TSTP Solution File: TOP005-1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : TOP005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n015.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 05:57:12 EDT 2023
% Result : Satisfiable 3.98s 1.20s
% Output : Model 3.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : TOP005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.18/0.36 % Computer : n015.cluster.edu
% 0.18/0.36 % Model : x86_64 x86_64
% 0.18/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36 % Memory : 8042.1875MB
% 0.18/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36 % CPULimit : 300
% 0.18/0.36 % WCLimit : 300
% 0.18/0.36 % DateTime : Sun Aug 27 00:11:38 EDT 2023
% 0.18/0.36 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.98/1.20 % SZS status Started for theBenchmark.p
% 3.98/1.20 % SZS status Satisfiable for theBenchmark.p
% 3.98/1.20
% 3.98/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 3.98/1.20
% 3.98/1.20 ------ iProver source info
% 3.98/1.20
% 3.98/1.20 git: date: 2023-05-31 18:12:56 +0000
% 3.98/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 3.98/1.20 git: non_committed_changes: false
% 3.98/1.20 git: last_make_outside_of_git: false
% 3.98/1.20
% 3.98/1.20 ------ Parsing...successful
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20 ------ 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
% 3.98/1.20
% 3.98/1.20 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 3.98/1.20 ------ Proving...
% 3.98/1.20 ------ Problem Properties
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20 clauses 98
% 3.98/1.20 conjectures 3
% 3.98/1.20 EPR 23
% 3.98/1.20 Horn 76
% 3.98/1.20 unary 3
% 3.98/1.20 binary 46
% 3.98/1.20 lits 298
% 3.98/1.20 lits eq 0
% 3.98/1.20 fd_pure 0
% 3.98/1.20 fd_pseudo 0
% 3.98/1.20 fd_cond 0
% 3.98/1.20 fd_pseudo_cond 0
% 3.98/1.20 AC symbols 0
% 3.98/1.20
% 3.98/1.20 ------ Input Options Time Limit: Unbounded
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20 ------
% 3.98/1.20 Current options:
% 3.98/1.20 ------
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20 ------ Proving...
% 3.98/1.20
% 3.98/1.20
% 3.98/1.20 % SZS status Satisfiable for theBenchmark.p
% 3.98/1.20
% 3.98/1.20 ------ Building Model...Done
% 3.98/1.20
% 3.98/1.20 %------ The model is defined over ground terms (initial term algebra).
% 3.98/1.20 %------ Predicates are defined as (\forall x_1,..,x_n ((~)P(x_1,..,x_n) <=> (\phi(x_1,..,x_n))))
% 3.98/1.20 %------ where \phi is a formula over the term algebra.
% 3.98/1.20 %------ If we have equality in the problem then it is also defined as a predicate above,
% 3.98/1.20 %------ with "=" on the right-hand-side of the definition interpreted over the term algebra term_algebra_type
% 3.98/1.20 %------ See help for --sat_out_model for different model outputs.
% 3.98/1.20 %------ equality_sorted(X0,X1,X2) can be used in the place of usual "="
% 3.98/1.20 %------ where the first argument stands for the sort ($i in the unsorted case)
% 3.98/1.20 % SZS output start Model for theBenchmark.p
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of basis
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X0_14] :
% 3.98/1.20 ( basis(X0_13,X0_14) <=>
% 3.98/1.20 (
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=cx & X0_14=f )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Negative definition of subset_collections
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_14,X1_14] :
% 3.98/1.20 ( ~(subset_collections(X0_14,X1_14)) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of element_of_collection
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X0_14] :
% 3.98/1.20 ( element_of_collection(X0_13,X0_14) <=>
% 3.98/1.20 (
% 3.98/1.20 ? [X0_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f2(X0_14,X0_15) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14] : ( X0_14!=X0_14 | X0_15!=f11(X1_14,intersection_of_members(X0_14)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_13,X1_13] : ( X0_14!=subspace_topology(X1_13,X0_14,X2_13) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_13] : ( X0_14!=subspace_topology(X1_13,X0_14,X2_13) | X0_15!=f7(X3_13,X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) | X0_15!=f11(X1_14,intersection_of_members(top_of_basis(X0_14))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(X0_14,X0_15) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=g | X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_13,X1_13] : ( X0_14!=subspace_topology(X1_13,X0_14,X2_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14] : ( X0_14!=subspace_topology(X1_13,X1_14,X2_13) | X0_15!=f11(X0_14,union_of_members(subspace_topology(X1_13,X1_14,X2_13))) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(g,f11(f,union_of_members(g))) & X0_14=g )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=union_of_members(top_of_basis(X1_14)) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X0_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f2(top_of_basis(X1_14),X0_15) & X0_14=top_of_basis(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_14] : ( X0_15!=f11(X2_14,intersection_of_members(top_of_basis(X1_14))) | X1_14!=X1_14 )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X0_15,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f2(top_of_basis(X1_14),X0_15) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_14] : ( X0_15!=f11(X3_14,intersection_of_members(top_of_basis(X2_14))) | X2_14!=X2_14 )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=intersection_of_members(top_of_basis(X1_14)) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X1_14,X2_13,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=union_of_members(subspace_topology(X1_13,X1_14,X2_13)) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(top_of_basis(X1_14),f11(X2_14,union_of_members(top_of_basis(X1_14)))) & X0_14=top_of_basis(X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14,X3_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(top_of_basis(X1_14),f11(X2_14,union_of_members(top_of_basis(X1_14)))) & X0_14=top_of_basis(X3_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f2(top_of_basis(X1_14),f11(X2_14,intersection_of_members(top_of_basis(X1_14)))) & X0_14=top_of_basis(X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X0_15,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(X0_14,f2(top_of_basis(X1_14),X0_15),f11(X2_14,f2(top_of_basis(X1_14),X0_15))) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_14] : ( X0_14!=X3_14 | X0_15!=f11(X0_14,intersection_of_members(top_of_basis(X3_14))) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_13,X1_13] : ( X0_14!=subspace_topology(X1_13,X0_14,X2_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X0_15,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(top_of_basis(X1_14),X0_15) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(X3_14,union_of_members(top_of_basis(X1_14))) | X1_14!=X1_14 )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_14] : ( X0_15!=f11(X1_14,intersection_of_members(X3_14)) | X1_14!=X2_14 | X2_14!=X2_14 )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14,X0_15,X3_14,X4_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(top_of_basis(X1_14),f2(top_of_basis(X2_14),X0_15),f11(X3_14,f2(top_of_basis(X2_14),X0_15))) & X0_14=top_of_basis(X4_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X3_14)))) | X1_14!=X1_14 | X2_14!=top_of_basis(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X4_14)))) | X4_14!=X4_14 )
% 3.98/1.20 &
% 3.98/1.20 ! [X5_14] : ( X0_15!=f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X5_14)))) )
% 3.98/1.20 &
% 3.98/1.20 ( X1_14!=X1_14 | X2_14!=top_of_basis(X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14,X3_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f2(top_of_basis(X1_14),f11(X2_14,intersection_of_members(top_of_basis(X3_14)))) & X0_14=top_of_basis(X3_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X0_15,X2_14,X3_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(top_of_basis(X1_14),f2(top_of_basis(top_of_basis(X1_14)),X0_15),f11(X2_14,f2(top_of_basis(top_of_basis(X1_14)),X0_15))) & X0_14=top_of_basis(X3_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X3_14)))) | X3_14!=X3_14 )
% 3.98/1.20 &
% 3.98/1.20 ! [X4_14] : ( X0_15!=f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X4_14)))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_14,X2_14,X3_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(top_of_basis(X1_14),f11(X2_14,intersection_of_members(X3_14))) & X0_14=top_of_basis(X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X2_13,X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=closure(X1_13,X2_13,X1_14) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X2_13,X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=boundary(X1_13,X2_13,X1_14) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X2_13,X1_14,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=interior(X1_13,X2_13,X1_14) & X0_14=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X1_14,X2_13,X0_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(X0_14,intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)),X0_15) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X4_13,X3_13] : ( X0_14!=subspace_topology(X3_13,X0_14,X4_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of element_of_set
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_15,X0_13] :
% 3.98/1.20 ( element_of_set(X0_15,X0_13) <=>
% 3.98/1.20 (
% 3.98/1.20 ? [X0_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=union_of_members(X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_13] : ( X0_14!=subspace_topology(X2_13,X0_14,X3_13) )
% 3.98/1.20 &
% 3.98/1.20 ! [X4_13,X3_13] : ( X0_14!=subspace_topology(X3_13,X0_14,X4_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14,X2_13] : ( X0_15!=f7(X2_13,X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f7(X3_13,X0_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f1(X0_14,X0_15) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=g | X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=top_of_basis(X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14] : ( X0_14!=top_of_basis(X1_14) | X0_15!=f11(X0_14,union_of_members(top_of_basis(X1_14))) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_14] : ( X0_14!=top_of_basis(X2_14) | X0_15!=f11(X0_14,intersection_of_members(X1_14)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_13] : ( X0_15!=f7(X1_13,X0_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X0_14,X2_13] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=intersection_of_members(subspace_topology(X1_13,X0_14,X2_13)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14,X3_13] : ( X0_15!=f7(X3_13,X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_13,X1_14,X2_13] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(X0_14,intersection_of_members(subspace_topology(X1_13,X1_14,X2_13)),X0_15) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_15!=f11(f,union_of_members(g)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_14,X3_13] : ( X0_15!=f7(X3_13,X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,X0_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(g) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(g) | X0_14!=f )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_13] : ( X0_13!=intersection_of_sets(X0_13,X1_13) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14] : ( X0_13!=intersection_of_members(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=closure(X0_13,X1_13,X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=boundary(X0_13,X1_13,X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=interior(X0_13,X1_13,X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(top_of_basis(X1_14)) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(subspace_topology(X0_13,X1_14,X1_13)) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=intersection_of_members(top_of_basis(X1_14)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_14] : ( X0_13!=f1(top_of_basis(X1_14),f11(X2_14,union_of_members(top_of_basis(X1_14)))) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_15] : ( X0_13!=f2(top_of_basis(X1_14),X1_15) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=f1(top_of_basis(X1_14),X1_15) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_14] : ( X0_13!=f10(top_of_basis(X1_14),f2(top_of_basis(X2_14),X1_15),f11(X3_14,f2(top_of_basis(X2_14),X1_15))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X1_13,X0_14,X2_13,X1_14,X3_13] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f7(X1_13,X0_14) & X0_13=intersection_of_members(subspace_topology(X2_13,X1_14,X3_13)) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,intersection_of_members(X1_14)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_13] : ( X0_13!=intersection_of_sets(X0_13,X1_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(top_of_basis(X2_14)) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=closure(X0_13,X1_13,X2_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=boundary(X0_13,X1_13,X2_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=interior(X0_13,X1_13,X2_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=f2(X2_14,f11(X0_14,intersection_of_members(X1_14))) | X0_14!=X0_14 | X1_14!=X1_14 )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=intersection_of_members(X2_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(subspace_topology(X0_13,X2_14,X1_13)) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=union_of_members(subspace_topology(X0_13,X2_14,X1_13)) | X1_14!=top_of_basis(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=intersection_of_members(top_of_basis(X1_14)) | X1_14!=top_of_basis(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_14] : ( X0_13!=f1(top_of_basis(X2_14),f11(X3_14,union_of_members(top_of_basis(X2_14)))) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=f2(top_of_basis(X2_14),X1_15) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_15,X2_14] : ( X0_13!=f10(X2_14,intersection_of_members(subspace_topology(X0_13,X1_14,X1_13)),X1_15) | X1_14!=subspace_topology(X0_13,X1_14,X1_13) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_13!=f1(top_of_basis(X2_14),X1_15) )
% 3.98/1.20 &
% 3.98/1.20 ! [X4_14] : ( X0_13!=f10(top_of_basis(X2_14),f2(top_of_basis(X3_14),X1_15),f11(X4_14,f2(top_of_basis(X3_14),X1_15))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,intersection_of_members(X1_14)) & X0_13=intersection_of_members(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X1_14!=top_of_basis(X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(f,union_of_members(g)) & X0_13=union_of_members(g) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(f,union_of_members(g)) & X0_13=f1(g,f11(f,union_of_members(g))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,union_of_members(g)) & X0_13=union_of_members(g) )
% 3.98/1.20 &
% 3.98/1.20 ( X0_14!=f )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f1(top_of_basis(X1_14),f11(f,union_of_members(g)))) & X0_13=f1(top_of_basis(X1_14),f11(f,union_of_members(g))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X2_14,X3_14,X4_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f10(top_of_basis(X1_14),f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X0_14))))),f11(X4_14,f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X0_14)))))))) & X0_13=f10(top_of_basis(X1_14),f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X0_14))))),f11(X4_14,f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X0_14))))))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X2_14,X3_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f10(top_of_basis(X1_14),f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X0_14))))),f11(X3_14,f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X0_14)))))))) & X0_13=f10(top_of_basis(X1_14),f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X0_14))))),f11(X3_14,f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X0_14))))))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X2_14,X3_14,X4_14,X5_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f10(top_of_basis(X1_14),f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X4_14))))),f11(X5_14,f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X4_14)))))))) & X0_13=f10(top_of_basis(X1_14),f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X4_14))))),f11(X5_14,f2(top_of_basis(X2_14),f11(X3_14,intersection_of_members(top_of_basis(top_of_basis(X4_14))))))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X2_14,X3_14,X4_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f10(top_of_basis(X1_14),f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X3_14))))),f11(X4_14,f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X3_14)))))))) & X0_13=f10(top_of_basis(X1_14),f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X3_14))))),f11(X4_14,f2(top_of_basis(top_of_basis(X1_14)),f11(X2_14,intersection_of_members(top_of_basis(top_of_basis(X3_14))))))) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_13,X2_13] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,intersection_of_sets(X1_13,X2_13)) & X0_13=intersection_of_sets(X1_13,X2_13) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X1_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f2(top_of_basis(X1_14),X1_15)) & X0_13=f10(X1_14,f2(top_of_basis(X1_14),X1_15),f11(X0_14,f2(top_of_basis(X1_14),X1_15))) )
% 3.98/1.20 &
% 3.98/1.20 ( X1_14!=top_of_basis(X1_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X1_15,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_15=f11(X0_14,f2(top_of_basis(X1_14),X1_15)) & X0_13=f10(X2_14,f2(top_of_basis(X1_14),X1_15),f11(X0_14,f2(top_of_basis(X1_14),X1_15))) )
% 3.98/1.20 &
% 3.98/1.20 ( X1_14!=top_of_basis(X1_14) | X2_14!=top_of_basis(X1_14) )
% 3.98/1.20 &
% 3.98/1.20 ( X2_14!=top_of_basis(X2_14) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of topological_space
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X0_14] :
% 3.98/1.20 ( topological_space(X0_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of equal_sets
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X1_13] :
% 3.98/1.20 ( equal_sets(X0_13,X1_13) <=>
% 3.98/1.20 (
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=union_of_members(f) & X1_13=cx )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of open
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X1_13,X0_14] :
% 3.98/1.20 ( open(X0_13,X1_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of closed
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X1_13,X0_14] :
% 3.98/1.20 ( closed(X0_13,X1_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of subset_sets
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X1_13] :
% 3.98/1.20 ( subset_sets(X0_13,X1_13) <=>
% 3.98/1.20 (
% 3.98/1.20 ? [X0_14,X2_13,X1_14,X3_13,X0_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(X0_14,intersection_of_members(subspace_topology(X2_13,X1_14,X3_13)),X0_15) & X1_13=intersection_of_members(subspace_topology(X2_13,X1_14,X3_13)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X2_14] : ( X0_15!=f11(X2_14,intersection_of_members(subspace_topology(X2_13,X1_14,X3_13))) | X1_14!=X1_14 | X2_13!=X2_13 | X3_13!=X3_13 )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X0_15,X1_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(X0_14,f2(top_of_basis(X0_14),X0_15),f11(X1_14,f2(top_of_basis(X0_14),X0_15))) & X1_13=f2(top_of_basis(X0_14),X0_15) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X0_14,X1_14,X0_15,X2_14] :
% 3.98/1.20 (
% 3.98/1.20 ( X0_13=f10(X0_14,f2(top_of_basis(X1_14),X0_15),f11(X2_14,f2(top_of_basis(X1_14),X0_15))) & X1_13=f2(top_of_basis(X1_14),X0_15) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 |
% 3.98/1.20 ? [X2_13,X0_14,X0_15] :
% 3.98/1.20 (
% 3.98/1.20 ( X1_13=f14(X0_13,X2_13,X0_14,X0_15) )
% 3.98/1.20 &
% 3.98/1.20 ! [X1_14] : ( X0_13!=union_of_members(top_of_basis(X1_14)) )
% 3.98/1.20 &
% 3.98/1.20 ! [X3_13] : ( X0_13!=union_of_members(subspace_topology(X0_13,X1_14,X3_13)) )
% 3.98/1.20 )
% 3.98/1.20
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of neighborhood
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X0_15,X1_13,X0_14] :
% 3.98/1.20 ( neighborhood(X0_13,X0_15,X1_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of limit_point
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_15,X0_13,X1_13,X0_14] :
% 3.98/1.20 ( limit_point(X0_15,X0_13,X1_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of hausdorff
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X0_14] :
% 3.98/1.20 ( hausdorff(X0_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of disjoint_s
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X1_13] :
% 3.98/1.20 ( disjoint_s(X0_13,X1_13) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of separation
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X1_13,X2_13,X0_14] :
% 3.98/1.20 ( separation(X0_13,X1_13,X2_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of open_covering
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_14,X0_13,X1_14] :
% 3.98/1.20 ( open_covering(X0_14,X0_13,X1_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of compact_space
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_13,X0_14] :
% 3.98/1.20 ( compact_space(X0_13,X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20
% 3.98/1.20 %------ Positive definition of finite
% 3.98/1.20 fof(lit_def,axiom,
% 3.98/1.20 (! [X0_14] :
% 3.98/1.20 ( finite(X0_14) <=>
% 3.98/1.20 $false
% 3.98/1.20 )
% 3.98/1.20 )
% 3.98/1.20 ).
% 3.98/1.20 % SZS output end Model for theBenchmark.p
% 3.98/1.20
%------------------------------------------------------------------------------