%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU794^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n009.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 08:29:19 AM UTC 2026
% Result : Theorem 28.68s 6.17s
% Output : Refutation 27.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 55 ( 20 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 83 ( 2 ~; 0 |; 8 &; 54 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 41 ( 3 ^; 28 !; 10 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(exu_decl,type,
exu: ( $i > $o ) > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetI1_decl,type,
subsetI1: $o ).
thf(setextsub_decl,type,
setextsub: $o ).
thf(image1Ex_decl,type,
image1Ex: $o ).
thf(exu_def,definition,
( exu
= ( ^ [A: $i > $o] :
? [B: $i] :
( ( A @ B )
& ! [C: $i] :
( ( A @ C )
=> ( B = C ) ) ) ) ) ).
thf(subsetI1_def,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(setextsub_def,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ) ).
thf(image1Ex_def,definition,
( image1Ex
= ( ! [A: $i,B: $i > $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ A )
& ( D
= ( B @ E ) ) ) ) ) ) ) ).
thf(1,conjecture,
( subsetI1
=> ( setextsub
=> ( image1Ex
=> ! [A: $i,B: $i > $i] :
( exu
@ ^ [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ A )
& ( D
= ( B @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Ex1) ).
thf(2,negated_conjecture,
~ ( subsetI1
=> ( setextsub
=> ( image1Ex
=> ! [A: $i,B: $i > $i] :
( exu
@ ^ [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ A )
& ( D
= ( B @ E ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i,B: $i > $i] :
? [C: $i] :
! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ A )
& ( D
= ( B @ E ) ) ) ) )
=> ! [A: $i,B: $i > $i] :
? [C: $i] :
( ! [D: $i] :
( ( in @ D @ C )
= ( ? [E: $i] :
( ( in @ E @ A )
& ( D
= ( B @ E ) ) ) ) )
& ! [D: $i] :
( ! [E: $i] :
( ( in @ E @ D )
= ( ? [F: $i] :
( ( in @ F @ A )
& ( E
= ( B @ F ) ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4096,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU794^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n009.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
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 14:30:30 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.83/0.68 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.99/0.78 % [INFO] Parsing done (102ms).
% 0.99/0.79 % [INFO] Running in sequential loop mode.
% 1.42/0.99 % [INFO] eprover registered as external prover.
% 1.42/1.00 % [INFO] Scanning for conjecture ...
% 1.74/1.06 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.74/1.08 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.74/1.08 % [INFO] Problem is higher-order (TPTP THF).
% 1.74/1.08 % [INFO] Type checking passed.
% 1.74/1.09 % [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 ...
% 28.68/6.17 % External prover 'e' found a proof!
% 28.68/6.17 % [INFO] Killing All external provers ...
% 28.68/6.17 % Time passed: 5809ms (effective reasoning time: 5376ms)
% 28.68/6.17 % 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)>
% 28.68/6.17 % Axioms used in derivation (0):
% 28.68/6.17 % No. of inferences in proof: 4
% 28.68/6.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5809 ms resp. 5376 ms w/o parsing
% 27.98/6.22 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 27.98/6.22 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------