%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU826^1 : TPTP v9.3.1. Released v3.7.0.
% 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 08:29:26 AM UTC 2026
% Result : Theorem 3.12s 2.05s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 42 ( 5 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 46 ( 2 ~; 4 |; 3 &; 37 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-3 aty)
% Number of variables : 10 ( 8 ^; 2 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
thf(seteq_decl,type,
seteq: ( $i > $o ) > ( $i > $o ) > $o ).
thf(u_decl,type,
u: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(n_decl,type,
n: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(a_decl,type,
a: $i > $o ).
thf(b_decl,type,
b: $i > $o ).
thf(c_decl,type,
c: $i > $o ).
thf(seteq_def,definition,
( seteq
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
= ( B @ C ) ) ) ) ).
thf(u_def,definition,
( u
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(n_def,definition,
( n
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
& ( B @ C ) ) ) ) ).
thf(1,conjecture,
seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(2,negated_conjecture,
~ ( seteq @ ( u @ a @ ( n @ b @ c ) ) @ ( n @ ( u @ a @ b ) @ ( u @ a @ c ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i] :
( ( ( a @ A )
| ( ( b @ A )
& ( c @ A ) ) )
= ( ( ( a @ A )
| ( b @ A ) )
& ( ( a @ A )
| ( c @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(31,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU826^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.11/0.21 % Computer : n002.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 14:37:52 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 0.85/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/0.98 % [INFO] Parsing done (189ms).
% 1.16/0.99 % [INFO] Running in sequential loop mode.
% 1.72/1.39 % [INFO] eprover registered as external prover.
% 1.89/1.40 % [INFO] Scanning for conjecture ...
% 2.05/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.05/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.05/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.05/1.53 % [INFO] Type checking passed.
% 2.05/1.54 % [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 ...
% 3.12/2.04 % External prover 'e' found a proof!
% 3.12/2.04 % [INFO] Killing All external provers ...
% 3.12/2.04 % Time passed: 1690ms (effective reasoning time: 1045ms)
% 3.12/2.04 % 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)>
% 3.12/2.05 % Axioms used in derivation (0):
% 3.12/2.05 % No. of inferences in proof: 4
% 3.12/2.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1690 ms resp. 1045 ms w/o parsing
% 3.12/2.08 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.12/2.08 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------