%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU816^2 : 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 : n010.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 08:29:24 AM UTC 2026
% Result : Theorem 4.40s 2.36s
% Output : Refutation 4.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 7
% Syntax : Number of formulae : 10 ( 7 unt; 0 typ; 6 def)
% Number of atoms : 99 ( 15 equ; 0 cnn)
% Maximal formula atoms : 50 ( 9 avg)
% Number of connectives : 239 ( 8 ~; 9 |; 18 &; 154 @)
% ( 0 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 5 ^; 41 !; 3 ?; 49 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(nonempty_decl,type,
nonempty: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(binintersect_decl,type,
binintersect: $i > $i > $i ).
thf(transitiveset_decl,type,
transitiveset: $i > $o ).
thf(binintTransitive_decl,type,
binintTransitive: $o ).
thf(stricttotalorderedByIn_decl,type,
stricttotalorderedByIn: $i > $o ).
thf(wellorderedByIn_decl,type,
wellorderedByIn: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(transitiveset_def,definition,
( transitiveset
= ( ^ [A: $i] :
! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) ) ) ) ).
thf(binintTransitive_def,definition,
( binintTransitive
= ( ! [A: $i] :
( ( transitiveset @ A )
=> ! [B: $i] :
( ( transitiveset @ B )
=> ( transitiveset @ ( binintersect @ A @ B ) ) ) ) ) ) ).
thf(stricttotalorderedByIn_def,definition,
( stricttotalorderedByIn
= ( ^ [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( ( in @ B @ C )
& ( in @ C @ D ) )
=> ( in @ B @ D ) ) ) ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( B = C )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ~ ( in @ B @ B ) ) ) ) ) ).
thf(wellorderedByIn_def,definition,
( wellorderedByIn
= ( ^ [A: $i] :
( ( stricttotalorderedByIn @ A )
& ! [B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( nonempty @ B )
=> ? [C: $i] :
( ( in @ C @ B )
& ! [D: $i] :
( ( in @ D @ B )
=> ( ( C = D )
| ( in @ C @ D ) ) ) ) ) ) ) ) ) ).
thf(ordinal_def,definition,
( ordinal
= ( ^ [A: $i] :
( ( transitiveset @ A )
& ( wellorderedByIn @ A ) ) ) ) ).
thf(1,conjecture,
( binintTransitive
=> ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( transitiveset @ ( binintersect @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordinalMinLem1) ).
thf(2,negated_conjecture,
~ ( binintTransitive
=> ! [A: $i] :
( ( ordinal @ A )
=> ! [B: $i] :
( ( ordinal @ B )
=> ( transitiveset @ ( binintersect @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) )
=> ! [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) )
=> ! [C: $i] :
( ( in @ C @ ( binintersect @ A @ B ) )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
=> ! [A: $i] :
( ( ! [B: $i] :
( ( in @ B @ A )
=> ( subset @ B @ A ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( ( ( in @ B @ C )
& ( in @ C @ D ) )
=> ( in @ B @ D ) ) ) ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( B = C )
| ( in @ B @ C )
| ( in @ C @ B ) ) ) )
& ! [B: $i] :
( ( in @ B @ A )
=> ~ ( in @ B @ B ) )
& ! [B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( B != emptyset )
=> ? [C: $i] :
( ( in @ C @ B )
& ! [D: $i] :
( ( in @ D @ B )
=> ( ( C = D )
| ( in @ C @ D ) ) ) ) ) ) )
=> ! [B: $i] :
( ( ! [C: $i] :
( ( in @ C @ B )
=> ( subset @ C @ B ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ B )
=> ! [E: $i] :
( ( in @ E @ B )
=> ( ( ( in @ C @ D )
& ( in @ D @ E ) )
=> ( in @ C @ E ) ) ) ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( C = D )
| ( in @ C @ D )
| ( in @ D @ C ) ) ) )
& ! [C: $i] :
( ( in @ C @ B )
=> ~ ( in @ C @ C ) )
& ! [C: $i] :
( ( in @ C @ ( powerset @ B ) )
=> ( ( C != emptyset )
=> ? [D: $i] :
( ( in @ D @ C )
& ! [E: $i] :
( ( in @ E @ C )
=> ( ( D = E )
| ( in @ D @ E ) ) ) ) ) ) )
=> ! [C: $i] :
( ( in @ C @ ( binintersect @ A @ B ) )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU816^2 : 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
% 0.08/0.18 % Computer : n010.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 14:34:18 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 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
% 0.89/0.76 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.99 % [INFO] Parsing done (234ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 2.17/1.41 % [INFO] eprover registered as external prover.
% 2.17/1.42 % [INFO] Scanning for conjecture ...
% 2.39/1.56 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.39/1.59 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.39/1.59 % [INFO] Problem is higher-order (TPTP THF).
% 2.39/1.59 % [INFO] Type checking passed.
% 2.59/1.60 % [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 ...
% 4.40/2.35 % External prover 'e' found a proof!
% 4.40/2.36 % [INFO] Killing All external provers ...
% 4.40/2.36 % Time passed: 2036ms (effective reasoning time: 1342ms)
% 4.40/2.36 % 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)>
% 4.40/2.36 % Axioms used in derivation (0):
% 4.40/2.36 % No. of inferences in proof: 4
% 4.40/2.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2036 ms resp. 1342 ms w/o parsing
% 4.77/2.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.77/2.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------