TSTP Solution File: SEU164+3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 : Fri May 19 11:57:20 EDT 2023
% Result : Theorem 94.35s 17.09s
% Output : Refutation 94.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 30 ( 10 unt; 6 typ; 0 def)
% Number of atoms : 81 ( 19 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 199 ( 6 ~; 0 |; 17 &; 136 @)
% ( 9 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 57 ( 0 ^; 48 !; 9 ?; 57 :)
% Comments :
%------------------------------------------------------------------------------
thf(union_type,type,
union: $i > $i ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(in_type,type,
in: $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(11,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(101,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B
= ( powerset @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( subset @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ( B
= ( powerset @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( subset @ C @ A ) )
& ( ( subset @ C @ A )
=> ( in @ C @ B ) ) )
=> ( B
= ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B
= ( union @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_tarski) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( B
= ( union @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) ) )
& ( ? [D: $i] :
( ( in @ C @ D )
& ( in @ D @ A ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( union @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(96,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,conjecture,
! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t99_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(98,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ( B
= ( singleton @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( C = A ) )
& ( ( C = A )
=> ( in @ C @ B ) ) )
=> ( B
= ( singleton @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(16,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) )
& ( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(103,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( in @ C @ A )
=> ( in @ C @ B ) )
& ( ( in @ C @ B )
=> ( in @ C @ A ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( ( subset @ ( singleton @ A ) @ B )
=> ( in @ A @ B ) )
& ( ( in @ A @ B )
=> ( subset @ ( singleton @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(51657,plain,
$false,
inference(e,[status(thm)],[101,38,65,96,13,98,18,16,58,103,91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SEU164+3 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n031.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 13:08:11 EDT 2023
% 0.16/0.37 % CPUTime :
% 1.08/0.93 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/1.13 % [INFO] Parsing done (196ms).
% 1.37/1.14 % [INFO] Running in sequential loop mode.
% 1.86/1.38 % [INFO] eprover registered as external prover.
% 1.86/1.39 % [INFO] cvc4 registered as external prover.
% 1.86/1.39 % [INFO] Scanning for conjecture ...
% 1.86/1.45 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 2.11/1.47 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.21/1.49 % [INFO] Problem is first-order (TPTP FOF).
% 2.21/1.50 % [INFO] Type checking passed.
% 2.21/1.50 % [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 ...
% 94.34/17.09 % External prover 'e' found a proof!
% 94.34/17.09 % [INFO] Killing All external provers ...
% 94.35/17.09 % Time passed: 16551ms (effective reasoning time: 15945ms)
% 94.35/17.09 % 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)>
% 94.35/17.09 % Axioms used in derivation (10): d1_tarski, t2_tarski, d4_tarski, l2_zfmisc_1, d1_zfmisc_1, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, d3_tarski, reflexivity_r1_tarski
% 94.35/17.09 % No. of inferences in proof: 24
% 94.35/17.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16551 ms resp. 15945 ms w/o parsing
% 94.35/17.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 94.35/17.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------