%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU664^2 : 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 : n008.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 3.43s 2.15s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 39 ( 12 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 100 ( 2 ~; 0 |; 4 &; 72 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 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; 0-2 aty)
% Number of variables : 35 ( 0 ^; 31 !; 4 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(kpair_decl,type,
kpair: $i > $i > $i ).
thf(cartprod_decl,type,
cartprod: $i > $i > $i ).
thf(cartprodmempair1_decl,type,
cartprodmempair1: $o ).
thf(kfst_decl,type,
kfst: $i > $i ).
thf(ksnd_decl,type,
ksnd: $i > $i ).
thf(cartprodfstpairEq_decl,type,
cartprodfstpairEq: $o ).
thf(cartprodsndpairEq_decl,type,
cartprodsndpairEq: $o ).
thf(cartprodmempair1_def,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) ) ) ) ).
thf(cartprodfstpairEq_def,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( kfst @ ( kpair @ C @ D ) )
= C ) ) ) ) ) ).
thf(cartprodsndpairEq_def,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( ksnd @ ( kpair @ C @ D ) )
= D ) ) ) ) ) ).
thf(1,conjecture,
( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ C ) @ ( ksnd @ C ) )
= C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(2,negated_conjecture,
~ ( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ C ) @ ( ksnd @ C ) )
= C ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ? [D: $i] :
( ( in @ D @ A )
& ? [E: $i] :
( ( in @ E @ B )
& ( C
= ( kpair @ D @ E ) ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( kfst @ ( kpair @ C @ D ) )
= C ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( ( ksnd @ ( kpair @ C @ D ) )
= D ) ) )
=> ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ C ) @ ( ksnd @ C ) )
= C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU664^2 : 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
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 14:05:10 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.98 % [INFO] Parsing done (195ms).
% 1.19/1.00 % [INFO] Running in sequential loop mode.
% 1.79/1.39 % [INFO] eprover registered as external prover.
% 1.96/1.40 % [INFO] Scanning for conjecture ...
% 2.14/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.14/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.14/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.56 % [INFO] Type checking passed.
% 2.14/1.57 % [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 ...
% 3.43/2.14 % External prover 'e' found a proof!
% 3.43/2.14 % [INFO] Killing All external provers ...
% 3.43/2.14 % Time passed: 1797ms (effective reasoning time: 1140ms)
% 3.43/2.15 % 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)>
% 3.43/2.15 % Axioms used in derivation (0):
% 3.43/2.15 % No. of inferences in proof: 4
% 3.43/2.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1797 ms resp. 1140 ms w/o parsing
% 3.43/2.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.43/2.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------