%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS156+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 : n018.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 07:44:47 AM UTC 2026
% Result : Theorem 5.77s 8.06s
% Output : Refutation 6.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 56
% Syntax : Number of formulae : 114 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 391 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 772 ( 20 ~; 0 |; 154 &; 475 @)
% ( 39 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 71 usr; 4 con; 0-2 aty)
% Number of variables : 165 ( 0 ^; 90 !; 75 ?; 165 :)
% 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(cC116_decl,type,
cC116: $i > $o ).
thf(iV5475_decl,type,
iV5475: $i ).
thf(cC140_decl,type,
cC140: $i > $o ).
thf(cC138_decl,type,
cC138: $i > $o ).
thf(cC70_decl,type,
cC70: $i > $o ).
thf(cC2_decl,type,
cC2: $i > $o ).
thf(cC68_decl,type,
cC68: $i > $o ).
thf(cC6_decl,type,
cC6: $i > $o ).
thf(cC4_decl,type,
cC4: $i > $o ).
thf(cC78_decl,type,
cC78: $i > $o ).
thf(cC76_decl,type,
cC76: $i > $o ).
thf(cC114_decl,type,
cC114: $i > $o ).
thf(ra_Px34_decl,type,
ra_Px34: $i > $i > $o ).
thf(cC92_decl,type,
cC92: $i > $o ).
thf(cC90_decl,type,
cC90: $i > $o ).
thf(cC126_decl,type,
cC126: $i > $o ).
thf(cC124_decl,type,
cC124: $i > $o ).
thf(cC100_decl,type,
cC100: $i > $o ).
thf(cC98xcomp_decl,type,
cC98xcomp: $i > $o ).
thf(cC94_decl,type,
cC94: $i > $o ).
thf(cC52_decl,type,
cC52: $i > $o ).
thf(cC50_decl,type,
cC50: $i > $o ).
thf(cC18_decl,type,
cC18: $i > $o ).
thf(cC16_decl,type,
cC16: $i > $o ).
thf(cC112_decl,type,
cC112: $i > $o ).
thf(ra_Px43_decl,type,
ra_Px43: $i > $i > $o ).
thf(cC72_decl,type,
cC72: $i > $o ).
thf(rR1_decl,type,
rR1: $i > $i > $o ).
thf(iV5478_decl,type,
iV5478: $i ).
thf(cC12xcomp_decl,type,
cC12xcomp: $i > $o ).
thf(cC36_decl,type,
cC36: $i > $o ).
thf(cC34_decl,type,
cC34: $i > $o ).
thf(cC118xcomp_decl,type,
cC118xcomp: $i > $o ).
thf(cC110xcomp_decl,type,
cC110xcomp: $i > $o ).
thf(cC80_decl,type,
cC80: $i > $o ).
thf(cC130xcomp_decl,type,
cC130xcomp: $i > $o ).
thf(cC34xcomp_decl,type,
cC34xcomp: $i > $o ).
thf(cC114xcomp_decl,type,
cC114xcomp: $i > $o ).
thf(cC120_decl,type,
cC120: $i > $o ).
thf(cC46_decl,type,
cC46: $i > $o ).
thf(cC44xcomp_decl,type,
cC44xcomp: $i > $o ).
thf(cC128_decl,type,
cC128: $i > $o ).
thf(cC102_decl,type,
cC102: $i > $o ).
thf(cC28xcomp_decl,type,
cC28xcomp: $i > $o ).
thf(cC54_decl,type,
cC54: $i > $o ).
thf(cC106_decl,type,
cC106: $i > $o ).
thf(cC104_decl,type,
cC104: $i > $o ).
thf(cC82_decl,type,
cC82: $i > $o ).
thf(cC80xcomp_decl,type,
cC80xcomp: $i > $o ).
thf(cC30xcomp_decl,type,
cC30xcomp: $i > $o ).
thf(cC112xcomp_decl,type,
cC112xcomp: $i > $o ).
thf(cC8_decl,type,
cC8: $i > $o ).
thf(cC58_decl,type,
cC58: $i > $o ).
thf(cC56_decl,type,
cC56: $i > $o ).
thf(cC20_decl,type,
cC20: $i > $o ).
thf(cC132_decl,type,
cC132: $i > $o ).
thf(cC130_decl,type,
cC130: $i > $o ).
thf(cC24_decl,type,
cC24: $i > $o ).
thf(cC22_decl,type,
cC22: $i > $o ).
thf(cC10xcomp_decl,type,
cC10xcomp: $i > $o ).
thf(cC14_decl,type,
cC14: $i > $o ).
thf(cC12_decl,type,
cC12: $i > $o ).
thf(cC136_decl,type,
cC136: $i > $o ).
thf(cC134_decl,type,
cC134: $i > $o ).
thf(cTOP_decl,type,
cTOP: $i > $o ).
thf(cTEST_decl,type,
cTEST: $i > $o ).
thf(iV5476_decl,type,
iV5476: $i ).
thf(24,axiom,
! [A: $i] :
( ( A @ cC120 )
<=> ? [B: $i] :
( ( B @ cC118xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(174,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC118xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC120 ) )
& ( ( A @ cC120 )
=> ? [B: $i] :
( ( B @ cC118xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cC72 )
<=> ? [B: $i] :
( ( B @ cC70 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_106) ).
thf(133,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC70 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC72 ) )
& ( ( A @ cC72 )
=> ? [B: $i] :
( ( B @ cC70 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ ( iV5475 @ rR1 ) )
=> ( A @ cC112xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_132) ).
thf(311,plain,
! [A: $i] :
( ( A @ ( iV5475 @ rR1 ) )
=> ( A @ cC112xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(21,axiom,
iV5478 @ cC130xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_141) ).
thf(166,plain,
iV5478 @ cC130xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cC140 )
<=> ( ( A @ cC138 )
& ( A @ cTOP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(304,plain,
! [A: $i] :
( ( ( ( A @ cC138 )
& ( A @ cTOP ) )
=> ( A @ cC140 ) )
& ( ( A @ cC140 )
=> ( ( A @ cC138 )
& ( A @ cTOP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(55,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(332,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cC82 )
<=> ? [B: $i] :
( ( B @ cC80xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_116) ).
thf(232,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC80xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC82 ) )
& ( ( A @ cC82 )
=> ? [B: $i] :
( ( B @ cC80xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cC18 )
<=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(120,plain,
! [A: $i] :
( ( ( ( A @ cC2 )
& ( A @ cC16 ) )
=> ( A @ cC18 ) )
& ( ( A @ cC18 )
=> ( ( A @ cC2 )
& ( A @ cC16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ ( iV5478 @ rR1 ) )
=> ( A @ cC28xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_144) ).
thf(202,plain,
! [A: $i] :
( ( A @ ( iV5478 @ rR1 ) )
=> ( A @ cC28xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(325,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ? [B: $i] :
( ( B @ cC110xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(152,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC110xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ? [B: $i] :
( ( B @ cC110xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(50,axiom,
iV5475 @ cC114xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_130) ).
thf(316,plain,
iV5475 @ cC114xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ( ( A @ cC94 )
& ( A @ cC98xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(106,plain,
! [A: $i] :
( ( ( ( A @ cC94 )
& ( A @ cC98xcomp ) )
=> ( A @ cC100 ) )
& ( ( A @ cC100 )
=> ( ( A @ cC94 )
& ( A @ cC98xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cC114 )
<=> ? [B: $i] :
( ( B @ cC112 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(211,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)],[30]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ? [B: $i] :
( ( B @ cC56 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_94) ).
thf(253,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)],[37]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cC20 )
<=> ? [B: $i] :
( ( B @ cC18 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(260,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)],[38]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cC138 )
<=> ? [B: $i] :
( ( B @ cC136 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(297,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)],[44]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cC92 )
<=> ( ( A @ cC90 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_121) ).
thf(92,plain,
! [A: $i] :
( ( ( ( A @ cC90 )
& ( A @ cC2 ) )
=> ( A @ cC92 ) )
& ( ( A @ cC92 )
=> ( ( A @ cC90 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cC70 )
<=> ( ( A @ cC68 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_105) ).
thf(65,plain,
! [A: $i] :
( ( ( ( A @ cC68 )
& ( A @ cC2 ) )
=> ( A @ cC70 ) )
& ( ( A @ cC70 )
=> ( ( A @ cC68 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(51,axiom,
iV5476 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_134) ).
thf(317,plain,
iV5476 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cC128 )
<=> ? [B: $i] :
( ( B @ cC126 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(188,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)],[26]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( iV5478 @ rR1 ) )
=> ( A @ cC2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_140) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( iV5478 @ rR1 ) )
=> ( A @ cC2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cC106 )
<=> ? [B: $i] :
( ( B @ cC104 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(225,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)],[32]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ cC116 )
<=> ( ( A @ cC114xcomp )
& ( A @ cTOP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(339,plain,
! [A: $i] :
( ( ( ( A @ cC114xcomp )
& ( A @ cTOP ) )
=> ( A @ cC116 ) )
& ( ( A @ cC116 )
=> ( ( A @ cC114xcomp )
& ( A @ cTOP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ ( iV5478 @ rR1 ) )
=> ( A @ cC10xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_143) ).
thf(281,plain,
! [A: $i] :
( ( A @ ( iV5478 @ rR1 ) )
=> ( A @ cC10xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cC94 )
<=> ? [B: $i] :
( ( B @ cC92 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_122) ).
thf(204,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)],[29]) ).
thf(47,axiom,
iV5475 @ cTEST,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_131) ).
thf(313,plain,
iV5475 @ cTEST,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cC36 )
<=> ? [B: $i] :
( ( B @ cC34 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_77) ).
thf(144,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC34 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC36 ) )
& ( ( A @ cC36 )
=> ? [B: $i] :
( ( B @ cC34 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cC46 )
<=> ? [B: $i] :
( ( B @ cC44xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_86) ).
thf(181,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC44xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC46 ) )
& ( ( A @ cC46 )
=> ? [B: $i] :
( ( B @ cC44xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cC114 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(86,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px34 ) )
=> ( A @ cC114 ) )
& ( ( A @ cC114 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cC80 )
<=> ? [B: $i] :
( ( B @ cC78 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_114) ).
thf(159,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC78 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC80 ) )
& ( ( A @ cC80 )
=> ? [B: $i] :
( ( B @ cC78 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cC52 )
<=> ( ( A @ cC50 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_89) ).
thf(113,plain,
! [A: $i] :
( ( ( ( A @ cC50 )
& ( A @ cC2 ) )
=> ( A @ cC52 ) )
& ( ( A @ cC52 )
=> ( ( A @ cC50 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cC24 )
<=> ? [B: $i] :
( ( B @ cC22 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(274,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC22 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC24 ) )
& ( ( A @ cC24 )
=> ? [B: $i] :
( ( B @ cC22 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cTEST )
<=> ( ( A @ cC116 )
& ( A @ cC140 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_127) ).
thf(318,plain,
! [A: $i] :
( ( ( ( A @ cC116 )
& ( A @ cC140 ) )
=> ( A @ cTEST ) )
& ( ( A @ cTEST )
=> ( ( A @ cC116 )
& ( A @ cC140 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(14,axiom,
iV5478 @ cC2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_137) ).
thf(140,plain,
iV5478 @ cC2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cC112xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px43 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(240,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px43 ) )
=> ( A @ cC112xcomp ) )
& ( ( A @ cC112xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px43 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cC132 )
<=> ? [B: $i] :
( ( B @ cC130 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(267,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC130 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC132 ) )
& ( ( A @ cC132 )
=> ? [B: $i] :
( ( B @ cC130 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(22,axiom,
iV5478 @ cC34xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_142) ).
thf(167,plain,
iV5478 @ cC34xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(54,axiom,
iV5476 @ ( iV5475 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_133) ).
thf(331,plain,
iV5476 @ ( iV5475 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px43 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(127,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px43 ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px43 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,axiom,
iV5478 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_138) ).
thf(338,plain,
iV5478 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cC6 )
<=> ( ( A @ cC4 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_97) ).
thf(72,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC2 ) )
=> ( A @ cC6 ) )
& ( ( A @ cC6 )
=> ( ( A @ cC4 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,axiom,
iV5475 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_129) ).
thf(314,plain,
iV5475 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(16,axiom,
iV5478 @ cC12xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_135) ).
thf(143,plain,
iV5478 @ cC12xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cC126 )
<=> ( ( A @ cC124 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_35) ).
thf(99,plain,
! [A: $i] :
( ( ( ( A @ cC124 )
& ( A @ cC2 ) )
=> ( A @ cC126 ) )
& ( ( A @ cC126 )
=> ( ( A @ cC124 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cC54 )
<=> ? [B: $i] :
( ( B @ cC52 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_91) ).
thf(218,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)],[31]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cC8 )
<=> ? [B: $i] :
( ( B @ cC6 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_110) ).
thf(246,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)],[36]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cC136 )
<=> ? [B: $i] :
( ( B @ cC134 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
thf(290,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC134 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC136 ) )
& ( ( A @ cC136 )
=> ? [B: $i] :
( ( B @ cC134 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(1,conjecture,
( ( iV5475 @ cC138 )
& ( iV5475 @ cowlThing )
& ( iV5475 @ cC140 )
& ( iV5475 @ cC116 )
& ! [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,
~ ( ( iV5475 @ cC138 )
& ( iV5475 @ cowlThing )
& ( iV5475 @ cC140 )
& ( iV5475 @ cC116 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(58,plain,
~ ( ( iV5475 @ cC138 )
& ( iV5475 @ cowlThing )
& ( iV5475 @ cC140 )
& ( iV5475 @ cC116 )
& ! [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(18,axiom,
iV5478 @ cC118xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_139) ).
thf(151,plain,
iV5478 @ cC118xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(49,axiom,
iV5475 @ cTOP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_128) ).
thf(315,plain,
iV5475 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cC114xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(168,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px34 ) )
=> ( A @ cC114xcomp ) )
& ( ( A @ cC114xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(34,axiom,
iV5478 @ cC30xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_136) ).
thf(239,plain,
iV5478 @ cC30xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cC78 )
<=> ( ( A @ cC76 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_109) ).
thf(79,plain,
! [A: $i] :
( ( ( ( A @ cC76 )
& ( A @ cC2 ) )
=> ( A @ cC78 ) )
& ( ( A @ cC78 )
=> ( ( A @ cC76 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cC102 )
<=> ? [B: $i] :
( ( B @ cC100 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(195,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC100 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC102 ) )
& ( ( A @ cC102 )
=> ? [B: $i] :
( ( B @ cC100 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cC14 )
<=> ? [B: $i] :
( ( B @ cC12 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
thf(283,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC12 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC14 ) )
& ( ( A @ cC14 )
=> ? [B: $i] :
( ( B @ cC12 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(346,plain,
$false,
inference(e,[status(thm)],[174,133,311,166,304,332,232,120,202,325,152,316,106,211,253,260,297,92,65,317,188,141,225,339,281,204,313,144,181,86,159,113,274,318,140,240,267,167,331,127,338,72,314,143,99,218,246,290,58,151,315,168,239,79,195,283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS156+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % 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
% 0.12/5.41 % Computer : n018.cluster.edu
% 0.12/5.41 % Model : x86_64 x86_64
% 0.12/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.41 % Memory : 8046.5625MB
% 0.12/5.41 % OS : Linux 6.8.0-71-generic
% 0.12/5.41 % CPULimit : 300
% 0.12/5.41 % WCLimit : 300
% 0.12/5.41 % DateTime : Fri Sep 25 19:44:12 UTC 2026
% 0.12/5.41 % CPUTime :
% 0.12/5.41 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
% 0.16/5.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.33/6.27 % [INFO] Parsing done (269ms).
% 1.33/6.28 % [INFO] Running in sequential loop mode.
% 2.25/6.68 % [INFO] eprover registered as external prover.
% 2.25/6.68 % [INFO] Scanning for conjecture ...
% 2.44/6.80 % [INFO] Found a conjecture (or negated_conjecture) and 145 axioms. Running axiom selection ...
% 2.83/6.90 % [INFO] Axiom selection finished. Selected 55 axioms (removed 90 axioms).
% 2.83/6.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.83/6.98 % [INFO] Type checking passed.
% 2.83/6.98 % [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 ...
% 5.77/8.06 % External prover 'e' found a proof!
% 5.77/8.06 % [INFO] Killing All external provers ...
% 5.77/8.06 % Time passed: 2504ms (effective reasoning time: 1774ms)
% 5.77/8.06 % 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)>
% 5.77/8.06 % Axioms used in derivation (55): axiom_22, axiom_77, axiom_110, axiom_129, axiom_132, axiom_133, axiom_122, axiom_20, axiom_24, axiom_131, axiom_55, axiom_136, axiom_114, axiom_10, axiom_49, axiom_121, axiom_141, axiom_130, axiom_51, axiom_21, axiom_19, axiom_89, axiom_43, axiom_137, axiom_143, axiom_32, axiom_6, axiom_91, axiom_144, axiom_140, axiom_46, axiom_1, axiom_138, axiom_127, axiom_116, axiom_105, axiom_35, axiom_97, axiom_86, axiom_5, axiom_47, axiom_134, axiom_128, axiom_109, axiom_25, axiom_139, axiom_0, axiom_58, axiom_23, axiom_106, axiom_48, axiom_142, axiom_37, axiom_135, axiom_94
% 5.77/8.06 % No. of inferences in proof: 114
% 5.77/8.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2504 ms resp. 1774 ms w/o parsing
% 6.06/8.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.06/8.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------