TSTP Solution File: SET014-4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET014-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:51:54 EDT 2023
% Result : Unsatisfiable 2.47s 1.51s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 50 ( 11 unt; 13 typ; 0 def)
% Number of atoms : 73 ( 8 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 250 ( 32 ~; 36 |; 0 &; 182 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 0 ^; 64 !; 0 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_type,type,
subset: $i > $i > $o ).
thf(union_type,type,
union: $i > $i > $i ).
thf(as_type,type,
as: $i ).
thf(bs_type,type,
bs: $i ).
thf(cs_type,type,
cs: $i ).
thf(little_set_type,type,
little_set: $i > $o ).
thf(f1_type,type,
f1: $i > $i > $i ).
thf(member_type,type,
member: $i > $i > $o ).
thf(intersection_type,type,
intersection: $i > $i > $i ).
thf(universal_set_type,type,
universal_set: $i ).
thf(complement_type,type,
complement: $i > $i ).
thf(empty_set_type,type,
empty_set: $i ).
thf(f17_type,type,
f17: $i > $i > $i ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset1) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset @ A @ B )
| ~ ( member @ C @ A )
| ( member @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( member @ ( f1 @ A @ B ) @ A )
| ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality2) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( member @ ( f1 @ A @ B ) @ A )
| ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(10,axiom,
! [A: $i] :
~ ( member @ A @ empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set) ).
thf(39,plain,
! [A: $i] :
~ ( member @ A @ empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i] :
( ( member @ A @ universal_set )
| ~ ( little_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',universal_set) ).
thf(35,plain,
! [A: $i] :
( ( member @ A @ universal_set )
| ~ ( little_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
~ ( subset @ ( union @ as @ bs ) @ cs ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
thf(19,plain,
~ ( subset @ ( union @ as @ bs ) @ cs ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( f17 @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ( member @ ( f17 @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( member @ ( f1 @ A @ B ) @ A )
| ~ ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality3) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( member @ ( f1 @ A @ B ) @ A )
| ~ ( member @ ( f1 @ A @ B ) @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( member @ A @ ( complement @ B ) )
| ~ ( little_set @ A )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( member @ A @ ( complement @ B ) )
| ~ ( little_set @ A )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
subset @ as @ cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_subset_of_c) ).
thf(46,plain,
subset @ as @ cs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( little_set @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ B )
| ( little_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( little_set @ ( f1 @ A @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',extensionality1) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( little_set @ ( f1 @ A @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
| ~ ( member @ A @ B )
| ~ ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( member @ A @ ( intersection @ B @ C ) )
| ~ ( member @ A @ B )
| ~ ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement1) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( member @ A @ ( complement @ B ) )
| ~ ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection1) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( union @ A @ B )
= ( complement @ ( intersection @ ( complement @ A ) @ ( complement @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
subset @ bs @ cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_subset_of_c) ).
thf(49,plain,
subset @ bs @ cs,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( member @ ( f17 @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset3) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( subset @ A @ B )
| ~ ( member @ ( f17 @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection2) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( member @ A @ ( intersection @ B @ C ) )
| ( member @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(56,plain,
$false,
inference(cvc4,[status(thm)],[52,41,39,35,19,47,24,37,46,29,21,33,44,27,54,49,50,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.08 % Problem : SET014-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.01/0.10 % Command : run_Leo-III %s %d
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Thu May 18 19:00:35 EDT 2023
% 0.10/0.28 % CPUTime :
% 0.68/0.68 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.92/0.79 % [INFO] Parsing done (110ms).
% 0.92/0.80 % [INFO] Running in sequential loop mode.
% 1.23/1.01 % [INFO] eprover registered as external prover.
% 1.23/1.01 % [INFO] cvc4 registered as external prover.
% 1.23/1.01 % [INFO] Scanning for conjecture ...
% 1.38/1.06 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.52/1.10 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 1.52/1.12 % [INFO] Problem is propositional (TPTP CNF).
% 1.52/1.12 % [INFO] Type checking passed.
% 1.52/1.12 % [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 ...
% 2.47/1.51 % External prover 'cvc4' found a proof!
% 2.47/1.51 % [INFO] Killing All external provers ...
% 2.47/1.51 % Time passed: 1120ms (effective reasoning time: 712ms)
% 2.47/1.51 % 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)>
% 2.47/1.51 % Axioms used in derivation (17): complement1, union, subset3, a_subset_of_c, intersection3, extensionality1, complement2, intersection2, a2, extensionality3, b_subset_of_c, empty_set, subset2, extensionality2, intersection1, universal_set, subset1
% 2.47/1.51 % No. of inferences in proof: 37
% 2.47/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1120 ms resp. 712 ms w/o parsing
% 2.47/1.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.47/1.55 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------