TSTP Solution File: KRS157+1 by Leo-III---1.7.10
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS157+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 7 07:52:01 EDT 2024
% Result : Theorem 5.47s 2.59s
% Output : Refutation 5.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 187
% Syntax : Number of formulae : 275 ( 25 unt; 101 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 : 115 ( 115 >; 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_type,type,
cowlThing: $i > $o ).
thf(cowlNothing_type,type,
cowlNothing: $i > $o ).
thf(xsd_string_type,type,
xsd_string: $i > $o ).
thf(xsd_integer_type,type,
xsd_integer: $i > $o ).
thf(cC14_type,type,
cC14: $i > $o ).
thf(iV3102_type,type,
iV3102: $i ).
thf(cC44_type,type,
cC44: $i > $o ).
thf(cC216_type,type,
cC216: $i > $o ).
thf(cC64_type,type,
cC64: $i > $o ).
thf(cC46_type,type,
cC46: $i > $o ).
thf(cC28_type,type,
cC28: $i > $o ).
thf(cC30_type,type,
cC30: $i > $o ).
thf(cC58_type,type,
cC58: $i > $o ).
thf(rR1_type,type,
rR1: $i > $i > $o ).
thf(cC56_type,type,
cC56: $i > $o ).
thf(cC94_type,type,
cC94: $i > $o ).
thf(cC92_type,type,
cC92: $i > $o ).
thf(cC152_type,type,
cC152: $i > $o ).
thf(cC150_type,type,
cC150: $i > $o ).
thf(cC40_type,type,
cC40: $i > $o ).
thf(ra_Px86_type,type,
ra_Px86: $i > $i > $o ).
thf(cC164_type,type,
cC164: $i > $o ).
thf(cC162_type,type,
cC162: $i > $o ).
thf(cC82_type,type,
cC82: $i > $o ).
thf(cC80_type,type,
cC80: $i > $o ).
thf(cC188_type,type,
cC188: $i > $o ).
thf(cC186_type,type,
cC186: $i > $o ).
thf(cC118_type,type,
cC118: $i > $o ).
thf(cC116_type,type,
cC116: $i > $o ).
thf(cC10_type,type,
cC10: $i > $o ).
thf(ra_Px87_type,type,
ra_Px87: $i > $i > $o ).
thf(cC130_type,type,
cC130: $i > $o ).
thf(cC128_type,type,
cC128: $i > $o ).
thf(cC200_type,type,
cC200: $i > $o ).
thf(cC198_type,type,
cC198: $i > $o ).
thf(cC180_type,type,
cC180: $i > $o ).
thf(cC16xcomp_type,type,
cC16xcomp: $i > $o ).
thf(cC126xcomp_type,type,
cC126xcomp: $i > $o ).
thf(cC114xcomp_type,type,
cC114xcomp: $i > $o ).
thf(cC50_type,type,
cC50: $i > $o ).
thf(cC156_type,type,
cC156: $i > $o ).
thf(ra_Px5_type,type,
ra_Px5: $i > $i > $o ).
thf(cC4_type,type,
cC4: $i > $o ).
thf(cC2xcomp_type,type,
cC2xcomp: $i > $o ).
thf(cC142_type,type,
cC142: $i > $o ).
thf(cC140xcomp_type,type,
cC140xcomp: $i > $o ).
thf(cC98_type,type,
cC98: $i > $o ).
thf(cC72xcomp_type,type,
cC72xcomp: $i > $o ).
thf(cC96xcomp_type,type,
cC96xcomp: $i > $o ).
thf(cC26xcomp_type,type,
cC26xcomp: $i > $o ).
thf(ra_Px9_type,type,
ra_Px9: $i > $i > $o ).
thf(cC214xcomp_type,type,
cC214xcomp: $i > $o ).
thf(ra_Px75_type,type,
ra_Px75: $i > $i > $o ).
thf(cC40xcomp_type,type,
cC40xcomp: $i > $o ).
thf(cC48_type,type,
cC48: $i > $o ).
thf(cC160xcomp_type,type,
cC160xcomp: $i > $o ).
thf(cC78xcomp_type,type,
cC78xcomp: $i > $o ).
thf(cC172_type,type,
cC172: $i > $o ).
thf(cC34_type,type,
cC34: $i > $o ).
thf(cC32xcomp_type,type,
cC32xcomp: $i > $o ).
thf(cC60xcomp_type,type,
cC60xcomp: $i > $o ).
thf(ra_Px85_type,type,
ra_Px85: $i > $i > $o ).
thf(cC148xcomp_type,type,
cC148xcomp: $i > $o ).
thf(ra_Px1_type,type,
ra_Px1: $i > $i > $o ).
thf(ra_Px10_type,type,
ra_Px10: $i > $i > $o ).
thf(cC136_type,type,
cC136: $i > $o ).
thf(cC8xcomp_type,type,
cC8xcomp: $i > $o ).
thf(cC108_type,type,
cC108: $i > $o ).
thf(cC106xcomp_type,type,
cC106xcomp: $i > $o ).
thf(cC110_type,type,
cC110: $i > $o ).
thf(cC122_type,type,
cC122: $i > $o ).
thf(cC102_type,type,
cC102: $i > $o ).
thf(cC62xcomp_type,type,
cC62xcomp: $i > $o ).
thf(ra_Px20_type,type,
ra_Px20: $i > $i > $o ).
thf(cC144_type,type,
cC144: $i > $o ).
thf(cC42xcomp_type,type,
cC42xcomp: $i > $o ).
thf(ra_Px14_type,type,
ra_Px14: $i > $i > $o ).
thf(cC100xcomp_type,type,
cC100xcomp: $i > $o ).
thf(ra_Px76_type,type,
ra_Px76: $i > $i > $o ).
thf(cC86_type,type,
cC86: $i > $o ).
thf(cC90xcomp_type,type,
cC90xcomp: $i > $o ).
thf(cC66_type,type,
cC66: $i > $o ).
thf(cC38xcomp_type,type,
cC38xcomp: $i > $o ).
thf(cC192_type,type,
cC192: $i > $o ).
thf(cC18_type,type,
cC18: $i > $o ).
thf(cC196xcomp_type,type,
cC196xcomp: $i > $o ).
thf(cC74_type,type,
cC74: $i > $o ).
thf(cC12xcomp_type,type,
cC12xcomp: $i > $o ).
thf(ra_Px4_type,type,
ra_Px4: $i > $i > $o ).
thf(cC24xcomp_type,type,
cC24xcomp: $i > $o ).
thf(ra_Px88_type,type,
ra_Px88: $i > $i > $o ).
thf(cC178_type,type,
cC178: $i > $o ).
thf(cC176xcomp_type,type,
cC176xcomp: $i > $o ).
thf(cC184xcomp_type,type,
cC184xcomp: $i > $o ).
thf(cC54xcomp_type,type,
cC54xcomp: $i > $o ).
thf(cC10xcomp_type,type,
cC10xcomp: $i > $o ).
thf(cC72_type,type,
cC72: $i > $o ).
thf(cC70xcomp_type,type,
cC70xcomp: $i > $o ).
thf(ra_Px34_type,type,
ra_Px34: $i > $i > $o ).
thf(cTOP_type,type,
cTOP: $i > $o ).
thf(cTEST_type,type,
cTEST: $i > $o ).
thf(16,axiom,
! [A: $i] :
( ( cC116 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC114xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_21) ).
thf(170,plain,
! [A: $i] :
( ( ( cC116 @ A )
=> ( ( cC16xcomp @ A )
& ( cC114xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC114xcomp @ A ) )
=> ( cC116 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(46,axiom,
! [A: $i] :
( ( cC92 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC90xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_191) ).
thf(340,plain,
! [A: $i] :
( ( ( cC92 @ A )
=> ( ( cC16xcomp @ A )
& ( cC90xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC90xcomp @ A ) )
=> ( cC92 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(87,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC24xcomp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_204) ).
thf(504,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC24xcomp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(17,axiom,
! [A: $i] :
( ( cC50 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_150) ).
thf(176,plain,
! [A: $i] :
( ( ( cC50 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC50 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,axiom,
! [A: $i] :
( ( cC110 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(295,plain,
! [A: $i] :
( ( ( cC110 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC110 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(14,axiom,
! [A: $i] :
( ( cC180 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_86) ).
thf(158,plain,
! [A: $i] :
( ( ( cC180 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC180 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ( cC14 @ iV3102 )
& ( cC44 @ iV3102 )
& ( cC216 @ iV3102 )
& ( cC64 @ iV3102 )
& ( cC46 @ iV3102 )
& ( cC28 @ iV3102 )
& ( cowlThing @ iV3102 )
& ( cC30 @ iV3102 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) )
& ( cC14 @ iV3102 )
& ( cC44 @ iV3102 )
& ( cC216 @ iV3102 )
& ( cC64 @ iV3102 )
& ( cC46 @ iV3102 )
& ( cC28 @ iV3102 )
& ( cowlThing @ iV3102 )
& ( cC30 @ iV3102 ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(88,plain,
~ ( ! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) )
& ! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) )
& ( cC14 @ iV3102 )
& ( cC44 @ iV3102 )
& ( cC216 @ iV3102 )
& ( cC64 @ iV3102 )
& ( cC46 @ iV3102 )
& ( cC28 @ iV3102 )
& ( cowlThing @ iV3102 )
& ( cC30 @ iV3102 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(48,axiom,
! [A: $i] :
( ( cC40 @ A )
<=> ( ( cC32xcomp @ A )
& ( cC38xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_142) ).
thf(352,plain,
! [A: $i] :
( ( ( cC40 @ A )
=> ( ( cC32xcomp @ A )
& ( cC38xcomp @ A ) ) )
& ( ( ( cC32xcomp @ A )
& ( cC38xcomp @ A ) )
=> ( cC40 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(57,axiom,
! [A: $i] :
( ( cC56 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC54xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_155) ).
thf(404,plain,
! [A: $i] :
( ( ( cC56 @ A )
=> ( ( cC16xcomp @ A )
& ( cC54xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC54xcomp @ A ) )
=> ( cC56 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
! [A: $i] :
( ( cC122 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_27) ).
thf(301,plain,
! [A: $i] :
( ( ( cC122 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC122 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(65,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC60xcomp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_209) ).
thf(436,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC60xcomp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(60,axiom,
! [A: $i] :
( ( cC98 @ A )
<=> ~ ? [B: $i] : ( ra_Px34 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_198) ).
thf(421,plain,
! [A: $i] :
( ( ( cC98 @ A )
=> ~ ? [B: $i] : ( ra_Px34 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px34 @ A @ B )
=> ( cC98 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(13,axiom,
! [A: $i] :
( ( cC200 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC198 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_103) ).
thf(152,plain,
! [A: $i] :
( ( ( cC200 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC198 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC198 @ B ) )
=> ( cC200 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(37,axiom,
! [A: $i] :
( ( cC108 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC106xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(289,plain,
! [A: $i] :
( ( ( cC108 @ A )
=> ( ( cC16xcomp @ A )
& ( cC106xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC106xcomp @ A ) )
=> ( cC108 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(32,axiom,
! [A: $i] :
( ( cC150 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC148xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_56) ).
thf(261,plain,
! [A: $i] :
( ( ( cC150 @ A )
=> ( ( cC16xcomp @ A )
& ( cC148xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC148xcomp @ A ) )
=> ( cC150 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(24,axiom,
! [A: $i] :
( ( cC214xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px75 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_120) ).
thf(216,plain,
! [A: $i] :
( ( ( cC214xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px75 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px75 @ A @ B )
=> ( cC214xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC10xcomp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_214) ).
thf(475,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC10xcomp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(15,axiom,
! [A: $i] :
( ( cC128 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC126xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_32) ).
thf(164,plain,
! [A: $i] :
( ( ( cC128 @ A )
=> ( ( cC16xcomp @ A )
& ( cC126xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC126xcomp @ A ) )
=> ( cC128 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(52,axiom,
! [A: $i] :
( ( cC74 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_175) ).
thf(376,plain,
! [A: $i] :
( ( ( cC74 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC74 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(23,axiom,
! [A: $i] :
( ( cC26xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px9 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_130) ).
thf(211,plain,
! [A: $i] :
( ( ( cC26xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px9 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px9 @ A @ B )
=> ( cC26xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [A: $i] :
( ( cC152 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC150 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_57) ).
thf(106,plain,
! [A: $i] :
( ( ( cC152 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC150 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC150 @ B ) )
=> ( cC152 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(28,axiom,
! [A: $i] :
( ( cC80 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC78xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_183) ).
thf(238,plain,
! [A: $i] :
( ( ( cC80 @ A )
=> ( ( cC16xcomp @ A )
& ( cC78xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC78xcomp @ A ) )
=> ( cC80 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(25,axiom,
! [A: $i] :
( ( cC40xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px86 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_143) ).
thf(221,plain,
! [A: $i] :
( ( ( cC40xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px86 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px86 @ A @ B )
=> ( cC40xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(62,axiom,
cC214xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_216) ).
thf(428,plain,
cC214xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(40,axiom,
! [A: $i] :
( ( cC102 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(307,plain,
! [A: $i] :
( ( ( cC102 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC102 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(7,axiom,
! [A: $i] :
( ( cC164 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC162 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_67) ).
thf(117,plain,
! [A: $i] :
( ( ( cC164 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC162 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC162 @ B ) )
=> ( cC164 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,axiom,
! [A: $i] :
( ( cC86 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_186) ).
thf(334,plain,
! [A: $i] :
( ( ( cC86 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC86 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(55,axiom,
! [A: $i] :
( ( cC178 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC176xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_83) ).
thf(392,plain,
! [A: $i] :
( ( ( cC178 @ A )
=> ( ( cC16xcomp @ A )
& ( cC176xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC176xcomp @ A ) )
=> ( cC178 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(63,axiom,
cTOP @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_205) ).
thf(429,plain,
cTOP @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(76,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC40xcomp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_213) ).
thf(467,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC40xcomp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(81,axiom,
! [A: $i] :
( ( cC28 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC26xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_131) ).
thf(484,plain,
! [A: $i] :
( ( ( cC28 @ A )
=> ( ( cC16xcomp @ A )
& ( cC26xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC26xcomp @ A ) )
=> ( cC28 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(44,axiom,
! [A: $i] :
( ( cC100xcomp @ A )
<=> ? [B: $i] : ( ra_Px76 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(329,plain,
! [A: $i] :
( ( ( cC100xcomp @ A )
=> ? [B: $i] : ( ra_Px76 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px76 @ A @ B )
=> ( cC100xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(43,axiom,
! [A: $i] :
( ( cC42xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px14 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_146) ).
thf(324,plain,
! [A: $i] :
( ( ( cC42xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px14 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px14 @ A @ B )
=> ( cC42xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(19,axiom,
! [A: $i] :
( ( cC16xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px5 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_62) ).
thf(188,plain,
! [A: $i] :
( ( ( cC16xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px5 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px5 @ A @ B )
=> ( cC16xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i] :
( ( cC10 @ A )
<=> ? [B: $i] : ( ra_Px87 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(141,plain,
! [A: $i] :
( ( ( cC10 @ A )
=> ? [B: $i] : ( ra_Px87 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px87 @ A @ B )
=> ( cC10 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [A: $i] :
( ( cC60xcomp @ A )
<=> ? [B: $i] : ( ra_Px85 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_162) ).
thf(256,plain,
! [A: $i] :
( ( ( cC60xcomp @ A )
=> ? [B: $i] : ( ra_Px85 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px85 @ A @ B )
=> ( cC60xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(20,axiom,
! [A: $i] :
( ( cC4 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_140) ).
thf(193,plain,
! [A: $i] :
( ( ( cC4 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC2xcomp @ B ) )
=> ( cC4 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(71,axiom,
cC12xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_215) ).
thf(457,plain,
cC12xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(9,axiom,
! [A: $i] :
( ( cC188 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC186 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_92) ).
thf(129,plain,
! [A: $i] :
( ( ( cC188 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC186 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC186 @ B ) )
=> ( cC188 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(86,axiom,
cC32xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_207) ).
thf(503,plain,
cC32xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(29,axiom,
! [A: $i] :
( ( cC172 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_77) ).
thf(244,plain,
! [A: $i] :
( ( ( cC172 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC172 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(22,axiom,
! [A: $i] :
( ( cC98 @ A )
<=> ( ( cC72xcomp @ A )
& ( cC96xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_199) ).
thf(205,plain,
! [A: $i] :
( ( ( cC98 @ A )
=> ( ( cC72xcomp @ A )
& ( cC96xcomp @ A ) ) )
& ( ( ( cC72xcomp @ A )
& ( cC96xcomp @ A ) )
=> ( cC98 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(56,axiom,
! [A: $i] :
( ( cC186 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC184xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_91) ).
thf(398,plain,
! [A: $i] :
( ( ( cC186 @ A )
=> ( ( cC16xcomp @ A )
& ( cC184xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC184xcomp @ A ) )
=> ( cC186 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(64,axiom,
! [A: $i] :
( ( cC216 @ A )
<=> ( ( cC64 @ A )
& ( cC214xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_121) ).
thf(430,plain,
! [A: $i] :
( ( ( cC216 @ A )
=> ( ( cC64 @ A )
& ( cC214xcomp @ A ) ) )
& ( ( ( cC64 @ A )
& ( cC214xcomp @ A ) )
=> ( cC216 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(67,axiom,
cC16xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_210) ).
thf(444,plain,
cC16xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(68,axiom,
cTEST @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_202) ).
thf(445,plain,
cTEST @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(53,axiom,
! [A: $i] :
( ( cC12xcomp @ A )
<=> ? [B: $i] : ( ra_Px4 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_25) ).
thf(382,plain,
! [A: $i] :
( ( ( cC12xcomp @ A )
=> ? [B: $i] : ( ra_Px4 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px4 @ A @ B )
=> ( cC12xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(41,axiom,
! [A: $i] :
( ( cC62xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px20 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_165) ).
thf(313,plain,
! [A: $i] :
( ( ( cC62xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px20 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px20 @ A @ B )
=> ( cC62xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(75,axiom,
cC42xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_211) ).
thf(466,plain,
cC42xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(70,axiom,
! [A: $i] :
( ( cC30 @ A )
<=> ( ( cC28 @ A )
& ( cC14 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_132) ).
thf(451,plain,
! [A: $i] :
( ( ( cC30 @ A )
=> ( ( cC28 @ A )
& ( cC14 @ A ) ) )
& ( ( ( cC28 @ A )
& ( cC14 @ A ) )
=> ( cC30 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(42,axiom,
! [A: $i] :
( ( cC144 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_51) ).
thf(318,plain,
! [A: $i] :
( ( ( cC144 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC144 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(79,axiom,
! [A: $i] :
( ( cC46 @ A )
<=> ( ( cC30 @ A )
& ( cC44 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_148) ).
thf(477,plain,
! [A: $i] :
( ( ( cC46 @ A )
=> ( ( cC30 @ A )
& ( cC44 @ A ) ) )
& ( ( ( cC30 @ A )
& ( cC44 @ A ) )
=> ( cC46 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(54,axiom,
! [A: $i] :
( ( cC24xcomp @ A )
<=> ? [B: $i] : ( ra_Px88 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_127) ).
thf(387,plain,
! [A: $i] :
( ( ( cC24xcomp @ A )
=> ? [B: $i] : ( ra_Px88 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px88 @ A @ B )
=> ( cC24xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(80,axiom,
cC2xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_203) ).
thf(483,plain,
cC2xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(10,axiom,
! [A: $i] :
( ( cC118 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC116 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_22) ).
thf(135,plain,
! [A: $i] :
( ( ( cC118 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC116 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC116 @ B ) )
=> ( cC118 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i] :
( ( cC48 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_149) ).
thf(226,plain,
! [A: $i] :
( ( ( cC48 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC48 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(33,axiom,
! [A: $i] :
( ( cC2xcomp @ A )
<=> ? [B: $i] : ( ra_Px1 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_101) ).
thf(267,plain,
! [A: $i] :
( ( ( cC2xcomp @ A )
=> ? [B: $i] : ( ra_Px1 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px1 @ A @ B )
=> ( cC2xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
! [A: $i] :
( ( cC44 @ A )
<=> ( ( cC42xcomp @ A )
& ( cC32xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_147) ).
thf(438,plain,
! [A: $i] :
( ( ( cC44 @ A )
=> ( ( cC42xcomp @ A )
& ( cC32xcomp @ A ) ) )
& ( ( ( cC42xcomp @ A )
& ( cC32xcomp @ A ) )
=> ( cC44 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(82,axiom,
! [A: $i] :
( ( cC64 @ A )
<=> ( ( cC62xcomp @ A )
& ( cTOP @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_166) ).
thf(490,plain,
! [A: $i] :
( ( ( cC64 @ A )
=> ( ( cC62xcomp @ A )
& ( cTOP @ A ) ) )
& ( ( ( cC62xcomp @ A )
& ( cTOP @ A ) )
=> ( cC64 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(61,axiom,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC98 @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_208) ).
thf(426,plain,
! [A: $i] :
( ( rR1 @ iV3102 @ A )
=> ( cC98 @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(6,axiom,
! [A: $i] :
( ( cC40 @ A )
<=> ? [B: $i] : ( ra_Px86 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_141) ).
thf(112,plain,
! [A: $i] :
( ( ( cC40 @ A )
=> ? [B: $i] : ( ra_Px86 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px86 @ A @ B )
=> ( cC40 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,axiom,
! [A: $i] :
( ( cC82 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC80 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_184) ).
thf(123,plain,
! [A: $i] :
( ( ( cC82 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC80 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC80 @ B ) )
=> ( cC82 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(72,axiom,
cC100xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_218) ).
thf(458,plain,
cC100xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,axiom,
! [A: $i] :
( ( cC142 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC140xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_48) ).
thf(199,plain,
! [A: $i] :
( ( ( cC142 @ A )
=> ( ( cC16xcomp @ A )
& ( cC140xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC140xcomp @ A ) )
=> ( cC142 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(18,axiom,
! [A: $i] :
( ( cC156 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_59) ).
thf(182,plain,
! [A: $i] :
( ( ( cC156 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC156 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(51,axiom,
! [A: $i] :
( ( cC198 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC196xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_99) ).
thf(370,plain,
! [A: $i] :
( ( ( cC198 @ A )
=> ( ( cC16xcomp @ A )
& ( cC196xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC196xcomp @ A ) )
=> ( cC198 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(85,axiom,
cC62xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_212) ).
thf(502,plain,
cC62xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(69,axiom,
! [A: $i] :
( ( xsd_string @ A )
<=> ~ ( xsd_integer @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(446,plain,
! [A: $i] :
( ( ( xsd_string @ A )
=> ~ ( xsd_integer @ A ) )
& ( ~ ( xsd_integer @ A )
=> ( xsd_string @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(84,axiom,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(497,plain,
! [A: $i] :
( ( cowlThing @ A )
& ~ ( cowlNothing @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(30,axiom,
! [A: $i] :
( ( cC34 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC32xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_135) ).
thf(250,plain,
! [A: $i] :
( ( ( cC34 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC32xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC32xcomp @ B ) )
=> ( cC34 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(74,axiom,
cC26xcomp @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_206) ).
thf(465,plain,
cC26xcomp @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [A: $i] :
( ( cC32xcomp @ A )
<=> ? [B: $i] : ( ra_Px10 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_134) ).
thf(272,plain,
! [A: $i] :
( ( ( cC32xcomp @ A )
=> ? [B: $i] : ( ra_Px10 @ A @ B ) )
& ( ? [B: $i] : ( ra_Px10 @ A @ B )
=> ( cC32xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(47,axiom,
! [A: $i] :
( ( cC66 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_167) ).
thf(346,plain,
! [A: $i] :
( ( ( cC66 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC66 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(58,axiom,
! [A: $i] :
( ( cC10xcomp @ A )
<=> ~ ? [B: $i] : ( ra_Px87 @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(410,plain,
! [A: $i] :
( ( ( cC10xcomp @ A )
=> ~ ? [B: $i] : ( ra_Px87 @ A @ B ) )
& ( ~ ? [B: $i] : ( ra_Px87 @ A @ B )
=> ( cC10xcomp @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(12,axiom,
! [A: $i] :
( ( cC130 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC128 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_33) ).
thf(146,plain,
! [A: $i] :
( ( ( cC130 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC128 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC128 @ B ) )
=> ( cC130 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(49,axiom,
! [A: $i] :
( ( cC192 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_94) ).
thf(358,plain,
! [A: $i] :
( ( ( cC192 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC192 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(3,axiom,
! [A: $i] :
( ( cC58 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC56 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_157) ).
thf(94,plain,
! [A: $i] :
( ( ( cC58 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC56 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC56 @ B ) )
=> ( cC58 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(36,axiom,
! [A: $i] :
( ( cC10 @ A )
<=> ( ( cC2xcomp @ A )
& ( cC8xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(283,plain,
! [A: $i] :
( ( ( cC10 @ A )
=> ( ( cC2xcomp @ A )
& ( cC8xcomp @ A ) ) )
& ( ( ( cC2xcomp @ A )
& ( cC8xcomp @ A ) )
=> ( cC10 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(59,axiom,
! [A: $i] :
( ( cC72 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC70xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_173) ).
thf(415,plain,
! [A: $i] :
( ( ( cC72 @ A )
=> ( ( cC16xcomp @ A )
& ( cC70xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC70xcomp @ A ) )
=> ( cC72 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(73,axiom,
! [A: $i] :
( ( cTEST @ A )
<=> ( ( cC216 @ A )
& ( cC46 @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_201) ).
thf(459,plain,
! [A: $i] :
( ( ( cTEST @ A )
=> ( ( cC216 @ A )
& ( cC46 @ A ) ) )
& ( ( ( cC216 @ A )
& ( cC46 @ A ) )
=> ( cTEST @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(35,axiom,
! [A: $i] :
( ( cC136 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_42) ).
thf(277,plain,
! [A: $i] :
( ( ( cC136 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC136 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(77,axiom,
! [A: $i] :
( ( cC14 @ A )
<=> ( ( cC2xcomp @ A )
& ( cC12xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_44) ).
thf(469,plain,
! [A: $i] :
( ( ( cC14 @ A )
=> ( ( cC2xcomp @ A )
& ( cC12xcomp @ A ) ) )
& ( ( ( cC2xcomp @ A )
& ( cC12xcomp @ A ) )
=> ( cC14 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(83,axiom,
cowlThing @ iV3102,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_217) ).
thf(496,plain,
cowlThing @ iV3102,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(50,axiom,
! [A: $i] :
( ( cC18 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_85) ).
thf(364,plain,
! [A: $i] :
( ( ( cC18 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC16xcomp @ B ) )
=> ( cC18 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(27,axiom,
! [A: $i] :
( ( cC162 @ A )
<=> ( ( cC16xcomp @ A )
& ( cC160xcomp @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_66) ).
thf(232,plain,
! [A: $i] :
( ( ( cC162 @ A )
=> ( ( cC16xcomp @ A )
& ( cC160xcomp @ A ) ) )
& ( ( ( cC16xcomp @ A )
& ( cC160xcomp @ A ) )
=> ( cC162 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
! [A: $i] :
( ( cC94 @ A )
<=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC92 @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_193) ).
thf(100,plain,
! [A: $i] :
( ( ( cC94 @ A )
=> ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC92 @ B ) ) )
& ( ? [B: $i] :
( ( rR1 @ A @ B )
& ( cC92 @ B ) )
=> ( cC94 @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(506,plain,
$false,
inference(e,[status(thm)],[170,340,504,176,295,158,88,352,404,301,436,421,152,289,261,216,475,164,376,211,106,238,221,428,307,117,334,392,429,467,484,329,324,188,141,256,193,457,129,503,244,205,398,430,444,445,382,313,466,451,318,477,387,483,135,226,267,438,490,426,112,123,458,199,182,370,502,446,497,250,465,272,346,410,146,358,94,283,415,459,277,469,496,364,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS157+1 : TPTP v8.1.2. Released v3.1.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.17/0.37 % Computer : n011.cluster.edu
% 0.17/0.37 % Model : x86_64 x86_64
% 0.17/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.37 % Memory : 8042.1875MB
% 0.17/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.37 % CPULimit : 300
% 0.17/0.37 % WCLimit : 300
% 0.17/0.37 % DateTime : Mon May 6 15:19:54 EDT 2024
% 0.17/0.37 % CPUTime :
% 0.95/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.20 % [INFO] Parsing done (260ms).
% 1.54/1.21 % [INFO] Running in sequential loop mode.
% 2.10/1.43 % [INFO] eprover registered as external prover.
% 2.10/1.43 % [INFO] cvc4 registered as external prover.
% 2.10/1.43 % [INFO] Scanning for conjecture ...
% 2.38/1.51 % [INFO] Found a conjecture and 219 axioms. Running axiom selection ...
% 2.44/1.58 % [INFO] Axiom selection finished. Selected 85 axioms (removed 134 axioms).
% 2.81/1.64 % [INFO] Problem is first-order (TPTP FOF).
% 2.81/1.65 % [INFO] Type checking passed.
% 2.81/1.65 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 5.47/2.58 % External prover 'e' found a proof!
% 5.47/2.58 % [INFO] Killing All external provers ...
% 5.47/2.59 % Time passed: 2001ms (effective reasoning time: 1375ms)
% 5.47/2.59 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 5.47/2.59 % 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
% 5.47/2.59 % No. of inferences in proof: 174
% 5.47/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2001 ms resp. 1375 ms w/o parsing
% 5.86/2.66 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.86/2.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------