%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE057+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n013.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 07:43:06 AM UTC 2026
% Result : Theorem 2.60s 1.46s
% Output : Refutation 2.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 10 unt; 0 typ; 1 def)
% Number of atoms : 20 ( 19 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 7 ~; 0 |; 1 &; 11 @)
% ( 0 <=>; 2 =>; 2 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 3 !; 0 ?; 4 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(domain_decl,type,
domain: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( A = zero )
=> ( ( A @ domain )
= zero ) ) ) ) ).
thf(17,axiom,
( ( zero @ domain )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(73,plain,
( ( zero @ domain )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(74,plain,
( ( zero @ domain )
= zero ),
inference(lifteq,[status(thm)],[73]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ domain )
= zero )
<= ( A = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ domain )
= zero )
<= ( A = zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i] :
( ( A = zero )
=> ( ( A @ domain )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
( ( ( sk1 @ domain )
!= zero )
& ( sk1 = zero ) ),
inference(cnf,[status(esa)],[20]) ).
thf(23,plain,
( ( sk1 @ domain )
!= zero ),
inference(cnfConj,[status(thm)],[21]) ).
thf(25,plain,
( ( sk1 @ domain )
!= zero ),
inference(lifteq,[status(thm)],[23]) ).
thf(22,plain,
sk1 = zero,
inference(cnfConj,[status(thm)],[21]) ).
thf(24,plain,
sk1 = zero,
inference(lifteq,[status(thm)],[22]) ).
thf(81,plain,
( ( zero @ domain )
!= zero ),
inference(rewrite,[status(thm)],[25,24]) ).
thf(82,plain,
$false,
inference(simplifyReflect,[status(thm)],[74,81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE057+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.16/0.41 % Computer : n013.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Fri Sep 25 19:18:36 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.94/0.82 % [INFO] Parsing done (102ms).
% 0.94/0.82 % [INFO] Running in sequential loop mode.
% 1.18/1.02 % [INFO] eprover registered as external prover.
% 1.18/1.02 % [INFO] Scanning for conjecture ...
% 1.51/1.07 % [INFO] Found a conjecture (or negated_conjecture) and 17 axioms. Running axiom selection ...
% 1.51/1.10 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.51/1.12 % [INFO] Problem is first-order (TPTP FOF).
% 1.51/1.12 % [INFO] Type checking passed.
% 1.51/1.13 % [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 ...
% 2.60/1.46 % [INFO] Killing All external provers ...
% 2.60/1.46 % Time passed: 958ms (effective reasoning time: 633ms)
% 2.60/1.46 % 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)>
% 2.60/1.46 % Axioms used in derivation (1): domain4
% 2.60/1.46 % No. of inferences in proof: 13
% 2.60/1.46 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 958 ms resp. 633 ms w/o parsing
% 2.60/1.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.60/1.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------