TSTP Solution File: TOP005-2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 12:38:39 EDT 2023
% Result : Unsatisfiable 2.67s 1.55s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 23
% Syntax : Number of formulae : 36 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 61 ( 0 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 246 ( 34 ~; 36 |; 0 &; 176 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_collections_type,type,
subset_collections: $i > $i > $o ).
thf(g_type,type,
g: $i ).
thf(top_of_basis_type,type,
top_of_basis: $i > $i ).
thf(f_type,type,
f: $i ).
thf(element_of_collection_type,type,
element_of_collection: $i > $i > $o ).
thf(union_of_members_type,type,
union_of_members: $i > $i ).
thf(element_of_set_type,type,
element_of_set: $i > $i > $o ).
thf(f1_type,type,
f1: $i > $i > $i ).
thf(f10_type,type,
f10: $i > $i > $i > $i ).
thf(subset_sets_type,type,
subset_sets: $i > $i > $o ).
thf(f11_type,type,
f11: $i > $i > $i ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ C @ A )
| ( subset_sets @ ( f10 @ B @ A @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ C @ A )
| ( subset_sets @ ( f10 @ B @ A @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(2,negated_conjecture,
~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).
thf(14,plain,
~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ C @ A )
| ( element_of_set @ C @ ( f10 @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_37) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ C @ A )
| ( element_of_set @ C @ ( f10 @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ ( f11 @ B @ A ) @ C )
| ~ ( element_of_collection @ C @ B )
| ~ ( subset_sets @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ ( f11 @ B @ A ) @ C )
| ~ ( element_of_collection @ C @ B )
| ~ ( subset_sets @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(1,negated_conjecture,
subset_collections @ g @ ( top_of_basis @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).
thf(13,plain,
subset_collections @ g @ ( top_of_basis @ f ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ C @ A )
| ( element_of_collection @ ( f10 @ B @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_38) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ~ ( element_of_set @ C @ A )
| ( element_of_collection @ ( f10 @ B @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
| ( element_of_collection @ ( f1 @ B @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).
thf(18,plain,
! [B: $i,A: $i] :
( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
| ( element_of_collection @ ( f1 @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
| ( element_of_set @ A @ ( f1 @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( element_of_set @ A @ ( union_of_members @ B ) )
| ( element_of_set @ A @ ( f1 @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ( element_of_set @ ( f11 @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( element_of_collection @ A @ ( top_of_basis @ B ) )
| ( element_of_set @ ( f11 @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( subset_sets @ A @ B )
| ~ ( element_of_set @ C @ A )
| ( element_of_set @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_19) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( subset_sets @ A @ B )
| ~ ( element_of_set @ C @ A )
| ( element_of_set @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset_sets @ A @ B )
| ~ ( element_of_collection @ B @ C )
| ( subset_sets @ A @ ( union_of_members @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset_sets @ A @ B )
| ~ ( element_of_collection @ B @ C )
| ( subset_sets @ A @ ( union_of_members @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( subset_collections @ A @ B )
| ~ ( element_of_collection @ C @ A )
| ( element_of_collection @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( subset_collections @ A @ B )
| ~ ( element_of_collection @ C @ A )
| ( element_of_collection @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(36,plain,
$false,
inference(e,[status(thm)],[24,14,20,28,13,22,18,16,26,30,32,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : TOP005-2 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n031.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 20:31:11 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.95/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/0.97 % [INFO] Parsing done (120ms).
% 1.15/0.98 % [INFO] Running in sequential loop mode.
% 1.67/1.16 % [INFO] eprover registered as external prover.
% 1.67/1.17 % [INFO] cvc4 registered as external prover.
% 1.67/1.17 % [INFO] Scanning for conjecture ...
% 1.67/1.22 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.82/1.24 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 1.82/1.26 % [INFO] Problem is propositional (TPTP CNF).
% 1.82/1.26 % [INFO] Type checking passed.
% 1.82/1.26 % [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 ...
% 2.67/1.54 % External prover 'e' found a proof!
% 2.67/1.55 % [INFO] Killing All external provers ...
% 2.67/1.55 % Time passed: 1015ms (effective reasoning time: 563ms)
% 2.67/1.55 % 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)>
% 2.67/1.55 % Axioms used in derivation (10): topology_generated_37, topology_generated_40, topology_generated_39, union_of_members_2, set_theory_20, topology_generated_38, union_of_members_1, topology_generated_41, set_theory_19, set_theory_21
% 2.67/1.55 % No. of inferences in proof: 25
% 2.67/1.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1015 ms resp. 563 ms w/o parsing
% 2.83/1.58 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.83/1.58 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------