%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS161+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 : 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 07:44:47 AM UTC 2026
% Result : Theorem 17.15s 6.53s
% Output : Refutation 18.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 247
% Syntax : Number of formulae : 496 ( 199 unt; 0 typ; 0 def)
% Number of atoms : 1266 ( 0 equ; 0 cnn)
% Maximal formula atoms : 51 ( 2 avg)
% Number of connectives : 2493 ( 113 ~; 0 |; 369 &;1610 @)
% ( 107 <=>; 294 =>; 0 <=; 0 <~>)
% Maximal formula depth : 49 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 148 ( 147 usr; 17 con; 0-2 aty)
% Number of variables : 543 ( 0 ^; 300 !; 243 ?; 543 :)
% 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(cC130_decl,type,
cC130: $i > $o ).
thf(iV16439_decl,type,
iV16439: $i ).
thf(cC108_decl,type,
cC108: $i > $o ).
thf(cC104_decl,type,
cC104: $i > $o ).
thf(cC106_decl,type,
cC106: $i > $o ).
thf(cC28_decl,type,
cC28: $i > $o ).
thf(cC98_decl,type,
cC98: $i > $o ).
thf(iV16440_decl,type,
iV16440: $i ).
thf(cC80_decl,type,
cC80: $i > $o ).
thf(cC82_decl,type,
cC82: $i > $o ).
thf(cC38_decl,type,
cC38: $i > $o ).
thf(iV16448_decl,type,
iV16448: $i ).
thf(cC76_decl,type,
cC76: $i > $o ).
thf(iV16453_decl,type,
iV16453: $i ).
thf(cC62_decl,type,
cC62: $i > $o ).
thf(cC60_decl,type,
cC60: $i > $o ).
thf(cC56_decl,type,
cC56: $i > $o ).
thf(iV16455_decl,type,
iV16455: $i ).
thf(cC44_decl,type,
cC44: $i > $o ).
thf(cC42_decl,type,
cC42: $i > $o ).
thf(iV16457_decl,type,
iV16457: $i ).
thf(cC50_decl,type,
cC50: $i > $o ).
thf(iV16459_decl,type,
iV16459: $i ).
thf(cC88_decl,type,
cC88: $i > $o ).
thf(cC34_decl,type,
cC34: $i > $o ).
thf(cC68_decl,type,
cC68: $i > $o ).
thf(iV16460_decl,type,
iV16460: $i ).
thf(iV16461_decl,type,
iV16461: $i ).
thf(iV16462_decl,type,
iV16462: $i ).
thf(iV16463_decl,type,
iV16463: $i ).
thf(iV16464_decl,type,
iV16464: $i ).
thf(iV16465_decl,type,
iV16465: $i ).
thf(cC36_decl,type,
cC36: $i > $o ).
thf(ra_Px7_decl,type,
ra_Px7: $i > $i > $o ).
thf(cC58_decl,type,
cC58: $i > $o ).
thf(ra_Px19_decl,type,
ra_Px19: $i > $i > $o ).
thf(cC78_decl,type,
cC78: $i > $o ).
thf(ra_Px28_decl,type,
ra_Px28: $i > $i > $o ).
thf(cC40_decl,type,
cC40: $i > $o ).
thf(ra_Px10_decl,type,
ra_Px10: $i > $i > $o ).
thf(cC100_decl,type,
cC100: $i > $o ).
thf(ra_Px37_decl,type,
ra_Px37: $i > $i > $o ).
thf(cC110_decl,type,
cC110: $i > $o ).
thf(cC4xcomp_decl,type,
cC4xcomp: $i > $o ).
thf(cC12xcomp_decl,type,
cC12xcomp: $i > $o ).
thf(cC22_decl,type,
cC22: $i > $o ).
thf(rR1_decl,type,
rR1: $i > $i > $o ).
thf(cC20_decl,type,
cC20: $i > $o ).
thf(cC8_decl,type,
cC8: $i > $o ).
thf(ra_Px9_decl,type,
ra_Px9: $i > $i > $o ).
thf(cC56xcomp_decl,type,
cC56xcomp: $i > $o ).
thf(cC2_decl,type,
cC2: $i > $o ).
thf(ra_Px2_decl,type,
ra_Px2: $i > $i > $o ).
thf(cC64_decl,type,
cC64: $i > $o ).
thf(ra_Px22_decl,type,
ra_Px22: $i > $i > $o ).
thf(cC84_decl,type,
cC84: $i > $o ).
thf(ra_Px31_decl,type,
ra_Px31: $i > $i > $o ).
thf(cC98xcomp_decl,type,
cC98xcomp: $i > $o ).
thf(cC126_decl,type,
cC126: $i > $o ).
thf(cC124_decl,type,
cC124: $i > $o ).
thf(cC86_decl,type,
cC86: $i > $o ).
thf(ra_Px32_decl,type,
ra_Px32: $i > $i > $o ).
thf(cC38xcomp_decl,type,
cC38xcomp: $i > $o ).
thf(ra_Px3_decl,type,
ra_Px3: $i > $i > $o ).
thf(cC32_decl,type,
cC32: $i > $o ).
thf(ra_Px5_decl,type,
ra_Px5: $i > $i > $o ).
thf(cC66_decl,type,
cC66: $i > $o ).
thf(ra_Px23_decl,type,
ra_Px23: $i > $i > $o ).
thf(cC76xcomp_decl,type,
cC76xcomp: $i > $o ).
thf(cC34xcomp_decl,type,
cC34xcomp: $i > $o ).
thf(cC46_decl,type,
cC46: $i > $o ).
thf(ra_Px13_decl,type,
ra_Px13: $i > $i > $o ).
thf(cC30_decl,type,
cC30: $i > $o ).
thf(ra_Px4_decl,type,
ra_Px4: $i > $i > $o ).
thf(cC24_decl,type,
cC24: $i > $o ).
thf(cC64xcomp_decl,type,
cC64xcomp: $i > $o ).
thf(cC100xcomp_decl,type,
cC100xcomp: $i > $o ).
thf(cC18xcomp_decl,type,
cC18xcomp: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(cC92xcomp_decl,type,
cC92xcomp: $i > $o ).
thf(ra_Px57_decl,type,
ra_Px57: $i > $i > $o ).
thf(cC50xcomp_decl,type,
cC50xcomp: $i > $o ).
thf(ra_Px15_decl,type,
ra_Px15: $i > $i > $o ).
thf(cC68xcomp_decl,type,
cC68xcomp: $i > $o ).
thf(ra_Px24_decl,type,
ra_Px24: $i > $i > $o ).
thf(cC94xcomp_decl,type,
cC94xcomp: $i > $o ).
thf(ra_Px48_decl,type,
ra_Px48: $i > $i > $o ).
thf(cC10xcomp_decl,type,
cC10xcomp: $i > $o ).
thf(ra_Px73_decl,type,
ra_Px73: $i > $i > $o ).
thf(cC90xcomp_decl,type,
cC90xcomp: $i > $o ).
thf(ra_Px50_decl,type,
ra_Px50: $i > $i > $o ).
thf(cC2xcomp_decl,type,
cC2xcomp: $i > $o ).
thf(ra_Px26_decl,type,
ra_Px26: $i > $i > $o ).
thf(cC32xcomp_decl,type,
cC32xcomp: $i > $o ).
thf(cC112_decl,type,
cC112: $i > $o ).
thf(cC102xcomp_decl,type,
cC102xcomp: $i > $o ).
thf(cC4_decl,type,
cC4: $i > $o ).
thf(cC70xcomp_decl,type,
cC70xcomp: $i > $o ).
thf(ra_Px51_decl,type,
ra_Px51: $i > $i > $o ).
thf(cC40xcomp_decl,type,
cC40xcomp: $i > $o ).
thf(cC14xcomp_decl,type,
cC14xcomp: $i > $o ).
thf(ra_Px74_decl,type,
ra_Px74: $i > $i > $o ).
thf(cC86xcomp_decl,type,
cC86xcomp: $i > $o ).
thf(cC48xcomp_decl,type,
cC48xcomp: $i > $o ).
thf(ra_Px14_decl,type,
ra_Px14: $i > $i > $o ).
thf(ra_Px18_decl,type,
ra_Px18: $i > $i > $o ).
thf(cC66xcomp_decl,type,
cC66xcomp: $i > $o ).
thf(cC54xcomp_decl,type,
cC54xcomp: $i > $o ).
thf(ra_Px16_decl,type,
ra_Px16: $i > $i > $o ).
thf(cC30xcomp_decl,type,
cC30xcomp: $i > $o ).
thf(cC72xcomp_decl,type,
cC72xcomp: $i > $o ).
thf(ra_Px58_decl,type,
ra_Px58: $i > $i > $o ).
thf(cC52xcomp_decl,type,
cC52xcomp: $i > $o ).
thf(ra_Px49_decl,type,
ra_Px49: $i > $i > $o ).
thf(cC16xcomp_decl,type,
cC16xcomp: $i > $o ).
thf(ra_Px27_decl,type,
ra_Px27: $i > $i > $o ).
thf(cC46xcomp_decl,type,
cC46xcomp: $i > $o ).
thf(cC36xcomp_decl,type,
cC36xcomp: $i > $o ).
thf(cC74xcomp_decl,type,
cC74xcomp: $i > $o ).
thf(ra_Px25_decl,type,
ra_Px25: $i > $i > $o ).
thf(cC8xcomp_decl,type,
cC8xcomp: $i > $o ).
thf(cC78xcomp_decl,type,
cC78xcomp: $i > $o ).
thf(ra_Px17_decl,type,
ra_Px17: $i > $i > $o ).
thf(cC12_decl,type,
cC12: $i > $o ).
thf(ra_Px36_decl,type,
ra_Px36: $i > $i > $o ).
thf(cC6xcomp_decl,type,
cC6xcomp: $i > $o ).
thf(ra_Px72_decl,type,
ra_Px72: $i > $i > $o ).
thf(ra_Px35_decl,type,
ra_Px35: $i > $i > $o ).
thf(cC96xcomp_decl,type,
cC96xcomp: $i > $o ).
thf(ra_Px34_decl,type,
ra_Px34: $i > $i > $o ).
thf(cC84xcomp_decl,type,
cC84xcomp: $i > $o ).
thf(cC128_decl,type,
cC128: $i > $o ).
thf(cC88xcomp_decl,type,
cC88xcomp: $i > $o ).
thf(ra_Px33_decl,type,
ra_Px33: $i > $i > $o ).
thf(ra_Px6_decl,type,
ra_Px6: $i > $i > $o ).
thf(cC58xcomp_decl,type,
cC58xcomp: $i > $o ).
thf(cC26_decl,type,
cC26: $i > $o ).
thf(ra_Px8_decl,type,
ra_Px8: $i > $i > $o ).
thf(iV16449_decl,type,
iV16449: $i ).
thf(cTEST_decl,type,
cTEST: $i > $o ).
thf(cTOP_decl,type,
cTOP: $i > $o ).
thf(iV16442_decl,type,
iV16442: $i ).
thf(iV16441_decl,type,
iV16441: $i ).
thf(148,axiom,
iV16464 @ cC72xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_273) ).
thf(892,plain,
iV16464 @ cC72xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(209,axiom,
! [A: $i] :
( ( A @ ( iV16440 @ rR1 ) )
=> ( A @ cC94xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_155) ).
thf(1036,plain,
! [A: $i] :
( ( A @ ( iV16440 @ rR1 ) )
=> ( A @ cC94xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(247,axiom,
iV16462 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_246) ).
thf(1105,plain,
iV16462 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_241) ).
thf(846,plain,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC38 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(149,axiom,
! [A: $i] :
( ( A @ cC42 )
<=> ? [B: $i] :
( ( B @ cC8xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_65) ).
thf(893,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC8xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC42 ) )
& ( ( A @ cC42 )
=> ? [B: $i] :
( ( B @ cC8xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(238,axiom,
iV16464 @ ( iV16463 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_263) ).
thf(1083,plain,
iV16464 @ ( iV16463 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(170,axiom,
iV16448 @ cC90xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_169) ).
thf(941,plain,
iV16448 @ cC90xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(101,axiom,
! [A: $i] :
( ( A @ ( iV16453 @ rR1 ) )
=> ( A @ cC92xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_179) ).
thf(777,plain,
! [A: $i] :
( ( A @ ( iV16453 @ rR1 ) )
=> ( A @ cC92xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(156,axiom,
iV16464 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_264) ).
thf(909,plain,
iV16464 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(205,axiom,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_194) ).
thf(1031,plain,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1,conjecture,
( ( iV16465 @ cowlThing )
& ( iV16465 @ cC38 )
& ( iV16464 @ cowlThing )
& ( iV16464 @ cC44 )
& ( iV16464 @ cC42 )
& ( iV16464 @ cC56 )
& ( iV16463 @ cC60 )
& ( iV16463 @ cowlThing )
& ( iV16463 @ cC62 )
& ( iV16463 @ cC76 )
& ( iV16462 @ cowlThing )
& ( iV16462 @ cC38 )
& ( iV16461 @ cowlThing )
& ( iV16461 @ cC44 )
& ( iV16461 @ cC56 )
& ( iV16461 @ cC42 )
& ( iV16460 @ cowlThing )
& ( iV16460 @ cC38 )
& ( iV16459 @ cowlThing )
& ( iV16459 @ cC68 )
& ( iV16459 @ cC34 )
& ( iV16459 @ cC88 )
& ( iV16459 @ cC50 )
& ( iV16457 @ cowlThing )
& ( iV16457 @ cC38 )
& ( iV16455 @ cowlThing )
& ( iV16455 @ cC42 )
& ( iV16455 @ cC44 )
& ( iV16455 @ cC56 )
& ( iV16453 @ cC60 )
& ( iV16453 @ cowlThing )
& ( iV16453 @ cC62 )
& ( iV16453 @ cC76 )
& ( iV16448 @ cowlThing )
& ( iV16448 @ cC38 )
& ( iV16440 @ cowlThing )
& ( iV16440 @ cC82 )
& ( iV16440 @ cC80 )
& ( iV16440 @ cC98 )
& ( iV16439 @ cowlThing )
& ( iV16439 @ cC28 )
& ( iV16439 @ cC106 )
& ( iV16439 @ cC104 )
& ( iV16439 @ cC108 )
& ( iV16439 @ cC130 )
& ! [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,
~ ( ( iV16465 @ cowlThing )
& ( iV16465 @ cC38 )
& ( iV16464 @ cowlThing )
& ( iV16464 @ cC44 )
& ( iV16464 @ cC42 )
& ( iV16464 @ cC56 )
& ( iV16463 @ cC60 )
& ( iV16463 @ cowlThing )
& ( iV16463 @ cC62 )
& ( iV16463 @ cC76 )
& ( iV16462 @ cowlThing )
& ( iV16462 @ cC38 )
& ( iV16461 @ cowlThing )
& ( iV16461 @ cC44 )
& ( iV16461 @ cC56 )
& ( iV16461 @ cC42 )
& ( iV16460 @ cowlThing )
& ( iV16460 @ cC38 )
& ( iV16459 @ cowlThing )
& ( iV16459 @ cC68 )
& ( iV16459 @ cC34 )
& ( iV16459 @ cC88 )
& ( iV16459 @ cC50 )
& ( iV16457 @ cowlThing )
& ( iV16457 @ cC38 )
& ( iV16455 @ cowlThing )
& ( iV16455 @ cC42 )
& ( iV16455 @ cC44 )
& ( iV16455 @ cC56 )
& ( iV16453 @ cC60 )
& ( iV16453 @ cowlThing )
& ( iV16453 @ cC62 )
& ( iV16453 @ cC76 )
& ( iV16448 @ cowlThing )
& ( iV16448 @ cC38 )
& ( iV16440 @ cowlThing )
& ( iV16440 @ cC82 )
& ( iV16440 @ cC80 )
& ( iV16440 @ cC98 )
& ( iV16439 @ cowlThing )
& ( iV16439 @ cC28 )
& ( iV16439 @ cC106 )
& ( iV16439 @ cC104 )
& ( iV16439 @ cC108 )
& ( iV16439 @ cC130 )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(249,plain,
~ ( ( iV16465 @ cowlThing )
& ( iV16465 @ cC38 )
& ( iV16464 @ cowlThing )
& ( iV16464 @ cC44 )
& ( iV16464 @ cC42 )
& ( iV16464 @ cC56 )
& ( iV16463 @ cC60 )
& ( iV16463 @ cowlThing )
& ( iV16463 @ cC62 )
& ( iV16463 @ cC76 )
& ( iV16462 @ cowlThing )
& ( iV16462 @ cC38 )
& ( iV16461 @ cowlThing )
& ( iV16461 @ cC44 )
& ( iV16461 @ cC56 )
& ( iV16461 @ cC42 )
& ( iV16460 @ cowlThing )
& ( iV16460 @ cC38 )
& ( iV16459 @ cowlThing )
& ( iV16459 @ cC68 )
& ( iV16459 @ cC34 )
& ( iV16459 @ cC88 )
& ( iV16459 @ cC50 )
& ( iV16457 @ cowlThing )
& ( iV16457 @ cC38 )
& ( iV16455 @ cowlThing )
& ( iV16455 @ cC42 )
& ( iV16455 @ cC44 )
& ( iV16455 @ cC56 )
& ( iV16453 @ cC60 )
& ( iV16453 @ cowlThing )
& ( iV16453 @ cC62 )
& ( iV16453 @ cC76 )
& ( iV16448 @ cowlThing )
& ( iV16448 @ cC38 )
& ( iV16440 @ cowlThing )
& ( iV16440 @ cC82 )
& ( iV16440 @ cC80 )
& ( iV16440 @ cC98 )
& ( iV16439 @ cowlThing )
& ( iV16439 @ cC28 )
& ( iV16439 @ cC106 )
& ( iV16439 @ cC104 )
& ( iV16439 @ cC108 )
& ( iV16439 @ cC130 )
& ! [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(231,axiom,
iV16440 @ cC102xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_157) ).
thf(1068,plain,
iV16440 @ cC102xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(86,axiom,
iV16439 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_147) ).
thf(741,plain,
iV16439 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(141,axiom,
! [A: $i] :
( ( A @ cC62 )
<=> ( ( A @ cC58xcomp )
& ( A @ cC60 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_92) ).
thf(873,plain,
! [A: $i] :
( ( ( ( A @ cC58xcomp )
& ( A @ cC60 ) )
=> ( A @ cC62 ) )
& ( ( A @ cC62 )
=> ( ( A @ cC58xcomp )
& ( A @ cC60 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ cC12xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(533,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px18 ) )
=> ( A @ cC12xcomp ) )
& ( ( A @ cC12xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px18 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ cC76 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_111) ).
thf(797,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px26 ) )
=> ( A @ cC76 ) )
& ( ( A @ cC76 )
=> ? [B: $i] : ( B @ ( A @ ra_Px26 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(173,axiom,
iV16463 @ cC16xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_257) ).
thf(945,plain,
iV16463 @ cC16xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(226,axiom,
iV16465 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_276) ).
thf(1063,plain,
iV16465 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(91,axiom,
iV16448 @ cTOP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_163) ).
thf(747,plain,
iV16448 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(160,axiom,
! [A: $i] :
( ( A @ cC38 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_58) ).
thf(913,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px8 ) )
=> ( A @ cC38 ) )
& ( ( A @ cC38 )
=> ? [B: $i] : ( B @ ( A @ ra_Px8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(125,axiom,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC88 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_278) ).
thf(829,plain,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC88 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(195,axiom,
iV16457 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_195) ).
thf(1001,plain,
iV16457 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(104,axiom,
iV16465 @ ( iV16464 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_274) ).
thf(782,plain,
iV16465 @ ( iV16464 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(212,axiom,
iV16457 @ cC70xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_204) ).
thf(1046,plain,
iV16457 @ cC70xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(220,axiom,
! [A: $i] :
( ( A @ ( iV16463 @ rR1 ) )
=> ( A @ cC92xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_258) ).
thf(1055,plain,
! [A: $i] :
( ( A @ ( iV16463 @ rR1 ) )
=> ( A @ cC92xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(77,axiom,
! [A: $i] :
( ( A @ cC26 )
<=> ? [B: $i] :
( ( B @ cC24 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_43) ).
thf(719,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)],[77]) ).
thf(223,axiom,
! [A: $i] :
( ( A @ ( iV16453 @ rR1 ) )
=> ( A @ cC56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_178) ).
thf(1059,plain,
! [A: $i] :
( ( A @ ( iV16453 @ rR1 ) )
=> ( A @ cC56 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ cC78xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_116) ).
thf(619,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px28 ) )
=> ( A @ cC78xcomp ) )
& ( ( A @ cC78xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(127,axiom,
iV16461 @ cC72xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_242) ).
thf(838,plain,
iV16461 @ cC72xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(151,axiom,
iV16448 @ cC70xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_171) ).
thf(902,plain,
iV16448 @ cC70xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(242,axiom,
iV16448 @ cC36xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_168) ).
thf(1087,plain,
iV16448 @ cC36xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(183,axiom,
! [A: $i] :
( ( A @ cC68 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_99) ).
thf(969,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px24 ) )
=> ( A @ cC68 ) )
& ( ( A @ cC68 )
=> ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(143,axiom,
iV16441 @ ( iV16439 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_152) ).
thf(881,plain,
iV16441 @ ( iV16439 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cC84 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_121) ).
thf(325,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px31 ) )
=> ( A @ cC84 ) )
& ( ( A @ cC84 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px31 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cC18xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_37) ).
thf(421,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cC18xcomp ) )
& ( ( A @ cC18xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(139,axiom,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_244) ).
thf(870,plain,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC50 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ cC78 )
<=> ? [B: $i] :
( ( B @ cC76xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_114) ).
thf(376,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC76xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC78 ) )
& ( ( A @ cC78 )
=> ? [B: $i] :
( ( B @ cC76xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(117,axiom,
! [A: $i] :
( ( A @ ( iV16440 @ rR1 ) )
=> ( A @ cC76 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_156) ).
thf(806,plain,
! [A: $i] :
( ( A @ ( iV16440 @ rR1 ) )
=> ( A @ cC76 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(216,axiom,
iV16455 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_184) ).
thf(1051,plain,
iV16455 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(153,axiom,
iV16462 @ cC8xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_249) ).
thf(905,plain,
iV16462 @ cC8xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(280,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px37 ) )
=> ( A @ cC100 ) )
& ( ( A @ cC100 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(81,axiom,
iV16463 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_256) ).
thf(734,plain,
iV16463 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ cC22 )
<=> ? [B: $i] :
( ( B @ cC20 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_41) ).
thf(293,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC20 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC22 ) )
& ( ( A @ cC22 )
=> ? [B: $i] :
( ( B @ cC20 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(234,axiom,
! [A: $i] :
( ( A @ ( iV16453 @ rR1 ) )
=> ( A @ cC72xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_176) ).
thf(1072,plain,
! [A: $i] :
( ( A @ ( iV16453 @ rR1 ) )
=> ( A @ cC72xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ cC30 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_45) ).
thf(396,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) )
=> ( A @ cC30 ) )
& ( ( A @ cC30 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(192,axiom,
iV16459 @ cC4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_214) ).
thf(998,plain,
iV16459 @ cC4,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(189,axiom,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC52xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_183) ).
thf(988,plain,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC52xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(132,axiom,
iV16459 @ cC46xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_212) ).
thf(849,plain,
iV16459 @ cC46xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cC48xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px14 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_72) ).
thf(527,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px14 ) )
=> ( A @ cC48xcomp ) )
& ( ( A @ cC48xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px14 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(235,axiom,
! [A: $i] :
( ( A @ cC88 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px33 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_127) ).
thf(1074,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px33 ) )
=> ( A @ cC88 ) )
& ( ( A @ cC88 )
=> ? [B: $i] : ( B @ ( A @ ra_Px33 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ cC94xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px48 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_138) ).
thf(452,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px48 ) )
=> ( A @ cC94xcomp ) )
& ( ( A @ cC94xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px48 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(162,axiom,
iV16459 @ cC2xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_219) ).
thf(920,plain,
iV16459 @ cC2xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(109,axiom,
iV16457 @ cC90xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_202) ).
thf(793,plain,
iV16457 @ cC90xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(166,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_142) ).
thf(925,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px35 ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(119,axiom,
iV16463 @ cC74xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_255) ).
thf(810,plain,
iV16463 @ cC74xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(230,axiom,
iV16465 @ cTOP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_277) ).
thf(1067,plain,
iV16465 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(171,axiom,
iV16465 @ cC8xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_280) ).
thf(942,plain,
iV16465 @ cC8xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cC68xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_101) ).
thf(439,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px24 ) )
=> ( A @ cC68xcomp ) )
& ( ( A @ cC68xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px24 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(213,axiom,
iV16440 @ cC78xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_158) ).
thf(1047,plain,
iV16440 @ cC78xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(221,axiom,
iV16463 @ ( iV16440 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_159) ).
thf(1057,plain,
iV16463 @ ( iV16440 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(157,axiom,
iV16462 @ cC70xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_254) ).
thf(910,plain,
iV16462 @ cC70xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(90,axiom,
iV16465 @ cC90xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_283) ).
thf(746,plain,
iV16465 @ cC90xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(202,axiom,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_224) ).
thf(1021,plain,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC34 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(178,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(952,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ ( iV16439 @ rR1 ) )
=> ( A @ cC98 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_146) ).
thf(820,plain,
! [A: $i] :
( ( A @ ( iV16439 @ rR1 ) )
=> ( A @ cC98 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ cC56xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_84) ).
thf(625,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px17 ) )
=> ( A @ cC56xcomp ) )
& ( ( A @ cC56xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px17 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ cC2xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_39) ).
thf(583,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px2 ) )
=> ( A @ cC2xcomp ) )
& ( ( A @ cC2xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(95,axiom,
! [A: $i] :
( ( A @ cC108 )
<=> ( ( A @ cC106 )
& ( A @ cC28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(757,plain,
! [A: $i] :
( ( ( ( A @ cC106 )
& ( A @ cC28 ) )
=> ( A @ cC108 ) )
& ( ( A @ cC108 )
=> ( ( A @ cC106 )
& ( A @ cC28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(71,axiom,
! [A: $i] :
( ( A @ cC4 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_60) ).
thf(682,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px3 ) )
=> ( A @ cC4 ) )
& ( ( A @ cC4 )
=> ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(200,axiom,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_167) ).
thf(1012,plain,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC34 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(248,axiom,
! [A: $i] :
( ( A @ cC56 )
<=> ( ( A @ cC44 )
& ( A @ cC54xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_82) ).
thf(1106,plain,
! [A: $i] :
( ( ( ( A @ cC44 )
& ( A @ cC54xcomp ) )
=> ( A @ cC56 ) )
& ( ( A @ cC56 )
=> ( ( A @ cC44 )
& ( A @ cC54xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(87,axiom,
iV16465 @ cC36xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_282) ).
thf(742,plain,
iV16465 @ cC36xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(176,axiom,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_166) ).
thf(948,plain,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(227,axiom,
iV16448 @ cC52xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_164) ).
thf(1064,plain,
iV16448 @ cC52xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(105,axiom,
! [A: $i] :
( ( A @ cC130 )
<=> ? [B: $i] :
( ( B @ cC128 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_29) ).
thf(783,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)],[105]) ).
thf(134,axiom,
! [A: $i] :
( ( A @ cC106 )
<=> ( ( A @ cC100xcomp )
& ( A @ cC104 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(857,plain,
! [A: $i] :
( ( ( ( A @ cC100xcomp )
& ( A @ cC104 ) )
=> ( A @ cC106 ) )
& ( ( A @ cC106 )
=> ( ( A @ cC100xcomp )
& ( A @ cC104 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cC36 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_54) ).
thf(256,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px7 ) )
=> ( A @ cC36 ) )
& ( ( A @ cC36 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ cC44 )
<=> ( ( A @ cC42 )
& ( A @ cC40xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_66) ).
thf(884,plain,
! [A: $i] :
( ( ( ( A @ cC42 )
& ( A @ cC40xcomp ) )
=> ( A @ cC44 ) )
& ( ( A @ cC44 )
=> ( ( A @ cC42 )
& ( A @ cC40xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(168,axiom,
! [A: $i] :
( ( A @ cC34 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_51) ).
thf(933,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px6 ) )
=> ( A @ cC34 ) )
& ( ( A @ cC34 )
=> ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(69,axiom,
! [A: $i] :
( ( A @ cC84 )
<=> ( ( A @ cC12 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_122) ).
thf(669,plain,
! [A: $i] :
( ( ( ( A @ cC12 )
& ( A @ cC2 ) )
=> ( A @ cC84 ) )
& ( ( A @ cC84 )
=> ( ( A @ cC12 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ cC102xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px36 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(637,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px36 ) )
=> ( A @ cC102xcomp ) )
& ( ( A @ cC102xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px36 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ cC112 )
<=> ( ( A @ cC102xcomp )
& ( A @ cC110 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(489,plain,
! [A: $i] :
( ( ( ( A @ cC102xcomp )
& ( A @ cC110 ) )
=> ( A @ cC112 ) )
& ( ( A @ cC112 )
=> ( ( A @ cC102xcomp )
& ( A @ cC110 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(211,axiom,
! [A: $i] :
( ( A @ cC98 )
<=> ( ( A @ cC82 )
& ( A @ cC96xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_143) ).
thf(1039,plain,
! [A: $i] :
( ( ( ( A @ cC82 )
& ( A @ cC96xcomp ) )
=> ( A @ cC98 ) )
& ( ( A @ cC98 )
=> ( ( A @ cC82 )
& ( A @ cC96xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(187,axiom,
iV16453 @ cC74xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_174) ).
thf(985,plain,
iV16453 @ cC74xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(74,axiom,
! [A: $i] :
( ( A @ cC88xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px33 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_129) ).
thf(701,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px33 ) )
=> ( A @ cC88xcomp ) )
& ( ( A @ cC88xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px33 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cC14xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px74 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_32) ).
thf(515,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px74 ) )
=> ( A @ cC14xcomp ) )
& ( ( A @ cC14xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px74 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(84,axiom,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_229) ).
thf(738,plain,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC50 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(158,axiom,
iV16461 @ cC40xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_234) ).
thf(911,plain,
iV16461 @ cC40xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(196,axiom,
iV16462 @ cC90xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_253) ).
thf(1002,plain,
iV16462 @ cC90xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(102,axiom,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_281) ).
thf(779,plain,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cC70xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px51 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_104) ).
thf(503,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px51 ) )
=> ( A @ cC70xcomp ) )
& ( ( A @ cC70xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px51 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(108,axiom,
iV16459 @ cC12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_211) ).
thf(792,plain,
iV16459 @ cC12,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(241,axiom,
iV16463 @ cC94xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_260) ).
thf(1086,plain,
iV16463 @ cC94xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(116,axiom,
iV16459 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_205) ).
thf(805,plain,
iV16459 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(163,axiom,
iV16457 @ cC8xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_199) ).
thf(921,plain,
iV16457 @ cC8xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(208,axiom,
iV16459 @ cC48xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_217) ).
thf(1035,plain,
iV16459 @ cC48xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(110,axiom,
iV16455 @ cC12xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_187) ).
thf(794,plain,
iV16455 @ cC12xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(97,axiom,
! [A: $i] :
( ( A @ ( iV16463 @ rR1 ) )
=> ( A @ cC72xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_259) ).
thf(765,plain,
! [A: $i] :
( ( A @ ( iV16463 @ rR1 ) )
=> ( A @ cC72xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(219,axiom,
iV16455 @ cC92xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_189) ).
thf(1054,plain,
iV16455 @ cC92xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ cC30xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_47) ).
thf(558,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px4 ) )
=> ( A @ cC30xcomp ) )
& ( ( A @ cC30xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(233,axiom,
iV16453 @ cC16xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_177) ).
thf(1071,plain,
iV16453 @ cC16xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(154,axiom,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_165) ).
thf(906,plain,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC50 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(94,axiom,
! [A: $i] :
( ( A @ cC82 )
<=> ( ( A @ cC78xcomp )
& ( A @ cC80 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_120) ).
thf(750,plain,
! [A: $i] :
( ( ( ( A @ cC78xcomp )
& ( A @ cC80 ) )
=> ( A @ cC82 ) )
& ( ( A @ cC82 )
=> ( ( A @ cC78xcomp )
& ( A @ cC80 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(80,axiom,
iV16455 @ cC40xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_185) ).
thf(733,plain,
iV16455 @ cC40xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ cC36xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_56) ).
thf(601,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px7 ) )
=> ( A @ cC36xcomp ) )
& ( ( A @ cC36xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(184,axiom,
iV16459 @ cC86xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_215) ).
thf(975,plain,
iV16459 @ cC86xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ cC128 )
<=> ? [B: $i] :
( ( B @ cC126 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_28) ).
thf(694,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)],[73]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cC24 )
<=> ? [B: $i] :
( ( B @ cC22 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_42) ).
thf(402,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)],[26]) ).
thf(79,axiom,
iV16449 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_173) ).
thf(732,plain,
iV16449 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ cC110 )
<=> ( ( A @ cC12xcomp )
& ( A @ cC4xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(286,plain,
! [A: $i] :
( ( ( ( A @ cC12xcomp )
& ( A @ cC4xcomp ) )
=> ( A @ cC110 ) )
& ( ( A @ cC110 )
=> ( ( A @ cC12xcomp )
& ( A @ cC4xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(88,axiom,
iV16439 @ cTEST,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_149) ).
thf(743,plain,
iV16439 @ cTEST,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cC52xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px49 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_78) ).
thf(577,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px49 ) )
=> ( A @ cC52xcomp ) )
& ( ( A @ cC52xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px49 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(179,axiom,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC70xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_272) ).
thf(958,plain,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC70xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ( ( A @ cC2xcomp )
& ( A @ cC12xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_124) ).
thf(545,plain,
! [A: $i] :
( ( ( ( A @ cC2xcomp )
& ( A @ cC12xcomp ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ( ( A @ cC2xcomp )
& ( A @ cC12xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ cC20 )
<=> ? [B: $i] :
( ( B @ cC18xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_40) ).
thf(445,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC18xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC20 ) )
& ( ( A @ cC20 )
=> ? [B: $i] :
( ( B @ cC18xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cC2 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_38) ).
thf(313,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px2 ) )
=> ( A @ cC2 ) )
& ( ( A @ cC2 )
=> ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,axiom,
! [A: $i] :
( ( A @ cC58xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_87) ).
thf(713,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px19 ) )
=> ( A @ cC58xcomp ) )
& ( ( A @ cC58xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px19 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(222,axiom,
iV16462 @ cC52xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_248) ).
thf(1058,plain,
iV16462 @ cC52xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(244,axiom,
! [A: $i] :
( ( A @ cC28 )
<=> ? [B: $i] :
( ( B @ cC26 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_44) ).
thf(1090,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC26 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC28 ) )
& ( ( A @ cC28 )
=> ? [B: $i] :
( ( B @ cC26 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(175,axiom,
iV16460 @ ( iV16455 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_193) ).
thf(947,plain,
iV16460 @ ( iV16455 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(161,axiom,
iV16461 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_233) ).
thf(919,plain,
iV16461 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(115,axiom,
iV16459 @ cC6xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_220) ).
thf(804,plain,
iV16459 @ cC6xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(96,axiom,
iV16453 @ cC94xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_180) ).
thf(764,plain,
iV16453 @ cC94xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC88 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_170) ).
thf(900,plain,
! [A: $i] :
( ( A @ ( iV16448 @ rR1 ) )
=> ( A @ cC88 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(126,axiom,
! [A: $i] :
( ( A @ cC104 )
<=> ? [B: $i] :
( ( B @ cC102xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(831,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC102xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC104 ) )
& ( ( A @ cC104 )
=> ? [B: $i] :
( ( B @ cC102xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_62) ).
thf(274,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px10 ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px10 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(199,axiom,
iV16461 @ ( iV16453 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_182) ).
thf(1011,plain,
iV16461 @ ( iV16453 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(214,axiom,
iV16464 @ cC54xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_270) ).
thf(1048,plain,
iV16464 @ cC54xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(190,axiom,
iV16459 @ cC84xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_210) ).
thf(990,plain,
iV16459 @ cC84xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(83,axiom,
iV16459 @ cC30xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_209) ).
thf(737,plain,
iV16459 @ cC30xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cC40xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px10 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_64) ).
thf(509,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px10 ) )
=> ( A @ cC40xcomp ) )
& ( ( A @ cC40xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px10 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(142,axiom,
iV16459 @ cC10xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_208) ).
thf(880,plain,
iV16459 @ cC10xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(66,axiom,
! [A: $i] :
( ( A @ cC66 )
<=> ( ( A @ cC8xcomp )
& ( A @ cC12xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_96) ).
thf(649,plain,
! [A: $i] :
( ( ( ( A @ cC8xcomp )
& ( A @ cC12xcomp ) )
=> ( A @ cC66 ) )
& ( ( A @ cC66 )
=> ( ( A @ cC8xcomp )
& ( A @ cC12xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ cC76xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px26 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_113) ).
thf(477,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px26 ) )
=> ( A @ cC76xcomp ) )
& ( ( A @ cC76xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px26 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(120,axiom,
iV16460 @ cTOP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_225) ).
thf(811,plain,
iV16460 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(236,axiom,
iV16453 @ cC58xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_181) ).
thf(1080,plain,
iV16453 @ cC58xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ cC12 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px18 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(631,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px18 ) )
=> ( A @ cC12 ) )
& ( ( A @ cC12 )
=> ? [B: $i] : ( B @ ( A @ ra_Px18 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(78,axiom,
! [A: $i] :
( ( A @ cC38xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_59) ).
thf(726,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px8 ) )
=> ( A @ cC38xcomp ) )
& ( ( A @ cC38xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ cC32xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_50) ).
thf(483,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) )
=> ( A @ cC32xcomp ) )
& ( ( A @ cC32xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(131,axiom,
iV16465 @ cC52xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_279) ).
thf(848,plain,
iV16465 @ cC52xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC90xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_186) ).
thf(1029,plain,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC90xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(172,axiom,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_284) ).
thf(943,plain,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC50 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(224,axiom,
iV16449 @ ( iV16448 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_172) ).
thf(1061,plain,
iV16449 @ ( iV16448 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ cC86 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_125) ).
thf(345,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px32 ) )
=> ( A @ cC86 ) )
& ( ( A @ cC86 )
=> ? [B: $i] : ( B @ ( A @ ra_Px32 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cC54xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px16 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_81) ).
thf(552,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px16 ) )
=> ( A @ cC54xcomp ) )
& ( ( A @ cC54xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px16 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(99,axiom,
! [A: $i] :
( ( A @ cC38 )
<=> ( ( A @ cC36xcomp )
& ( A @ cTOP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_57) ).
thf(768,plain,
! [A: $i] :
( ( ( ( A @ cC36xcomp )
& ( A @ cTOP ) )
=> ( A @ cC38 ) )
& ( ( A @ cC38 )
=> ( ( A @ cC36xcomp )
& ( A @ cTOP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(145,axiom,
iV16459 @ cC18xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_218) ).
thf(883,plain,
iV16459 @ cC18xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(194,axiom,
iV16460 @ cC8xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_227) ).
thf(1000,plain,
iV16460 @ cC8xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(164,axiom,
iV16462 @ cC36xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_252) ).
thf(922,plain,
iV16462 @ cC36xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(159,axiom,
iV16442 @ ( iV16439 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_151) ).
thf(912,plain,
iV16442 @ ( iV16439 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cC86xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px32 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_126) ).
thf(521,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px32 ) )
=> ( A @ cC86xcomp ) )
& ( ( A @ cC86xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px32 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(229,axiom,
iV16460 @ cC52xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_226) ).
thf(1066,plain,
iV16460 @ cC52xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(138,axiom,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC70xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_236) ).
thf(868,plain,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC70xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(188,axiom,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_222) ).
thf(986,plain,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ? [B: $i] :
( ( B @ cC56xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_85) ).
thf(306,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC56xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC58 ) )
& ( ( A @ cC58 )
=> ? [B: $i] :
( ( B @ cC56xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(207,axiom,
iV16461 @ cC12xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_237) ).
thf(1034,plain,
iV16461 @ cC12xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ cC16xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_34) ).
thf(589,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px27 ) )
=> ( A @ cC16xcomp ) )
& ( ( A @ cC16xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px27 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(111,axiom,
iV16439 @ cC100xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_148) ).
thf(795,plain,
iV16439 @ cC100xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ cC98xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_144) ).
thf(663,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px35 ) )
=> ( A @ cC98xcomp ) )
& ( ( A @ cC98xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px35 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(121,axiom,
iV16440 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_153) ).
thf(812,plain,
iV16440 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(169,axiom,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_250) ).
thf(939,plain,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC34 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(215,axiom,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC90xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_271) ).
thf(1049,plain,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC90xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(237,axiom,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC52xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_268) ).
thf(1081,plain,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC52xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(93,axiom,
iV16460 @ cC70xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_232) ).
thf(749,plain,
iV16460 @ cC70xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(182,axiom,
iV16440 @ ( iV16439 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_150) ).
thf(968,plain,
iV16440 @ ( iV16439 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cC10xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px73 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(458,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px73 ) )
=> ( A @ cC10xcomp ) )
& ( ( A @ cC10xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px73 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(197,axiom,
! [A: $i] :
( ( A @ cC50 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_74) ).
thf(1003,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px15 ) )
=> ( A @ cC50 ) )
& ( ( A @ cC50 )
=> ? [B: $i] : ( B @ ( A @ ra_Px15 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(140,axiom,
iV16448 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_162) ).
thf(872,plain,
iV16448 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(75,axiom,
! [A: $i] :
( ( A @ cC34xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_53) ).
thf(707,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px6 ) )
=> ( A @ cC34xcomp ) )
& ( ( A @ cC34xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ cC64xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_95) ).
thf(409,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px22 ) )
=> ( A @ cC64xcomp ) )
& ( ( A @ cC64xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(246,axiom,
! [A: $i] :
( ( A @ cTEST )
<=> ( ( A @ cC130 )
& ( A @ cC108 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_145) ).
thf(1098,plain,
! [A: $i] :
( ( ( ( A @ cC130 )
& ( A @ cC108 ) )
=> ( A @ cTEST ) )
& ( ( A @ cTEST )
=> ( ( A @ cC130 )
& ( A @ cC108 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(218,axiom,
iV16464 @ cC92xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_269) ).
thf(1053,plain,
iV16464 @ cC92xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(107,axiom,
iV16460 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_223) ).
thf(791,plain,
iV16460 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cC100 )
<=> ? [B: $i] :
( ( B @ cC98xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(331,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC98xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC100 ) )
& ( ( A @ cC100 )
=> ? [B: $i] :
( ( B @ cC98xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ cC126 )
<=> ? [B: $i] :
( ( B @ cC124 )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_27) ).
thf(338,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC124 )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC126 ) )
& ( ( A @ cC126 )
=> ? [B: $i] :
( ( B @ cC124 )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(118,axiom,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC50 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_203) ).
thf(808,plain,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC50 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(65,axiom,
! [A: $i] :
( ( A @ cC6xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px72 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_90) ).
thf(643,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px72 ) )
=> ( A @ cC6xcomp ) )
& ( ( A @ cC6xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px72 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(210,axiom,
iV16459 @ cC8xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_207) ).
thf(1038,plain,
iV16459 @ cC8xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cC66 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_97) ).
thf(370,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px23 ) )
=> ( A @ cC66 ) )
& ( ( A @ cC66 )
=> ? [B: $i] : ( B @ ( A @ ra_Px23 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(240,axiom,
iV16462 @ cTOP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_247) ).
thf(1085,plain,
iV16462 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ cC32 )
<=> ( ( A @ cC2xcomp )
& ( A @ cC4xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_49) ).
thf(470,plain,
! [A: $i] :
( ( ( ( A @ cC2xcomp )
& ( A @ cC4xcomp ) )
=> ( A @ cC32 ) )
& ( ( A @ cC32 )
=> ( ( A @ cC2xcomp )
& ( A @ cC4xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(89,axiom,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC90xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_235) ).
thf(744,plain,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC90xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ cC8xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_118) ).
thf(613,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) )
=> ( A @ cC8xcomp ) )
& ( ( A @ cC8xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(217,axiom,
iV16440 @ cC96xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_154) ).
thf(1052,plain,
iV16440 @ cC96xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(135,axiom,
iV16457 @ cC52xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_198) ).
thf(864,plain,
iV16457 @ cC52xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ cC80 )
<=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_119) ).
thf(978,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC80 ) )
& ( ( A @ cC80 )
=> ? [B: $i] :
( ( B @ cC16xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cC72xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px58 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_107) ).
thf(571,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px58 ) )
=> ( A @ cC72xcomp ) )
& ( ( A @ cC72xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px58 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ cC46xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_69) ).
thf(595,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px13 ) )
=> ( A @ cC46xcomp ) )
& ( ( A @ cC46xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px13 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(191,axiom,
! [A: $i] :
( ( A @ cC34 )
<=> ( ( A @ cC32xcomp )
& ( A @ cC30xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_52) ).
thf(991,plain,
! [A: $i] :
( ( ( ( A @ cC32xcomp )
& ( A @ cC30xcomp ) )
=> ( A @ cC34 ) )
& ( ( A @ cC34 )
=> ( ( A @ cC32xcomp )
& ( A @ cC30xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ cC64 )
<=> ( ( A @ cC12 )
& ( A @ cC8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_93) ).
thf(656,plain,
! [A: $i] :
( ( ( ( A @ cC12 )
& ( A @ cC8 ) )
=> ( A @ cC64 ) )
& ( ( A @ cC64 )
=> ( ( A @ cC12 )
& ( A @ cC8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(203,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(1023,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(129,axiom,
iV16442 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_161) ).
thf(845,plain,
iV16442 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(239,axiom,
iV16455 @ cC72xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_192) ).
thf(1084,plain,
iV16455 @ cC72xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(147,axiom,
iV16457 @ cC36xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_201) ).
thf(891,plain,
iV16457 @ cC36xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(167,axiom,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC88 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_230) ).
thf(931,plain,
! [A: $i] :
( ( A @ ( iV16460 @ rR1 ) )
=> ( A @ cC88 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cC66xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px23 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_98) ).
thf(539,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px23 ) )
=> ( A @ cC66xcomp ) )
& ( ( A @ cC66xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px23 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(185,axiom,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_265) ).
thf(976,plain,
! [A: $i] :
( ( A @ ( iV16464 @ rR1 ) )
=> ( A @ cC38 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(72,axiom,
! [A: $i] :
( ( A @ cC84xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px31 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_123) ).
thf(688,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px31 ) )
=> ( A @ cC84xcomp ) )
& ( ( A @ cC84xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px31 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(152,axiom,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_275) ).
thf(903,plain,
! [A: $i] :
( ( A @ ( iV16465 @ rR1 ) )
=> ( A @ cC34 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cC64 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_94) ).
thf(319,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px22 ) )
=> ( A @ cC64 ) )
& ( ( A @ cC64 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px22 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(92,axiom,
iV16464 @ cC12xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_267) ).
thf(748,plain,
iV16464 @ cC12xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(225,axiom,
iV16453 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_175) ).
thf(1062,plain,
iV16453 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(174,axiom,
iV16457 @ cTOP,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_197) ).
thf(946,plain,
iV16457 @ cTOP,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ cC40 )
<=> ? [B: $i] :
( ( B @ cC38xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_63) ).
thf(351,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC38xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC40 ) )
& ( ( A @ cC40 )
=> ? [B: $i] :
( ( B @ cC38xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cC46 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_67) ).
thf(390,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px13 ) )
=> ( A @ cC46 ) )
& ( ( A @ cC46 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px13 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(103,axiom,
iV16462 @ ( iV16461 @ rR1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_243) ).
thf(781,plain,
iV16462 @ ( iV16461 @ rR1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(181,axiom,
! [A: $i] :
( ( A @ cC76 )
<=> ( ( A @ cC62 )
& ( A @ cC74xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_112) ).
thf(961,plain,
! [A: $i] :
( ( ( ( A @ cC62 )
& ( A @ cC74xcomp ) )
=> ( A @ cC76 ) )
& ( ( A @ cC76 )
=> ( ( A @ cC62 )
& ( A @ cC74xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(122,axiom,
! [A: $i] :
( ( A @ cC60 )
<=> ? [B: $i] :
( ( B @ cC12xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_91) ).
thf(813,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC12xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC60 ) )
& ( ( A @ cC60 )
=> ? [B: $i] :
( ( B @ cC12xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(31,axiom,
! [A: $i] :
( ( A @ cC50xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_75) ).
thf(433,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px15 ) )
=> ( A @ cC50xcomp ) )
& ( ( A @ cC50xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px15 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cC36 )
<=> ? [B: $i] :
( ( B @ cC34xcomp )
& ( B @ ( A @ rR1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_55) ).
thf(383,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ cC34xcomp )
& ( B @ ( A @ rR1 ) ) )
=> ( A @ cC36 ) )
& ( ( A @ cC36 )
=> ? [B: $i] :
( ( B @ cC34xcomp )
& ( B @ ( A @ rR1 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cC8 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_117) ).
thf(300,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px9 ) )
=> ( A @ cC8 ) )
& ( ( A @ cC8 )
=> ? [B: $i] : ( B @ ( A @ ra_Px9 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(193,axiom,
iV16441 @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_160) ).
thf(999,plain,
iV16441 @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(106,axiom,
iV16464 @ cC40xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_266) ).
thf(790,plain,
iV16464 @ cC40xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(137,axiom,
iV16459 @ cC14xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_206) ).
thf(867,plain,
iV16459 @ cC14xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(136,axiom,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC38 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_188) ).
thf(865,plain,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC38 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(82,axiom,
! [A: $i] :
( ( A @ ( iV16463 @ rR1 ) )
=> ( A @ cC56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_261) ).
thf(735,plain,
! [A: $i] :
( ( A @ ( iV16463 @ rR1 ) )
=> ( A @ cC56 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(177,axiom,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC68 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_245) ).
thf(950,plain,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC68 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(245,axiom,
iV16459 @ cC32xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_216) ).
thf(1097,plain,
iV16459 @ cC32xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ cC58 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px19 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_86) ).
thf(262,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px19 ) )
=> ( A @ cC58 ) )
& ( ( A @ cC58 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px19 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cC30 )
<=> ( ( A @ cC4 )
& ( A @ cC2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_46) ).
thf(564,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC2 ) )
=> ( A @ cC30 ) )
& ( ( A @ cC30 )
=> ( ( A @ cC4 )
& ( A @ cC2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cC78 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_115) ).
thf(268,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px28 ) )
=> ( A @ cC78 ) )
& ( ( A @ cC78 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px28 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cC4xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_61) ).
thf(358,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px3 ) )
=> ( A @ cC4xcomp ) )
& ( ( A @ cC4xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(98,axiom,
iV16460 @ cC36xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_228) ).
thf(767,plain,
iV16460 @ cC36xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(206,axiom,
iV16459 @ cC66xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_221) ).
thf(1033,plain,
iV16459 @ cC66xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(180,axiom,
iV16463 @ cC58xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_262) ).
thf(960,plain,
iV16463 @ cC58xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(228,axiom,
iV16459 @ cC64xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_213) ).
thf(1065,plain,
iV16459 @ cC64xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(112,axiom,
iV16461 @ cC92xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_239) ).
thf(796,plain,
iV16461 @ cC92xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ cC100xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(415,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px37 ) )
=> ( A @ cC100xcomp ) )
& ( ( A @ cC100xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px37 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(128,axiom,
! [A: $i] :
( ( A @ cC56 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_83) ).
thf(839,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px17 ) )
=> ( A @ cC56 ) )
& ( ( A @ cC56 )
=> ? [B: $i] : ( B @ ( A @ ra_Px17 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(85,axiom,
iV16455 @ cC54xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_190) ).
thf(740,plain,
iV16455 @ cC54xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cC90xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px50 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_132) ).
thf(464,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px50 ) )
=> ( A @ cC90xcomp ) )
& ( ( A @ cC90xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px50 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cC92xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px57 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_135) ).
thf(427,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px57 ) )
=> ( A @ cC92xcomp ) )
& ( ( A @ cC92xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px57 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(155,axiom,
iV16465 @ cC70xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_285) ).
thf(908,plain,
iV16465 @ cC70xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(124,axiom,
! [A: $i] :
( ( A @ cC50 )
<=> ( ( A @ cC48xcomp )
& ( A @ cC46xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_73) ).
thf(822,plain,
! [A: $i] :
( ( ( ( A @ cC48xcomp )
& ( A @ cC46xcomp ) )
=> ( A @ cC50 ) )
& ( ( A @ cC50 )
=> ( ( A @ cC48xcomp )
& ( A @ cC46xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(133,axiom,
! [A: $i] :
( ( A @ cC68 )
<=> ( ( A @ cC66xcomp )
& ( A @ cC64xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_100) ).
thf(850,plain,
! [A: $i] :
( ( ( ( A @ cC66xcomp )
& ( A @ cC64xcomp ) )
=> ( A @ cC68 ) )
& ( ( A @ cC68 )
=> ( ( A @ cC66xcomp )
& ( A @ cC64xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ cC74xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px25 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_110) ).
thf(607,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px25 ) )
=> ( A @ cC74xcomp ) )
& ( ( A @ cC74xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px25 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(114,axiom,
iV16461 @ cC54xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_240) ).
thf(803,plain,
iV16461 @ cC54xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(198,axiom,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC88 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_251) ).
thf(1009,plain,
! [A: $i] :
( ( A @ ( iV16462 @ rR1 ) )
=> ( A @ cC88 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(165,axiom,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC70xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_191) ).
thf(923,plain,
! [A: $i] :
( ( A @ ( iV16455 @ rR1 ) )
=> ( A @ cC70xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(100,axiom,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC88 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_200) ).
thf(775,plain,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC88 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(70,axiom,
! [A: $i] :
( ( A @ cC96xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_141) ).
thf(676,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px34 ) )
=> ( A @ cC96xcomp ) )
& ( ( A @ cC96xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px34 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(243,axiom,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_196) ).
thf(1088,plain,
! [A: $i] :
( ( A @ ( iV16457 @ rR1 ) )
=> ( A @ cC34 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cC32 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_48) ).
thf(364,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px5 ) )
=> ( A @ cC32 ) )
& ( ( A @ cC32 )
=> ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(144,axiom,
iV16460 @ cC90xcomp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_231) ).
thf(882,plain,
iV16460 @ cC90xcomp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ cC88 )
<=> ( ( A @ cC86xcomp )
& ( A @ cC84xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_128) ).
thf(1014,plain,
! [A: $i] :
( ( ( ( A @ cC86xcomp )
& ( A @ cC84xcomp ) )
=> ( A @ cC88 ) )
& ( ( A @ cC88 )
=> ( ( A @ cC86xcomp )
& ( A @ cC84xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ cC46 )
<=> ( ( A @ cC4 )
& ( A @ cC8 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_68) ).
thf(496,plain,
! [A: $i] :
( ( ( ( A @ cC4 )
& ( A @ cC8 ) )
=> ( A @ cC46 ) )
& ( ( A @ cC46 )
=> ( ( A @ cC4 )
& ( A @ cC8 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(232,axiom,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC52xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_238) ).
thf(1069,plain,
! [A: $i] :
( ( A @ ( iV16461 @ rR1 ) )
=> ( A @ cC52xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(1193,plain,
$false,
inference(e,[status(thm)],[892,1036,1105,846,893,1083,941,777,909,1031,249,1068,741,873,533,797,945,1063,747,913,829,1001,782,1046,1055,719,1059,619,838,902,1087,969,881,325,421,870,376,806,1051,905,280,734,293,1072,396,998,988,849,527,1074,452,920,793,925,810,1067,942,439,1047,1057,910,746,1021,952,820,625,583,757,682,1012,1106,742,948,1064,783,857,256,884,933,669,637,489,1039,985,701,515,738,911,1002,779,503,792,1086,805,921,1035,794,765,1054,558,1071,906,750,733,601,975,694,402,732,286,743,577,958,545,445,313,713,1058,1090,947,919,804,764,900,831,274,1011,1048,990,737,509,880,649,477,811,1080,631,726,483,848,1029,943,1061,345,552,768,883,1000,922,912,521,1066,868,986,306,1034,589,795,663,812,939,1049,1081,749,968,458,1003,872,707,409,1098,1053,791,331,338,808,643,1038,370,1085,470,744,613,1052,864,978,571,595,991,656,1023,845,1084,891,931,539,976,688,903,319,748,1062,946,351,390,781,961,813,433,383,300,999,790,867,865,735,950,1097,262,564,268,358,767,1033,960,1065,796,415,839,740,464,427,908,822,850,607,803,1009,923,775,676,1088,364,882,1014,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS161+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n004.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Fri Sep 25 19:41:39 UTC 2026
% 0.22/0.49 % CPUTime :
% 0.22/0.49 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
% 1.43/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.83/1.81 % [INFO] Parsing done (464ms).
% 2.83/1.83 % [INFO] Running in sequential loop mode.
% 3.83/2.44 % [INFO] eprover registered as external prover.
% 3.83/2.45 % [INFO] Scanning for conjecture ...
% 4.46/2.71 % [INFO] Found a conjecture (or negated_conjecture) and 286 axioms. Running axiom selection ...
% 4.95/2.97 % [INFO] Axiom selection finished. Selected 246 axioms (removed 40 axioms).
% 5.47/3.15 % [INFO] Problem is first-order (TPTP FOF).
% 5.70/3.19 % [INFO] Type checking passed.
% 5.70/3.19 % [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 ...
% 17.15/6.52 % External prover 'e' found a proof!
% 17.15/6.52 % [INFO] Killing All external provers ...
% 17.15/6.52 % Time passed: 5825ms (effective reasoning time: 4685ms)
% 17.15/6.52 % 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)>
% 17.15/6.53 % Axioms used in derivation (246): axiom_7, axiom_243, axiom_248, axiom_55, axiom_232, axiom_114, axiom_119, axiom_174, axiom_254, axiom_181, axiom_10, axiom_40, axiom_221, axiom_271, axiom_152, axiom_163, axiom_282, axiom_59, axiom_259, axiom_125, axiom_237, axiom_265, axiom_185, axiom_217, axiom_44, axiom_49, axiom_198, axiom_214, axiom_168, axiom_206, axiom_95, axiom_191, axiom_121, axiom_179, axiom_233, axiom_260, axiom_73, axiom_141, axiom_226, axiom_67, axiom_276, axiom_51, axiom_157, axiom_195, axiom_99, axiom_84, axiom_69, axiom_258, axiom_21, axiom_244, axiom_222, axiom_203, axiom_63, axiom_110, axiom_38, axiom_146, axiom_170, axiom_147, axiom_220, axiom_184, axiom_266, axiom_151, axiom_285, axiom_129, axiom_158, axiom_255, axiom_43, axiom_107, axiom_173, axiom_27, axiom_162, axiom_267, axiom_143, axiom_180, axiom_218, axiom_32, axiom_6, axiom_91, axiom_169, axiom_60, axiom_144, axiom_281, axiom_238, axiom_118, axiom_132, axiom_126, axiom_208, axiom_274, axiom_155, axiom_78, axiom_187, axiom_54, axiom_196, axiom_100, axiom_234, axiom_148, axiom_245, axiom_92, axiom_64, axiom_277, axiom_263, axiom_159, axiom_50, axiom_176, axiom_227, axiom_122, axiom_81, axiom_74, axiom_111, axiom_213, axiom_207, axiom_270, axiom_96, axiom_249, axiom_192, axiom_202, axiom_68, axiom_46, axiom_104, axiom_241, axiom_154, axiom_20, axiom_256, axiom_85, axiom_165, axiom_223, axiom_115, axiom_205, axiom_156, axiom_145, axiom_42, axiom_273, axiom_280, axiom_90, axiom_1, axiom_212, axiom_57, axiom_230, axiom_257, axiom_138, axiom_127, axiom_246, axiom_224, axiom_252, axiom_209, axiom_235, axiom_116, axiom_61, axiom_229, axiom_28, axiom_150, axiom_216, axiom_53, axiom_197, axiom_167, axiom_189, axiom_101, axiom_112, axiom_65, axiom_219, axiom_39, axiom_251, axiom_97, axiom_161, axiom_193, axiom_86, axiom_201, axiom_279, axiom_262, axiom_149, axiom_172, axiom_268, axiom_75, axiom_183, axiom_278, axiom_47, axiom_240, axiom_166, axiom_13, axiom_93, axiom_177, axiom_284, axiom_5, axiom_123, axiom_82, axiom_188, axiom_41, axiom_128, axiom_171, axiom_242, axiom_164, axiom_225, axiom_200, axiom_211, axiom_52, axiom_34, axiom_182, axiom_194, axiom_247, axiom_204, axiom_153, axiom_0, axiom_58, axiom_62, axiom_231, axiom_45, axiom_253, axiom_11, axiom_199, axiom_272, axiom_215, axiom_117, axiom_160, axiom_261, axiom_56, axiom_175, axiom_29, axiom_264, axiom_186, axiom_236, axiom_239, axiom_228, axiom_87, axiom_113, axiom_12, axiom_9, axiom_98, axiom_250, axiom_178, axiom_48, axiom_142, axiom_283, axiom_275, axiom_83, axiom_14, axiom_124, axiom_72, axiom_120, axiom_269, axiom_190, axiom_4, axiom_210, axiom_66, axiom_37, axiom_135, axiom_94
% 17.15/6.53 % No. of inferences in proof: 496
% 17.15/6.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5825 ms resp. 4685 ms w/o parsing
% 18.14/6.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 18.14/6.85 % [INFO] Killing All external provers ...
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