%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KRS162+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 : n017.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 07:44:47 AM UTC 2026
% Result : Theorem 4.45s 2.63s
% Output : Refutation 4.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 20
% Syntax : Number of formulae : 42 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 189 ( 66 equ; 0 cnn)
% Maximal formula atoms : 30 ( 4 avg)
% Number of connectives : 393 ( 58 ~; 0 |; 105 &; 188 @)
% ( 3 <=>; 39 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 121 ( 0 ^; 91 !; 30 ?; 121 :)
% 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(rp_decl,type,
rp: $i > $i > $o ).
thf(rq_decl,type,
rq: $i > $i > $o ).
thf(rr_decl,type,
rr: $i > $i > $o ).
thf(cA_decl,type,
cA: $i > $o ).
thf(cB_decl,type,
cB: $i > $o ).
thf(9,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(69,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rr ) )
& ( A = B ) )
=> ( C @ ( B @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(5,axiom,
! [A: $i] :
~ ( ( A @ cA )
& ( A @ cB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
thf(52,plain,
! [A: $i] :
~ ( ( A @ cA )
& ( A @ cB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,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(61,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_string )
& ( A = B ) )
=> ( B @ xsd_string ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
=> ( B @ cB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
=> ( B @ cB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlThing_substitution_1) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlThing )
& ( A = B ) )
=> ( B @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(16,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(91,plain,
! [A: $i,B: $i] :
( ( ( A @ xsd_integer )
& ( A = B ) )
=> ( B @ xsd_integer ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1) ).
thf(55,plain,
! [A: $i] :
( ( ~ ( A @ xsd_integer )
=> ( A @ xsd_string ) )
& ( ( A @ xsd_string )
=> ~ ( A @ xsd_integer ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( A = B ) )
=> ( C @ ( B @ rp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rp_substitution_1) ).
thf(79,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rp ) )
& ( A = B ) )
=> ( C @ ( B @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ( A @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
thf(109,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ ( A @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ cA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(77,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rp ) )
=> ( B @ cA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,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(73,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rr ) )
& ( A = B ) )
=> ( B @ ( C @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rq ) )
& ( A = B ) )
=> ( B @ ( C @ rq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rq_substitution_2) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rq ) )
& ( A = B ) )
=> ( B @ ( C @ rq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(1,conjecture,
( ! [A: $i] :
( ( ? [B: $i,C: $i,D: $i] :
( ( C != D )
& ( B != D )
& ( B != C )
& ( D @ ( A @ rq ) )
& ( C @ ( A @ rq ) )
& ( B @ ( A @ rq ) ) )
& ? [B: $i,C: $i] :
( ( B != C )
& ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) ) )
=> ? [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E != F )
& ( D != F )
& ( D != E )
& ( C != F )
& ( C != E )
& ( C != D )
& ( B != F )
& ( B != E )
& ( B != D )
& ( B != C )
& ( F @ ( A @ rr ) )
& ( E @ ( A @ rr ) )
& ( D @ ( A @ rr ) )
& ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) ) )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',the_axiom) ).
thf(2,negated_conjecture,
~ ( ! [A: $i] :
( ( ? [B: $i,C: $i,D: $i] :
( ( C != D )
& ( B != D )
& ( B != C )
& ( D @ ( A @ rq ) )
& ( C @ ( A @ rq ) )
& ( B @ ( A @ rq ) ) )
& ? [B: $i,C: $i] :
( ( B != C )
& ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) ) )
=> ? [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E != F )
& ( D != F )
& ( D != E )
& ( C != F )
& ( C != E )
& ( C != D )
& ( B != F )
& ( B != E )
& ( B != D )
& ( B != C )
& ( F @ ( A @ rr ) )
& ( E @ ( A @ rr ) )
& ( D @ ( A @ rr ) )
& ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) ) )
& ! [A: $i] :
( ( A @ xsd_string )
<=> ~ ( A @ xsd_integer ) )
& ! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(22,plain,
~ ( ! [A: $i] :
( ( ? [B: $i,C: $i,D: $i] :
( ( C != D )
& ( B != D )
& ( B != C )
& ( D @ ( A @ rq ) )
& ( C @ ( A @ rq ) )
& ( B @ ( A @ rq ) ) )
& ? [B: $i,C: $i] :
( ( B != C )
& ( C @ ( A @ rp ) )
& ( B @ ( A @ rp ) ) ) )
=> ? [B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E != F )
& ( D != F )
& ( D != E )
& ( C != F )
& ( C != E )
& ( C != D )
& ( B != F )
& ( B != E )
& ( B != D )
& ( B != C )
& ( F @ ( A @ rr ) )
& ( E @ ( A @ rr ) )
& ( D @ ( A @ rr ) )
& ( C @ ( A @ rr ) )
& ( B @ ( A @ rr ) ) ) )
& ! [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(3,axiom,
! [A: $i,B: $i] :
( ( ( A @ cA )
& ( A = B ) )
=> ( B @ cA ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cA_substitution_1) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ( A @ cA )
& ( A = B ) )
=> ( B @ cA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( ( A @ cB )
& ( A = B ) )
=> ( B @ cB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cB_substitution_1) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( A @ cB )
& ( A = B ) )
=> ( B @ cB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rq ) )
& ( A = B ) )
=> ( C @ ( B @ rq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rq_substitution_1) ).
thf(95,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ rq ) )
& ( A = B ) )
=> ( C @ ( B @ rq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,axiom,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_0) ).
thf(99,plain,
! [A: $i] :
( ~ ( A @ cowlNothing )
& ( A @ cowlThing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rp ) )
& ( A = B ) )
=> ( B @ ( C @ rp ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rp_substitution_2) ).
thf(87,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ rp ) )
& ( A = B ) )
=> ( B @ ( C @ rp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cowlNothing_substitution_1) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( ( A @ cowlNothing )
& ( A = B ) )
=> ( B @ cowlNothing ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
=> ( B @ ( A @ rr ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ rq ) )
=> ( B @ ( A @ rr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(117,plain,
$false,
inference(e,[status(thm)],[69,52,61,85,65,91,55,79,109,77,73,105,22,44,48,95,99,87,111,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS162+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.08 % 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
% 0.11/0.38 % Computer : n017.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 19:37:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 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
% 0.84/0.95 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.23/1.16 % [INFO] Parsing done (206ms).
% 1.23/1.18 % [INFO] Running in sequential loop mode.
% 1.93/1.57 % [INFO] eprover registered as external prover.
% 1.93/1.58 % [INFO] Scanning for conjecture ...
% 2.33/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 19 axioms. Running axiom selection ...
% 2.33/1.79 % [INFO] Axiom selection finished. Selected 19 axioms (removed 0 axioms).
% 2.50/1.81 % [INFO] Problem is first-order (TPTP FOF).
% 2.50/1.82 % [INFO] Type checking passed.
% 2.50/1.83 % [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 ...
% 4.45/2.63 % External prover 'e' found a proof!
% 4.45/2.63 % [INFO] Killing All external provers ...
% 4.45/2.63 % Time passed: 2109ms (effective reasoning time: 1443ms)
% 4.45/2.63 % 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)>
% 4.45/2.63 % Axioms used in derivation (19): cA_substitution_1, rr_substitution_1, axiom_6, cowlThing_substitution_1, axiom_3, axiom_5, axiom_0, rp_substitution_1, rr_substitution_2, axiom_4, cowlNothing_substitution_1, cB_substitution_1, axiom_2, rp_substitution_2, xsd_string_substitution_1, rq_substitution_1, axiom_1, xsd_integer_substitution_1, rq_substitution_2
% 4.45/2.63 % No. of inferences in proof: 42
% 4.45/2.63 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2109 ms resp. 1443 ms w/o parsing
% 4.45/2.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.45/2.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------