TSTP Solution File: SEU681^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n020.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 03:39:02 EDT 2024
% Result : Theorem 2.92s 1.81s
% Output : Refutation 3.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 11
% Syntax : Number of formulae : 14 ( 4 unt; 7 typ; 3 def)
% Number of atoms : 41 ( 5 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 124 ( 2 ~; 0 |; 4 &; 88 @)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 3 ^ 33 !; 4 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(subsetE_type,type,
subsetE: $o ).
thf(subsetE_def,definition,
( subsetE
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ) ).
thf(kpair_type,type,
kpair: $i > $i > $i ).
thf(cartprod_type,type,
cartprod: $i > $i > $i ).
thf(cartprodmempair1_type,type,
cartprodmempair1: $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(breln_type,type,
breln: $i > $i > $i > $o ).
thf(breln_def,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
thf(1,conjecture,
( subsetE
=> ( cartprodmempair1
=> ! [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 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(2,negated_conjecture,
~ ( subsetE
=> ( cartprodmempair1
=> ! [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 ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( in @ C @ A )
=> ( in @ C @ B ) ) )
=> ( ! [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] :
( ( 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 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,plain,
$false,
inference(cvc4,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU681^2 : TPTP v8.2.0. Released v3.7.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 15:32:23 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.92/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/0.98 % [INFO] Parsing done (144ms).
% 1.29/1.00 % [INFO] Running in sequential loop mode.
% 1.69/1.26 % [INFO] eprover registered as external prover.
% 1.69/1.26 % [INFO] cvc4 registered as external prover.
% 1.77/1.27 % [INFO] Scanning for conjecture ...
% 1.97/1.35 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.06/1.37 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.06/1.38 % [INFO] Problem is higher-order (TPTP THF).
% 2.06/1.38 % [INFO] Type checking passed.
% 2.06/1.38 % [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 ...
% 2.92/1.80 % External prover 'cvc4' found a proof!
% 2.92/1.80 % [INFO] Killing All external provers ...
% 2.92/1.81 % Time passed: 1302ms (effective reasoning time: 802ms)
% 2.92/1.81 % 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)>
% 2.92/1.81 % Axioms used in derivation (0):
% 2.92/1.81 % No. of inferences in proof: 4
% 2.92/1.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1302 ms resp. 802 ms w/o parsing
% 3.06/1.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.06/1.83 % [INFO] Killing All external provers ...
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