%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO355^5 : 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 : n003.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 08:45:38 AM UTC 2026
% Result : Theorem 3.64s 2.21s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 18 ( 17 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 8 ~; 0 |; 1 &; 2 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 21 ( 0 ^; 19 !; 0 ?; 21 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(sk1_decl,type,
sk1: $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $i] :
~ ! [B: $i > $i] : ( A = B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $i] : ( sk1 != A ) ) ) ).
thf(1,conjecture,
( ! [A: $i,B: $i] : ( A = B )
=> ! [A: $i > $i,B: $i > $i] : ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM613) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] : ( A = B )
=> ! [A: $i > $i,B: $i > $i] : ( A = B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] : ( A = B )
=> ! [A: $i > $i,B: $i > $i] : ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ( A = B )
& ( sk1 != sk2 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[6]) ).
thf(9,plain,
( ( sk2 @ sk3 )
!= ( sk1 @ sk3 ) ),
inference(func_ext,[status(esa)],[8]) ).
thf(5,plain,
! [B: $i,A: $i] : ( A = B ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i] : ( A = B ),
inference(lifteq,[status(thm)],[5]) ).
thf(10,plain,
$false,
inference(simplifyReflect,[status(thm)],[9,7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO355^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.08/0.22 % Computer : n003.cluster.edu
% 0.08/0.22 % Model : x86_64 x86_64
% 0.08/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.22 % Memory : 8046.5625MB
% 0.08/0.22 % OS : Linux 6.8.0-71-generic
% 0.08/0.22 % CPULimit : 300
% 0.08/0.22 % WCLimit : 300
% 0.08/0.22 % DateTime : Tue Sep 29 16:50:14 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 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
% 1.23/0.92 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.10 % [INFO] Parsing done (176ms).
% 1.48/1.12 % [INFO] Running in sequential loop mode.
% 2.22/1.52 % [INFO] eprover registered as external prover.
% 2.22/1.52 % [INFO] Scanning for conjecture ...
% 2.37/1.60 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.37/1.64 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.37/1.64 % [INFO] Problem is higher-order (TPTP THF).
% 2.37/1.64 % [INFO] Type checking passed.
% 2.37/1.65 % [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 ...
% 3.64/2.20 % [INFO] Killing All external provers ...
% 3.64/2.21 % Time passed: 1809ms (effective reasoning time: 1082ms)
% 3.64/2.21 % 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)>
% 3.64/2.21 % Axioms used in derivation (0):
% 3.64/2.21 % No. of inferences in proof: 10
% 3.64/2.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1809 ms resp. 1082 ms w/o parsing
% 3.64/2.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.64/2.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------