%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS174+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 : n014.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 6.00s 8.58s
% Output : Refutation 6.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 104 ( 26 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 163 ( 14 ~; 7 |; 31 &; 77 @)
% ( 8 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 ^; 47 !; 0 ?; 47 :)
% 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(cA_and_B_decl,type,
cA_and_B: $i > $o ).
thf(cB_decl,type,
cB: $i > $o ).
thf(cA_decl,type,
cA: $i > $o ).
thf(ia_decl,type,
ia: $i ).
thf(ib_decl,type,
ib: $i ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( ( A @ cB )
& ( A = B ) )
=> ( B @ cB ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cB_substitution_1) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( ( A @ cB )
& ( A = B ) )
=> ( B @ cB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cA_and_B )
& ( A = B ) )
=> ( B @ cA_and_B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cA_and_B_substitution_1) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( A @ cA_and_B )
& ( A = B ) )
=> ( B @ cA_and_B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,axiom,
ib @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(97,plain,
ib @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,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(53,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(8,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(49,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(63,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cA )
<=> ( A = ia ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(69,plain,
! [A: $i] :
( ( ( A = ia )
=> ( A @ cA ) )
& ( ( A @ cA )
=> ( A = ia ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ cB )
<=> ( A = ib ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(88,plain,
! [A: $i] :
( ( ( A = ib )
=> ( A @ cB ) )
& ( ( A @ cB )
=> ( A = ib ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_0) ).
thf(57,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cA )
& ( A = B ) )
=> ( B @ cA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cA_substitution_1) ).
thf(29,plain,
! [A: $i,B: $i] :
( ( ( A @ cA )
& ( A = B ) )
=> ( B @ cA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ cA_and_B )
<=> ( ( A = ia )
| ( A = ib ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(77,plain,
! [A: $i] :
( ( ( ( A = ia )
| ( A = ib ) )
=> ( A @ cA_and_B ) )
& ( ( A @ cA_and_B )
=> ( ( A = ia )
| ( A = ib ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
ia @ cowlThing,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(96,plain,
ia @ cowlThing,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( A @ cA_and_B )
<=> ( ( A @ cA )
| ( A @ cB ) ) )
& ! [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 @ cA_and_B )
<=> ( ( A @ cA )
| ( A @ cB ) ) )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ( ! [A: $i] :
( ( ( ( A @ cA )
| ( A @ cB ) )
=> ( A @ cA_and_B ) )
& ( ( A @ cA_and_B )
=> ( ( A @ cA )
| ( A @ cB ) ) ) )
& ! [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(98,plain,
$false,
inference(e,[status(thm)],[37,33,97,53,41,49,63,69,88,57,29,77,96,45,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KRS174+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.13 % 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
% 0.26/5.54 % Computer : n014.cluster.edu
% 0.26/5.54 % Model : x86_64 x86_64
% 0.26/5.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/5.54 % Memory : 8046.5625MB
% 0.26/5.54 % OS : Linux 6.8.0-71-generic
% 0.26/5.54 % CPULimit : 300
% 0.26/5.54 % WCLimit : 300
% 0.26/5.54 % DateTime : Fri Sep 25 19:42:23 UTC 2026
% 0.26/5.54 % CPUTime :
% 0.26/5.54 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
% 1.27/6.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/6.57 % [INFO] Parsing done (282ms).
% 1.81/6.59 % [INFO] Running in sequential loop mode.
% 3.00/7.22 % [INFO] eprover registered as external prover.
% 3.00/7.23 % [INFO] Scanning for conjecture ...
% 3.21/7.38 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 3.38/7.44 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 3.38/7.49 % [INFO] Problem is first-order (TPTP FOF).
% 3.38/7.50 % [INFO] Type checking passed.
% 3.57/7.51 % [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 ...
% 6.00/8.58 % External prover 'e' found a proof!
% 6.00/8.58 % [INFO] Killing All external provers ...
% 6.00/8.58 % Time passed: 2815ms (effective reasoning time: 1976ms)
% 6.00/8.58 % 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)>
% 6.00/8.58 % Axioms used in derivation (14): cA_substitution_1, xsd_string_substitution_1, axiom_6, cowlThing_substitution_1, axiom_3, axiom_5, axiom_0, axiom_4, cowlNothing_substitution_1, cB_substitution_1, cA_and_B_substitution_1, axiom_2, axiom_1, xsd_integer_substitution_1
% 6.00/8.58 % No. of inferences in proof: 32
% 6.00/8.58 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2815 ms resp. 1976 ms w/o parsing
% 6.35/8.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.35/8.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------