%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU656^2 : 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 : n001.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 08:28:55 AM UTC 2026
% Result : Theorem 10.44s 4.36s
% Output : Refutation 10.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 13 ( 10 unt; 0 typ; 9 def)
% Number of atoms : 62 ( 27 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 285 ( 2 ~; 0 |; 9 &; 251 @)
% ( 0 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 47 ( 10 ^; 28 !; 9 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrER_decl,type,
dsetconstrER: $o ).
thf(iskpair_decl,type,
iskpair: $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(kpairp_decl,type,
kpairp: $o ).
thf(singleton_decl,type,
singleton: $i > $o ).
thf(theprop_decl,type,
theprop: $o ).
thf(kfst_decl,type,
kfst: $i > $i ).
thf(setukpairinjR_decl,type,
setukpairinjR: $o ).
thf(ksndsingleton_decl,type,
ksndsingleton: $o ).
thf(ksnd_decl,type,
ksnd: $i > $i ).
thf(dsetconstrER_def,definition,
( dsetconstrER
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) ) ) ) ).
thf(iskpair_def,definition,
( iskpair
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ ( setunion @ A ) )
& ? [C: $i] :
( ( in @ C @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
thf(kpair_def,definition,
( kpair
= ( ^ [A: $i,B: $i] : ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) ) ).
thf(kpairp_def,definition,
( kpairp
= ( ! [A: $i,B: $i] : ( iskpair @ ( kpair @ A @ B ) ) ) ) ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(theprop_def,definition,
( theprop
= ( ! [A: $i] :
( ( singleton @ A )
=> ( in @ ( setunion @ A ) @ A ) ) ) ) ).
thf(setukpairinjR_def,definition,
( setukpairinjR
= ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( kpair @ A @ B )
= ( kpair @ C @ D ) )
=> ( B = D ) ) ) ) ).
thf(ksndsingleton_def,definition,
( ksndsingleton
= ( ! [A: $i] :
( ( iskpair @ A )
=> ( singleton
@ ( dsetconstr @ ( setunion @ A )
@ ^ [B: $i] :
( A
= ( kpair @ ( kfst @ A ) @ B ) ) ) ) ) ) ) ).
thf(ksnd_def,definition,
( ksnd
= ( ^ [A: $i] :
( setunion
@ ( dsetconstr @ ( setunion @ A )
@ ^ [B: $i] :
( A
= ( kpair @ ( kfst @ A ) @ B ) ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [A: $i,B: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ksndpairEq) ).
thf(2,negated_conjecture,
~ ( dsetconstrER
=> ( kpairp
=> ( theprop
=> ( setukpairinjR
=> ( ksndsingleton
=> ! [A: $i,B: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ ( dsetconstr @ A @ B ) )
=> ( B @ C ) )
=> ( ! [A: $i,B: $i] :
? [C: $i] :
( ( in @ C @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) )
& ? [D: $i] :
( ( in @ D @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [A: $i] :
( ? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) )
=> ( in @ ( setunion @ A ) @ A ) )
=> ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ C @ emptyset ) @ ( setadjoin @ ( setadjoin @ C @ ( setadjoin @ D @ emptyset ) ) @ emptyset ) ) )
=> ( B = D ) )
=> ( ! [A: $i] :
( ? [B: $i] :
( ( in @ B @ ( setunion @ A ) )
& ? [C: $i] :
( ( in @ C @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ B @ emptyset ) @ ( setadjoin @ ( setadjoin @ B @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [B: $i] :
( ( in @ B
@ ( dsetconstr @ ( setunion @ A )
@ ^ [C: $i] :
( A
= ( setadjoin @ ( setadjoin @ ( kfst @ A ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ A ) @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) )
& ( ( dsetconstr @ ( setunion @ A )
@ ^ [C: $i] :
( A
= ( setadjoin @ ( setadjoin @ ( kfst @ A ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ A ) @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) )
= ( setadjoin @ B @ emptyset ) ) ) )
=> ! [A: $i,B: $i] :
( ( setunion
@ ( dsetconstr @ ( setunion @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) )
@ ^ [C: $i] :
( ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( kfst @ ( setadjoin @ ( setadjoin @ A @ emptyset ) @ ( setadjoin @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) @ emptyset ) ) ) @ ( setadjoin @ C @ emptyset ) ) @ emptyset ) ) ) ) )
= B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(119,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU656^2 : 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
% 0.11/0.18 % Computer : n001.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Tue Sep 29 14:09:20 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 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
% 1.20/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/1.29 % [INFO] Parsing done (298ms).
% 1.99/1.31 % [INFO] Running in sequential loop mode.
% 3.11/1.93 % [INFO] eprover registered as external prover.
% 3.11/1.95 % [INFO] Scanning for conjecture ...
% 3.40/2.15 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.62/2.20 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.70/2.20 % [INFO] Problem is higher-order (TPTP THF).
% 3.70/2.20 % [INFO] Type checking passed.
% 3.70/2.21 % [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 ...
% 10.44/4.35 % External prover 'e' found a proof!
% 10.44/4.35 % [INFO] Killing All external provers ...
% 10.44/4.35 % Time passed: 4003ms (effective reasoning time: 3030ms)
% 10.44/4.35 % 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)>
% 10.44/4.35 % Axioms used in derivation (0):
% 10.44/4.35 % No. of inferences in proof: 4
% 10.44/4.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4003 ms resp. 3030 ms w/o parsing
% 10.89/4.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.89/4.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------