TSTP Solution File: SEU160+3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SEU160+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:57:18 EDT 2023
% Result : Theorem 2.48s 1.60s
% Output : Refutation 2.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 10
% Syntax : Number of formulae : 18 ( 9 unt; 4 typ; 0 def)
% Number of atoms : 30 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 4 ~; 7 |; 2 &; 38 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 13 !; 4 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(singleton_type,type,
singleton: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(empty_type,type,
empty: $i > $o ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(20,plain,
empty @ empty_set,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(21,plain,
? [A: $i] : ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(18,plain,
! [A: $i] : ( subset @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( subset @ A @ ( singleton @ B ) )
<=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( subset @ A @ ( singleton @ B ) )
=> ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) ) )
& ( ( ( A = empty_set )
| ( A
= ( singleton @ B ) ) )
=> ( subset @ A @ ( singleton @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(6,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(23,plain,
? [A: $i] :
~ ( empty @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(40,plain,
$false,
inference(e,[status(thm)],[20,21,18,8,26,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU160+3 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.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 12:42:58 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.11/0.99 % [INFO] Parsing done (121ms).
% 1.11/1.00 % [INFO] Running in sequential loop mode.
% 1.62/1.19 % [INFO] eprover registered as external prover.
% 1.62/1.19 % [INFO] cvc4 registered as external prover.
% 1.62/1.20 % [INFO] Scanning for conjecture ...
% 1.74/1.25 % [INFO] Found a conjecture and 5 axioms. Running axiom selection ...
% 1.74/1.27 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.74/1.27 % [INFO] Problem is first-order (TPTP FOF).
% 1.74/1.28 % [INFO] Type checking passed.
% 1.74/1.28 % [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 ...
% 2.48/1.60 % External prover 'e' found a proof!
% 2.48/1.60 % [INFO] Killing All external provers ...
% 2.48/1.60 % Time passed: 1089ms (effective reasoning time: 604ms)
% 2.48/1.60 % 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)>
% 2.48/1.60 % Axioms used in derivation (5): fc1_xboole_0, l4_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0
% 2.48/1.60 % No. of inferences in proof: 14
% 2.48/1.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1089 ms resp. 604 ms w/o parsing
% 2.81/1.67 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.81/1.67 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------