84: $i > $o ).
thf(cC96_decl,type,
cC96: $i > $o ).
thf(ra_Px38_decl,type,
ra_Px38: $i > $i > $o ).
thf(cC102_decl,type,
cC102: $i > $o ).
thf(ra_Px35_decl,type,
ra_Px35: $i > $i > $o ).
thf(ra_Px53_decl,type,
ra_Px53: $i > $i > $o ).
thf(ra_Px64_decl,type,
ra_Px64: $i > $i > $o ).
thf(cC66_decl,type,
cC66: $i > $o ).
thf(cC94xcomp_decl,type,
cC94xcomp: $i > $o ).
thf(ra_Px30_decl,type,
ra_Px30: $i > $i > $o ).
thf(cC100xcomp_decl,type,
cC100xcomp: $i > $o ).
thf(cC90xcomp_decl,type,
cC90xcomp: $i > $o ).
thf(cC8_decl,type,
cC8: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(cC92xcomp_decl,type,
cC92xcomp: $i > $o ).
thf(ra_Px29_decl,type,
ra_Px29: $i > $i > $o ).
thf(cC108xcomp_decl,type,
cC108xcomp: $i > $o ).
thf(ra_Px36_decl,type,
ra_Px36: $i > $i > $o ).
thf(cC110xcomp_decl,type,
cC110xcomp: $i > $o ).
thf(ra_Px37_decl,type,
ra_Px37: $i > $i > $o ).
thf(cC138_decl,type,
cC138: $i > $o ).
thf(cC136xcomp_decl,type,
cC136xcomp: $i > $o ).
thf(cC24_decl,type,
cC24: $i > $o ).
thf(cC16_decl,type,
cC16: $i > $o ).
thf(cC2_decl,type,
cC2: $i > $o ).
thf(cC10xcomp_decl,type,
cC10xcomp: $i > $o ).
thf(ra_Px16_decl,type,
ra_Px16: $i > $i > $o ).
thf(ra_Px46_decl,type,
ra_Px46: $i > $i > $o ).
thf(cC34_decl,type,
cC34: $i > $o ).
thf(cC42_decl,type,
cC42: $i > $o ).
thf(cC134xcomp_decl,type,
cC134xcomp: $i > $o ).
thf(ra_Px45_decl,type,
ra_Px45: $i > $i > $o ).
thf(cC50_decl,type,
cC50: $i > $o ).
thf(cC48xcomp_decl,type,
cC48xcomp: $i > $o ).
thf(cC120_decl,type,
cC120: $i > $o ).
thf(cC118_decl,type,
cC118: $i > $o ).
thf(cC44_decl,type,
cC44: $i > $o ).
thf(cC96xcomp_decl,type,
cC96xcomp: $i > $o ).
thf(cC26_decl,type,
cC26: $i > $o ).
thf(cC84xcomp_decl,type,
cC84xcomp: $i > $o ).
thf(cC112xcomp_decl,type,
cC112xcomp: $i > $o ).
thf(cC106_decl,type,
cC106: $i > $o ).
thf(cC104_decl,type,
cC104: $i > $o ).
thf(cC38_decl,type,
cC38: $i > $o ).
thf(cC82xcomp_decl,type,
cC82xcomp: $i > $o ).
thf(cC88xcomp_decl,type,
cC88xcomp: $i > $o ).
thf(cC22_decl,type,
cC22: $i > $o ).
thf(cC20_decl,type,
cC20: $i > $o ).
thf(cC18xcomp_decl,type,
cC18xcomp: $i > $o ).
thf(cC32_decl,type,
cC32: $i > $o ).
thf(cC30xcomp_decl,type,
cC30xcomp: $i > $o ).
thf(cC132xcomp_decl,type,
cC132xcomp: $i > $o ).
thf(ra_Px48_decl,type,
ra_Px48: $i > $i > $o ).
thf(cC86xcomp_decl,type,
cC86xcomp: $i > $o ).
thf(cC40_decl,type,
cC40: $i > $o ).
thf(cC102xcomp_decl,type,
cC102xcomp: $i > $o ).
thf(cC98xcomp_decl,type,
cC98xcomp: $i > $o ).
thf(cC78xcomp_decl,type,
cC78xcomp: $i > $o ).
thf(ra_Px25_decl,type,
ra_Px25: $i > $i > $o ).
thf(ra_Px4_decl,type,
ra_Px4: $i > $i > $o ).
thf(cC76xcomp_decl,type,
cC76xcomp: $i > $o ).
thf(cC68_decl,type,
cC68: $i > $o ).
thf(cC60_decl,type,
cC60: $i > $o ).
thf(93,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(651,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cC138 )
<=> ? [B: $i] :
( ( B @ cC136xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(325,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC136xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC138 ) )
& ( ( A @ cC138 )
=> ? [B: $i] :
( ( B @ cC136xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(109,axiom,
iV822576 @ cC92xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_168) ).
thf(710,plain,
iV822576 @ cC92xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ cC94 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_137) ).
thf(612,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px30 ) )
=> ( A @ cC94 ) )
& ( ( A @ cC94 )
=> ? [B: $i] : ( B @ ( A @ ra_Px30 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ cC80 )
<=> ( ( A @ cC76xcomp )
& ( A @ cC78xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_117) ).
thf(666,plain,
! [A: $i] :
( ( ( ( A @ cC76xcomp )
& ( A @ cC78xcomp ) )
=> ( A @ cC80 ) )
& ( ( A @ cC80 )
=> ( ( A @ cC76xcomp )
& ( A @ cC78xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cC136xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px46 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(352,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px46 ) )
=> ( A @ cC136xcomp ) )
& ( ( A @ cC136xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px46 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ cC20 )
<=> ? [B: $i] :
( ( B @ cC18 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(523,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC18 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC20 ) )
& ( ( A @ cC20 )
=> ? [B: $i] :
( ( B @ cC18 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(1,conjecture,
( ( iV822576 @ cC56 )
& ( iV822576 @ cC136 )
& ( iV822576 @ cC110 )
& ( iV822576 @ cC80 )
& ( iV822576 @ cC94 )
& ( iV822576 @ cowlThing )
& ( iV822576 @ cC114 )
& ( iV822576 @ cC116 )
& ( iV822576 @ cC58 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ( iV822576 @ cC56 )
& ( iV822576 @ cC136 )
& ( iV822576 @ cC110 )
& ( iV822576 @ cC80 )
& ( iV822576 @ cC94 )
& ( iV822576 @ cowlThing )
& ( iV822576 @ cC114 )
& ( iV822576 @ cC116 )
& ( iV822576 @ cC58 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(115,plain,
~ ( ( iV822576 @ cC56 )
& ( iV822576 @ cC136 )
& ( iV822576 @ cC110 )
& ( iV822576 @ cC80 )
& ( iV822576 @ cC94 )
& ( iV822576 @ cowlThing )
& ( iV822576 @ cC114 )
& ( iV822576 @ cC116 )
& ( iV822576 @ cC58 )
& ! [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(102,axiom,
iV822576 @ cC112xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_151) ).
thf(683,plain,
iV822576 @ cC112xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cC94xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_138) ).
thf(269,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px30 ) )
=> ( A @ cC94xcomp ) )
& ( ( A @ cC94xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px30 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cC134xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px45 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(385,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px45 ) )
=> ( A @ cC134xcomp ) )
& ( ( A @ cC134xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px45 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ( ( A @ cC38 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_78) ).
thf(550,plain,
! [A: $i] :
( ( ( ( A @ cC38 )
& ( A @ cC34 ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ( ( A @ cC38 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ( A @ cC98xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_156) ).
thf(698,plain,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ( A @ cC98xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ( ( A @ cC4 )
& ( A @ cC34xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_143) ).
thf(153,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC34xcomp ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ( ( A @ cC4 )
& ( A @ cC34xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ cC56 )
<=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_93) ).
thf(719,plain,
! [A: $i] :
( ( ( ( A @ cC10xcomp )
& ( A @ cC4 ) )
=> ( A @ cC56 ) )
& ( ( A @ cC56 )
=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ cC118 )
<=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(587,plain,
! [A: $i] :
( ( ( ( A @ cC10xcomp )
& ( A @ cC4 ) )
=> ( A @ cC118 ) )
& ( ( A @ cC118 )
=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ cC116 )
<=> ( ( A @ cC80 )
& ( A @ cC114 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(619,plain,
! [A: $i] :
( ( ( ( A @ cC80 )
& ( A @ cC114 ) )
=> ( A @ cC116 ) )
& ( ( A @ cC116 )
=> ( ( A @ cC80 )
& ( A @ cC114 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cC130 )
<=> ( ( A @ cC122 )
& ( A @ cC128 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(211,plain,
! [A: $i] :
( ( ( ( A @ cC122 )
& ( A @ cC128 ) )
=> ( A @ cC130 ) )
& ( ( A @ cC130 )
=> ( ( A @ cC122 )
& ( A @ cC128 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cC96 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px38 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_139) ).
thf(238,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px38 ) )
=> ( A @ cC96 ) )
& ( ( A @ cC96 )
=> ? [B: $i] : ( B @ ( A @ ra_Px38 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cC82 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px65 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_118) ).
thf(147,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px65 ) )
=> ( A @ cC82 ) )
& ( ( A @ cC82 )
=> ? [B: $i] : ( B @ ( A @ ra_Px65 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(86,axiom,
iV822576 @ cC108xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_148) ).
thf(634,plain,
iV822576 @ cC108xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cC126 )
<=> ( ( A @ cC124 )
& ( A @ cC34xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_30) ).
thf(160,plain,
! [A: $i] :
( ( ( ( A @ cC124 )
& ( A @ cC34xcomp ) )
=> ( A @ cC126 ) )
& ( ( A @ cC126 )
=> ( ( A @ cC124 )
& ( A @ cC34xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cC100xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px49 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(275,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px49 ) )
=> ( A @ cC100xcomp ) )
& ( ( A @ cC100xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px49 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(92,axiom,
iV822576 @ cC78xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_158) ).
thf(650,plain,
iV822576 @ cC78xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cC34xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_72) ).
thf(141,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) )
=> ( A @ cC34xcomp ) )
& ( ( A @ cC34xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(79,axiom,
iV822576 @ cC76xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_152) ).
thf(610,plain,
iV822576 @ cC76xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cC88 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px64 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_128) ).
thf(256,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px64 ) )
=> ( A @ cC88 ) )
& ( ( A @ cC88 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px64 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(225,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px39 ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ? [B: $i] : ( B @ ( A @ ra_Px39 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cC88 )
<=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_127) ).
thf(339,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ( A @ cC16 ) )
=> ( A @ cC88 ) )
& ( ( A @ cC88 )
=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ cC22 )
<=> ( ( A @ cC20 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_57) ).
thf(476,plain,
! [A: $i] :
( ( ( ( A @ cC20 )
& ( A @ cC16 ) )
=> ( A @ cC22 ) )
& ( ( A @ cC22 )
=> ( ( A @ cC20 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(642,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ( ( A @ cC84 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_124) ).
thf(489,plain,
! [A: $i] :
( ( ( ( A @ cC84 )
& ( A @ cC16 ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ( ( A @ cC84 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cC76 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_108) ).
thf(193,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px24 ) )
=> ( A @ cC76 ) )
& ( ( A @ cC76 )
=> ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ cC86xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_126) ).
thf(537,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px28 ) )
=> ( A @ cC86xcomp ) )
& ( ( A @ cC86xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ cC38 )
<=> ? [B: $i] :
( ( B @ cC36 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_74) ).
thf(457,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)],[55]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cC90 )
<=> ? [B: $i] :
( ( B @ cC88 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_130) ).
thf(173,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)],[11]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ cC78xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_113) ).
thf(569,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px25 ) )
=> ( A @ cC78xcomp ) )
& ( ( A @ cC78xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px25 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cC42 )
<=> ( ( A @ cC34 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_80) ).
thf(371,plain,
! [A: $i] :
( ( ( ( A @ cC34 )
& ( A @ cC4 ) )
=> ( A @ cC42 ) )
& ( ( A @ cC42 )
=> ( ( A @ cC34 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ cC102 )
<=> ( ( A @ cC100 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(503,plain,
! [A: $i] :
( ( ( ( A @ cC100 )
& ( A @ cC34 ) )
=> ( A @ cC102 ) )
& ( ( A @ cC102 )
=> ( ( A @ cC100 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cC36 )
<=> ( ( A @ cC4 )
& ( A @ cC34xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_73) ).
thf(128,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC34xcomp ) )
=> ( A @ cC36 ) )
& ( ( A @ cC36 )
=> ( ( A @ cC4 )
& ( A @ cC34xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cC102 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(244,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px35 ) )
=> ( A @ cC102 ) )
& ( ( A @ cC102 )
=> ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px49 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(205,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px49 ) )
=> ( A @ cC100 ) )
& ( ( A @ cC100 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px49 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(94,axiom,
iV822576 @ cC134xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_160) ).
thf(657,plain,
iV822576 @ cC134xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cC120 )
<=> ( ( A @ cC34 )
& ( A @ cC118 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(398,plain,
! [A: $i] :
( ( ( ( A @ cC34 )
& ( A @ cC118 ) )
=> ( A @ cC120 ) )
& ( ( A @ cC120 )
=> ( ( A @ cC34 )
& ( A @ cC118 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(99,axiom,
iV822576 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_166) ).
thf(674,plain,
iV822576 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ cC122 )
<=> ? [B: $i] :
( ( B @ cC120 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(530,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC120 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC122 ) )
& ( ( A @ cC122 )
=> ? [B: $i] :
( ( B @ cC120 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(112,axiom,
iV822576 @ cC86xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_161) ).
thf(718,plain,
iV822576 @ cC86xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cC96 )
<=> ( ( A @ cC94xcomp )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_140) ).
thf(412,plain,
! [A: $i] :
( ( ( ( A @ cC94xcomp )
& ( A @ cC2 ) )
=> ( A @ cC96 ) )
& ( ( A @ cC96 )
=> ( ( A @ cC94xcomp )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(82,axiom,
iV822576 @ cC90xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_157) ).
thf(618,plain,
iV822576 @ cC90xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cC96xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px38 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_141) ).
thf(425,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px38 ) )
=> ( A @ cC96xcomp ) )
& ( ( A @ cC96xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px38 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_125) ).
thf(180,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px28 ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cC112xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(444,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px39 ) )
=> ( A @ cC112xcomp ) )
& ( ( A @ cC112xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px39 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ cC104 )
<=> ( ( A @ cC34 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(601,plain,
! [A: $i] :
( ( ( ( A @ cC34 )
& ( A @ cC4 ) )
=> ( A @ cC104 ) )
& ( ( A @ cC104 )
=> ( ( A @ cC34 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(110,axiom,
iV822576 @ cC2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_165) ).
thf(711,plain,
iV822576 @ cC2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ cC90xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px52 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_132) ).
thf(281,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px52 ) )
=> ( A @ cC90xcomp ) )
& ( ( A @ cC90xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px52 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(88,axiom,
iV822576 @ cC34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_162) ).
thf(641,plain,
iV822576 @ cC34,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cC50 )
<=> ( ( A @ cC48xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_89) ).
thf(391,plain,
! [A: $i] :
( ( ( ( A @ cC48xcomp )
& ( A @ cC4 ) )
=> ( A @ cC50 ) )
& ( ( A @ cC50 )
=> ( ( A @ cC48xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cC108xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(313,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px36 ) )
=> ( A @ cC108xcomp ) )
& ( ( A @ cC108xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px36 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(80,axiom,
iV822576 @ cC18xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_150) ).
thf(611,plain,
iV822576 @ cC18xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cC2 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_54) ).
thf(419,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px22 ) )
=> ( A @ cC2 ) )
& ( ( A @ cC2 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(91,axiom,
iV822576 @ cC96xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_153) ).
thf(649,plain,
iV822576 @ cC96xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ cC68 )
<=> ( ( A @ cC60 )
& ( A @ cC66 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_100) ).
thf(594,plain,
! [A: $i] :
( ( ( ( A @ cC60 )
& ( A @ cC66 ) )
=> ( A @ cC68 ) )
& ( ( A @ cC68 )
=> ( ( A @ cC60 )
& ( A @ cC66 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(114,axiom,
iV822576 @ cC10xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_167) ).
thf(726,plain,
iV822576 @ cC10xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ cC18xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px56 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
thf(483,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px56 ) )
=> ( A @ cC18xcomp ) )
& ( ( A @ cC18xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px56 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(106,axiom,
! [A: $i] :
( ( A @ cC60 )
<=> ? [B: $i] :
( ( B @ cC58 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_96) ).
thf(700,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC58 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC60 ) )
& ( ( A @ cC60 )
=> ? [B: $i] :
( ( B @ cC58 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(84,axiom,
iV822576 @ cC102xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_147) ).
thf(626,plain,
iV822576 @ cC102xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ( A @ cC82xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_159) ).
thf(608,plain,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ( A @ cC82xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cC76 )
<=> ( ( A @ cC2xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_109) ).
thf(306,plain,
! [A: $i] :
( ( ( ( A @ cC2xcomp )
& ( A @ cC4 ) )
=> ( A @ cC76 ) )
& ( ( A @ cC76 )
=> ( ( A @ cC2xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cC84xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px53 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_123) ).
thf(438,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px53 ) )
=> ( A @ cC84xcomp ) )
& ( ( A @ cC84xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px53 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ cC26 )
<=> ? [B: $i] :
( ( B @ cC24 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(431,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)],[51]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cC2xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(167,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px22 ) )
=> ( A @ cC2xcomp ) )
& ( ( A @ cC2xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(95,axiom,
iV822576 @ cC16,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_146) ).
thf(658,plain,
iV822576 @ cC16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cC90 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px52 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_131) ).
thf(135,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px52 ) )
=> ( A @ cC90 ) )
& ( ( A @ cC90 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px52 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ cC98xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px63 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_144) ).
thf(563,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px63 ) )
=> ( A @ cC98xcomp ) )
& ( ( A @ cC98xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px63 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(100,axiom,
iV822576 @ cC4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_149) ).
thf(675,plain,
iV822576 @ cC4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(90,axiom,
iV822576 @ cC84xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_163) ).
thf(648,plain,
iV822576 @ cC84xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ cC62 )
<=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_97) ).
thf(516,plain,
! [A: $i] :
( ( ( ( A @ cC10xcomp )
& ( A @ cC4 ) )
=> ( A @ cC62 ) )
& ( ( A @ cC62 )
=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(107,axiom,
iV822576 @ cC132xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_154) ).
thf(707,plain,
iV822576 @ cC132xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(111,axiom,
! [A: $i] :
( ( A @ cC136 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px46 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(712,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px46 ) )
=> ( A @ cC136 ) )
& ( ( A @ cC136 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px46 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ cC102xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(557,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px35 ) )
=> ( A @ cC102xcomp ) )
& ( ( A @ cC102xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ cC88xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px64 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_129) ).
thf(470,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px64 ) )
=> ( A @ cC88xcomp ) )
& ( ( A @ cC88xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px64 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cC18 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px56 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(199,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px56 ) )
=> ( A @ cC18 ) )
& ( ( A @ cC18 )
=> ? [B: $i] : ( B @ ( A @ ra_Px56 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(98,axiom,
iV822576 @ cC100xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_155) ).
thf(673,plain,
iV822576 @ cC100xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(85,axiom,
! [A: $i] :
( ( A @ cC114 )
<=> ( ( A @ cC96xcomp )
& ( A @ cC112xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(627,plain,
! [A: $i] :
( ( ( ( A @ cC96xcomp )
& ( A @ cC112xcomp ) )
=> ( A @ cC114 ) )
& ( ( A @ cC114 )
=> ( ( A @ cC96xcomp )
& ( A @ cC112xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cC106 )
<=> ? [B: $i] :
( ( B @ cC104 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(450,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)],[54]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ cC76xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_110) ).
thf(581,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px24 ) )
=> ( A @ cC76xcomp ) )
& ( ( A @ cC76xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ? [B: $i] :
( ( B @ cC98 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(218,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)],[18]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cC84 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px53 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_121) ).
thf(250,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px53 ) )
=> ( A @ cC84 ) )
& ( ( A @ cC84 )
=> ? [B: $i] : ( B @ ( A @ ra_Px53 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cC84 )
<=> ? [B: $i] :
( ( B @ cC82 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_122) ).
thf(231,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)],[20]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ cC110xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(319,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px37 ) )
=> ( A @ cC110xcomp ) )
& ( ( A @ cC110xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cC64 )
<=> ( ( A @ cC62 )
& ( A @ cC34xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_98) ).
thf(186,plain,
! [A: $i] :
( ( ( ( A @ cC62 )
& ( A @ cC34xcomp ) )
=> ( A @ cC64 ) )
& ( ( A @ cC64 )
=> ( ( A @ cC62 )
& ( A @ cC34xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ( ( A @ cC110xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(378,plain,
! [A: $i] :
( ( ( ( A @ cC110xcomp )
& ( A @ cC4 ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ( ( A @ cC110xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ cC132xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(510,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px48 ) )
=> ( A @ cC132xcomp ) )
& ( ( A @ cC132xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px48 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(103,axiom,
! [A: $i] :
( ( A @ cC94 )
<=> ( ( A @ cC92xcomp )
& ( A @ cC86xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_136) ).
thf(684,plain,
! [A: $i] :
( ( ( ( A @ cC92xcomp )
& ( A @ cC86xcomp ) )
=> ( A @ cC94 ) )
& ( ( A @ cC94 )
=> ( ( A @ cC92xcomp )
& ( A @ cC86xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cC10xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(346,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px16 ) )
=> ( A @ cC10xcomp ) )
& ( ( A @ cC10xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cC8 )
<=> ( ( A @ cC2xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_115) ).
thf(287,plain,
! [A: $i] :
( ( ( ( A @ cC2xcomp )
& ( A @ cC4 ) )
=> ( A @ cC8 ) )
& ( ( A @ cC8 )
=> ( ( A @ cC2xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cC92xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px29 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_135) ).
thf(300,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px29 ) )
=> ( A @ cC92xcomp ) )
& ( ( A @ cC92xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px29 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cC66 )
<=> ? [B: $i] :
( ( B @ cC64 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_99) ).
thf(262,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC64 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC66 ) )
& ( ( A @ cC66 )
=> ? [B: $i] :
( ( B @ cC64 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ cC44 )
<=> ? [B: $i] :
( ( B @ cC42 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_81) ).
thf(405,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC42 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC44 ) )
& ( ( A @ cC44 )
=> ? [B: $i] :
( ( B @ cC42 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cC4 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_75) ).
thf(294,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cC4 ) )
& ( ( A @ cC4 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cC34 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_71) ).
thf(358,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px9 ) )
=> ( A @ cC34 ) )
& ( ( A @ cC34 )
=> ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ cC110 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(635,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px37 ) )
=> ( A @ cC110 ) )
& ( ( A @ cC110 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ cC82xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px65 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_120) ).
thf(464,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px65 ) )
=> ( A @ cC82xcomp ) )
& ( ( A @ cC82xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px65 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cC24 )
<=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(332,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ( A @ cC16 ) )
=> ( A @ cC24 ) )
& ( ( A @ cC24 )
=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ cC16 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(575,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) )
=> ( A @ cC16 ) )
& ( ( A @ cC16 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(104,axiom,
! [A: $i] :
( ( A @ cC136 )
<=> ( ( A @ cC116 )
& ( A @ cC134xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(691,plain,
! [A: $i] :
( ( ( ( A @ cC116 )
& ( A @ cC134xcomp ) )
=> ( A @ cC136 ) )
& ( ( A @ cC136 )
=> ( ( A @ cC116 )
& ( A @ cC134xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px63 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_142) ).
thf(122,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px63 ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ? [B: $i] : ( B @ ( A @ ra_Px63 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ( ( A @ cC56 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_94) ).
thf(659,plain,
! [A: $i] :
( ( ( ( A @ cC56 )
& ( A @ cC34 ) )
=> ( A @ cC58 ) )
& ( ( A @ cC58 )
=> ( ( A @ cC56 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ cC128 )
<=> ? [B: $i] :
( ( B @ cC126 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_31) ).
thf(543,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC126 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC128 ) )
& ( ( A @ cC128 )
=> ? [B: $i] :
( ( B @ cC126 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ cC110 )
<=> ( ( A @ cC108xcomp )
& ( A @ cC102xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(676,plain,
! [A: $i] :
( ( ( ( A @ cC108xcomp )
& ( A @ cC102xcomp ) )
=> ( A @ cC110 ) )
& ( ( A @ cC110 )
=> ( ( A @ cC108xcomp )
& ( A @ cC102xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ cC32 )
<=> ( ( A @ cC30xcomp )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_68) ).
thf(496,plain,
! [A: $i] :
( ( ( ( A @ cC30xcomp )
& ( A @ cC2 ) )
=> ( A @ cC32 ) )
& ( ( A @ cC32 )
=> ( ( A @ cC30xcomp )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ cC124 )
<=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
thf(364,plain,
! [A: $i] :
( ( ( ( A @ cC10xcomp )
& ( A @ cC4 ) )
=> ( A @ cC124 ) )
& ( ( A @ cC124 )
=> ( ( A @ cC10xcomp )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(108,axiom,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ( A @ cC88xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_164) ).
thf(708,plain,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ( A @ cC88xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(729,plain,
$false,
inference(e,[status(thm)],[651,325,710,612,666,352,523,115,683,269,385,550,698,153,719,587,619,211,238,147,634,160,275,650,141,610,256,225,339,476,642,489,193,537,457,173,569,371,503,128,244,205,657,398,674,530,718,412,618,425,180,444,601,711,281,641,391,313,611,419,649,594,726,483,700,626,608,306,438,431,167,658,135,563,675,648,516,707,712,557,470,199,673,627,450,581,218,250,231,319,186,378,510,684,346,287,300,262,405,294,358,635,464,332,575,691,122,659,543,676,496,364,708]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS154+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.47 % Computer : n017.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Fri Sep 25 19:36:47 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.99/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.75/1.30 % [INFO] Parsing done (314ms).
% 2.21/1.31 % [INFO] Running in sequential loop mode.
% 2.97/1.66 % [INFO] eprover registered as external prover.
% 2.97/1.66 % [INFO] Scanning for conjecture ...
% 3.27/1.78 % [INFO] Found a conjecture (or negated_conjecture) and 169 axioms. Running axiom selection ...
% 3.81/1.91 % [INFO] Axiom selection finished. Selected 112 axioms (removed 57 axioms).
% 3.81/2.01 % [INFO] Problem is first-order (TPTP FOF).
% 3.81/2.03 % [INFO] Type checking passed.
% 3.81/2.03 % [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 ...
% 11.33/4.11 % External prover 'e' found a proof!
% 11.33/4.11 % [INFO] Killing All external provers ...
% 11.33/4.11 % Time passed: 3499ms (effective reasoning time: 2799ms)
% 11.33/4.11 % 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)>
% 11.33/4.12 % Axioms used in derivation (112): axiom_44, axiom_7, axiom_55, axiom_136, axiom_108, axiom_10, axiom_40, axiom_22, axiom_152, axiom_163, axiom_125, axiom_49, axiom_168, axiom_15, axiom_121, axiom_73, axiom_141, axiom_130, axiom_21, axiom_157, axiom_19, axiom_99, axiom_110, axiom_147, axiom_146, axiom_151, axiom_129, axiom_158, axiom_89, axiom_43, axiom_27, axiom_162, axiom_137, axiom_143, axiom_32, axiom_6, axiom_60, axiom_144, axiom_118, axiom_132, axiom_126, axiom_155, axiom_78, axiom_54, axiom_100, axiom_148, axiom_16, axiom_159, axiom_74, axiom_122, axiom_81, axiom_3, axiom_96, axiom_140, axiom_68, axiom_154, axiom_20, axiom_165, axiom_115, axiom_156, axiom_42, axiom_31, axiom_1, axiom_57, axiom_138, axiom_127, axiom_61, axiom_28, axiom_150, axiom_53, axiom_167, axiom_80, axiom_71, axiom_8, axiom_97, axiom_17, axiom_161, axiom_149, axiom_75, axiom_5, axiom_166, axiom_93, axiom_123, axiom_41, axiom_128, axiom_109, axiom_164, axiom_52, axiom_139, axiom_153, axiom_0, axiom_29, axiom_11, axiom_117, axiom_160, axiom_56, axiom_30, axiom_23, axiom_18, axiom_131, axiom_113, axiom_9, axiom_98, axiom_142, axiom_14, axiom_124, axiom_72, axiom_120, axiom_4, axiom_37, axiom_135, axiom_94
% 11.33/4.12 % No. of inferences in proof: 228
% 11.33/4.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3499 ms resp. 2799 ms w/o parsing
% 12.12/4.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.12/4.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------