%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU663^2 : 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 : 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 08:28:57 AM UTC 2026
% Result : Theorem 2.99s 1.85s
% Output : Refutation 2.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 12 unt; 0 typ; 6 def)
% Number of atoms : 47 ( 23 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 10 ~; 0 |; 3 &; 83 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 32 !; 0 ?; 36 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(ksnd_decl,type,
ksnd: $i > $i ).
thf(ksndpairEq_decl,type,
ksndpairEq: $o ).
thf(cartprodmempaircEq_decl,type,
cartprodmempaircEq: $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(ksndpairEq_def,definition,
( ksndpairEq
= ( ! [A: $i,B: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ) ) ) ).
thf(cartprodmempaircEq_def,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( kpair @ C @ D )
= ( kpair @ C @ D ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( ksnd @ ( kpair @ C @ D ) )
= D ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( in @ B @ sk1 )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( ( ksnd @ ( kpair @ B @ C ) )
= C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( in @ A @ sk1 )
=> ! [B: $i] :
( ( in @ B @ sk2 )
=> ( ( ksnd @ ( kpair @ A @ B ) )
= B ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( in @ A @ sk2 )
=> ( ( ksnd @ ( kpair @ sk3 @ A ) )
= A ) ) ) ) ).
thf(1,conjecture,
( ksndpairEq
=> ( cartprodmempaircEq
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( ksnd @ ( kpair @ C @ D ) )
= D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(2,negated_conjecture,
~ ( ksndpairEq
=> ( cartprodmempaircEq
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( ksnd @ ( kpair @ C @ D ) )
= D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( ksnd @ ( kpair @ C @ D ) )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ( ( ksnd @ ( kpair @ A @ B ) )
= B )
& ( in @ sk3 @ sk1 )
& ( in @ sk4 @ sk2 )
& ( ( ksnd @ ( kpair @ sk3 @ sk4 ) )
!= sk4 ) ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( ( ksnd @ ( kpair @ sk3 @ sk4 ) )
!= sk4 ),
inference(cnfConj,[status(thm)],[4]) ).
thf(10,plain,
( ( ksnd @ ( kpair @ sk3 @ sk4 ) )
!= sk4 ),
inference(lifteq,[status(thm)],[8]) ).
thf(5,plain,
! [B: $i,A: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[5]) ).
thf(11,plain,
sk4 != sk4,
inference(rewrite,[status(thm)],[10,9]) ).
thf(12,plain,
$false,
inference(simp,[status(thm)],[11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU663^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 14:10:05 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.26/0.98 % [INFO] Parsing done (183ms).
% 1.26/0.99 % [INFO] Running in sequential loop mode.
% 2.02/1.41 % [INFO] eprover registered as external prover.
% 2.02/1.42 % [INFO] Scanning for conjecture ...
% 2.18/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.18/1.55 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.18/1.55 % [INFO] Problem is higher-order (TPTP THF).
% 2.18/1.55 % [INFO] Type checking passed.
% 2.18/1.55 % [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 ...
% 2.99/1.84 % [INFO] Killing All external provers ...
% 2.99/1.85 % Time passed: 1500ms (effective reasoning time: 845ms)
% 2.99/1.85 % 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)>
% 2.99/1.85 % Axioms used in derivation (0):
% 2.99/1.85 % No. of inferences in proof: 10
% 2.99/1.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1500 ms resp. 845 ms w/o parsing
% 2.99/1.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.99/1.88 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------