TSTP Solution File: SEU663^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU663^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:38:56 EDT 2024
% Result : Theorem 3.04s 1.66s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 18 ( 8 unt; 7 typ; 2 def)
% Number of atoms : 28 ( 13 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 65 ( 5 ~; 0 |; 0 &; 47 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 24 ( 0 ^ 24 !; 0 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(ksnd_type,type,
ksnd: $i > $i ).
thf(ksndpairEq_type,type,
ksndpairEq: $o ).
thf(ksndpairEq_def,definition,
( ksndpairEq
= ( ! [A: $i,B: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ) ) ) ).
thf(cartprodmempaircEq_type,type,
cartprodmempaircEq: $o ).
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(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i ).
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,
( ( ksnd @ ( kpair @ sk3 @ sk4 ) )
!= sk4 ),
inference(cnf,[status(esa)],[3]) ).
thf(8,plain,
( ( ksnd @ ( kpair @ sk3 @ sk4 ) )
!= sk4 ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
! [B: $i,A: $i] :
( ( ksnd @ ( kpair @ A @ B ) )
= B ),
inference(lifteq,[status(thm)],[7]) ).
thf(10,plain,
sk4 != sk4,
inference(rewrite,[status(thm)],[8,9]) ).
thf(11,plain,
$false,
inference(simp,[status(thm)],[10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU663^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n002.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 15:56:54 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.98/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.12/0.99 % [INFO] Parsing done (105ms).
% 1.12/1.00 % [INFO] Running in sequential loop mode.
% 1.63/1.22 % [INFO] eprover registered as external prover.
% 1.63/1.23 % [INFO] cvc4 registered as external prover.
% 1.63/1.23 % [INFO] Scanning for conjecture ...
% 1.88/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.01/1.32 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.01/1.32 % [INFO] Problem is higher-order (TPTP THF).
% 2.01/1.32 % [INFO] Type checking passed.
% 2.01/1.32 % [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 ...
% 3.04/1.66 % [INFO] Killing All external provers ...
% 3.04/1.66 % Time passed: 1111ms (effective reasoning time: 651ms)
% 3.04/1.66 % 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)>
% 3.04/1.66 % Axioms used in derivation (0):
% 3.04/1.66 % No. of inferences in proof: 9
% 3.04/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1111 ms resp. 651 ms w/o parsing
% 3.04/1.69 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.04/1.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------