%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU805^2 : 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 : n026.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 08:29:21 AM UTC 2026
% Result : Theorem 3.69s 2.16s
% Output : Refutation 3.93s
% 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 : 43 ( 12 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 83 ( 9 ~; 0 |; 9 &; 47 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 25 ( 1 ^; 11 !; 13 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(foundationAx_decl,type,
foundationAx: $o ).
thf(nonempty_decl,type,
nonempty: $i > $o ).
thf(nonemptyE1_decl,type,
nonemptyE1: $o ).
thf(binintersect_decl,type,
binintersect: $i > $i > $i ).
thf(disjointsetsI1_decl,type,
disjointsetsI1: $o ).
thf(foundationAx_def,definition,
( foundationAx
= ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) ) ) ) ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(nonemptyE1_def,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] : ( in @ B @ A ) ) ) ) ).
thf(disjointsetsI1_def,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ) ).
thf(1,conjecture,
( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ( ( binintersect @ B @ A )
= emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundation2) ).
thf(2,negated_conjecture,
~ ( foundationAx
=> ( nonemptyE1
=> ( disjointsetsI1
=> ! [A: $i] :
( ( nonempty @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ( ( binintersect @ B @ A )
= emptyset ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [C: $i] :
( ( in @ C @ B )
& ( in @ C @ A ) ) ) )
=> ( ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] : ( in @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [C: $i] :
( ( in @ C @ A )
& ( in @ C @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ! [A: $i] :
( ( A != emptyset )
=> ? [B: $i] :
( ( in @ B @ A )
& ( ( binintersect @ B @ A )
= emptyset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU805^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.22 % Computer : n026.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
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:35:12 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.06/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (189ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.07/1.40 % [INFO] eprover registered as external prover.
% 2.07/1.41 % [INFO] Scanning for conjecture ...
% 2.28/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.28/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.28/1.57 % [INFO] Problem is higher-order (TPTP THF).
% 2.28/1.57 % [INFO] Type checking passed.
% 2.28/1.58 % [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 ...
% 3.69/2.16 % External prover 'e' found a proof!
% 3.69/2.16 % [INFO] Killing All external provers ...
% 3.69/2.16 % Time passed: 1798ms (effective reasoning time: 1147ms)
% 3.69/2.16 % 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)>
% 3.69/2.16 % Axioms used in derivation (0):
% 3.69/2.16 % No. of inferences in proof: 4
% 3.69/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1798 ms resp. 1147 ms w/o parsing
% 3.93/2.21 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.93/2.21 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------