TSTP Solution File: SEU768^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU768^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 03:39:44 EDT 2024
% Result : Theorem 2.92s 1.92s
% Output : Refutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of formulae : 12 ( 3 unt; 6 typ; 2 def)
% Number of atoms : 33 ( 2 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 122 ( 2 ~; 0 |; 0 &; 87 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 15 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 1 ^ 32 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(brelnall2_type,type,
brelnall2: $o ).
thf(brelnall2_def,definition,
( brelnall2
= ( ! [A: $i,B: $i,C: $i] :
( ( breln @ A @ B @ C )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) ) ) ) ).
thf(breln1_type,type,
breln1: $i > $i > $o ).
thf(breln1_def,definition,
( breln1
= ( ^ [A: $i] : ( breln @ A @ A ) ) ) ).
thf(1,conjecture,
( brelnall2
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i > $o] :
( ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ B )
=> ( C @ ( kpair @ D @ E ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( C @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1all2) ).
thf(2,negated_conjecture,
~ ( brelnall2
=> ! [A: $i,B: $i] :
( ( breln1 @ A @ B )
=> ! [C: $i > $o] :
( ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ B )
=> ( C @ ( kpair @ D @ E ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( C @ D ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ ( cartprod @ A @ B ) )
=> ! [D: $i > $o] :
( ! [E: $i] :
( ( in @ E @ A )
=> ! [F: $i] :
( ( in @ F @ B )
=> ( ( in @ ( kpair @ E @ F ) @ C )
=> ( D @ ( kpair @ E @ F ) ) ) ) )
=> ! [E: $i] :
( ( in @ E @ C )
=> ( D @ E ) ) ) )
=> ! [A: $i,B: $i] :
( ( subset @ B @ ( cartprod @ A @ A ) )
=> ! [C: $i > $o] :
( ! [D: $i] :
( ( in @ D @ A )
=> ! [E: $i] :
( ( in @ E @ A )
=> ( ( in @ ( kpair @ D @ E ) @ B )
=> ( C @ ( kpair @ D @ E ) ) ) ) )
=> ! [D: $i] :
( ( in @ D @ B )
=> ( C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU768^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n015.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 18:06:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.08/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/1.13 % [INFO] Parsing done (115ms).
% 1.25/1.14 % [INFO] Running in sequential loop mode.
% 1.78/1.39 % [INFO] eprover registered as external prover.
% 1.78/1.40 % [INFO] cvc4 registered as external prover.
% 1.78/1.40 % [INFO] Scanning for conjecture ...
% 2.01/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.09/1.51 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.09/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.09/1.52 % [INFO] Type checking passed.
% 2.09/1.52 % [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 ...
% 2.92/1.92 % External prover 'e' found a proof!
% 2.92/1.92 % [INFO] Killing All external provers ...
% 2.92/1.92 % Time passed: 1354ms (effective reasoning time: 774ms)
% 2.92/1.92 % 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)>
% 2.92/1.92 % Axioms used in derivation (0):
% 2.92/1.92 % No. of inferences in proof: 4
% 2.92/1.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1354 ms resp. 774 ms w/o parsing
% 3.28/2.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.28/2.02 % [INFO] Killing All external provers ...
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