TSTP Solution File: SEU164+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:57:19 EDT 2023
% Result : Theorem 33.64s 7.97s
% Output : Refutation 33.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 17
% Syntax : Number of formulae : 31 ( 12 unt; 5 typ; 0 def)
% Number of atoms : 83 ( 19 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 193 ( 4 ~; 0 |; 17 &; 132 @)
% ( 9 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 53 ( 0 ^; 48 !; 5 ?; 53 :)
% 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(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(14,plain,
~ ! [A: $i] :
( ( union @ ( powerset @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(93,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,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(102,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)],[13]) ).
thf(8,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(92,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(17,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(59,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(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(39,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(66,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(11,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ B )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(95,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)],[11]) ).
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(19,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(10,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).
thf(94,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(100,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16185,plain,
$false,
inference(cvc4,[status(thm)],[14,93,102,92,17,59,39,66,95,19,94,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU164+1 : TPTP v8.1.2. Released v3.3.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n016.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 14:00:27 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.98/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.35/1.05 % [INFO] Parsing done (134ms).
% 1.35/1.06 % [INFO] Running in sequential loop mode.
% 1.74/1.26 % [INFO] eprover registered as external prover.
% 1.74/1.26 % [INFO] cvc4 registered as external prover.
% 1.74/1.27 % [INFO] Scanning for conjecture ...
% 1.96/1.32 % [INFO] Found a conjecture and 11 axioms. Running axiom selection ...
% 1.96/1.34 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.96/1.36 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/1.36 % [INFO] Type checking passed.
% 1.96/1.37 % [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 ...
% 33.64/7.96 % External prover 'cvc4' found a proof!
% 33.64/7.97 % [INFO] Killing All external provers ...
% 33.64/7.97 % Time passed: 7443ms (effective reasoning time: 6905ms)
% 33.64/7.97 % 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)>
% 33.64/7.97 % Axioms used in derivation (11): d1_tarski, dt_k1_tarski, dt_k3_tarski, t2_tarski, d4_tarski, dt_k1_zfmisc_1, l2_zfmisc_1, d1_zfmisc_1, antisymmetry_r2_hidden, d3_tarski, reflexivity_r1_tarski
% 33.64/7.97 % No. of inferences in proof: 26
% 33.64/7.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7443 ms resp. 6905 ms w/o parsing
% 33.64/8.00 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 33.64/8.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------