%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO356^5 : 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 08:45:38 AM UTC 2026
% Result : Theorem 3.63s 1.76s
% Output : Refutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 26 ( 15 equ; 4 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 82 ( 15 ~; 5 |; 2 &; 50 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 1 ^; 11 !; 0 ?; 14 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(v_decl,type,
v: a ).
thf(u_decl,type,
u: a ).
thf(sk1_decl,type,
sk1: ( a > a > $o ) > a ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: a > a > $o] :
@+[B: a] :
~ ( A @ B @ B ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ( ( A @ u )
=> ( A @ v ) ) ) ) ).
thf(1,conjecture,
( ! [A: a > a > $o] :
( ! [B: a] : ( A @ B @ B )
=> ( A @ u @ v ) )
=> ! [A: a > $o] :
( ( A @ u )
=> ( A @ v ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE1LEIBEQ2_pme) ).
thf(2,negated_conjecture,
~ ( ! [A: a > a > $o] :
( ! [B: a] : ( A @ B @ B )
=> ( A @ u @ v ) )
=> ! [A: a > $o] :
( ( A @ u )
=> ( A @ v ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: a > a > $o] :
( ! [B: a] : ( A @ B @ B )
=> ( A @ u @ v ) )
=> ! [A: a > $o] :
( ( A @ u )
=> ( A @ v ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: a > a > $o] :
( ( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ u @ v ) )
& ( sk2 @ u )
& ~ ( sk2 @ v ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
sk2 @ u,
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ ( sk2 @ v ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ~ $true
| ( ( sk2 @ u )
!= ( sk2 @ v ) ) ),
inference(paramod_ordered,[status(thm)],[6,7]) ).
thf(12,plain,
( ( sk2 @ u )
!= ( sk2 @ v ) ),
inference(simp,[status(thm)],[11]) ).
thf(13,plain,
u != v,
inference(simp,[status(thm)],[12]) ).
thf(5,plain,
! [A: a > a > $o] :
( ~ ( A @ ( sk1 @ A ) @ ( sk1 @ A ) )
| ( A @ u @ v ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
( ( ( sk1 @ ( (=) @ a ) )
!= ( sk1 @ ( (=) @ a ) ) )
| ( u = v ) ),
inference(replace_andrewseq,[status(thm)],[5:[bind(A,$thf( (=) @ a ))]]) ).
thf(9,plain,
( ( ( sk1 @ ( (=) @ a ) )
!= ( sk1 @ ( (=) @ a ) ) )
| ( u = v ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
u = v,
inference(simp,[status(thm)],[9]) ).
thf(15,plain,
v != v,
inference(rewrite,[status(thm)],[13,10]) ).
thf(16,plain,
$false,
inference(simp,[status(thm)],[15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO356^5 : 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
% 0.26/0.28 % Computer : n002.cluster.edu
% 0.26/0.28 % Model : x86_64 x86_64
% 0.26/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.28 % Memory : 8046.5625MB
% 0.26/0.28 % OS : Linux 6.8.0-71-generic
% 0.26/0.28 % CPULimit : 300
% 0.26/0.28 % WCLimit : 300
% 0.26/0.28 % DateTime : Tue Sep 29 16:51:07 UTC 2026
% 0.26/0.29 % CPUTime :
% 0.26/0.29 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
% 0.98/0.74 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/0.85 % [INFO] Parsing done (108ms).
% 1.26/0.86 % [INFO] Running in sequential loop mode.
% 1.96/1.14 % [INFO] eprover registered as external prover.
% 1.96/1.15 % [INFO] Scanning for conjecture ...
% 2.11/1.22 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.11/1.24 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.11/1.24 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.25 % [INFO] Type checking passed.
% 2.11/1.25 % [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 ...
% 3.63/1.75 % [INFO] Killing All external provers ...
% 3.63/1.75 % Time passed: 1310ms (effective reasoning time: 886ms)
% 3.63/1.75 % 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)>
% 3.63/1.76 % Axioms used in derivation (0):
% 3.63/1.76 % No. of inferences in proof: 15
% 3.63/1.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1310 ms resp. 886 ms w/o parsing
% 3.89/1.83 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.89/1.83 % [INFO] Killing All external provers ...
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