TSTP Solution File: SEU320+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 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 : Fri May 19 11:58:14 EDT 2023
% Result : Theorem 3.09s 1.67s
% Output : Refutation 3.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 39 ( 17 unt; 9 typ; 0 def)
% Number of atoms : 59 ( 2 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 166 ( 2 ~; 0 |; 3 &; 135 @)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 0 ^; 29 !; 6 ?; 35 :)
% Comments :
%------------------------------------------------------------------------------
thf(top_str_type,type,
top_str: $i > $o ).
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(the_carrier_type,type,
the_carrier: $i > $i ).
thf(open_subset_type,type,
open_subset: $i > $i > $o ).
thf(closed_subset_type,type,
closed_subset: $i > $i > $o ).
thf(subset_complement_type,type,
subset_complement: $i > $i > $i ).
thf(one_sorted_str_type,type,
one_sorted_str: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(7,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_subset_1) ).
thf(29,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
thf(45,plain,
! [A: $i,B: $i] :
( ( ( element @ A @ ( powerset @ B ) )
=> ( subset @ A @ B ) )
& ( ( subset @ A @ B )
=> ( element @ A @ ( powerset @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(35,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u1_struct_0) ).
thf(30,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( closed_subset @ B @ A )
<=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).
thf(42,plain,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( closed_subset @ B @ A )
=> ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) )
& ( ( open_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A )
=> ( closed_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( element @ ( subset_complement @ A @ B ) @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( subset_complement @ A @ ( subset_complement @ A @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_struct_0) ).
thf(28,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
? [A: $i] : ( one_sorted_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(33,plain,
? [A: $i] : ( one_sorted_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( open_subset @ B @ A )
<=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] :
( ( top_str @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ ( the_carrier @ A ) ) )
=> ( ( ( open_subset @ B @ A )
=> ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A ) )
& ( ( closed_subset @ ( subset_complement @ ( the_carrier @ A ) @ B ) @ A )
=> ( open_subset @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
? [A: $i] : ( top_str @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_pre_topc) ).
thf(31,plain,
? [A: $i] : ( top_str @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(40,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
thf(26,plain,
! [A: $i] :
( ( top_str @ A )
=> ( one_sorted_str @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_zfmisc_1) ).
thf(23,plain,
$true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(60,plain,
$false,
inference(cvc4,[status(thm)],[29,45,35,30,42,24,37,28,33,16,31,40,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 13:54:53 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.92/0.85 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.18/0.96 % [INFO] Parsing done (111ms).
% 1.18/0.97 % [INFO] Running in sequential loop mode.
% 1.61/1.15 % [INFO] eprover registered as external prover.
% 1.61/1.15 % [INFO] cvc4 registered as external prover.
% 1.61/1.16 % [INFO] Scanning for conjecture ...
% 1.70/1.21 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.89/1.23 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 1.89/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.89/1.25 % [INFO] Type checking passed.
% 1.89/1.25 % [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 ...
% 3.09/1.67 % External prover 'cvc4' found a proof!
% 3.09/1.67 % [INFO] Killing All external provers ...
% 3.09/1.67 % Time passed: 1148ms (effective reasoning time: 703ms)
% 3.09/1.67 % 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)>
% 3.09/1.67 % Axioms used in derivation (13): involutiveness_k3_subset_1, dt_l1_pre_topc, dt_k1_zfmisc_1, existence_l1_struct_0, dt_l1_struct_0, t3_subset, existence_m1_subset_1, existence_l1_pre_topc, reflexivity_r1_tarski, dt_m1_subset_1, dt_u1_struct_0, dt_k3_subset_1, t29_tops_1
% 3.09/1.67 % No. of inferences in proof: 30
% 3.09/1.67 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1148 ms resp. 703 ms w/o parsing
% 3.18/1.70 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.18/1.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------