%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS113+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 : n016.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 4.35s 2.60s
% Output : Refutation 4.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 25
% Syntax : Number of formulae : 51 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 167 ( 35 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 318 ( 8 ~; 0 |; 58 &; 194 @)
% ( 6 <=>; 52 =>; 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 : 15 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 121 ( 0 ^; 109 !; 12 ?; 121 :)
% Comments :
%------------------------------------------------------------------------------
thf(cUnsatisfiable_decl,type,
cUnsatisfiable: $i > $o ).
thf(ca_Vx2_decl,type,
ca_Vx2: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(cp_decl,type,
cp: $i > $o ).
thf(cpxcomp_decl,type,
cpxcomp: $i > $o ).
thf(ra_Px1_decl,type,
ra_Px1: $i > $i > $o ).
thf(rinvS_decl,type,
rinvS: $i > $i > $o ).
thf(rr_decl,type,
rr: $i > $i > $o ).
thf(rs_decl,type,
rs: $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_22376_decl,type,
i2003_11_14_17_21_22376: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ cp )
& ( A = B ) )
=> ( B @ cp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp_substitution_1) ).
thf(42,plain,
! [A: $i,B: $i] :
( ( ( A @ cp )
& ( A = B ) )
=> ( B @ cp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ cpxcomp )
<=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(125,plain,
! [A: $i] :
( ( ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cpxcomp ) )
& ( ( A @ cpxcomp )
=> ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rs ) )
& ( A = B ) )
=> ( C @ ( B @ rs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rs_substitution_1) ).
thf(74,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rs ) )
& ( A = B ) )
=> ( C @ ( B @ rs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cUnsatisfiable )
<=> ( ( A @ cpxcomp )
& ? [B: $i] :
( ( B @ cp )
& ( B @ ( A @ rs ) ) )
& ? [B: $i] :
( ( B @ ca_Vx2 )
& ( B @ ( A @ rr ) ) )
& ! [B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( B = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(102,plain,
! [A: $i] :
( ( ( ( A @ cpxcomp )
& ? [B: $i] :
( ( B @ cp )
& ( B @ ( A @ rs ) ) )
& ? [B: $i] :
( ( B @ ca_Vx2 )
& ( B @ ( A @ rr ) ) )
& ! [B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( B = C ) ) )
=> ( A @ cUnsatisfiable ) )
& ( ( A @ cUnsatisfiable )
=> ( ( A @ cpxcomp )
& ? [B: $i] :
( ( B @ cp )
& ( B @ ( A @ rs ) ) )
& ? [B: $i] :
( ( B @ ca_Vx2 )
& ( B @ ( A @ rr ) ) )
& ! [B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) )
=> ( B = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(96,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_substitution_1) ).
thf(66,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
i2003_11_14_17_21_22376 @ cUnsatisfiable,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
thf(145,plain,
i2003_11_14_17_21_22376 @ cUnsatisfiable,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,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(50,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)],[7]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(90,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ cpxcomp )
& ( A = B ) )
=> ( B @ cpxcomp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cpxcomp_substitution_1) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( ( A @ cpxcomp )
& ( A = B ) )
=> ( B @ cpxcomp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rs ) )
& ( A = B ) )
=> ( B @ ( C @ rs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rs_substitution_2) ).
thf(78,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rs ) )
& ( A = B ) )
=> ( B @ ( C @ rs ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_substitution_2) ).
thf(70,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,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(54,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)],[8]) ).
thf(16,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(86,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,axiom,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cUnsatisfiable_substitution_1) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( A @ cUnsatisfiable )
& ( A = B ) )
=> ( B @ cUnsatisfiable ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rinvS ) )
<=> ( A @ ( B @ rs ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(139,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ rs ) )
=> ( B @ ( A @ rinvS ) ) )
& ( ( B @ ( A @ rinvS ) )
=> ( A @ ( B @ rs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,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(82,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ cp )
<=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(119,plain,
! [A: $i] :
( ( ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) )
=> ( A @ cp ) )
& ( ( A @ cp )
=> ~ ? [B: $i] : ( B @ ( A @ ra_Px1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvS ) )
& ( A = B ) )
=> ( C @ ( B @ rinvS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvS_substitution_1) ).
thf(58,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rinvS ) )
& ( A = B ) )
=> ( C @ ( B @ rinvS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rs ) )
=> ( B @ ( A @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rs ) )
=> ( B @ ( A @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(2,axiom,
! [A: $i,B: $i] :
( ( ( A @ ca_Vx2 )
& ( A = B ) )
=> ( B @ ca_Vx2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca_Vx2_substitution_1) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( A @ ca_Vx2 )
& ( A = B ) )
=> ( B @ ca_Vx2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ca_Vx2 )
<=> ! [B: $i] :
( ( B @ ( A @ rinvS ) )
=> ( B @ cp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(131,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ ( A @ rinvS ) )
=> ( B @ cp ) )
=> ( A @ ca_Vx2 ) )
& ( ( A @ ca_Vx2 )
=> ! [B: $i] :
( ( B @ ( A @ rinvS ) )
=> ( B @ cp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvS ) )
& ( A = B ) )
=> ( B @ ( C @ rinvS ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rinvS_substitution_2) ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rinvS ) )
& ( A = B ) )
=> ( B @ ( C @ rinvS ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(148,plain,
$false,
inference(e,[status(thm)],[42,125,74,102,96,34,66,145,50,90,46,78,38,70,54,86,26,139,82,119,58,146,30,131,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS113+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n016.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Fri Sep 25 19:45:14 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.82/1.00 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.16/1.19 % [INFO] Parsing done (183ms).
% 1.33/1.20 % [INFO] Running in sequential loop mode.
% 2.00/1.61 % [INFO] eprover registered as external prover.
% 2.00/1.62 % [INFO] Scanning for conjecture ...
% 2.00/1.67 % [INFO] 25 axioms and no conjecture found.
% 2.19/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.19/1.78 % [INFO] Type checking passed.
% 2.19/1.78 % [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 ...
% 4.06/2.60 % External prover 'e' found a proof!
% 4.06/2.60 % [INFO] Killing All external provers ...
% 4.35/2.60 % Time passed: 2028ms (effective reasoning time: 1388ms)
% 4.35/2.60 % Axioms used in derivation (25): cpxcomp_substitution_1, rr_substitution_1, axiom_2, xsd_string_substitution_1, rinvS_substitution_2, cowlThing_substitution_1, axiom_3, rinvS_substitution_1, axiom_5, axiom_0, ca_Vx2_substitution_1, cp_substitution_1, axiom_4, axiom_7, cowlNothing_substitution_1, axiom_6, ra_Px1_substitution_1, ra_Px1_substitution_2, cUnsatisfiable_substitution_1, axiom_1, xsd_integer_substitution_1, axiom_8, rs_substitution_2, rs_substitution_1, rr_substitution_2
% 4.35/2.60 % No. of inferences in proof: 51
% 4.35/2.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 2028 ms resp. 1388 ms w/o parsing
% 4.35/2.67 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.35/2.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------