TSTP Solution File: SET986+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET986+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:54:59 EDT 2023
% Result : Theorem 8.86s 2.69s
% Output : Refutation 8.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 21
% Syntax : Number of formulae : 38 ( 11 unt; 6 typ; 0 def)
% Number of atoms : 105 ( 27 equ; 0 cnn)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 299 ( 22 ~; 5 |; 23 &; 204 @)
% ( 9 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 74 ( 0 ^; 70 !; 4 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_type,type,
in: $i > $i > $o ).
thf(set_union2_type,type,
set_union2: $i > $i > $i ).
thf(set_difference_type,type,
set_difference: $i > $i > $i ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(empty_type,type,
empty: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(37,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)],[6]) ).
thf(13,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(125,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_union2 @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
| ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_union2 @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
| ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
| ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_union2 @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( set_difference @ B @ ( singleton @ A ) ) @ ( singleton @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t140_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( set_difference @ B @ ( singleton @ A ) ) @ ( singleton @ A ) )
= B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,plain,
~ ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ( ( set_union2 @ ( set_difference @ B @ ( singleton @ A ) ) @ ( singleton @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(130,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(127,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(119,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( in @ A @ ( set_difference @ B @ ( singleton @ C ) ) )
<=> ( ( in @ A @ B )
& ( A != C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t64_zfmisc_1) ).
thf(132,plain,
! [A: $i,B: $i,C: $i] :
( ( ( in @ A @ ( set_difference @ B @ ( singleton @ C ) ) )
=> ( ( in @ A @ B )
& ( A != C ) ) )
& ( ( ( in @ A @ B )
& ( A != C ) )
=> ( in @ A @ ( set_difference @ B @ ( singleton @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(116,plain,
! [A: $i,B: $i] :
( ~ ( empty @ A )
=> ~ ( empty @ ( set_union2 @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( subset @ A @ B )
& ( subset @ B @ A ) ) )
& ( ( ( subset @ A @ B )
& ( subset @ B @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(23,plain,
! [A: $i,B: $i] :
( ( set_union2 @ A @ B )
= ( set_union2 @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( set_difference @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(90,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C
= ( set_difference @ A @ B ) )
=> ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ~ ( in @ D @ B ) )
=> ( in @ D @ C ) ) ) )
& ( ! [D: $i] :
( ( ( in @ D @ C )
=> ( ( in @ D @ A )
& ~ ( in @ D @ B ) ) )
& ( ( ( in @ D @ A )
& ~ ( in @ D @ B ) )
=> ( in @ D @ C ) ) )
=> ( C
= ( set_difference @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( set_union2 @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(122,plain,
! [A: $i] :
( ( set_union2 @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ B )
<=> ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(83,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)],[8]) ).
thf(1263,plain,
$false,
inference(e,[status(thm)],[37,125,57,21,17,130,127,119,132,116,26,23,90,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET986+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu May 18 19:05:59 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.84/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.94 % [INFO] Parsing done (117ms).
% 1.18/0.95 % [INFO] Running in sequential loop mode.
% 1.47/1.14 % [INFO] eprover registered as external prover.
% 1.47/1.14 % [INFO] cvc4 registered as external prover.
% 1.47/1.14 % [INFO] Scanning for conjecture ...
% 1.73/1.20 % [INFO] Found a conjecture and 14 axioms. Running axiom selection ...
% 1.73/1.22 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 1.91/1.24 % [INFO] Problem is first-order (TPTP FOF).
% 1.91/1.25 % [INFO] Type checking passed.
% 1.91/1.25 % [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 ...
% 8.86/2.68 % External prover 'e' found a proof!
% 8.86/2.68 % [INFO] Killing All external provers ...
% 8.86/2.68 % Time passed: 2180ms (effective reasoning time: 1732ms)
% 8.86/2.69 % 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)>
% 8.86/2.69 % Axioms used in derivation (14): d1_tarski, fc2_xboole_0, commutativity_k2_xboole_0, t64_zfmisc_1, d4_xboole_0, rc1_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, fc3_xboole_0, d2_xboole_0, d3_tarski, reflexivity_r1_tarski, idempotence_k2_xboole_0, d10_xboole_0
% 8.86/2.69 % No. of inferences in proof: 32
% 8.86/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2180 ms resp. 1732 ms w/o parsing
% 8.86/2.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.86/2.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------