%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n013.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 5.30s 2.84s
% Output : Refutation 5.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 53
% Syntax : Number of formulae : 107 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 315 ( 74 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 611 ( 8 ~; 0 |; 100 &; 395 @)
% ( 6 <=>; 102 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 2 con; 0-2 aty)
% Number of variables : 263 ( 0 ^; 248 !; 15 ?; 263 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(ca_Ax2_decl,type,
ca_Ax2: $i > $o ).
thf(ca_Cx1_decl,type,
ca_Cx1: $i > $o ).
thf(ca_Cx1xcomp_decl,type,
ca_Cx1xcomp: $i > $o ).
thf(cc1_decl,type,
cc1: $i > $o ).
thf(cc2_decl,type,
cc2: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(rrx_decl,type,
rrx: $i > $i > $o ).
thf(rrx1_decl,type,
rrx1: $i > $i > $o ).
thf(rrx1a_decl,type,
rrx1a: $i > $i > $o ).
thf(rrx2_decl,type,
rrx2: $i > $i > $o ).
thf(rrx2a_decl,type,
rrx2a: $i > $i > $o ).
thf(rrx3_decl,type,
rrx3: $i > $i > $o ).
thf(rrx3a_decl,type,
rrx3a: $i > $i > $o ).
thf(rrx4_decl,type,
rrx4: $i > $i > $o ).
thf(rrx4a_decl,type,
rrx4a: $i > $i > $o ).
thf(rrxa_decl,type,
rrxa: $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_01226_decl,type,
i2003_11_14_17_21_01226: $i ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx3 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx3_substitution_2) ).
thf(138,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx3 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx3a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx3a_substitution_1) ).
thf(142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx3a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_integer_substitution_1) ).
thf(174,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx1a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx1a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx1a_substitution_1) ).
thf(110,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx1a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx1a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ cc2 )
& ( A = B ) )
=> ( B @ cc2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_substitution_1) ).
thf(74,plain,
! [A: $i,B: $i] :
( ( ( A @ cc2 )
& ( A = B ) )
=> ( B @ cc2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(188,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3a ) )
=> ( B @ ( A @ rrx1a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_18) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3a ) )
=> ( B @ ( A @ rrx1a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx3_substitution_1) ).
thf(134,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrxa ) )
& ( A = B ) )
=> ( C @ ( B @ rrxa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrxa_substitution_1) ).
thf(166,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrxa ) )
& ( A = B ) )
=> ( C @ ( B @ rrxa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1xcomp )
& ( A = B ) )
=> ( B @ ca_Cx1xcomp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca_Cx1xcomp_substitution_1) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1xcomp )
& ( A = B ) )
=> ( B @ ca_Cx1xcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx2a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx2a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx2a_substitution_2) ).
thf(130,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx2a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx2a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx4_substitution_1) ).
thf(150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(182,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx4 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx4 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx4_substitution_2) ).
thf(154,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx4 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx4 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4a ) )
=> ( B @ ( A @ rrxa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_15) ).
thf(250,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4a ) )
=> ( B @ ( A @ rrxa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx3a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx3a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx3a_substitution_2) ).
thf(146,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx3a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx3a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrxa ) )
& ( A = B ) )
=> ( B @ ( C @ rrxa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrxa_substitution_2) ).
thf(170,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrxa ) )
& ( A = B ) )
=> ( B @ ( C @ rrxa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ ca_Cx1xcomp )
<=> ? [B: $i] :
( ( B @ ca_Ax2 )
& ( B @ ( A @ rrx3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(217,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( B @ ca_Ax2 )
& ( B @ ( A @ rrx3 ) ) )
=> ( A @ ca_Cx1xcomp ) )
& ( ( A @ ca_Cx1xcomp )
=> ? [B: $i] :
( ( B @ ca_Ax2 )
& ( B @ ( A @ rrx3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ca_Cx1 )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(211,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)],[37]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx1 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx1_substitution_2) ).
thf(106,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx1 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3 ) )
& ( B @ ( A @ rrx3 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(233,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3 ) )
& ( B @ ( A @ rrx3 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3a ) )
=> ( B @ ( A @ rrxa ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
thf(248,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3a ) )
=> ( B @ ( A @ rrxa ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx1 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx1_substitution_1) ).
thf(102,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx1 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3 ) )
=> ( B @ ( A @ rrx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_20) ).
thf(260,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3 ) )
=> ( B @ ( A @ rrx ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ cc1 )
& ( A = B ) )
=> ( B @ cc1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_substitution_1) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( A @ cc1 )
& ( A = B ) )
=> ( B @ cc1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4 ) )
=> ( B @ ( A @ rrx2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_16) ).
thf(252,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4 ) )
=> ( B @ ( A @ rrx2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ca_Cx1xcomp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(224,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)],[39]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx2 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx2_substitution_1) ).
thf(118,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx2 ) )
& ( A = B ) )
=> ( C @ ( B @ rrx2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ca_Ax2 )
<=> ( ( A @ cc1 )
& ( A @ cc2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(204,plain,
! [A: $i] :
( ( ( ( A @ cc1 )
& ( A @ cc2 ) )
=> ( A @ ca_Ax2 ) )
& ( ( A @ ca_Ax2 )
=> ( ( A @ cc1 )
& ( A @ cc2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3a ) )
& ( B @ ( A @ rrx3a ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
thf(236,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx3a ) )
& ( B @ ( A @ rrx3a ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ ra_Px1 ) )
& ( A = B ) )
=> ( C @ ( B @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ra_Px1_substitution_1) ).
thf(86,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)],[9]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx ) )
& ( B @ ( A @ rrx ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx ) )
& ( B @ ( A @ rrx ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(45,axiom,
i2003_11_14_17_21_01226 @ cUnsatisfiable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
thf(245,plain,
i2003_11_14_17_21_01226 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx ) )
& ( A = B ) )
=> ( B @ ( C @ rrx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx_substitution_2) ).
thf(98,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx ) )
& ( A = B ) )
=> ( B @ ( C @ rrx ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx4a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx4a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx4a_substitution_2) ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx4a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx4a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ( ( A @ ca_Cx1 )
& ? [B: $i] :
( ( B @ cc2 )
& ( B @ ( A @ rrx4 ) ) )
& ? [B: $i] :
( ( B @ cc1 )
& ( B @ ( A @ rrx3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(194,plain,
! [A: $i] :
( ( ( ( A @ ca_Cx1 )
& ? [B: $i] :
( ( B @ cc2 )
& ( B @ ( A @ rrx4 ) ) )
& ? [B: $i] :
( ( B @ cc1 )
& ( B @ ( A @ rrx3 ) ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ( ( A @ ca_Cx1 )
& ? [B: $i] :
( ( B @ cc2 )
& ( B @ ( A @ rrx4 ) ) )
& ? [B: $i] :
( ( B @ cc1 )
& ( B @ ( A @ rrx3 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4a ) )
=> ( B @ ( A @ rrx2a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_19) ).
thf(258,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4a ) )
=> ( B @ ( A @ rrx2a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx4a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx4a_substitution_1) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx4a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx1a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx1a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx1a_substitution_2) ).
thf(114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx1a ) )
& ( A = B ) )
=> ( B @ ( C @ rrx1a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Ax2 )
& ( A = B ) )
=> ( B @ ca_Ax2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca_Ax2_substitution_1) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Ax2 )
& ( A = B ) )
=> ( B @ ca_Ax2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3 ) )
=> ( B @ ( A @ rrx1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
thf(246,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx3 ) )
=> ( B @ ( A @ rrx1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx2a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx2a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx2a_substitution_1) ).
thf(126,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx2a ) )
& ( A = B ) )
=> ( C @ ( B @ rrx2a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx ) )
& ( A = B ) )
=> ( C @ ( B @ rrx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx_substitution_1) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx ) )
& ( A = B ) )
=> ( C @ ( B @ rrx ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4 ) )
& ( B @ ( A @ rrx4 ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
thf(239,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4 ) )
& ( B @ ( A @ rrx4 ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4a ) )
& ( B @ ( A @ rrx4a ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
thf(242,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rrx4a ) )
& ( B @ ( A @ rrx4a ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1 )
& ( A = B ) )
=> ( B @ ca_Cx1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca_Cx1_substitution_1) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Cx1 )
& ( A = B ) )
=> ( B @ ca_Cx1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xsd_string_substitution_1) ).
thf(178,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ ra_Px1 ) )
& ( A = B ) )
=> ( B @ ( C @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ra_Px1_substitution_2) ).
thf(90,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)],[10]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4 ) )
=> ( B @ ( A @ rrx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_17) ).
thf(254,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rrx4 ) )
=> ( B @ ( A @ rrx ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx2 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rrx2_substitution_2) ).
thf(122,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rrx2 ) )
& ( A = B ) )
=> ( B @ ( C @ rrx2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(262,plain,
$false,
inference(e,[status(thm)],[138,142,174,110,78,74,188,256,134,166,66,130,150,182,154,250,146,170,217,211,106,233,248,102,260,70,252,224,118,204,54,236,86,230,245,98,162,194,258,158,114,58,246,82,126,94,239,242,62,178,90,254,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS107+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.13/0.40 % Computer : n013.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Fri Sep 25 19:39:06 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.86/0.97 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.45/1.20 % [INFO] Parsing done (235ms).
% 1.45/1.22 % [INFO] Running in sequential loop mode.
% 2.17/1.63 % [INFO] eprover registered as external prover.
% 2.17/1.64 % [INFO] Scanning for conjecture ...
% 2.17/1.69 % [INFO] 53 axioms and no conjecture found.
% 2.62/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.62/1.84 % [INFO] Type checking passed.
% 2.62/1.85 % [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 ...
% 5.30/2.84 % External prover 'e' found a proof!
% 5.30/2.84 % [INFO] Killing All external provers ...
% 5.30/2.84 % Time passed: 2301ms (effective reasoning time: 1611ms)
% 5.30/2.84 % Axioms used in derivation (53): axiom_10, rrx_substitution_1, xsd_string_substitution_1, axiom_16, rrx_substitution_2, rrx4_substitution_1, axiom_8, axiom_17, axiom_14, axiom_4, axiom_7, cowlNothing_substitution_1, rrx3_substitution_2, axiom_15, rrx2_substitution_2, cc1_substitution_1, axiom_19, ca_Ax2_substitution_1, rrx3a_substitution_2, axiom_2, rrx4_substitution_2, rrxa_substitution_1, axiom_6, ra_Px1_substitution_1, cowlThing_substitution_1, ca_Cx1_substitution_1, axiom_3, ca_Cx1xcomp_substitution_1, axiom_20, rrx3a_substitution_1, rrx2a_substitution_1, ra_Px1_substitution_2, rrx1a_substitution_2, cUnsatisfiable_substitution_1, rrxa_substitution_2, axiom_1, rrx1_substitution_2, xsd_integer_substitution_1, axiom_5, axiom_13, rrx1a_substitution_1, rrx3_substitution_1, rrx2a_substitution_2, axiom_0, axiom_11, rrx4a_substitution_2, rrx2_substitution_1, cc2_substitution_1, rrx4a_substitution_1, axiom_18, axiom_12, axiom_9, rrx1_substitution_1
% 5.30/2.84 % No. of inferences in proof: 107
% 5.30/2.84 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2301 ms resp. 1611 ms w/o parsing
% 5.76/2.94 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.76/2.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------