TSTP Solution File: SEU706^2 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 03:39:12 EDT 2024
% Result : Theorem 2.80s 1.67s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 20 ( 7 unt; 10 typ; 6 def)
% Number of atoms : 61 ( 31 equ; 0 cnn)
% Maximal formula atoms : 15 ( 6 avg)
% Number of connectives : 90 ( 2 ~; 0 |; 2 &; 53 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 35 ( 1 ^ 32 !; 2 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(emptyset_type,type,
emptyset: $i ).
thf(setadjoin_type,type,
setadjoin: $i > $i > $i ).
thf(setunion_type,type,
setunion: $i > $i ).
thf(uniqinunit_type,type,
uniqinunit: $o ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(in__Cong_type,type,
in__Cong: $o ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(setadjoin__Cong_type,type,
setadjoin__Cong: $o ).
thf(setadjoin__Cong_def,definition,
( setadjoin__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( setadjoin @ A @ C )
= ( setadjoin @ B @ D ) ) ) ) ) ) ).
thf(setunion__Cong_type,type,
setunion__Cong: $o ).
thf(setunion__Cong_def,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ) ).
thf(setunionsingleton_type,type,
setunionsingleton: $o ).
thf(setunionsingleton_def,definition,
( setunionsingleton
= ( ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A ) ) ) ).
thf(singleton_type,type,
singleton: $i > $o ).
thf(singleton_def,definition,
( singleton
= ( ^ [A: $i] :
? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(1,conjecture,
( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [A: $i] :
( ( singleton @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theeq) ).
thf(2,negated_conjecture,
~ ( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [A: $i] :
( ( singleton @ A )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( setadjoin @ A @ C )
= ( setadjoin @ B @ D ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ! [A: $i] :
( ( setunion @ ( setadjoin @ A @ emptyset ) )
= A )
=> ! [A: $i] :
( ? [B: $i] :
( ( in @ B @ A )
& ( A
= ( setadjoin @ B @ emptyset ) ) )
=> ! [B: $i] :
( ( in @ B @ A )
=> ( ( setunion @ A )
= B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU706^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n012.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 17:37:09 EDT 2024
% 0.15/0.37 % CPUTime :
% 1.02/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.33/1.03 % [INFO] Parsing done (121ms).
% 1.33/1.04 % [INFO] Running in sequential loop mode.
% 1.64/1.24 % [INFO] eprover registered as external prover.
% 1.64/1.24 % [INFO] cvc4 registered as external prover.
% 1.64/1.24 % [INFO] Scanning for conjecture ...
% 2.00/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.04/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.04/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 2.04/1.34 % [INFO] Type checking passed.
% 2.04/1.34 % [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 ...
% 2.80/1.67 % External prover 'e' found a proof!
% 2.80/1.67 % [INFO] Killing All external provers ...
% 2.80/1.67 % Time passed: 1140ms (effective reasoning time: 627ms)
% 2.80/1.67 % 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)>
% 2.80/1.67 % Axioms used in derivation (0):
% 2.80/1.67 % No. of inferences in proof: 4
% 2.80/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1140 ms resp. 627 ms w/o parsing
% 2.80/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.80/1.70 % [INFO] Killing All external provers ...
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