%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS167+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 : n005.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 07:44:48 AM UTC 2026
% Result : Theorem 3.84s 2.73s
% Output : Refutation 3.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 13
% Syntax : Number of formulae : 28 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 22 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 211 ( 14 ~; 0 |; 44 &; 114 @)
% ( 7 <=>; 32 =>; 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 : 9 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 71 ( 0 ^; 65 !; 6 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
thf(cowlThing_decl,type,
cowlThing: $i > $o ).
thf(cowlNothing_decl,type,
cowlNothing: $i > $o ).
thf(xsd_string_decl,type,
xsd_string: $i > $o ).
thf(xsd_integer_decl,type,
xsd_integer: $i > $o ).
thf(cc1_decl,type,
cc1: $i > $o ).
thf(cc2_decl,type,
cc2: $i > $o ).
thf(rp_decl,type,
rp: $i > $i > $o ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( A = B ) )
=> ( C @ ( B @ rp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rp_substitution_1) ).
thf(42,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( A = B ) )
=> ( C @ ( B @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rp ) )
& ( A = B ) )
=> ( B @ ( C @ rp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rp_substitution_2) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rp ) )
& ( A = B ) )
=> ( B @ ( C @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,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(54,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(9,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(50,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cc1 )
& ( A = B ) )
=> ( B @ cc1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_substitution_1) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( A @ cc1 )
& ( A = B ) )
=> ( B @ cc1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(58,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cc2 )
& ( A = B ) )
=> ( B @ cc2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_substitution_1) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( ( A @ cc2 )
& ( A = B ) )
=> ( B @ cc2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( A @ cc1 )
<=> ( A @ cc2 ) )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( A @ cc1 )
<=> ( A @ cc2 ) )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ( ! [A: $i] :
( ( ( A @ cc2 )
=> ( A @ cc1 ) )
& ( ( A @ cc1 )
=> ( A @ cc2 ) ) )
& ! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cc2 )
<=> ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) )
& ? [B: $i] : ( B @ ( A @ rp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(83,plain,
! [A: $i] :
( ( ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) )
& ? [B: $i] : ( B @ ( A @ rp ) ) )
=> ( A @ cc2 ) )
& ( ( A @ cc2 )
=> ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) )
& ? [B: $i] : ( B @ ( A @ rp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox2/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)],[6]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cc1 )
<=> ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) )
& ? [B: $i] : ( B @ ( A @ rp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(70,plain,
! [A: $i] :
( ( ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) )
& ? [B: $i] : ( B @ ( A @ rp ) ) )
=> ( A @ cc1 ) )
& ( ( A @ cc1 )
=> ( ! [B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) )
& ? [B: $i] : ( B @ ( A @ rp ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox2/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)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(64,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(96,plain,
$false,
inference(e,[status(thm)],[42,46,54,50,26,58,30,15,83,38,70,34,64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.23 % Problem : KRS167+1 : TPTP v9.3.1. Released v3.1.0.
% 0.03/0.28 % 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
% 0.13/0.60 % Computer : n005.cluster.edu
% 0.13/0.60 % Model : x86_64 x86_64
% 0.13/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.60 % Memory : 8046.5625MB
% 0.13/0.60 % OS : Linux 6.8.0-71-generic
% 0.13/0.60 % CPULimit : 300
% 0.13/0.60 % WCLimit : 300
% 0.13/0.60 % DateTime : Fri Sep 25 19:41:48 UTC 2026
% 0.13/0.60 % CPUTime :
% 0.13/0.60 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
% 0.90/1.19 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/1.40 % [INFO] Parsing done (203ms).
% 1.35/1.42 % [INFO] Running in sequential loop mode.
% 1.78/1.79 % [INFO] eprover registered as external prover.
% 1.95/1.80 % [INFO] Scanning for conjecture ...
% 1.95/1.89 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.11/1.93 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.11/1.96 % [INFO] Problem is first-order (TPTP FOF).
% 2.11/1.97 % [INFO] Type checking passed.
% 2.11/1.97 % [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 ...
% 3.84/2.72 % External prover 'e' found a proof!
% 3.84/2.72 % [INFO] Killing All external provers ...
% 3.84/2.72 % Time passed: 1976ms (effective reasoning time: 1302ms)
% 3.84/2.72 % 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)>
% 3.84/2.73 % Axioms used in derivation (12): cowlNothing_substitution_1, cc1_substitution_1, xsd_string_substitution_1, cowlThing_substitution_1, axiom_3, axiom_0, cc2_substitution_1, rp_substitution_1, axiom_2, rp_substitution_2, axiom_1, xsd_integer_substitution_1
% 3.84/2.73 % No. of inferences in proof: 28
% 3.84/2.73 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1976 ms resp. 1302 ms w/o parsing
% 3.84/2.78 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.84/2.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------