TSTP Solution File: TOP008-1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : TOP008-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n011.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 Sep 1 05:57:13 EDT 2023
% Result : Satisfiable 3.67s 1.19s
% Output : Model 3.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : TOP008-1 : TPTP v8.1.2. Released v1.0.0.
% 0.12/0.14 % Command : run_iprover %s %d THM
% 0.13/0.36 % Computer : n011.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 23:22:40 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.67/1.19 % SZS status Started for theBenchmark.p
% 3.67/1.19 % SZS status Satisfiable for theBenchmark.p
% 3.67/1.19
% 3.67/1.19 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.67/1.19
% 3.67/1.19 ------ iProver source info
% 3.67/1.19
% 3.67/1.19 git: date: 2023-05-31 18:12:56 +0000
% 3.67/1.19 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.67/1.19 git: non_committed_changes: false
% 3.67/1.19 git: last_make_outside_of_git: false
% 3.67/1.19
% 3.67/1.19 ------ Parsing...successful
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 3.67/1.19
% 3.67/1.19 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.67/1.19 ------ Proving...
% 3.67/1.19 ------ Problem Properties
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19 clauses 98
% 3.67/1.19 conjectures 3
% 3.67/1.19 EPR 24
% 3.67/1.19 Horn 76
% 3.67/1.19 unary 3
% 3.67/1.19 binary 46
% 3.67/1.19 lits 298
% 3.67/1.19 lits eq 0
% 3.67/1.19 fd_pure 0
% 3.67/1.19 fd_pseudo 0
% 3.67/1.19 fd_cond 0
% 3.67/1.19 fd_pseudo_cond 0
% 3.67/1.19 AC symbols 0
% 3.67/1.19
% 3.67/1.19 ------ Input Options Time Limit: Unbounded
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19 ------
% 3.67/1.19 Current options:
% 3.67/1.19 ------
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19 ------ Proving...
% 3.67/1.19
% 3.67/1.19
% 3.67/1.19 % SZS status Satisfiable for theBenchmark.p
% 3.67/1.19
% 3.67/1.19 ------ Building Model...Done
% 3.67/1.19
% 3.67/1.19 %------ The model is defined over ground terms (initial term algebra).
% 3.67/1.19 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n))))
% 3.67/1.19 %------ where \phi is a formula over the term algebra.
% 3.67/1.19 %------ If we have equality in the problem then it is also defined as a predicate above,
% 3.67/1.19 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 3.67/1.19 %------ See help for --sat_out_model for different model outputs.
% 3.67/1.19 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 3.67/1.19 %------ where the first argument stands for the sort ($i in the unsorted case)
% 3.67/1.19 % SZS output start Model for theBenchmark.p
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of topological_space
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X0_14] :
% 3.67/1.19 ( topological_space(X0_13,X0_14) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cx & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of subset_sets
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X1_13] :
% 3.67/1.19 ( subset_sets(X0_13,X1_13) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cy & X1_13=cx )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X0_15] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cy & X1_13=f14(cy,cx,ct,X0_15) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of element_of_set
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_15,X0_13] :
% 3.67/1.19 ( element_of_set(X0_15,X0_13) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=closure(cy,cx,ct) )
% 3.67/1.19 &
% 3.67/1.19 ! [X1_13,X0_14] : ( X0_15!=f11(X0_14,X1_13) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_15!=f7(X1_13,X0_14) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X0_14,X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=intersection_of_members(subspace_topology(X1_13,X0_14,X2_13)) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_15!=f11(X0_14,X1_13) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_15!=f7(X1_13,X0_14) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_15!=f7(X3_13,X1_14) )
% 3.67/1.19 &
% 3.67/1.19 ! [X3_13,X1_14] : ( X0_15!=f11(X1_14,X3_13) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X0_14,X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_15=f11(X0_14,X1_13) & X0_13=closure(cy,cx,ct) )
% 3.67/1.19 &
% 3.67/1.19 ( X1_13!=closure(cy,cx,ct) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X0_14,X1_13,X2_13,X1_14,X3_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_15=f11(X0_14,X1_13) & X0_13=intersection_of_members(subspace_topology(X2_13,X1_14,X3_13)) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X0_14] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_15=f7(X1_13,X0_14) & X0_13=closure(cy,cx,ct) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X0_14,X2_13,X1_14,X3_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_15=f7(X1_13,X0_14) & X0_13=intersection_of_members(subspace_topology(X2_13,X1_14,X3_13)) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X0_14] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_15=f11(X0_14,closure(cy,cx,ct)) & X0_13=closure(cy,cx,ct) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X0_14,X1_13,X1_14,X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_15=f11(X0_14,intersection_of_members(subspace_topology(X1_13,X1_14,X2_13))) & X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Negative definition of element_of_collection
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X0_14] :
% 3.67/1.19 ( ~(element_of_collection(X0_13,X0_14)) <=>
% 3.67/1.19 (
% 3.67/1.19 ? [X1_13,X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=relative_complement_sets(X1_13,X2_13) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=closure(cy,cx,ct) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_14] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=closure(cy,cx,ct) & X0_14=top_of_basis(X1_14) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13,X0_15] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=f2(subspace_topology(X1_13,X1_14,X2_13),X0_15) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_14!=ct )
% 3.67/1.19 &
% 3.67/1.19 ( X0_14!=top_of_basis(X0_14) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_14!=subspace_topology(X1_13,X1_14,X2_13) | X1_13!=X1_13 | X1_14!=X1_14 | X2_13!=X2_13 )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13,X0_15] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=f2(subspace_topology(X1_13,X1_14,X2_13),X0_15) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13,X0_15] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=f2(subspace_topology(X1_13,X1_14,X2_13),X0_15) & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_14!=ct )
% 3.67/1.19 &
% 3.67/1.19 ( X0_14!=top_of_basis(X0_14) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13,X2_14] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) & X0_14=top_of_basis(X2_14) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=closure(X1_13,cx,ct) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_14!=top_of_basis(X0_14) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=closure(X1_13,cx,ct) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=relative_complement_sets(X1_13,cx) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=f4(X1_13,ct) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=intersection_of_sets(f3(X1_13,ct),f4(X1_13,ct)) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=relative_complement_sets(X1_13,empty_set) & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13,X3_13,X2_14] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=f2(subspace_topology(X1_13,X1_14,X2_13),f7(X3_13,X2_14)) & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 ? [X1_13,X1_14,X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 3.67/1.19 &
% 3.67/1.19 ! [X1_15] : ( X0_13!=f2(subspace_topology(X1_13,X1_14,X2_13),X1_15) | X1_13!=X1_13 | X1_14!=X1_14 | X2_13!=X2_13 )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of equal_sets
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X1_13] :
% 3.67/1.19 ( equal_sets(X0_13,X1_13) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=union_of_members(ct) & X1_13=cx )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Negative definition of subset_collections
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_14,X1_14] :
% 3.67/1.19 ( ~(subset_collections(X0_14,X1_14)) <=>
% 3.67/1.19 $false
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of open
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X1_13,X0_14] :
% 3.67/1.19 ( open(X0_13,X1_13,X0_14) <=>
% 3.67/1.19 (
% 3.67/1.19 ? [X2_13] :
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=union_of_members(f5(X2_13,ct)) & X1_13=cx & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 |
% 3.67/1.19 (
% 3.67/1.19 ( X1_13=cx & X0_14=ct )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=closure(X0_13,cx,ct) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=relative_complement_sets(X0_13,cx) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=f4(X0_13,ct) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=intersection_of_sets(f3(X0_13,ct),f4(X0_13,ct)) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=union_of_members(f5(X0_13,ct)) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=relative_complement_sets(X0_13,empty_set) )
% 3.67/1.19 &
% 3.67/1.19 ! [X2_13] : ( X0_13!=relative_complement_sets(X0_13,X2_13) )
% 3.67/1.19 &
% 3.67/1.19 ! [X0_15,X1_14] : ( X0_13!=f2(subspace_topology(X0_13,X1_14,X2_13),X0_15) )
% 3.67/1.19 &
% 3.67/1.19 ( X0_13!=intersection_of_members(subspace_topology(X0_13,X1_14,X2_13)) )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of closed
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X1_13,X0_14] :
% 3.67/1.19 ( closed(X0_13,X1_13,X0_14) <=>
% 3.67/1.19 $false
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of basis
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X0_14] :
% 3.67/1.19 ( basis(X0_13,X0_14) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cx & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of neighborhood
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X0_15,X1_13,X0_14] :
% 3.67/1.19 ( neighborhood(X0_13,X0_15,X1_13,X0_14) <=>
% 3.67/1.19 $false
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of limit_point
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_15,X0_13,X1_13,X0_14] :
% 3.67/1.19 ( limit_point(X0_15,X0_13,X1_13,X0_14) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cy & X1_13=cx & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of hausdorff
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X0_14] :
% 3.67/1.19 ( hausdorff(X0_13,X0_14) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cx & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of separation
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X1_13,X2_13,X0_14] :
% 3.67/1.19 ( separation(X0_13,X1_13,X2_13,X0_14) <=>
% 3.67/1.19 $false
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of open_covering
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_14,X0_13,X1_14] :
% 3.67/1.19 ( open_covering(X0_14,X0_13,X1_14) <=>
% 3.67/1.19 $false
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19
% 3.67/1.19 %------ Positive definition of compact_space
% 3.67/1.19 fof(lit_def,axiom,
% 3.67/1.19 (! [X0_13,X0_14] :
% 3.67/1.19 ( compact_space(X0_13,X0_14) <=>
% 3.67/1.19 (
% 3.67/1.19 (
% 3.67/1.19 ( X0_13=cx & X0_14=ct )
% 3.67/1.19 )
% 3.67/1.19
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 )
% 3.67/1.19 ).
% 3.67/1.19 % SZS output end Model for theBenchmark.p
% 3.67/1.20
%------------------------------------------------------------------------------