%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO218^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n002.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 08:45:25 AM UTC 2026
% Result : Theorem 2.39s 1.17s
% Output : Refutation 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 44 ( 43 equ; 16 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 72 ( 10 ~; 3 |; 1 &; 48 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 15 !; 0 ?; 17 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ! [C: ( $i > $o ) > $i] :
( ( A
= ( C @ ( (=) @ $i @ A ) ) )
=> ( B
= ( C @ ( (=) @ $i @ B ) ) ) )
=> ( A = B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ! [B: ( $i > $o ) > $i] :
( ( sk1
= ( B @ ( (=) @ $i @ sk1 ) ) )
=> ( A
= ( B @ ( (=) @ $i @ A ) ) ) )
=> ( sk1 = A ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ! [C: ( $i > $o ) > $i] :
( ( A
= ( C @ ( (=) @ $i @ A ) ) )
=> ( B
= ( C @ ( (=) @ $i @ B ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM7B_pme) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ! [C: ( $i > $o ) > $i] :
( ( A
= ( C @ ( (=) @ $i @ A ) ) )
=> ( B
= ( C @ ( (=) @ $i @ B ) ) ) )
=> ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i,B: $i] :
( ! [C: ( $i > $o ) > $i] :
( ( A
= ( C @ ( (=) @ $i @ A ) ) )
=> ( B
= ( C @ ( (=) @ $i @ B ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: ( $i > $o ) > $i] :
( ( ( sk1
!= ( A @ ( (=) @ $i @ sk1 ) ) )
| ( sk2
= ( A @ ( (=) @ $i @ sk2 ) ) ) )
& ( sk1 != sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [A: ( $i > $o ) > $i] :
( ( sk1
!= ( A @ ( (=) @ $i @ sk1 ) ) )
| ( sk2
= ( A @ ( (=) @ $i @ sk2 ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [A: ( $i > $o ) > $i] :
( ( ( A @ ( (=) @ $i @ sk1 ) )
!= sk1 )
| ( ( A @ ( (=) @ $i @ sk2 ) )
= sk2 ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
sk2 = sk1,
inference(pre_uni,[status(thm)],[7:[bind(A,$thf( ^ [B: $i > $o] : sk1 ))]]) ).
thf(6,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[6]) ).
thf(28,plain,
$false,
inference(simplifyReflect,[status(thm)],[9,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO218^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % 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
% 0.10/0.18 % Computer : n002.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:42:22 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 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
% 0.66/0.49 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.89/0.58 % [INFO] Parsing done (91ms).
% 0.89/0.59 % [INFO] Running in sequential loop mode.
% 1.16/0.78 % [INFO] eprover registered as external prover.
% 1.16/0.78 % [INFO] Scanning for conjecture ...
% 1.38/0.82 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.38/0.84 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.38/0.84 % [INFO] Problem is higher-order (TPTP THF).
% 1.38/0.84 % [INFO] Type checking passed.
% 1.38/0.84 % [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 ...
% 2.39/1.17 % [INFO] Killing All external provers ...
% 2.39/1.17 % Time passed: 897ms (effective reasoning time: 576ms)
% 2.39/1.17 % 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)>
% 2.39/1.17 % Axioms used in derivation (0):
% 2.39/1.17 % No. of inferences in proof: 10
% 2.39/1.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 897 ms resp. 576 ms w/o parsing
% 2.39/1.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.39/1.19 % [INFO] Killing All external provers ...
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