%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU707^2 : 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 : n019.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 08:29:05 AM UTC 2026
% Result : Theorem 4.87s 2.68s
% Output : Refutation 5.20s
% 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 : 53 ( 21 equ; 0 cnn)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 122 ( 8 ~; 6 |; 12 &; 64 @)
% ( 0 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 42 ( 10 ^; 32 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(singleton_decl,type,
singleton: $i > $o ).
thf(iftrueProp1_decl,type,
iftrueProp1: $o ).
thf(ifSingleton_decl,type,
ifSingleton: $o ).
thf(if_decl,type,
if: $i > $o > $i > $i > $i ).
thf(theeq_decl,type,
theeq: $o ).
thf(iftrueProp1_def,definition,
( iftrueProp1
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) ) ) ) ).
thf(ifSingleton_def,definition,
( ifSingleton
= ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) ) ) ).
thf(if_def,definition,
( if
= ( ^ [A: $i,B: $o,C: $i,D: $i] :
( setunion
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) ).
thf(theeq_def,definition,
( theeq
= ( ! [A: $i] :
( ( singleton @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ).
thf(1,conjecture,
( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( if @ A @ B @ C @ D )
= C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',iftrue) ).
thf(2,negated_conjecture,
~ ( iftrueProp1
=> ( ifSingleton
=> ( theeq
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( if @ A @ B @ C @ D )
= C ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( in @ C
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) ) )
=> ( ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) ) ) )
=> ( ! [A: $i] :
( ( singleton @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) )
=> ! [A: $i,B: $o,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ A )
=> ( B
=> ( ( setunion
@ ( dsetconstr @ A
@ ^ [E: $i] :
( ( B
& ( E = C ) )
| ( ~ B
& ( E = D ) ) ) ) )
= C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU707^2 : 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
% 0.11/0.21 % Computer : n019.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 14:13:02 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.03/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.42/1.11 % [INFO] Parsing done (273ms).
% 1.70/1.14 % [INFO] Running in sequential loop mode.
% 2.41/1.63 % [INFO] eprover registered as external prover.
% 2.41/1.63 % [INFO] Scanning for conjecture ...
% 2.66/1.77 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.87/1.81 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.87/1.81 % [INFO] Problem is higher-order (TPTP THF).
% 2.87/1.81 % [INFO] Type checking passed.
% 2.87/1.82 % [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 ...
% 4.87/2.67 % External prover 'e' found a proof!
% 4.87/2.67 % [INFO] Killing All external provers ...
% 4.87/2.67 % Time passed: 2319ms (effective reasoning time: 1527ms)
% 4.87/2.67 % 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)>
% 4.87/2.68 % Axioms used in derivation (0):
% 4.87/2.68 % No. of inferences in proof: 4
% 4.87/2.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2319 ms resp. 1527 ms w/o parsing
% 5.20/2.74 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.20/2.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------