%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS172+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 : n008.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 07:44:49 AM UTC 2026
% Result : Theorem 4.59s 2.99s
% Output : Refutation 4.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 19
% Syntax : Number of formulae : 40 ( 3 unt; 0 typ; 0 def)
% Number of atoms : 121 ( 22 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 235 ( 14 ~; 0 |; 38 &; 140 @)
% ( 7 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 ^; 84 !; 0 ?; 84 :)
% 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(rq_decl,type,
rq: $i > $i > $o ).
thf(rp_decl,type,
rp: $i > $i > $o ).
thf(cd_decl,type,
cd: $i > $o ).
thf(iv_decl,type,
iv: $i ).
thf(17,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(88,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(8,axiom,
iv @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(56,plain,
iv @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,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(42,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rq ) )
& ( A = B ) )
=> ( C @ ( B @ rq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rq_substitution_1) ).
thf(84,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rq ) )
& ( A = B ) )
=> ( C @ ( B @ rq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
<=> ( B @ ( A @ rp ) ) )
& ! [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,B: $i] :
( ( B @ ( A @ rq ) )
<=> ( B @ ( A @ rp ) ) )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ( ! [A: $i,B: $i] :
( ( ( B @ ( A @ rp ) )
=> ( B @ ( A @ rq ) ) )
& ( ( B @ ( A @ rq ) )
=> ( B @ ( A @ rp ) ) ) )
& ! [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(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
=> ( A @ cd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(73,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
=> ( A @ cd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,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(80,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(36,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rq ) )
& ( A = B ) )
=> ( B @ ( C @ rq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rq_substitution_2) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rq ) )
& ( A = B ) )
=> ( B @ ( C @ rq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(46,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(60,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rp ) )
=> ( A @ cd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(102,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rp ) )
=> ( A @ cd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cd )
& ( A = B ) )
=> ( B @ cd ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cd_substitution_1) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( ( A @ cd )
& ( A = B ) )
=> ( B @ cd ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rq ) )
& ( B @ ( A @ rq ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(64,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rq ) )
& ( B @ ( A @ rq ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,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(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rp ) )
& ( A = B ) )
=> ( B @ ( C @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,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(98,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( A = B ) )
=> ( C @ ( B @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ cd )
<=> ( iv @ ( A @ rp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(50,plain,
! [A: $i] :
( ( ( iv @ ( A @ rp ) )
=> ( A @ cd ) )
& ( ( A @ cd )
=> ( iv @ ( A @ rp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cd )
<=> ( iv @ ( A @ rq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(67,plain,
! [A: $i] :
( ( ( iv @ ( A @ rq ) )
=> ( A @ cd ) )
& ( ( A @ cd )
=> ( iv @ ( A @ rq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(106,plain,
$false,
inference(e,[status(thm)],[88,56,42,84,21,73,80,36,94,46,57,60,102,32,64,76,98,50,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS172+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.12 % 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
% 0.24/0.48 % Computer : n008.cluster.edu
% 0.24/0.48 % Model : x86_64 x86_64
% 0.24/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.48 % Memory : 8046.5625MB
% 0.24/0.48 % OS : Linux 6.8.0-71-generic
% 0.24/0.48 % CPULimit : 300
% 0.24/0.48 % WCLimit : 300
% 0.24/0.48 % DateTime : Fri Sep 25 19:43:29 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 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
% 1.31/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.84/1.59 % [INFO] Parsing done (294ms).
% 2.08/1.61 % [INFO] Running in sequential loop mode.
% 2.73/2.07 % [INFO] eprover registered as external prover.
% 2.73/2.08 % [INFO] Scanning for conjecture ...
% 2.89/2.18 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.95/2.25 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.95/2.29 % [INFO] Problem is first-order (TPTP FOF).
% 2.95/2.29 % [INFO] Type checking passed.
% 3.15/2.30 % [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 ...
% 4.59/2.98 % External prover 'e' found a proof!
% 4.59/2.98 % [INFO] Killing All external provers ...
% 4.59/2.99 % Time passed: 2294ms (effective reasoning time: 1367ms)
% 4.59/2.99 % 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)>
% 4.59/2.99 % Axioms used in derivation (18): axiom_6, axiom_3, axiom_8, axiom_5, axiom_0, rp_substitution_1, axiom_4, axiom_7, cowlNothing_substitution_1, axiom_2, rp_substitution_2, xsd_string_substitution_1, rq_substitution_1, cowlThing_substitution_1, cd_substitution_1, axiom_1, xsd_integer_substitution_1, rq_substitution_2
% 4.59/2.99 % No. of inferences in proof: 40
% 4.59/2.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2294 ms resp. 1367 ms w/o parsing
% 4.94/3.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.94/3.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------