%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO527^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n007.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 : Wed Sep 30 08:46:03 AM UTC 2026
% Result : Theorem 3.55s 2.15s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 19 ( 4 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 50 ( 7 ~; 1 |; 0 &; 42 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 2 ^; 11 !; 5 ?; 20 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(b_type,type,
b: $tType ).
thf(r_decl,type,
r: a > b > $o ).
thf(sk1_decl,type,
sk1: ( a > b ) > a ).
thf(sk2_decl,type,
sk2: a > b ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > b] :
@+[B: a] :
~ ( r @ B @ ( A @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: a] :
@+[B: b] : ( r @ A @ B ) ) ) ).
thf(3,axiom,
! [A: a] :
? [B: b] : ( r @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rtotal) ).
thf(6,plain,
! [A: a] :
? [B: b] : ( r @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(7,plain,
! [A: a] : ( r @ A @ ( sk2 @ A ) ),
inference(cnf,[status(esa)],[6]) ).
thf(1,conjecture,
? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',skolem) ).
thf(2,negated_conjecture,
~ ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(4,plain,
~ ? [A: a > b] :
! [B: a] : ( r @ B @ ( A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,plain,
! [A: a > b] :
~ ( r @ ( sk1 @ A ) @ ( A @ ( sk1 @ A ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
! [B: a > b,A: a] :
( ~ $true
| ( ( r @ A @ ( sk2 @ A ) )
!= ( r @ ( sk1 @ B ) @ ( B @ ( sk1 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[7,5]) ).
thf(9,plain,
! [B: a > b,A: a] :
( ( r @ A @ ( sk2 @ A ) )
!= ( r @ ( sk1 @ B ) @ ( B @ ( sk1 @ B ) ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(10,plain,
$false,
inference(pre_uni,[status(thm)],[9:[bind(A,$thf( sk1 @ sk2 )),bind(B,$thf( sk2 ))]]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO527^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % 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
% 0.10/0.22 % Computer : n007.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 17:10:56 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.04/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.99 % [INFO] Parsing done (177ms).
% 1.21/1.01 % [INFO] Running in sequential loop mode.
% 2.01/1.42 % [INFO] eprover registered as external prover.
% 2.01/1.43 % [INFO] Scanning for conjecture ...
% 2.20/1.51 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.20/1.55 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.20/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.55 % [INFO] Type checking passed.
% 2.20/1.56 % [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 ...
% 3.55/2.15 % [INFO] Killing All external provers ...
% 3.55/2.15 % Time passed: 1776ms (effective reasoning time: 1137ms)
% 3.55/2.15 % 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)>
% 3.55/2.15 % Axioms used in derivation (1): rtotal
% 3.55/2.15 % No. of inferences in proof: 10
% 3.55/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1776 ms resp. 1137 ms w/o parsing
% 3.72/2.20 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.72/2.20 % [INFO] Killing All external provers ...
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