%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS146+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 : n004.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 10.72s 4.58s
% Output : Refutation 11.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 90
% Syntax : Number of formulae : 182 ( 41 unt; 0 typ; 0 def)
% Number of atoms : 680 ( 0 equ; 0 cnn)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1410 ( 188 ~; 0 |; 293 &; 724 @)
% ( 67 <=>; 138 =>; 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 : 77 ( 76 usr; 2 con; 0-2 aty)
% Number of variables : 183 ( 0 ^; 144 !; 39 ?; 183 :)
% 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(cC94_decl,type,
cC94: $i > $o ).
thf(iV822576_decl,type,
iV822576: $i ).
thf(cC58_decl,type,
cC58: $i > $o ).
thf(cC116_decl,type,
cC116: $i > $o ).
thf(cC56_decl,type,
cC56: $i > $o ).
thf(cC110_decl,type,
cC110: $i > $o ).
thf(cC114_decl,type,
cC114: $i > $o ).
thf(cC136_decl,type,
cC136: $i > $o ).
thf(cC80_decl,type,
cC80: $i > $o ).
thf(cC72_decl,type,
cC72: $i > $o ).
thf(cC68_decl,type,
cC68: $i > $o ).
thf(cC70_decl,type,
cC70: $i > $o ).
thf(cC130_decl,type,
cC130: $i > $o ).
thf(cC122_decl,type,
cC122: $i > $o ).
thf(cC128_decl,type,
cC128: $i > $o ).
thf(cC52_decl,type,
cC52: $i > $o ).
thf(cC50_decl,type,
cC50: $i > $o ).
thf(cC32_decl,type,
cC32: $i > $o ).
thf(cTEST_decl,type,
cTEST: $i > $o ).
thf(cC140_decl,type,
cC140: $i > $o ).
thf(cC6_decl,type,
cC6: $i > $o ).
thf(cC30_decl,type,
cC30: $i > $o ).
thf(cC28_decl,type,
cC28: $i > $o ).
thf(cC22_decl,type,
cC22: $i > $o ).
thf(cC14_decl,type,
cC14: $i > $o ).
thf(cC8_decl,type,
cC8: $i > $o ).
thf(cC12_decl,type,
cC12: $i > $o ).
thf(cC48_decl,type,
cC48: $i > $o ).
thf(cC40_decl,type,
cC40: $i > $o ).
thf(cC46_decl,type,
cC46: $i > $o ).
thf(cC84_decl,type,
cC84: $i > $o ).
thf(rR1_decl,type,
rR1: $i > $i > $o ).
thf(cC82_decl,type,
cC82: $i > $o ).
thf(cC124_decl,type,
cC124: $i > $o ).
thf(cC10_decl,type,
cC10: $i > $o ).
thf(cC4_decl,type,
cC4: $i > $o ).
thf(cC2_decl,type,
cC2: $i > $o ).
thf(cC120_decl,type,
cC120: $i > $o ).
thf(cC90_decl,type,
cC90: $i > $o ).
thf(cC88_decl,type,
cC88: $i > $o ).
thf(cC118_decl,type,
cC118: $i > $o ).
thf(cC126_decl,type,
cC126: $i > $o ).
thf(cC34_decl,type,
cC34: $i > $o ).
thf(cC66_decl,type,
cC66: $i > $o ).
thf(cC64_decl,type,
cC64: $i > $o ).
thf(cC20_decl,type,
cC20: $i > $o ).
thf(cC18_decl,type,
cC18: $i > $o ).
thf(cC44_decl,type,
cC44: $i > $o ).
thf(cC86_decl,type,
cC86: $i > $o ).
thf(cC16_decl,type,
cC16: $i > $o ).
thf(cC78_decl,type,
cC78: $i > $o ).
thf(cC62_decl,type,
cC62: $i > $o ).
thf(cC106_decl,type,
cC106: $i > $o ).
thf(cC104_decl,type,
cC104: $i > $o ).
thf(cC38_decl,type,
cC38: $i > $o ).
thf(cC102_decl,type,
cC102: $i > $o ).
thf(cC100_decl,type,
cC100: $i > $o ).
thf(cC76_decl,type,
cC76: $i > $o ).
thf(cC92_decl,type,
cC92: $i > $o ).
thf(cC132_decl,type,
cC132: $i > $o ).
thf(cC42_decl,type,
cC42: $i > $o ).
thf(cC138_decl,type,
cC138: $i > $o ).
thf(cC74_decl,type,
cC74: $i > $o ).
thf(cC60_decl,type,
cC60: $i > $o ).
thf(cC36_decl,type,
cC36: $i > $o ).
thf(cC26_decl,type,
cC26: $i > $o ).
thf(cC24_decl,type,
cC24: $i > $o ).
thf(cC134_decl,type,
cC134: $i > $o ).
thf(cC98_decl,type,
cC98: $i > $o ).
thf(cC108_decl,type,
cC108: $i > $o ).
thf(cC112_decl,type,
cC112: $i > $o ).
thf(cC96_decl,type,
cC96: $i > $o ).
thf(30,axiom,
! [A: $i] :
( ( A @ cC128 )
<=> ? [B: $i] :
( ( B @ cC126 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(288,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)],[30]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cC12 )
<=> ( ~ ( A @ cC4 )
& ( A @ cC10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(428,plain,
! [A: $i] :
( ( ( ~ ( A @ cC4 )
& ( A @ cC10 ) )
=> ( A @ cC12 ) )
& ( ( A @ cC12 )
=> ( ~ ( A @ cC4 )
& ( A @ cC10 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cC84 )
<=> ? [B: $i] :
( ( B @ cC82 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(148,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)],[10]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ( ( A @ cC38 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_35) ).
thf(267,plain,
! [A: $i] :
( ( ( ( A @ cC38 )
& ( A @ cC34 ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ( ( A @ cC38 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cC44 )
<=> ? [B: $i] :
( ( B @ cC42 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_37) ).
thf(386,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)],[44]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cC68 )
<=> ( ( A @ cC66 )
& ( A @ cC60 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_50) ).
thf(351,plain,
! [A: $i] :
( ( ( ( A @ cC66 )
& ( A @ cC60 ) )
=> ( A @ cC68 ) )
& ( ( A @ cC68 )
=> ( ( A @ cC66 )
& ( A @ cC60 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cC62 )
<=> ( ~ ( A @ cC10 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_47) ).
thf(246,plain,
! [A: $i] :
( ( ( ~ ( A @ cC10 )
& ( A @ cC4 ) )
=> ( A @ cC62 ) )
& ( ( A @ cC62 )
=> ( ~ ( A @ cC10 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ cC26 )
<=> ? [B: $i] :
( ( B @ cC24 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_29) ).
thf(365,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)],[41]) ).
thf(80,axiom,
~ ( iV822576 @ cC18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).
thf(555,plain,
~ ( iV822576 @ cC18 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cC28 )
<=> ( ( A @ cC26 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_30) ).
thf(449,plain,
! [A: $i] :
( ( ( ( A @ cC26 )
& ~ ( A @ cC16 ) )
=> ( A @ cC28 ) )
& ( ( A @ cC28 )
=> ( ( A @ cC26 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cTEST )
<=> ( ( A @ cC6 )
& ( A @ cC140 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).
thf(120,plain,
! [A: $i] :
( ( ( ( A @ cC6 )
& ( A @ cC140 ) )
=> ( A @ cTEST ) )
& ( ( A @ cTEST )
=> ( ( A @ cC6 )
& ( A @ cC140 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cC134 )
<=> ( ( A @ cC132 )
& ~ ( A @ cC130 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(379,plain,
! [A: $i] :
( ( ( ( A @ cC132 )
& ~ ( A @ cC130 ) )
=> ( A @ cC134 ) )
& ( ( A @ cC134 )
=> ( ( A @ cC132 )
& ~ ( A @ cC130 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(74,axiom,
~ ( iV822576 @ cC96 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_76) ).
thf(533,plain,
~ ( iV822576 @ cC96 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ~ ( A @ cC98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_81) ).
thf(472,plain,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ~ ( A @ cC98 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cC36 )
<=> ( ( A @ cC4 )
& ~ ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(372,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ~ ( A @ cC34 ) )
=> ( A @ cC36 ) )
& ( ( A @ cC36 )
=> ( ( A @ cC4 )
& ~ ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cC8 )
<=> ( ~ ( A @ cC2 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(344,plain,
! [A: $i] :
( ( ( ~ ( A @ cC2 )
& ( A @ cC4 ) )
=> ( A @ cC8 ) )
& ( ( A @ cC8 )
=> ( ~ ( A @ cC2 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cC70 )
<=> ( ( A @ cC2 )
& ~ ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(421,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ~ ( A @ cC4 ) )
=> ( A @ cC70 ) )
& ( ( A @ cC70 )
=> ( ( A @ cC2 )
& ~ ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ cC42 )
<=> ( ( A @ cC4 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_36) ).
thf(316,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC34 ) )
=> ( A @ cC42 ) )
& ( ( A @ cC42 )
=> ( ( A @ cC4 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ cC94 )
<=> ( ~ ( A @ cC92 )
& ~ ( A @ cC86 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_64) ).
thf(475,plain,
! [A: $i] :
( ( ( ~ ( A @ cC92 )
& ~ ( A @ cC86 ) )
=> ( A @ cC94 ) )
& ( ( A @ cC94 )
=> ( ~ ( A @ cC92 )
& ~ ( A @ cC86 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cC130 )
<=> ( ( A @ cC128 )
& ( A @ cC122 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(106,plain,
! [A: $i] :
( ( ( ( A @ cC128 )
& ( A @ cC122 ) )
=> ( A @ cC130 ) )
& ( ( A @ cC130 )
=> ( ( A @ cC128 )
& ( A @ cC122 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(85,axiom,
iV822576 @ cC4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_75) ).
thf(574,plain,
iV822576 @ cC4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cC46 )
<=> ( ~ ( A @ cC34 )
& ( A @ cC44 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_38) ).
thf(211,plain,
! [A: $i] :
( ( ( ~ ( A @ cC34 )
& ( A @ cC44 ) )
=> ( A @ cC46 ) )
& ( ( A @ cC46 )
=> ( ~ ( A @ cC34 )
& ( A @ cC44 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cC120 )
<=> ( ( A @ cC118 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(253,plain,
! [A: $i] :
( ( ( ( A @ cC118 )
& ( A @ cC34 ) )
=> ( A @ cC120 ) )
& ( ( A @ cC120 )
=> ( ( A @ cC118 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(72,axiom,
~ ( iV822576 @ cC112 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_87) ).
thf(529,plain,
~ ( iV822576 @ cC112 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ cC138 )
<=> ? [B: $i] :
( ~ ( B @ cC136 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(546,plain,
! [A: $i] :
( ( ? [B: $i] :
( ~ ( B @ cC136 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC138 ) )
& ( ( A @ cC138 )
=> ? [B: $i] :
( ~ ( B @ cC136 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cC92 )
<=> ( ~ ( A @ cC16 )
& ( A @ cC90 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_63) ).
thf(302,plain,
! [A: $i] :
( ( ( ~ ( A @ cC16 )
& ( A @ cC90 ) )
=> ( A @ cC92 ) )
& ( ( A @ cC92 )
=> ( ~ ( A @ cC16 )
& ( A @ cC90 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cC106 )
<=> ? [B: $i] :
( ( B @ cC104 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(260,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)],[26]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ? [B: $i] :
( ( B @ cC98 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(407,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)],[47]) ).
thf(1,conjecture,
( ( iV822576 @ cC80 )
& ( iV822576 @ cC136 )
& ( iV822576 @ cC114 )
& ( iV822576 @ cC110 )
& ( iV822576 @ cC56 )
& ( iV822576 @ cC116 )
& ( iV822576 @ cC58 )
& ( iV822576 @ cowlThing )
& ( iV822576 @ cC94 )
& ! [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,
~ ( ( iV822576 @ cC80 )
& ( iV822576 @ cC136 )
& ( iV822576 @ cC114 )
& ( iV822576 @ cC110 )
& ( iV822576 @ cC56 )
& ( iV822576 @ cC116 )
& ( iV822576 @ cC58 )
& ( iV822576 @ cowlThing )
& ( iV822576 @ cC94 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(92,plain,
~ ( ( iV822576 @ cC80 )
& ( iV822576 @ cC136 )
& ( iV822576 @ cC114 )
& ( iV822576 @ cC110 )
& ( iV822576 @ cC56 )
& ( iV822576 @ cC116 )
& ( iV822576 @ cC58 )
& ( iV822576 @ cowlThing )
& ( iV822576 @ cC94 )
& ! [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(61,axiom,
! [A: $i] :
( ( A @ cC136 )
<=> ( ~ ( A @ cC134 )
& ( A @ cC116 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(484,plain,
! [A: $i] :
( ( ( ~ ( A @ cC134 )
& ( A @ cC116 ) )
=> ( A @ cC136 ) )
& ( ( A @ cC136 )
=> ( ~ ( A @ cC134 )
& ( A @ cC116 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cC66 )
<=> ? [B: $i] :
( ( B @ cC64 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_49) ).
thf(197,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)],[17]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ cC108 )
<=> ( ( A @ cC106 )
& ~ ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(435,plain,
! [A: $i] :
( ( ( ( A @ cC106 )
& ~ ( A @ cC34 ) )
=> ( A @ cC108 ) )
& ( ( A @ cC108 )
=> ( ( A @ cC106 )
& ~ ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(63,axiom,
~ ( iV822576 @ cC76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).
thf(493,plain,
~ ( iV822576 @ cC76 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cC64 )
<=> ( ~ ( A @ cC34 )
& ( A @ cC62 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(456,plain,
! [A: $i] :
( ( ( ~ ( A @ cC34 )
& ( A @ cC62 ) )
=> ( A @ cC64 ) )
& ( ( A @ cC64 )
=> ( ~ ( A @ cC34 )
& ( A @ cC62 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(88,axiom,
~ ( iV822576 @ cC78 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_88) ).
thf(583,plain,
~ ( iV822576 @ cC78 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(68,axiom,
~ ( iV822576 @ cC86 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).
thf(522,plain,
~ ( iV822576 @ cC86 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cC122 )
<=> ? [B: $i] :
( ( B @ cC120 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(169,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)],[13]) ).
thf(91,axiom,
! [A: $i] :
( ( A @ cC96 )
<=> ( ( A @ cC2 )
& ~ ( A @ cC94 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_65) ).
thf(593,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ~ ( A @ cC94 ) )
=> ( A @ cC96 ) )
& ( ( A @ cC96 )
=> ( ( A @ cC2 )
& ~ ( A @ cC94 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cC48 )
<=> ( ~ ( A @ cC46 )
& ~ ( A @ cC40 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_39) ).
thf(141,plain,
! [A: $i] :
( ( ( ~ ( A @ cC46 )
& ~ ( A @ cC40 ) )
=> ( A @ cC48 ) )
& ( ( A @ cC48 )
=> ( ~ ( A @ cC46 )
& ~ ( A @ cC40 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cC78 )
<=> ( ( A @ cC10 )
& ~ ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_55) ).
thf(225,plain,
! [A: $i] :
( ( ( ( A @ cC10 )
& ~ ( A @ cC4 ) )
=> ( A @ cC78 ) )
& ( ( A @ cC78 )
=> ( ( A @ cC10 )
& ~ ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,axiom,
~ ( iV822576 @ cC134 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_71) ).
thf(537,plain,
~ ( iV822576 @ cC134 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(70,axiom,
~ ( iV822576 @ cC108 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_79) ).
thf(526,plain,
~ ( iV822576 @ cC108 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cC88 )
<=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_61) ).
thf(393,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ( A @ cC16 ) )
=> ( A @ cC88 ) )
& ( ( A @ cC88 )
=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ cC56 )
<=> ( ~ ( A @ cC10 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_43) ).
thf(515,plain,
! [A: $i] :
( ( ( ~ ( A @ cC10 )
& ( A @ cC4 ) )
=> ( A @ cC56 ) )
& ( ( A @ cC56 )
=> ( ~ ( A @ cC10 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cC14 )
<=> ( ~ ( A @ cC12 )
& ~ ( A @ cC8 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_23) ).
thf(134,plain,
! [A: $i] :
( ( ( ~ ( A @ cC12 )
& ~ ( A @ cC8 ) )
=> ( A @ cC14 ) )
& ( ( A @ cC14 )
=> ( ~ ( A @ cC12 )
& ~ ( A @ cC8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ cC110 )
<=> ( ~ ( A @ cC108 )
& ~ ( A @ cC102 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(508,plain,
! [A: $i] :
( ( ( ~ ( A @ cC108 )
& ~ ( A @ cC102 ) )
=> ( A @ cC110 ) )
& ( ( A @ cC110 )
=> ( ~ ( A @ cC108 )
& ~ ( A @ cC102 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(82,axiom,
~ ( iV822576 @ cC132 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_69) ).
thf(558,plain,
~ ( iV822576 @ cC132 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ cC80 )
<=> ( ~ ( A @ cC76 )
& ~ ( A @ cC78 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(586,plain,
! [A: $i] :
( ( ( ~ ( A @ cC76 )
& ~ ( A @ cC78 ) )
=> ( A @ cC80 ) )
& ( ( A @ cC80 )
=> ( ~ ( A @ cC76 )
& ~ ( A @ cC78 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cC90 )
<=> ? [B: $i] :
( ( B @ cC88 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(176,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)],[14]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cC102 )
<=> ( ( A @ cC100 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(281,plain,
! [A: $i] :
( ( ( ( A @ cC100 )
& ( A @ cC34 ) )
=> ( A @ cC102 ) )
& ( ( A @ cC102 )
=> ( ( A @ cC100 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ cC20 )
<=> ? [B: $i] :
( ( B @ cC18 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_26) ).
thf(204,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)],[18]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cC52 )
<=> ( ~ ( A @ cC32 )
& ~ ( A @ cC50 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_41) ).
thf(113,plain,
! [A: $i] :
( ( ( ~ ( A @ cC32 )
& ~ ( A @ cC50 ) )
=> ( A @ cC52 ) )
& ( ( A @ cC52 )
=> ( ~ ( A @ cC32 )
& ~ ( A @ cC50 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ cC50 )
<=> ( ~ ( A @ cC48 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_40) ).
thf(274,plain,
! [A: $i] :
( ( ( ~ ( A @ cC48 )
& ( A @ cC4 ) )
=> ( A @ cC50 ) )
& ( ( A @ cC50 )
=> ( ~ ( A @ cC48 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ cC114 )
<=> ( ~ ( A @ cC112 )
& ~ ( A @ cC96 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(567,plain,
! [A: $i] :
( ( ( ~ ( A @ cC112 )
& ~ ( A @ cC96 ) )
=> ( A @ cC114 ) )
& ( ( A @ cC114 )
=> ( ~ ( A @ cC112 )
& ~ ( A @ cC96 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(75,axiom,
~ ( iV822576 @ cC100 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).
thf(535,plain,
~ ( iV822576 @ cC100 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cC140 )
<=> ( ( A @ cC74 )
& ~ ( A @ cC138 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_24) ).
thf(323,plain,
! [A: $i] :
( ( ( ( A @ cC74 )
& ~ ( A @ cC138 ) )
=> ( A @ cC140 ) )
& ( ( A @ cC140 )
=> ( ( A @ cC74 )
& ~ ( A @ cC138 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cC124 )
<=> ( ( A @ cC4 )
& ~ ( A @ cC10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(155,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ~ ( A @ cC10 ) )
=> ( A @ cC124 ) )
& ( ( A @ cC124 )
=> ( ( A @ cC4 )
& ~ ( A @ cC10 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cC104 )
<=> ( ( A @ cC4 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(330,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC34 ) )
=> ( A @ cC104 ) )
& ( ( A @ cC104 )
=> ( ( A @ cC4 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(79,axiom,
~ ( iV822576 @ cC90 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_82) ).
thf(553,plain,
~ ( iV822576 @ cC90 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cC6 )
<=> ( ~ ( A @ cC4 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_45) ).
thf(162,plain,
! [A: $i] :
( ( ( ~ ( A @ cC4 )
& ( A @ cC2 ) )
=> ( A @ cC6 ) )
& ( ( A @ cC6 )
=> ( ~ ( A @ cC4 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ~ ( A @ cC82 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_90) ).
thf(531,plain,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ~ ( A @ cC82 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(81,axiom,
iV822576 @ cC2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_89) ).
thf(557,plain,
iV822576 @ cC2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cC76 )
<=> ( ( A @ cC4 )
& ~ ( A @ cC2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_54) ).
thf(295,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ~ ( A @ cC2 ) )
=> ( A @ cC76 ) )
& ( ( A @ cC76 )
=> ( ( A @ cC4 )
& ~ ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cC18 )
<=> ( ( A @ cC2 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(414,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ~ ( A @ cC16 ) )
=> ( A @ cC18 ) )
& ( ( A @ cC18 )
=> ( ( A @ cC2 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(89,axiom,
iV822576 @ cowlThing,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_80) ).
thf(585,plain,
iV822576 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ( ( A @ cC4 )
& ~ ( A @ cC110 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(463,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ~ ( A @ cC110 ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ( ( A @ cC4 )
& ~ ( A @ cC110 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cC30 )
<=> ( ~ ( A @ cC22 )
& ~ ( A @ cC28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_31) ).
thf(127,plain,
! [A: $i] :
( ( ( ~ ( A @ cC22 )
& ~ ( A @ cC28 ) )
=> ( A @ cC30 ) )
& ( ( A @ cC30 )
=> ( ~ ( A @ cC22 )
& ~ ( A @ cC28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,axiom,
~ ( iV822576 @ cC92 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_78) ).
thf(470,plain,
~ ( iV822576 @ cC92 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cC72 )
<=> ( ( A @ cC70 )
& ~ ( A @ cC68 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_52) ).
thf(99,plain,
! [A: $i] :
( ( ( ( A @ cC70 )
& ~ ( A @ cC68 ) )
=> ( A @ cC72 ) )
& ( ( A @ cC72 )
=> ( ( A @ cC70 )
& ~ ( A @ cC68 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ cC60 )
<=> ? [B: $i] :
( ( B @ cC58 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_46) ).
thf(539,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)],[77]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ~ ( A @ cC88 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_73) ).
thf(482,plain,
! [A: $i] :
( ( A @ ( iV822576 @ rR1 ) )
=> ~ ( A @ cC88 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(64,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(495,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ( ( A @ cC84 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_60) ).
thf(218,plain,
! [A: $i] :
( ( ( ( A @ cC84 )
& ( A @ cC16 ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ( ( A @ cC84 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(69,axiom,
~ ( iV822576 @ cC84 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_68) ).
thf(524,plain,
~ ( iV822576 @ cC84 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(87,axiom,
~ ( iV822576 @ cC102 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_70) ).
thf(581,plain,
~ ( iV822576 @ cC102 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ cC126 )
<=> ( ( A @ cC124 )
& ~ ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(190,plain,
! [A: $i] :
( ( ( ( A @ cC124 )
& ~ ( A @ cC34 ) )
=> ( A @ cC126 ) )
& ( ( A @ cC126 )
=> ( ( A @ cC124 )
& ~ ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cC118 )
<=> ( ( A @ cC4 )
& ~ ( A @ cC10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(183,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ~ ( A @ cC10 ) )
=> ( A @ cC118 ) )
& ( ( A @ cC118 )
=> ( ( A @ cC4 )
& ~ ( A @ cC10 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cC32 )
<=> ( ( A @ cC2 )
& ~ ( A @ cC30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(239,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ~ ( A @ cC30 ) )
=> ( A @ cC32 ) )
& ( ( A @ cC32 )
=> ( ( A @ cC2 )
& ~ ( A @ cC30 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cC38 )
<=> ? [B: $i] :
( ( B @ cC36 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_34) ).
thf(358,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)],[40]) ).
thf(58,axiom,
iV822576 @ cC16,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_72) ).
thf(474,plain,
iV822576 @ cC16,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ( ~ ( A @ cC34 )
& ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).
thf(400,plain,
! [A: $i] :
( ( ( ~ ( A @ cC34 )
& ( A @ cC4 ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ( ~ ( A @ cC34 )
& ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(86,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(575,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(71,axiom,
iV822576 @ cC34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_74) ).
thf(528,plain,
iV822576 @ cC34,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cC24 )
<=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_28) ).
thf(442,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ( A @ cC16 ) )
=> ( A @ cC24 ) )
& ( ( A @ cC24 )
=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ( ( A @ cC56 )
& ( A @ cC34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(501,plain,
! [A: $i] :
( ( ( ( A @ cC56 )
& ( A @ cC34 ) )
=> ( A @ cC58 ) )
& ( ( A @ cC58 )
=> ( ( A @ cC56 )
& ( A @ cC34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cC22 )
<=> ( ( A @ cC20 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(337,plain,
! [A: $i] :
( ( ( ( A @ cC20 )
& ( A @ cC16 ) )
=> ( A @ cC22 ) )
& ( ( A @ cC22 )
=> ( ( A @ cC20 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cC132 )
<=> ( ( A @ cC2 )
& ~ ( A @ cC4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(309,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ~ ( A @ cC4 ) )
=> ( A @ cC132 ) )
& ( ( A @ cC132 )
=> ( ( A @ cC2 )
& ~ ( A @ cC4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(83,axiom,
! [A: $i] :
( ( A @ cC116 )
<=> ( ( A @ cC80 )
& ( A @ cC114 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(560,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(62,axiom,
~ ( iV822576 @ cC10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_84) ).
thf(491,plain,
~ ( iV822576 @ cC10 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cC82 )
<=> ( ( A @ cC2 )
& ~ ( A @ cC16 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_58) ).
thf(232,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ~ ( A @ cC16 ) )
=> ( A @ cC82 ) )
& ( ( A @ cC82 )
=> ( ( A @ cC2 )
& ~ ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(600,plain,
$false,
inference(e,[status(thm)],[288,428,148,267,386,351,246,365,555,449,120,379,533,472,372,344,421,316,475,106,574,211,253,529,546,302,260,407,92,484,197,435,493,456,583,522,169,593,141,225,537,526,393,515,134,508,558,586,176,281,204,113,274,567,535,323,155,330,553,162,531,557,295,414,585,463,127,470,99,539,482,495,218,524,581,190,183,239,358,474,400,575,528,442,501,337,309,560,491,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS146+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.13 % 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
% 0.25/0.49 % Computer : n004.cluster.edu
% 0.25/0.49 % Model : x86_64 x86_64
% 0.25/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.49 % Memory : 8046.5625MB
% 0.25/0.49 % OS : Linux 6.8.0-71-generic
% 0.25/0.49 % CPULimit : 300
% 0.25/0.49 % WCLimit : 300
% 0.25/0.49 % DateTime : Fri Sep 25 19:41:08 UTC 2026
% 0.25/0.50 % CPUTime :
% 0.25/0.50 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
% 1.23/1.18 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.00/1.53 % [INFO] Parsing done (350ms).
% 2.00/1.56 % [INFO] Running in sequential loop mode.
% 3.06/2.09 % [INFO] eprover registered as external prover.
% 3.06/2.10 % [INFO] Scanning for conjecture ...
% 3.45/2.23 % [INFO] Found a conjecture (or negated_conjecture) and 91 axioms. Running axiom selection ...
% 3.95/2.40 % [INFO] Axiom selection finished. Selected 89 axioms (removed 2 axioms).
% 4.19/2.52 % [INFO] Problem is first-order (TPTP FOF).
% 4.19/2.54 % [INFO] Type checking passed.
% 4.19/2.55 % [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 ...
% 10.72/4.58 % External prover 'e' found a proof!
% 10.72/4.58 % [INFO] Killing All external provers ...
% 10.72/4.58 % Time passed: 3874ms (effective reasoning time: 3010ms)
% 10.72/4.58 % 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)>
% 10.72/4.58 % Axioms used in derivation (89): axiom_64, axiom_75, axiom_7, axiom_26, axiom_55, axiom_88, axiom_33, axiom_10, axiom_40, axiom_22, axiom_59, axiom_77, axiom_44, axiom_49, axiom_15, axiom_73, axiom_67, axiom_69, axiom_51, axiom_21, axiom_19, axiom_84, axiom_63, axiom_38, axiom_2, axiom_79, axiom_89, axiom_43, axiom_27, axiom_32, axiom_6, axiom_60, axiom_78, axiom_54, axiom_16, axiom_81, axiom_50, axiom_74, axiom_3, axiom_68, axiom_46, axiom_20, axiom_85, axiom_70, axiom_31, axiom_24, axiom_90, axiom_1, axiom_57, axiom_61, axiom_35, axiom_28, axiom_65, axiom_36, axiom_39, axiom_80, axiom_71, axiom_8, axiom_17, axiom_86, axiom_5, axiom_47, axiom_13, axiom_82, axiom_41, axiom_25, axiom_76, axiom_52, axiom_34, axiom_0, axiom_58, axiom_62, axiom_45, axiom_29, axiom_11, axiom_56, axiom_30, axiom_23, axiom_18, axiom_87, axiom_12, axiom_9, axiom_48, axiom_83, axiom_14, axiom_72, axiom_4, axiom_66, axiom_37
% 10.72/4.58 % No. of inferences in proof: 182
% 10.72/4.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3874 ms resp. 3010 ms w/o parsing
% 11.74/4.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.74/4.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------