TSTP Solution File: TOP003-1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : TOP003-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 05:57:11 EDT 2023
% Result : Satisfiable 24.27s 4.18s
% Output : Model 24.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : TOP003-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 00:20:34 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.47 Running first-order theorem proving
% 0.18/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.27/4.18 % SZS status Started for theBenchmark.p
% 24.27/4.18 % SZS status Satisfiable for theBenchmark.p
% 24.27/4.18
% 24.27/4.18 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 24.27/4.18
% 24.27/4.18 ------ iProver source info
% 24.27/4.18
% 24.27/4.18 git: date: 2023-05-31 18:12:56 +0000
% 24.27/4.18 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 24.27/4.18 git: non_committed_changes: false
% 24.27/4.18 git: last_make_outside_of_git: false
% 24.27/4.18
% 24.27/4.18 ------ Parsing...successful
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18 ------ Preprocessing... sf_s rm: 0 0s sf_e
% 24.27/4.18
% 24.27/4.18 ------ Preprocessing...
% 24.27/4.18 ------ Proving...
% 24.27/4.18 ------ Problem Properties
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18 clauses 111
% 24.27/4.18 conjectures 6
% 24.27/4.18 EPR 33
% 24.27/4.18 Horn 88
% 24.27/4.18 unary 2
% 24.27/4.18 binary 55
% 24.27/4.18 lits 334
% 24.27/4.18 lits eq 0
% 24.27/4.18 fd_pure 0
% 24.27/4.18 fd_pseudo 0
% 24.27/4.18 fd_cond 0
% 24.27/4.18 fd_pseudo_cond 0
% 24.27/4.18 AC symbols 0
% 24.27/4.18
% 24.27/4.18 ------ Input Options Time Limit: Unbounded
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18 ------
% 24.27/4.18 Current options:
% 24.27/4.18 ------
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18 ------ Proving...
% 24.27/4.18
% 24.27/4.18
% 24.27/4.18 % SZS status Satisfiable for theBenchmark.p
% 24.27/4.18
% 24.27/4.18 ------ Building Model...Done
% 24.27/4.18
% 24.27/4.18 %------ The model is defined over ground terms (initial term algebra).
% 24.27/4.18 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n))))
% 24.27/4.18 %------ where \phi is a formula over the term algebra.
% 24.27/4.18 %------ If we have equality in the problem then it is also defined as a predicate above,
% 24.27/4.18 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 24.27/4.18 %------ See help for --sat_out_model for different model outputs.
% 24.27/4.18 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 24.27/4.18 %------ where the first argument stands for the sort ($i in the unsorted case)
% 24.27/4.18 % SZS output start Model for theBenchmark.p
% 24.27/4.18
% 24.27/4.18 %------ Negative definition of basis
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_14] :
% 24.27/4.18 ( ~(basis(X0_13,X0_14)) <=>
% 24.27/4.18 (
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=empty_set & X0_14=top_of_basis(X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=empty_set & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=closure(X1_13,X2_13,X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=boundary(X1_13,X2_13,X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(subspace_topology(X1_13,X1_14,X2_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=interior(X1_13,X2_13,X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=top_of_basis(X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Negative definition of element_of_collection
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_14] :
% 24.27/4.18 ( ~(element_of_collection(X0_13,X0_14)) <=>
% 24.27/4.18 (
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=f )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=top_of_basis(f) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=top_of_basis(X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=top_of_basis(subspace_topology(X1_13,X1_14,X2_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14,X3_13,X4_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=top_of_basis(subspace_topology(X1_13,subspace_topology(X2_13,X1_14,X3_13),X4_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=cx & X0_14=f5(X1_13,top_of_basis(X1_14)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=empty_set & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(X1_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) | X1_14!=top_of_basis(X1_14) )
% 24.27/4.18 &
% 24.27/4.18 ! [X2_13,X1_13] : ( X0_14!=top_of_basis(X0_14) | X1_14!=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 &
% 24.27/4.18 ! [X1_13] : ( X0_14!=top_of_basis(X0_14) | X1_14!=f5(X1_13,top_of_basis(X0_14)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) | X1_14!=f5(X1_13,top_of_basis(X1_14)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X1_14) | X1_14!=f5(X1_13,top_of_basis(X1_14)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(X1_14) & X0_14=f )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X1_13,X2_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(X1_14) & X0_14=subspace_topology(X1_13,X2_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(top_of_basis(X1_14)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ! [X2_13,X1_13] : ( X0_14!=top_of_basis(subspace_topology(X1_13,X0_14,X2_13)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(top_of_basis(X0_14)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X1_13,X2_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(top_of_basis(X1_14)) & X0_14=subspace_topology(X1_13,X2_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13,X2_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) & X0_14=top_of_basis(X2_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13,X3_13,X2_14,X4_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) & X0_14=top_of_basis(subspace_topology(X3_13,X2_14,X4_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13,X3_13,X4_13,X2_14,X5_13,X6_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)) & X0_14=top_of_basis(subspace_topology(X3_13,subspace_topology(X4_13,X2_14,X5_13),X6_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13,X0_15] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f2(subspace_topology(X1_13,X1_14,X2_13),X0_15) & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(f5(X1_13,X0_14)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X2_14,X3_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,union_of_members(X2_14),f11(X3_14,union_of_members(X2_14))) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X2_14,X1_13,X3_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,union_of_members(X2_14),f11(subspace_topology(X1_13,X3_14,X2_13),union_of_members(X2_14))) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X2_14,X1_13,X3_14,X2_13,X4_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,union_of_members(X2_14),f11(subspace_topology(X1_13,X3_14,X2_13),union_of_members(X2_14))) & X0_14=top_of_basis(X4_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X2_14,X1_13,X3_14,X2_13,X3_13,X4_14,X4_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,union_of_members(X2_14),f11(subspace_topology(X1_13,X3_14,X2_13),union_of_members(X2_14))) & X0_14=top_of_basis(subspace_topology(X3_13,X4_14,X4_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X2_14,X1_13,X3_14,X2_13,X3_13,X4_13,X4_14,X5_13,X6_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,union_of_members(X2_14),f11(subspace_topology(X1_13,X3_14,X2_13),union_of_members(X2_14))) & X0_14=top_of_basis(subspace_topology(X3_13,subspace_topology(X4_13,X4_14,X5_13),X6_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_sets(f3(X1_13,X0_14),f4(X1_13,X0_14)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13,X2_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f1(subspace_topology(X1_13,X1_14,X2_13),f11(X2_14,union_of_members(subspace_topology(X1_13,X1_14,X2_13)))) & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14,X3_13,X4_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,subspace_topology(X2_13,X1_14,X3_13),X4_13)) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14,X3_13,X4_13,X2_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,subspace_topology(X2_13,X1_14,X3_13),X4_13)) & X0_14=top_of_basis(X2_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(f5(X1_13,top_of_basis(X1_14))) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X1_14) | X1_14!=X1_14 )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(subspace_topology(X1_13,X1_14,X2_13)) | X1_14!=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 &
% 24.27/4.18 ! [X3_13,X2_13] : ( X0_14!=top_of_basis(subspace_topology(X2_13,X1_14,X3_13)) | X1_14!=subspace_topology(X2_13,X1_14,X3_13) )
% 24.27/4.18 &
% 24.27/4.18 ! [X5_13,X4_13] : ( X0_14!=top_of_basis(subspace_topology(X2_13,subspace_topology(X3_13,X1_14,X4_13),X5_13)) | X1_14!=subspace_topology(X2_13,subspace_topology(X3_13,X1_14,X4_13),X5_13) )
% 24.27/4.18 &
% 24.27/4.18 ! [X4_13,X3_13,X2_13] : ( X0_14!=top_of_basis(subspace_topology(X1_13,subspace_topology(X2_13,X1_14,X3_13),X4_13)) | X1_14!=subspace_topology(X1_13,subspace_topology(X2_13,X1_14,X3_13),X4_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X1_13,X2_14,X2_13,X0_15] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,intersection_of_members(subspace_topology(X1_13,X2_14,X2_13)),X0_15) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14,X3_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(f5(X1_13,top_of_basis(subspace_topology(X2_13,X1_14,X3_13)))) & X0_14=subspace_topology(X2_13,X1_14,X3_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f1(subspace_topology(X1_13,X1_14,X2_13),f11(f,cx)) & X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X1_13,X2_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f1(X1_14,f11(subspace_topology(X1_13,X2_14,X2_13),union_of_members(X1_14))) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X1_14) | X1_14!=top_of_basis(X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14,X2_14,X3_14,X1_13,X4_14,X2_13,X5_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=f10(X1_14,f10(X2_14,union_of_members(X3_14),f11(subspace_topology(X1_13,X4_14,X2_13),union_of_members(X3_14))),f11(X5_14,f10(X2_14,union_of_members(X3_14),f11(subspace_topology(X1_13,X4_14,X2_13),union_of_members(X3_14))))) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=subspace_topology(X1_13,X1_14,X2_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X1_14,X3_13,X4_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=subspace_topology(X1_13,subspace_topology(X2_13,X1_14,X3_13),X4_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_13,X2_13,X3_13,X1_14,X4_13,X5_13,X6_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=subspace_topology(X1_13,subspace_topology(X2_13,subspace_topology(X3_13,X1_14,X4_13),X5_13),X6_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X1_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=subspace_topology(cx,X1_14,cx) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of element_of_set
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_15,X0_13] :
% 24.27/4.18 ( element_of_set(X0_15,X0_13) <=>
% 24.27/4.18 (
% 24.27/4.18 ? [X1_13,X0_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=intersection_of_members(subspace_topology(X1_13,X0_14,X2_13)) )
% 24.27/4.18 &
% 24.27/4.18 ! [X3_13,X1_14] : ( X0_15!=f11(X1_14,X3_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X0_14,X1_13,X2_13,X1_14,X3_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_15=f11(X0_14,X1_13) & X0_13=intersection_of_members(subspace_topology(X2_13,X1_14,X3_13)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 (
% 24.27/4.18 ( X0_15=f11(f,cx) & X0_13=cx )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X0_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_15=f11(X0_14,cx) & X0_13=cx )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X0_14,X1_14,X2_14,X1_13,X3_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_15=f11(X0_14,f10(X1_14,union_of_members(X2_14),f11(subspace_topology(X1_13,X3_14,X2_13),union_of_members(X2_14)))) & X0_13=f10(X1_14,union_of_members(X2_14),f11(subspace_topology(X1_13,X3_14,X2_13),union_of_members(X2_14))) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X0_14,X1_13,X1_14,X2_13] :
% 24.27/4.18 (
% 24.27/4.18 ( 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)) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of topological_space
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_14] :
% 24.27/4.18 ( topological_space(X0_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of equal_sets
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13] :
% 24.27/4.18 ( equal_sets(X0_13,X1_13) <=>
% 24.27/4.18 (
% 24.27/4.18 ? [X0_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ! [X2_13] : ( X0_14!=subspace_topology(X1_13,X0_14,X2_13) | X1_13!=empty_set )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) | X1_13!=empty_set )
% 24.27/4.18 &
% 24.27/4.18 ! [X3_13] : ( X0_14!=subspace_topology(X2_13,X0_14,X3_13) )
% 24.27/4.18 &
% 24.27/4.18 ( X1_13!=empty_set )
% 24.27/4.18 &
% 24.27/4.18 ( X1_13!=intersection_of_members(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X1_13!=union_of_members(subspace_topology(X1_13,X0_14,X2_13)) )
% 24.27/4.18 &
% 24.27/4.18 ( X1_13!=boundary(X1_13,X2_13,X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X1_13!=closure(X1_13,X2_13,X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ( X1_13!=interior(X1_13,X2_13,X0_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 |
% 24.27/4.18 ? [X0_14] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_13=union_of_members(X0_14) & X1_13=empty_set )
% 24.27/4.18 &
% 24.27/4.18 ( X0_14!=top_of_basis(X0_14) )
% 24.27/4.18 &
% 24.27/4.18 ! [X3_13,X2_13] : ( X0_14!=subspace_topology(X2_13,X0_14,X3_13) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of subset_collections
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_14,X1_14] :
% 24.27/4.18 ( subset_collections(X0_14,X1_14) <=>
% 24.27/4.18 (
% 24.27/4.18 ? [X0_13] :
% 24.27/4.18 (
% 24.27/4.18 ( X0_14=f5(X0_13,X1_14) )
% 24.27/4.18 )
% 24.27/4.18
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of open
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13,X0_14] :
% 24.27/4.18 ( open(X0_13,X1_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of closed
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13,X0_14] :
% 24.27/4.18 ( closed(X0_13,X1_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of finer
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_14,X1_14,X0_13] :
% 24.27/4.18 ( finer(X0_14,X1_14,X0_13) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Negative definition of subset_sets
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13] :
% 24.27/4.18 ( ~(subset_sets(X0_13,X1_13)) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of neighborhood
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_15,X1_13,X0_14] :
% 24.27/4.18 ( neighborhood(X0_13,X0_15,X1_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of limit_point
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_15,X0_13,X1_13,X0_14] :
% 24.27/4.18 ( limit_point(X0_15,X0_13,X1_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of eq_p
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_15,X1_15] :
% 24.27/4.18 ( eq_p(X0_15,X1_15) <=>
% 24.27/4.18 $true
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of hausdorff
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_14] :
% 24.27/4.18 ( hausdorff(X0_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of disjoint_s
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13] :
% 24.27/4.18 ( disjoint_s(X0_13,X1_13) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of separation
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13,X2_13,X0_14] :
% 24.27/4.18 ( separation(X0_13,X1_13,X2_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of connected_space
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_14] :
% 24.27/4.18 ( connected_space(X0_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of connected_set
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13,X0_14] :
% 24.27/4.18 ( connected_set(X0_13,X1_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of open_covering
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_14,X0_13,X1_14] :
% 24.27/4.18 ( open_covering(X0_14,X0_13,X1_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of compact_space
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X0_14] :
% 24.27/4.18 ( compact_space(X0_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of finite
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_14] :
% 24.27/4.18 ( finite(X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18
% 24.27/4.18 %------ Positive definition of compact_set
% 24.27/4.18 fof(lit_def,axiom,
% 24.27/4.18 (! [X0_13,X1_13,X0_14] :
% 24.27/4.18 ( compact_set(X0_13,X1_13,X0_14) <=>
% 24.27/4.18 $false
% 24.27/4.18 )
% 24.27/4.18 )
% 24.27/4.18 ).
% 24.27/4.18 % SZS output end Model for theBenchmark.p
% 24.27/4.18
%------------------------------------------------------------------------------