%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS157+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 : n012.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 6.29s 2.74s
% Output : Refutation 6.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 86
% Syntax : Number of formulae : 174 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 639 ( 0 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1277 ( 38 ~; 0 |; 250 &; 774 @)
% ( 69 <=>; 146 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 102 ( 101 usr; 2 con; 0-2 aty)
% Number of variables : 278 ( 0 ^; 152 !; 126 ?; 278 :)
% 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(cC14_decl,type,
cC14: $i > $o ).
thf(iV3102_decl,type,
iV3102: $i ).
thf(cC44_decl,type,
cC44: $i > $o ).
thf(cC216_decl,type,
cC216: $i > $o ).
thf(cC64_decl,type,
cC64: $i > $o ).
thf(cC46_decl,type,
cC46: $i > $o ).
thf(cC28_decl,type,
cC28: $i > $o ).
thf(cC30_decl,type,
cC30: $i > $o ).
thf(cC58_decl,type,
cC58: $i > $o ).
thf(rR1_decl,type,
rR1: $i > $i > $o ).
thf(cC56_decl,type,
cC56: $i > $o ).
thf(cC94_decl,type,
cC94: $i > $o ).
thf(cC92_decl,type,
cC92: $i > $o ).
thf(cC152_decl,type,
cC152: $i > $o ).
thf(cC150_decl,type,
cC150: $i > $o ).
thf(cC40_decl,type,
cC40: $i > $o ).
thf(ra_Px86_decl,type,
ra_Px86: $i > $i > $o ).
thf(cC164_decl,type,
cC164: $i > $o ).
thf(cC162_decl,type,
cC162: $i > $o ).
thf(cC82_decl,type,
cC82: $i > $o ).
thf(cC80_decl,type,
cC80: $i > $o ).
thf(cC188_decl,type,
cC188: $i > $o ).
thf(cC186_decl,type,
cC186: $i > $o ).
thf(cC118_decl,type,
cC118: $i > $o ).
thf(cC116_decl,type,
cC116: $i > $o ).
thf(cC10_decl,type,
cC10: $i > $o ).
thf(ra_Px87_decl,type,
ra_Px87: $i > $i > $o ).
thf(cC130_decl,type,
cC130: $i > $o ).
thf(cC128_decl,type,
cC128: $i > $o ).
thf(cC200_decl,type,
cC200: $i > $o ).
thf(cC198_decl,type,
cC198: $i > $o ).
thf(cC180_decl,type,
cC180: $i > $o ).
thf(cC16xcomp_decl,type,
cC16xcomp: $i > $o ).
thf(cC126xcomp_decl,type,
cC126xcomp: $i > $o ).
thf(cC114xcomp_decl,type,
cC114xcomp: $i > $o ).
thf(cC50_decl,type,
cC50: $i > $o ).
thf(cC156_decl,type,
cC156: $i > $o ).
thf(ra_Px5_decl,type,
ra_Px5: $i > $i > $o ).
thf(cC4_decl,type,
cC4: $i > $o ).
thf(cC2xcomp_decl,type,
cC2xcomp: $i > $o ).
thf(cC142_decl,type,
cC142: $i > $o ).
thf(cC140xcomp_decl,type,
cC140xcomp: $i > $o ).
thf(cC98_decl,type,
cC98: $i > $o ).
thf(cC72xcomp_decl,type,
cC72xcomp: $i > $o ).
thf(cC96xcomp_decl,type,
cC96xcomp: $i > $o ).
thf(cC26xcomp_decl,type,
cC26xcomp: $i > $o ).
thf(ra_Px9_decl,type,
ra_Px9: $i > $i > $o ).
thf(cC214xcomp_decl,type,
cC214xcomp: $i > $o ).
thf(ra_Px75_decl,type,
ra_Px75: $i > $i > $o ).
thf(cC40xcomp_decl,type,
cC40xcomp: $i > $o ).
thf(cC48_decl,type,
cC48: $i > $o ).
thf(cC160xcomp_decl,type,
cC160xcomp: $i > $o ).
thf(cC78xcomp_decl,type,
cC78xcomp: $i > $o ).
thf(cC172_decl,type,
cC172: $i > $o ).
thf(cC34_decl,type,
cC34: $i > $o ).
thf(cC32xcomp_decl,type,
cC32xcomp: $i > $o ).
thf(cC60xcomp_decl,type,
cC60xcomp: $i > $o ).
thf(ra_Px85_decl,type,
ra_Px85: $i > $i > $o ).
thf(cC148xcomp_decl,type,
cC148xcomp: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(ra_Px10_decl,type,
ra_Px10: $i > $i > $o ).
thf(cC136_decl,type,
cC136: $i > $o ).
thf(cC8xcomp_decl,type,
cC8xcomp: $i > $o ).
thf(cC108_decl,type,
cC108: $i > $o ).
thf(cC106xcomp_decl,type,
cC106xcomp: $i > $o ).
thf(cC110_decl,type,
cC110: $i > $o ).
thf(cC122_decl,type,
cC122: $i > $o ).
thf(cC102_decl,type,
cC102: $i > $o ).
thf(cC62xcomp_decl,type,
cC62xcomp: $i > $o ).
thf(ra_Px20_decl,type,
ra_Px20: $i > $i > $o ).
thf(cC144_decl,type,
cC144: $i > $o ).
thf(cC42xcomp_decl,type,
cC42xcomp: $i > $o ).
thf(ra_Px14_decl,type,
ra_Px14: $i > $i > $o ).
thf(cC100xcomp_decl,type,
cC100xcomp: $i > $o ).
thf(ra_Px76_decl,type,
ra_Px76: $i > $i > $o ).
thf(cC86_decl,type,
cC86: $i > $o ).
thf(cC90xcomp_decl,type,
cC90xcomp: $i > $o ).
thf(cC66_decl,type,
cC66: $i > $o ).
thf(cC38xcomp_decl,type,
cC38xcomp: $i > $o ).
thf(cC192_decl,type,
cC192: $i > $o ).
thf(cC18_decl,type,
cC18: $i > $o ).
thf(cC196xcomp_decl,type,
cC196xcomp: $i > $o ).
thf(cC74_decl,type,
cC74: $i > $o ).
thf(cC12xcomp_decl,type,
cC12xcomp: $i > $o ).
thf(ra_Px4_decl,type,
ra_Px4: $i > $i > $o ).
thf(cC24xcomp_decl,type,
cC24xcomp: $i > $o ).
thf(ra_Px88_decl,type,
ra_Px88: $i > $i > $o ).
thf(cC178_decl,type,
cC178: $i > $o ).
thf(cC176xcomp_decl,type,
cC176xcomp: $i > $o ).
thf(cC184xcomp_decl,type,
cC184xcomp: $i > $o ).
thf(cC54xcomp_decl,type,
cC54xcomp: $i > $o ).
thf(cC10xcomp_decl,type,
cC10xcomp: $i > $o ).
thf(cC72_decl,type,
cC72: $i > $o ).
thf(cC70xcomp_decl,type,
cC70xcomp: $i > $o ).
thf(ra_Px34_decl,type,
ra_Px34: $i > $i > $o ).
thf(cTOP_decl,type,
cTOP: $i > $o ).
thf(cTEST_decl,type,
cTEST: $i > $o ).
thf(14,axiom,
! [A: $i] :
( ( A @ cC180 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).
thf(170,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC180 ) )
& ( ( A @ cC180 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ cC32xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_134) ).
thf(304,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px10 ) )
=> ( A @ cC32xcomp ) )
& ( ( A @ cC32xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px10 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cC192 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_94) ).
thf(405,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC192 ) )
& ( ( A @ cC192 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cC42xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px14 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_146) ).
thf(365,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px14 ) )
=> ( A @ cC42xcomp ) )
& ( ( A @ cC42xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px14 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_198) ).
thf(479,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px34 ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(1,conjecture,
( ( iV3102 @ cC30 )
& ( iV3102 @ cowlThing )
& ( iV3102 @ cC28 )
& ( iV3102 @ cC46 )
& ( iV3102 @ cC64 )
& ( iV3102 @ cC216 )
& ( iV3102 @ cC44 )
& ( iV3102 @ cC14 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ( iV3102 @ cC30 )
& ( iV3102 @ cowlThing )
& ( iV3102 @ cC28 )
& ( iV3102 @ cC46 )
& ( iV3102 @ cC64 )
& ( iV3102 @ cC216 )
& ( iV3102 @ cC44 )
& ( iV3102 @ cC14 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(88,plain,
~ ( ( iV3102 @ cC30 )
& ( iV3102 @ cowlThing )
& ( iV3102 @ cC28 )
& ( iV3102 @ cC46 )
& ( iV3102 @ cC64 )
& ( iV3102 @ cC216 )
& ( iV3102 @ cC44 )
& ( iV3102 @ cC14 )
& ! [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(41,axiom,
! [A: $i] :
( ( A @ cC62xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px20 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_165) ).
thf(352,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px20 ) )
=> ( A @ cC62xcomp ) )
& ( ( A @ cC62xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px20 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cC92 )
<=> ( ( A @ cC90xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_191) ).
thf(384,plain,
! [A: $i] :
( ( ( ( A @ cC90xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC92 ) )
& ( ( A @ cC92 )
=> ( ( A @ cC90xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ cC14 )
<=> ( ( A @ cC12xcomp )
& ( A @ cC2xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(533,plain,
! [A: $i] :
( ( ( ( A @ cC12xcomp )
& ( A @ cC2xcomp ) )
=> ( A @ cC14 ) )
& ( ( A @ cC14 )
=> ( ( A @ cC12xcomp )
& ( A @ cC2xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(81,axiom,
! [A: $i] :
( ( A @ cC28 )
<=> ( ( A @ cC26xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_131) ).
thf(550,plain,
! [A: $i] :
( ( ( ( A @ cC26xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC28 ) )
& ( ( A @ cC28 )
=> ( ( A @ cC26xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ cC72 )
<=> ( ( A @ cC70xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_173) ).
thf(472,plain,
! [A: $i] :
( ( ( ( A @ cC70xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC72 ) )
& ( ( A @ cC72 )
=> ( ( A @ cC70xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(84,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(565,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cC162 )
<=> ( ( A @ cC160xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).
thf(257,plain,
! [A: $i] :
( ( ( ( A @ cC160xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC162 ) )
& ( ( A @ cC162 )
=> ( ( A @ cC160xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ cC116 )
<=> ( ( A @ cC114xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(184,plain,
! [A: $i] :
( ( ( ( A @ cC114xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC116 ) )
& ( ( A @ cC116 )
=> ( ( A @ cC114xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ cC46 )
<=> ( ( A @ cC44 )
& ( A @ cC30 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_148) ).
thf(542,plain,
! [A: $i] :
( ( ( ( A @ cC44 )
& ( A @ cC30 ) )
=> ( A @ cC46 ) )
& ( ( A @ cC46 )
=> ( ( A @ cC44 )
& ( A @ cC30 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cC4 )
<=> ? [B: $i] :
( ( B @ cC2xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_140) ).
thf(211,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC2xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC4 ) )
& ( ( A @ cC4 )
=> ? [B: $i] :
( ( B @ cC2xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC98 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_208) ).
thf(485,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC98 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cC214xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px75 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_120) ).
thf(238,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px75 ) )
=> ( A @ cC214xcomp ) )
& ( ( A @ cC214xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px75 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px86 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_141) ).
thf(116,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px86 ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ? [B: $i] : ( B @ ( A @ ra_Px86 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(507,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ cC186 )
<=> ( ( A @ cC184xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_91) ).
thf(452,plain,
! [A: $i] :
( ( ( ( A @ cC184xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC186 ) )
& ( ( A @ cC186 )
=> ( ( A @ cC184xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cC24xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px88 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_127) ).
thf(439,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px88 ) )
=> ( A @ cC24xcomp ) )
& ( ( A @ cC24xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px88 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(74,axiom,
iV3102 @ cC26xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_206) ).
thf(529,plain,
iV3102 @ cC26xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cC94 )
<=> ? [B: $i] :
( ( B @ cC92 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_193) ).
thf(102,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)],[4]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ cTEST )
<=> ( ( A @ cC46 )
& ( A @ cC216 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_201) ).
thf(522,plain,
! [A: $i] :
( ( ( ( A @ cC46 )
& ( A @ cC216 ) )
=> ( A @ cTEST ) )
& ( ( A @ cTEST )
=> ( ( A @ cC46 )
& ( A @ cC216 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cC108 )
<=> ( ( A @ cC106xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(324,plain,
! [A: $i] :
( ( ( ( A @ cC106xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC108 ) )
& ( ( A @ cC108 )
=> ( ( A @ cC106xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cC60xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px85 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_162) ).
thf(285,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px85 ) )
=> ( A @ cC60xcomp ) )
& ( ( A @ cC60xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px85 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cC10 )
<=> ( ( A @ cC8xcomp )
& ( A @ cC2xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(317,plain,
! [A: $i] :
( ( ( ( A @ cC8xcomp )
& ( A @ cC2xcomp ) )
=> ( A @ cC10 ) )
& ( ( A @ cC10 )
=> ( ( A @ cC8xcomp )
& ( A @ cC2xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cC130 )
<=> ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(156,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC130 ) )
& ( ( A @ cC130 )
=> ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cC152 )
<=> ? [B: $i] :
( ( B @ cC150 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(109,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC150 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC152 ) )
& ( ( A @ cC152 )
=> ? [B: $i] :
( ( B @ cC150 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(63,axiom,
iV3102 @ cTOP,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_205) ).
thf(488,plain,
iV3102 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ( ( A @ cC96xcomp )
& ( A @ cC72xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_199) ).
thf(225,plain,
! [A: $i] :
( ( ( ( A @ cC96xcomp )
& ( A @ cC72xcomp ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ( ( A @ cC96xcomp )
& ( A @ cC72xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ cC216 )
<=> ( ( A @ cC214xcomp )
& ( A @ cC64 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_121) ).
thf(489,plain,
! [A: $i] :
( ( ( ( A @ cC214xcomp )
& ( A @ cC64 ) )
=> ( A @ cC216 ) )
& ( ( A @ cC216 )
=> ( ( A @ cC214xcomp )
& ( A @ cC64 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cC82 )
<=> ? [B: $i] :
( ( B @ cC80 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_184) ).
thf(129,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC80 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC82 ) )
& ( ( A @ cC82 )
=> ? [B: $i] :
( ( B @ cC80 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cC100xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px76 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(371,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px76 ) )
=> ( A @ cC100xcomp ) )
& ( ( A @ cC100xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px76 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cC40xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px86 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_143) ).
thf(244,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px86 ) )
=> ( A @ cC40xcomp ) )
& ( ( A @ cC40xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px86 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cC16xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(205,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) )
=> ( A @ cC16xcomp ) )
& ( ( A @ cC16xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ( ( A @ cC38xcomp )
& ( A @ cC32xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_142) ).
thf(398,plain,
! [A: $i] :
( ( ( ( A @ cC38xcomp )
& ( A @ cC32xcomp ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ( ( A @ cC38xcomp )
& ( A @ cC32xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(75,axiom,
iV3102 @ cC42xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_211) ).
thf(530,plain,
iV3102 @ cC42xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cC2xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_101) ).
thf(298,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cC2xcomp ) )
& ( ( A @ cC2xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cC18 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).
thf(412,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC18 ) )
& ( ( A @ cC18 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ cC30 )
<=> ( ( A @ cC14 )
& ( A @ cC28 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_132) ).
thf(513,plain,
! [A: $i] :
( ( ( ( A @ cC14 )
& ( A @ cC28 ) )
=> ( A @ cC30 ) )
& ( ( A @ cC30 )
=> ( ( A @ cC14 )
& ( A @ cC28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ cC80 )
<=> ( ( A @ cC78xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_183) ).
thf(264,plain,
! [A: $i] :
( ( ( ( A @ cC78xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC80 ) )
& ( ( A @ cC80 )
=> ( ( A @ cC78xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC24xcomp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_204) ).
thf(573,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC24xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cC50 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_150) ).
thf(191,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC50 ) )
& ( ( A @ cC50 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cC150 )
<=> ( ( A @ cC148xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(291,plain,
! [A: $i] :
( ( ( ( A @ cC148xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC150 ) )
& ( ( A @ cC150 )
=> ( ( A @ cC148xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ cC66 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_167) ).
thf(391,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC66 ) )
& ( ( A @ cC66 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ cC178 )
<=> ( ( A @ cC176xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).
thf(445,plain,
! [A: $i] :
( ( ( ( A @ cC176xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC178 ) )
& ( ( A @ cC178 )
=> ( ( A @ cC176xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(86,axiom,
iV3102 @ cC32xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_207) ).
thf(572,plain,
iV3102 @ cC32xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ cC44 )
<=> ( ( A @ cC32xcomp )
& ( A @ cC42xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_147) ).
thf(498,plain,
! [A: $i] :
( ( ( ( A @ cC32xcomp )
& ( A @ cC42xcomp ) )
=> ( A @ cC44 ) )
& ( ( A @ cC44 )
=> ( ( A @ cC32xcomp )
& ( A @ cC42xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ cC10xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px87 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(466,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px87 ) )
=> ( A @ cC10xcomp ) )
& ( ( A @ cC10xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px87 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC10xcomp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_214) ).
thf(540,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC10xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ cC198 )
<=> ( ( A @ cC196xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_99) ).
thf(419,plain,
! [A: $i] :
( ( ( ( A @ cC196xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC198 ) )
& ( ( A @ cC198 )
=> ( ( A @ cC196xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_186) ).
thf(377,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cC172 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).
thf(271,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC172 ) )
& ( ( A @ cC172 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cC102 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(345,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC102 ) )
& ( ( A @ cC102 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(71,axiom,
iV3102 @ cC12xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_215) ).
thf(520,plain,
iV3102 @ cC12xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ cC156 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(198,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC156 ) )
& ( ( A @ cC156 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(72,axiom,
iV3102 @ cC100xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_218) ).
thf(521,plain,
iV3102 @ cC100xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cC34 )
<=> ? [B: $i] :
( ( B @ cC32xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_135) ).
thf(278,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC32xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC34 ) )
& ( ( A @ cC34 )
=> ? [B: $i] :
( ( B @ cC32xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(67,axiom,
iV3102 @ cC16xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_210) ).
thf(505,plain,
iV3102 @ cC16xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cC74 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_175) ).
thf(426,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC74 ) )
& ( ( A @ cC74 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC40xcomp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_213) ).
thf(531,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC40xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(62,axiom,
iV3102 @ cC214xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_216) ).
thf(487,plain,
iV3102 @ cC214xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ cC64 )
<=> ( ( A @ cTOP )
& ( A @ cC62xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_166) ).
thf(557,plain,
! [A: $i] :
( ( ( ( A @ cTOP )
& ( A @ cC62xcomp ) )
=> ( A @ cC64 ) )
& ( ( A @ cC64 )
=> ( ( A @ cTOP )
& ( A @ cC62xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cC10 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px87 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(150,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px87 ) )
=> ( A @ cC10 ) )
& ( ( A @ cC10 )
=> ? [B: $i] : ( B @ ( A @ ra_Px87 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ? [B: $i] :
( ( B @ cC56 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_157) ).
thf(95,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)],[3]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cC136 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(310,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC136 ) )
& ( ( A @ cC136 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cC128 )
<=> ( ( A @ cC126xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(177,plain,
! [A: $i] :
( ( ( ( A @ cC126xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC128 ) )
& ( ( A @ cC128 )
=> ( ( A @ cC126xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cC110 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(331,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC110 ) )
& ( ( A @ cC110 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cC122 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(338,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC122 ) )
& ( ( A @ cC122 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(85,axiom,
iV3102 @ cC62xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_212) ).
thf(571,plain,
iV3102 @ cC62xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cC118 )
<=> ? [B: $i] :
( ( B @ cC116 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(143,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC116 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC118 ) )
& ( ( A @ cC118 )
=> ? [B: $i] :
( ( B @ cC116 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cC48 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_149) ).
thf(250,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC48 ) )
& ( ( A @ cC48 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cC142 )
<=> ( ( A @ cC140xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(218,plain,
! [A: $i] :
( ( ( ( A @ cC140xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC142 ) )
& ( ( A @ cC142 )
=> ( ( A @ cC140xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cC12xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(433,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px4 ) )
=> ( A @ cC12xcomp ) )
& ( ( A @ cC12xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(80,axiom,
iV3102 @ cC2xcomp,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_203) ).
thf(549,plain,
iV3102 @ cC2xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(83,axiom,
iV3102 @ cowlThing,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_217) ).
thf(564,plain,
iV3102 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cC188 )
<=> ? [B: $i] :
( ( B @ cC186 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_92) ).
thf(136,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC186 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC188 ) )
& ( ( A @ cC188 )
=> ? [B: $i] :
( ( B @ cC186 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(68,axiom,
iV3102 @ cTEST,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_202) ).
thf(506,plain,
iV3102 @ cTEST,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cC144 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(358,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC144 ) )
& ( ( A @ cC144 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ cC56 )
<=> ( ( A @ cC54xcomp )
& ( A @ cC16xcomp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_155) ).
thf(459,plain,
! [A: $i] :
( ( ( ( A @ cC54xcomp )
& ( A @ cC16xcomp ) )
=> ( A @ cC56 ) )
& ( ( A @ cC56 )
=> ( ( A @ cC54xcomp )
& ( A @ cC16xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cC200 )
<=> ? [B: $i] :
( ( B @ cC198 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_103) ).
thf(163,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC198 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC200 ) )
& ( ( A @ cC200 )
=> ? [B: $i] :
( ( B @ cC198 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cC164 )
<=> ? [B: $i] :
( ( B @ cC162 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).
thf(122,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC162 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC164 ) )
& ( ( A @ cC164 )
=> ? [B: $i] :
( ( B @ cC162 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC60xcomp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_209) ).
thf(496,plain,
! [A: $i] :
( ( A @ ( iV3102 @ rR1 ) )
=> ( A @ cC60xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cC26xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_130) ).
thf(232,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) )
=> ( A @ cC26xcomp ) )
& ( ( A @ cC26xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(575,plain,
$false,
inference(e,[status(thm)],[170,304,405,365,479,88,352,384,533,550,472,565,257,184,542,211,485,238,116,507,452,439,529,102,522,324,285,317,156,109,488,225,489,129,371,244,205,398,530,298,412,513,264,573,191,291,391,445,572,498,466,540,419,377,271,345,520,198,521,278,505,426,531,487,557,150,95,310,177,331,338,571,143,250,218,433,549,564,136,506,358,459,163,122,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS157+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % 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
% 0.14/0.40 % Computer : n012.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 19:41:39 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.73/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/1.08 % [INFO] Parsing done (233ms).
% 1.17/1.09 % [INFO] Running in sequential loop mode.
% 1.98/1.37 % [INFO] eprover registered as external prover.
% 1.98/1.37 % [INFO] Scanning for conjecture ...
% 2.21/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 219 axioms. Running axiom selection ...
% 2.39/1.56 % [INFO] Axiom selection finished. Selected 85 axioms (removed 134 axioms).
% 2.75/1.62 % [INFO] Problem is first-order (TPTP FOF).
% 2.75/1.63 % [INFO] Type checking passed.
% 2.75/1.64 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.29/2.74 % External prover 'e' found a proof!
% 6.29/2.74 % [INFO] Killing All external provers ...
% 6.29/2.74 % Time passed: 2227ms (effective reasoning time: 1645ms)
% 6.29/2.74 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.29/2.74 % Axioms used in derivation (85): axiom_7, axiom_33, axiom_209, axiom_186, axiom_131, axiom_22, axiom_59, axiom_77, axiom_217, axiom_44, axiom_198, axiom_214, axiom_206, axiom_191, axiom_121, axiom_67, axiom_141, axiom_130, axiom_51, axiom_21, axiom_157, axiom_99, axiom_203, axiom_103, axiom_147, axiom_146, axiom_184, axiom_2, axiom_173, axiom_27, axiom_162, axiom_143, axiom_218, axiom_32, axiom_91, axiom_132, axiom_208, axiom_155, axiom_92, axiom_148, axiom_16, axiom_213, axiom_207, axiom_3, axiom_140, axiom_202, axiom_85, axiom_165, axiom_205, axiom_42, axiom_1, axiom_212, axiom_57, axiom_127, axiom_150, axiom_216, axiom_167, axiom_101, axiom_8, axiom_193, axiom_86, axiom_201, axiom_149, axiom_183, axiom_166, axiom_13, axiom_134, axiom_25, axiom_211, axiom_204, axiom_0, axiom_62, axiom_175, axiom_199, axiom_215, axiom_56, axiom_48, axiom_142, axiom_83, axiom_120, axiom_4, axiom_210, axiom_66, axiom_135, axiom_94
% 6.29/2.74 % No. of inferences in proof: 174
% 6.29/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2227 ms resp. 1645 ms w/o parsing
% 6.70/2.85 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.70/2.85 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------