%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS108+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 07:44:40 AM UTC 2026
% Result : Unsatisfiable 6.15s 3.46s
% Output : Refutation 6.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 66
% Syntax : Number of formulae : 133 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 419 ( 81 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 781 ( 26 ~; 0 |; 134 &; 469 @)
% ( 21 <=>; 131 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 31 usr; 2 con; 0-2 aty)
% Number of variables : 300 ( 0 ^; 252 !; 48 ?; 300 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(ca_Ax14_decl,type,
ca_Ax14: $i > $o ).
thf(ca_Cx1_decl,type,
ca_Cx1: $i > $o ).
thf(ca_Cx1xcomp_decl,type,
ca_Cx1xcomp: $i > $o ).
thf(ca_Cx2_decl,type,
ca_Cx2: $i > $o ).
thf(ca_Cx2xcomp_decl,type,
ca_Cx2xcomp: $i > $o ).
thf(ca_Cx3_decl,type,
ca_Cx3: $i > $o ).
thf(ca_Cx3xcomp_decl,type,
ca_Cx3xcomp: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(cp1_decl,type,
cp1: $i > $o ).
thf(cp2_decl,type,
cp2: $i > $o ).
thf(cp2xcomp_decl,type,
cp2xcomp: $i > $o ).
thf(cp3_decl,type,
cp3: $i > $o ).
thf(cp3xcomp_decl,type,
cp3xcomp: $i > $o ).
thf(cp4_decl,type,
cp4: $i > $o ).
thf(cp4xcomp_decl,type,
cp4xcomp: $i > $o ).
thf(cp5_decl,type,
cp5: $i > $o ).
thf(cp5xcomp_decl,type,
cp5xcomp: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(ra_Px2_decl,type,
ra_Px2: $i > $i > $o ).
thf(ra_Px3_decl,type,
ra_Px3: $i > $i > $o ).
thf(ra_Px4_decl,type,
ra_Px4: $i > $i > $o ).
thf(ra_Px5_decl,type,
ra_Px5: $i > $i > $o ).
thf(ra_Px6_decl,type,
ra_Px6: $i > $i > $o ).
thf(ra_Px7_decl,type,
ra_Px7: $i > $i > $o ).
thf(rinvR_decl,type,
rinvR: $i > $i > $o ).
thf(rr_decl,type,
rr: $i > $i > $o ).
thf(xsd_integer_decl,type,
xsd_integer: $i > $o ).
thf(xsd_string_decl,type,
xsd_string: $i > $o ).
thf(i2003_11_14_17_21_04740_decl,type,
i2003_11_14_17_21_04740: $i ).
thf(59,axiom,
! [A: $i] :
( ( A @ ca_Cx2 )
<=> ( ( A @ cp4xcomp )
& ( A @ cp3xcomp )
& ( A @ cp5xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_19) ).
thf(334,plain,
! [A: $i] :
( ( ( ( A @ cp4xcomp )
& ( A @ cp3xcomp )
& ( A @ cp5xcomp ) )
=> ( A @ ca_Cx2 ) )
& ( ( A @ ca_Cx2 )
=> ( ( A @ cp4xcomp )
& ( A @ cp3xcomp )
& ( A @ cp5xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(229,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ ca_Cx1xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_18) ).
thf(328,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ ca_Cx1xcomp ) )
& ( ( A @ ca_Cx1xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ ca_Cx3 )
<=> ( ( A @ cp4xcomp )
& ( A @ cp5xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_23) ).
thf(360,plain,
! [A: $i] :
( ( ( ( A @ cp4xcomp )
& ( A @ cp5xcomp ) )
=> ( A @ ca_Cx3 ) )
& ( ( A @ ca_Cx3 )
=> ( ( A @ cp4xcomp )
& ( A @ cp5xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ cp4 )
=> ( A @ cp5xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(279,plain,
! [A: $i] :
( ( A @ cp4 )
=> ( A @ cp5xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx3xcomp )
& ( A = B ) )
=> ( B @ ca_Cx3xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Cx3xcomp_substitution_1) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx3xcomp )
& ( A = B ) )
=> ( B @ ca_Cx3xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp2xcomp )
& ( A = B ) )
=> ( B @ cp2xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2xcomp_substitution_1) ).
thf(115,plain,
! [A: $i,B: $i] :
( ( ( A @ cp2xcomp )
& ( A = B ) )
=> ( B @ cp2xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(66,axiom,
i2003_11_14_17_21_04740 @ cUnsatisfiable,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
thf(379,plain,
i2003_11_14_17_21_04740 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px5 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px5_substitution_2) ).
thf(179,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px5 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ ca_Cx2xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_21) ).
thf(348,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px2 ) )
=> ( A @ ca_Cx2xcomp ) )
& ( ( A @ ca_Cx2xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rr_substitution_2) ).
thf(211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cp2xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(253,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) )
=> ( A @ cp2xcomp ) )
& ( ( A @ cp2xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px1 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_2) ).
thf(147,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px1 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cp5xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_14) ).
thf(293,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px4 ) )
=> ( A @ cp5xcomp ) )
& ( ( A @ cp5xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cp1 )
=> ( A @ ca_Cx1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(243,plain,
! [A: $i] :
( ( A @ cp1 )
=> ( A @ ca_Cx1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ cp3 )
=> ( A @ ca_Cx3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(265,plain,
! [A: $i] :
( ( A @ cp3 )
=> ( A @ ca_Cx3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px7 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px7_substitution_1) ).
thf(191,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px7 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px7 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(52,axiom,
! [A: $i] :
( ( A @ cp4xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
thf(281,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px7 ) )
=> ( A @ cp4xcomp ) )
& ( ( A @ cp4xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ cp3 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(259,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px6 ) )
=> ( A @ cp3 ) )
& ( ( A @ cp3 )
=> ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Ax14 )
& ( A = B ) )
=> ( B @ ca_Ax14 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Ax14_substitution_1) ).
thf(71,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Ax14 )
& ( A = B ) )
=> ( B @ ca_Ax14 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ ca_Cx1 )
<=> ( ( A @ cp4xcomp )
& ( A @ cp3xcomp )
& ( A @ cp5xcomp )
& ( A @ cp2xcomp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
thf(313,plain,
! [A: $i] :
( ( ( ( A @ cp4xcomp )
& ( A @ cp3xcomp )
& ( A @ cp5xcomp )
& ( A @ cp2xcomp ) )
=> ( A @ ca_Cx1 ) )
& ( ( A @ ca_Cx1 )
=> ( ( A @ cp4xcomp )
& ( A @ cp3xcomp )
& ( A @ cp5xcomp )
& ( A @ cp2xcomp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px3 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px3_substitution_1) ).
thf(159,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px3 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px6 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px6_substitution_2) ).
thf(187,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px6 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ cp2 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(245,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px5 ) )
=> ( A @ cp2 ) )
& ( ( A @ cp2 )
=> ? [B: $i] : ( B @ ( A @ ra_Px5 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ ca_Cx3xcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_24) ).
thf(367,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px3 ) )
=> ( A @ ca_Cx3xcomp ) )
& ( ( A @ ca_Cx3xcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx3 )
& ( A = B ) )
=> ( B @ ca_Cx3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Cx3_substitution_1) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx3 )
& ( A = B ) )
=> ( B @ ca_Cx3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ cp2 )
=> ( A @ ca_Cx2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(251,plain,
! [A: $i] :
( ( A @ cp2 )
=> ( A @ ca_Cx2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px2 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px2_substitution_2) ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px2 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(40,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(223,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp5 )
& ( A = B ) )
=> ( B @ cp5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp5_substitution_1) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( ( A @ cp5 )
& ( A = B ) )
=> ( B @ cp5 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(55,axiom,
! [A: $i] :
( ( A @ ca_Ax14 )
<=> ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( B = C ) )
& ? [B: $i] :
( ( B @ cp1 )
& ( B @ ( A @ rr ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
thf(299,plain,
! [A: $i] :
( ( ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( B = C ) )
& ? [B: $i] :
( ( B @ cp1 )
& ( B @ ( A @ rr ) ) ) )
=> ( A @ ca_Ax14 ) )
& ( ( A @ ca_Ax14 )
=> ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( B = C ) )
& ? [B: $i] :
( ( B @ cp1 )
& ( B @ ( A @ rr ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cp3xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(267,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px6 ) )
=> ( A @ cp3xcomp ) )
& ( ( A @ cp3xcomp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px6 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px4 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px4_substitution_1) ).
thf(167,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px4 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ ca_Cx2 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_20) ).
thf(342,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px2 ) )
=> ( A @ ca_Cx2 ) )
& ( ( A @ ca_Cx2 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp3xcomp )
& ( A = B ) )
=> ( B @ cp3xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp3xcomp_substitution_1) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ( A @ cp3xcomp )
& ( A = B ) )
=> ( B @ cp3xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvR ) )
& ( A = B ) )
=> ( C @ ( B @ rinvR ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvR_substitution_1) ).
thf(199,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvR ) )
& ( A = B ) )
=> ( C @ ( B @ rinvR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp4 )
& ( A = B ) )
=> ( B @ cp4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp4_substitution_1) ).
thf(127,plain,
! [A: $i,B: $i] :
( ( ( A @ cp4 )
& ( A = B ) )
=> ( B @ cp4 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px5 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px5_substitution_1) ).
thf(175,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px5 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px5 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px1 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px1_substitution_1) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px1 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx2xcomp )
& ( A = B ) )
=> ( B @ ca_Cx2xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Cx2xcomp_substitution_1) ).
thf(87,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx2xcomp )
& ( A = B ) )
=> ( B @ ca_Cx2xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvR ) )
& ( A = B ) )
=> ( B @ ( C @ rinvR ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rinvR_substitution_2) ).
thf(203,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvR ) )
& ( A = B ) )
=> ( B @ ( C @ rinvR ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px4 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px4_substitution_2) ).
thf(171,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px4 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp5xcomp )
& ( A = B ) )
=> ( B @ cp5xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp5xcomp_substitution_1) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( A @ cp5xcomp )
& ( A = B ) )
=> ( B @ cp5xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1 )
& ( A = B ) )
=> ( B @ ca_Cx1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Cx1_substitution_1) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1 )
& ( A = B ) )
=> ( B @ ca_Cx1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp3 )
& ( A = B ) )
=> ( B @ cp3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp3_substitution_1) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( ( A @ cp3 )
& ( A = B ) )
=> ( B @ cp3 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ( ( A @ cp2 )
& ? [B: $i] :
( ( B @ ca_Ax14 )
& ( B @ ( A @ rinvR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(235,plain,
! [A: $i] :
( ( ( ( A @ cp2 )
& ? [B: $i] :
( ( B @ ca_Ax14 )
& ( B @ ( A @ rinvR ) ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ( ( A @ cp2 )
& ? [B: $i] :
( ( B @ ca_Ax14 )
& ( B @ ( A @ rinvR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rr_substitution_1) ).
thf(207,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(53,axiom,
! [A: $i] :
( ( A @ cp5 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
thf(287,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) )
=> ( A @ cp5 ) )
& ( ( A @ cp5 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px4 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px2 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px2_substitution_1) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px2 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px6 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px6_substitution_1) ).
thf(183,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px6 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px6 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
! [A: $i] :
( ( A @ cp4 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(273,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px7 ) )
=> ( A @ cp4 ) )
& ( ( A @ cp4 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px7 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvR ) )
<=> ( A @ ( B @ rr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
thf(373,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rr ) )
=> ( B @ ( A @ rinvR ) ) )
& ( ( B @ ( A @ rinvR ) )
=> ( A @ ( B @ rr ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp1 )
& ( A = B ) )
=> ( B @ cp1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1_substitution_1) ).
thf(107,plain,
! [A: $i,B: $i] :
( ( ( A @ cp1 )
& ( A = B ) )
=> ( B @ cp1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1xcomp )
& ( A = B ) )
=> ( B @ ca_Cx1xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Cx1xcomp_substitution_1) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1xcomp )
& ( A = B ) )
=> ( B @ ca_Cx1xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px7 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px7 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px7_substitution_2) ).
thf(195,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px7 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px7 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp4xcomp )
& ( A = B ) )
=> ( B @ cp4xcomp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp4xcomp_substitution_1) ).
thf(131,plain,
! [A: $i,B: $i] :
( ( ( A @ cp4xcomp )
& ( A = B ) )
=> ( B @ cp4xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px3 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ra_Px3_substitution_2) ).
thf(163,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px3 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp2 )
& ( A = B ) )
=> ( B @ cp2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2_substitution_1) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( A @ cp2 )
& ( A = B ) )
=> ( B @ cp2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ ca_Cx1 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_17) ).
thf(322,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ ca_Cx1 ) )
& ( ( A @ ca_Cx1 )
=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(215,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(62,axiom,
! [A: $i] :
( ( A @ ca_Cx3 )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_22) ).
thf(354,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px3 ) )
=> ( A @ ca_Cx3 ) )
& ( ( A @ ca_Cx3 )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx2 )
& ( A = B ) )
=> ( B @ ca_Cx2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ca_Cx2_substitution_1) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx2 )
& ( A = B ) )
=> ( B @ ca_Cx2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(380,plain,
$false,
inference(e,[status(thm)],[334,229,328,360,279,95,115,379,179,348,211,253,147,293,243,265,191,281,259,71,313,159,187,219,245,367,103,91,251,155,223,135,299,267,167,342,123,67,199,127,175,143,99,87,203,171,139,75,119,235,207,287,151,183,273,373,107,79,195,131,163,111,322,215,354,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS108+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Fri Sep 25 19:39:36 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 1.27/1.26 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.08/1.63 % [INFO] Parsing done (365ms).
% 2.08/1.65 % [INFO] Running in sequential loop mode.
% 3.09/2.21 % [INFO] eprover registered as external prover.
% 3.09/2.21 % [INFO] Scanning for conjecture ...
% 3.09/2.27 % [INFO] 66 axioms and no conjecture found.
% 3.45/2.41 % [INFO] Problem is first-order (TPTP FOF).
% 3.45/2.42 % [INFO] Type checking passed.
% 3.45/2.42 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 6.15/3.45 % External prover 'e' found a proof!
% 6.15/3.45 % [INFO] Killing All external provers ...
% 6.15/3.45 % Time passed: 2845ms (effective reasoning time: 1795ms)
% 6.15/3.45 % Axioms used in derivation (66): cp3_substitution_1, cp5_substitution_1, axiom_16, axiom_20, ca_Cx2_substitution_1, axiom_8, cp4_substitution_1, axiom_25, axiom_23, axiom_7, axiom_26, cowlNothing_substitution_1, axiom_10, ra_Px7_substitution_2, axiom_22, ra_Px5_substitution_1, ca_Cx3xcomp_substitution_1, cp5xcomp_substitution_1, cp2xcomp_substitution_1, ra_Px6_substitution_2, axiom_15, ca_Cx3_substitution_1, ra_Px3_substitution_1, rr_substitution_1, ra_Px2_substitution_1, axiom_21, axiom_19, ra_Px4_substitution_1, axiom_2, ra_Px2_substitution_2, ra_Px7_substitution_1, xsd_string_substitution_1, ra_Px5_substitution_2, ca_Ax14_substitution_1, ra_Px4_substitution_2, axiom_6, ra_Px1_substitution_1, cowlThing_substitution_1, ca_Cx1_substitution_1, axiom_3, ca_Cx2xcomp_substitution_1, ca_Cx1xcomp_substitution_1, ra_Px1_substitution_2, cUnsatisfiable_substitution_1, axiom_24, axiom_1, xsd_integer_substitution_1, ra_Px6_substitution_1, axiom_17, rinvR_substitution_1, axiom_5, cp2_substitution_1, axiom_13, cp4xcomp_substitution_1, axiom_0, cp1_substitution_1, axiom_11, ra_Px3_substitution_2, axiom_18, axiom_12, axiom_9, rr_substitution_2, axiom_14, rinvR_substitution_2, cp3xcomp_substitution_1, axiom_4
% 6.15/3.45 % No. of inferences in proof: 133
% 6.15/3.46 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2845 ms resp. 1795 ms w/o parsing
% 6.52/3.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.52/3.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------