TSTP Solution File: SET985+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 2.92s 1.69s
% Output : Refutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 22 ( 11 unt; 4 typ; 0 def)
% Number of atoms : 40 ( 11 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 118 ( 7 ~; 8 |; 3 &; 89 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 ^; 29 !; 4 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_type,type,
empty: $i > $o ).
thf(subset_type,type,
subset: $i > $i > $o ).
thf(cartesian_product2_type,type,
cartesian_product2: $i > $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(1,conjecture,
! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ D @ C ) ) )
=> ( subset @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t139_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ D @ C ) ) )
=> ( subset @ B @ D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(10,plain,
~ ! [A: $i] :
( ~ ( empty @ A )
=> ! [B: $i,C: $i,D: $i] :
( ( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
| ( subset @ ( cartesian_product2 @ B @ A ) @ ( cartesian_product2 @ D @ C ) ) )
=> ( subset @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i] : ( subset @ empty_set @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(37,plain,
! [A: $i] : ( subset @ empty_set @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(14,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(20,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( ( cartesian_product2 @ A @ B )
= empty_set )
<=> ( ( A = empty_set )
| ( B = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t113_zfmisc_1) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( ( ( cartesian_product2 @ A @ B )
= empty_set )
=> ( ( A = empty_set )
| ( B = empty_set ) ) )
& ( ( ( A = empty_set )
| ( B = empty_set ) )
=> ( ( cartesian_product2 @ A @ B )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(15,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t138_zfmisc_1) ).
thf(32,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( subset @ ( cartesian_product2 @ A @ B ) @ ( cartesian_product2 @ C @ D ) )
=> ( ( ( cartesian_product2 @ A @ B )
= empty_set )
| ( ( subset @ A @ C )
& ( subset @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(5,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(17,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,plain,
$false,
inference(e,[status(thm)],[10,37,14,20,22,15,32,17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET985+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n007.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 19:07:24 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.83/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (114ms).
% 1.21/0.96 % [INFO] Running in sequential loop mode.
% 1.50/1.17 % [INFO] eprover registered as external prover.
% 1.50/1.17 % [INFO] cvc4 registered as external prover.
% 1.50/1.17 % [INFO] Scanning for conjecture ...
% 1.79/1.23 % [INFO] Found a conjecture and 7 axioms. Running axiom selection ...
% 1.85/1.25 % [INFO] Axiom selection finished. Selected 7 axioms (removed 0 axioms).
% 1.85/1.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.85/1.27 % [INFO] Type checking passed.
% 1.85/1.27 % [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 ...
% 2.92/1.64 % External prover 'e' found a proof!
% 2.92/1.68 % [INFO] Killing All external provers ...
% 2.92/1.68 % Time passed: 1171ms (effective reasoning time: 721ms)
% 2.92/1.68 % 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)>
% 2.92/1.69 % Axioms used in derivation (7): t138_zfmisc_1, reflexivity_r1_tarski, t2_xboole_1, rc1_xboole_0, rc2_xboole_0, fc1_xboole_0, t113_zfmisc_1
% 2.92/1.69 % No. of inferences in proof: 18
% 2.92/1.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1171 ms resp. 721 ms w/o parsing
% 3.17/1.72 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.17/1.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------