TSTP Solution File: SEU118+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:57:03 EDT 2023
% Result : Theorem 3.72s 1.82s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 52
% Syntax : Number of formulae : 87 ( 15 unt; 19 typ; 0 def)
% Number of atoms : 198 ( 7 equ; 0 cnn)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 472 ( 36 ~; 2 |; 79 &; 306 @)
% ( 3 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 19 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 0 ^; 92 !; 20 ?; 112 :)
% Comments :
%------------------------------------------------------------------------------
thf(element_type,type,
element: $i > $i > $o ).
thf(powerset_type,type,
powerset: $i > $i ).
thf(finite_type,type,
finite: $i > $o ).
thf(finite_subsets_type,type,
finite_subsets: $i > $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(empty_set_type,type,
empty_set: $i ).
thf(cup_closed_type,type,
cup_closed: $i > $o ).
thf(diff_closed_type,type,
diff_closed: $i > $o ).
thf(preboolean_type,type,
preboolean: $i > $o ).
thf(in_type,type,
in: $i > $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(cap_closed_type,type,
cap_closed: $i > $o ).
thf(relation_type,type,
relation: $i > $o ).
thf(function_type,type,
function: $i > $o ).
thf(one_to_one_type,type,
one_to_one: $i > $o ).
thf(epsilon_transitive_type,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_type,type,
epsilon_connected: $i > $o ).
thf(ordinal_type,type,
ordinal: $i > $o ).
thf(natural_type,type,
natural: $i > $o ).
thf(22,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(102,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( empty @ ( finite_subsets @ A ) )
& ( cup_closed @ ( finite_subsets @ A ) )
& ( diff_closed @ ( finite_subsets @ A ) )
& ( preboolean @ ( finite_subsets @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).
thf(70,plain,
! [A: $i] :
( ~ ( empty @ ( finite_subsets @ A ) )
& ( cup_closed @ ( finite_subsets @ A ) )
& ( diff_closed @ ( finite_subsets @ A ) )
& ( preboolean @ ( finite_subsets @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(19,axiom,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(92,plain,
! [A: $i] :
( ( empty @ A )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(53,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_finsub_1) ).
thf(124,plain,
! [A: $i,B: $i] :
( ( element @ B @ ( finite_subsets @ A ) )
=> ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) ) )
=> ( element @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(23,axiom,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(105,plain,
! [A: $i] :
( ( finite @ A )
=> ! [B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( finite @ A )
=> ( element @ B @ ( finite_subsets @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( finite @ A )
=> ( element @ B @ ( finite_subsets @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(35,plain,
~ ! [A: $i,B: $i] :
( ( element @ B @ ( powerset @ A ) )
=> ( ( finite @ A )
=> ( element @ B @ ( finite_subsets @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(48,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(67,plain,
! [A: $i] :
( ( empty @ A )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(43,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(55,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( cup_closed @ A )
& ( cap_closed @ A )
& ( diff_closed @ A )
& ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( element @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(31,axiom,
! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
thf(131,plain,
! [A: $i] : ( preboolean @ ( finite_subsets @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).
thf(121,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ B )
& ( finite @ B ) )
=> ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( element @ A @ B )
=> ( ( empty @ B )
| ( in @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(61,plain,
! [A: $i,B: $i] :
~ ( ( in @ A @ B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
thf(116,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( in @ A @ B )
& ( element @ B @ ( powerset @ C ) )
& ( empty @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(18,axiom,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(89,plain,
? [A: $i] :
( ~ ( empty @ A )
& ( finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(133,plain,
! [A: $i] :
? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ( empty @ B )
& ( relation @ B )
& ( function @ B )
& ( one_to_one @ B )
& ( epsilon_transitive @ B )
& ( epsilon_connected @ B )
& ( ordinal @ B )
& ( natural @ B )
& ( finite @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(45,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(64,plain,
! [A: $i] :
( ( preboolean @ A )
=> ( ( cup_closed @ A )
& ( diff_closed @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(33,axiom,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(144,plain,
! [A: $i] :
? [B: $i] : ( element @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(7,axiom,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(49,plain,
! [A: $i] :
( ( ( cup_closed @ A )
& ( diff_closed @ A ) )
=> ( preboolean @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(86,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(39,plain,
! [A: $i,B: $i] :
~ ( ( empty @ A )
& ( A != B )
& ( empty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(21,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_finset_1) ).
thf(98,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( preboolean @ B )
=> ( ( B
= ( finite_subsets @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( ( subset @ C @ A )
& ( finite @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
thf(146,plain,
! [A: $i,B: $i] :
( ( preboolean @ B )
=> ( ( ( B
= ( finite_subsets @ A ) )
=> ! [C: $i] :
( ( ( in @ C @ B )
=> ( ( subset @ C @ A )
& ( finite @ C ) ) )
& ( ( ( subset @ C @ A )
& ( finite @ C ) )
=> ( in @ C @ B ) ) ) )
& ( ! [C: $i] :
( ( ( in @ C @ B )
=> ( ( subset @ C @ A )
& ( finite @ C ) ) )
& ( ( ( subset @ C @ A )
& ( finite @ C ) )
=> ( in @ C @ B ) ) )
=> ( B
= ( finite_subsets @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(24,axiom,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_finsub_1) ).
thf(107,plain,
! [A: $i] :
( ~ ( empty @ ( powerset @ A ) )
& ( cup_closed @ ( powerset @ A ) )
& ( diff_closed @ ( powerset @ A ) )
& ( preboolean @ ( powerset @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(29,axiom,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(126,plain,
! [A: $i] :
~ ( empty @ ( powerset @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( element @ A @ ( powerset @ B ) )
<=> ( subset @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(79,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(20,axiom,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
thf(94,plain,
! [A: $i] :
( ~ ( empty @ A )
=> ? [B: $i] :
( ( element @ B @ ( powerset @ A ) )
& ~ ( empty @ B )
& ( finite @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(167,plain,
$false,
inference(e,[status(thm)],[102,70,92,53,124,129,105,35,48,67,43,55,119,131,121,84,61,116,89,133,45,64,144,49,86,39,98,146,51,107,126,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU118+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n013.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 : Thu May 18 12:21:52 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.92/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/0.98 % [INFO] Parsing done (129ms).
% 1.34/0.99 % [INFO] Running in sequential loop mode.
% 1.73/1.17 % [INFO] eprover registered as external prover.
% 1.73/1.18 % [INFO] cvc4 registered as external prover.
% 1.73/1.18 % [INFO] Scanning for conjecture ...
% 1.89/1.24 % [INFO] Found a conjecture and 32 axioms. Running axiom selection ...
% 1.97/1.28 % [INFO] Axiom selection finished. Selected 32 axioms (removed 0 axioms).
% 1.97/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 1.97/1.32 % [INFO] Type checking passed.
% 1.97/1.32 % [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 ...
% 3.72/1.82 % External prover 'e' found a proof!
% 3.72/1.82 % [INFO] Killing All external provers ...
% 3.72/1.82 % Time passed: 1292ms (effective reasoning time: 829ms)
% 3.72/1.82 % 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)>
% 3.72/1.82 % Axioms used in derivation (32): cc2_finset_1, cc2_finsub_1, t5_subset, t4_subset, rc1_subset_1, cc3_finsub_1, t2_subset, antisymmetry_r2_hidden, fc1_finsub_1, rc4_finset_1, rc1_finsub_1, fc1_xboole_0, t1_subset, t6_boole, rc2_subset_1, t7_boole, fc1_subset_1, t13_finset_1, t3_subset, existence_m1_subset_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, rc3_finset_1, fc2_finsub_1, rc1_finset_1, cc1_finset_1, t8_boole, rc1_xboole_0, dt_k5_finsub_1, d5_finsub_1, rc2_xboole_0
% 3.72/1.82 % No. of inferences in proof: 68
% 3.72/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1292 ms resp. 829 ms w/o parsing
% 3.81/1.87 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/1.87 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------