%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET657^3 : TPTP v9.3.1. Released v3.6.0.
% 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 : n005.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 08:23:06 AM UTC 2026
% Result : Theorem 2.76s 1.51s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 9 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 24 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 27 ( 2 ~; 2 |; 0 &; 22 @)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 20 ( 15 ^; 3 !; 2 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(subset_decl,type,
subset: ( $i > $o ) > ( $i > $o ) > $o ).
thf(rel_codomain_decl,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(rel_domain_decl,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(rel_field_decl,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(subset_def,definition,
( subset
= ( ^ [A: $i > $o,B: $i > $o] :
! [C: $i] :
( ( A @ C )
=> ( B @ C ) ) ) ) ).
thf(rel_codomain_def,definition,
( rel_codomain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ C @ B ) ) ) ).
thf(rel_domain_def,definition,
( rel_domain
= ( ^ [A: $i > $i > $o,B: $i] :
? [C: $i] : ( A @ B @ C ) ) ) ).
thf(rel_field_def,definition,
( rel_field
= ( ^ [A: $i > $i > $o,B: $i] :
( ( rel_domain @ A @ B )
| ( rel_codomain @ A @ B ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $i > $o] :
( subset @ ( rel_field @ A )
@ ( union
@ ^ [B: $i] : $true
@ ^ [B: $i] : $true ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $i > $o] :
( subset @ ( rel_field @ A )
@ ( union
@ ^ [B: $i] : $true
@ ^ [B: $i] : $true ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
$false,
inference(simp,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET657^3 : TPTP v9.3.1. Released v3.6.0.
% 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
% 0.10/0.21 % Computer : n005.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 13:40:16 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.85/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.54/1.06 % [INFO] Parsing done (276ms).
% 1.54/1.08 % [INFO] Running in sequential loop mode.
% 2.19/1.31 % [INFO] eprover registered as external prover.
% 2.19/1.32 % [INFO] Scanning for conjecture ...
% 2.49/1.41 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.49/1.42 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.49/1.42 % [INFO] Problem is higher-order (TPTP THF).
% 2.49/1.43 % [INFO] Type checking passed.
% 2.49/1.43 % [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 ...
% 2.76/1.50 % [INFO] Killing All external provers ...
% 2.76/1.51 % Time passed: 1154ms (effective reasoning time: 416ms)
% 2.76/1.51 % 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)>
% 2.76/1.51 % Axioms used in derivation (0):
% 2.76/1.51 % No. of inferences in proof: 4
% 2.76/1.51 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1154 ms resp. 416 ms w/o parsing
% 2.76/1.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.76/1.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------