TSTP Solution File: TOP002-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : TOP002-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.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 : Tue Apr 30 18:25:12 EDT 2024
% Result : Satisfiable 0.21s 0.41s
% Output : FiniteModel 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : TOP002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 01:49:05 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (22194)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (22199)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (22201)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.21/0.38 % (22200)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.21/0.38 % (22198)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.38 % (22202)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.21/0.38 % (22203)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.21/0.38 % (22204)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [1]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [2]
% 0.21/0.39 TRYING [1,1,1,1,1,1,1,1,1,1,1,1]
% 0.21/0.39 TRYING [1,1,1,1,1,1,1,1,1,1,1,1]
% 0.21/0.39 TRYING [1,2,1,1,1,1,1,1,1,1,1,1]
% 0.21/0.39 TRYING [1,2,1,1,1,1,1,1,1,1,1,1]
% 0.21/0.40 TRYING [2,2,1,1,1,1,1,1,1,1,1,1]
% 0.21/0.40 TRYING [2,2,1,1,1,1,1,1,1,1,1,1]
% 0.21/0.41 Finite Model Found!
% 0.21/0.41 % SZS status Satisfiable for theBenchmark
% 0.21/0.41 % (22198)First to succeed.
% 0.21/0.41 % SZS output start FiniteModel for theBenchmark
% 0.21/0.41 tff(declare_$i,type,$i:$tType).
% 0.21/0.41 tff(declare_$i1,type,empty_set:$i).
% 0.21/0.41 tff(declare_$i2,type,fmb_$i_2:$i).
% 0.21/0.41 tff(finite_domain,axiom,
% 0.21/0.41 ! [X:$i] : (
% 0.21/0.41 X = empty_set | X = fmb_$i_2
% 0.21/0.41 ) ).
% 0.21/0.41
% 0.21/0.41 tff(distinct_domain,axiom,
% 0.21/0.41 empty_set != fmb_$i_2
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_bool,type,$o:$tType).
% 0.21/0.41 tff(declare_bool1,type,fmb_bool_1:$o).
% 0.21/0.41 tff(finite_domain,axiom,
% 0.21/0.41 ! [X:$o] : (
% 0.21/0.41 X = fmb_bool_1
% 0.21/0.41 ) ).
% 0.21/0.41
% 0.21/0.41 tff(declare_cx,type,cx:$i).
% 0.21/0.41 tff(cx_definition,axiom,cx = empty_set).
% 0.21/0.41 tff(declare_f,type,f:$i).
% 0.21/0.41 tff(f_definition,axiom,f = empty_set).
% 0.21/0.41 tff(declare_union_of_members,type,union_of_members: $i > $i).
% 0.21/0.41 tff(function_union_of_members,axiom,
% 0.21/0.41 union_of_members(empty_set) = fmb_$i_2
% 0.21/0.41 & union_of_members(fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f1,type,f1: $i * $i > $i).
% 0.21/0.41 tff(function_f1,axiom,
% 0.21/0.41 f1(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f1(empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f1(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f1(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_intersection_of_members,type,intersection_of_members: $i > $i).
% 0.21/0.41 tff(function_intersection_of_members,axiom,
% 0.21/0.41 intersection_of_members(empty_set) = fmb_$i_2
% 0.21/0.41 & intersection_of_members(fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f2,type,f2: $i * $i > $i).
% 0.21/0.41 tff(function_f2,axiom,
% 0.21/0.41 f2(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f2(empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f2(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f2(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_intersection_of_sets,type,intersection_of_sets: $i * $i > $i).
% 0.21/0.41 tff(function_intersection_of_sets,axiom,
% 0.21/0.41 intersection_of_sets(empty_set,empty_set) = empty_set
% 0.21/0.41 & intersection_of_sets(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & intersection_of_sets(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & intersection_of_sets(fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f3,type,f3: $i * $i > $i).
% 0.21/0.41 tff(function_f3,axiom,
% 0.21/0.41 f3(empty_set,empty_set) = empty_set
% 0.21/0.41 & f3(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f3(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f3(fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f5,type,f5: $i * $i > $i).
% 0.21/0.41 tff(function_f5,axiom,
% 0.21/0.41 f5(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f5(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f5(fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f5(fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f4,type,f4: $i * $i > $i).
% 0.21/0.41 tff(function_f4,axiom,
% 0.21/0.41 f4(empty_set,empty_set) = empty_set
% 0.21/0.41 & f4(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f4(fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f4(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_relative_complement_sets,type,relative_complement_sets: $i * $i > $i).
% 0.21/0.41 tff(function_relative_complement_sets,axiom,
% 0.21/0.41 relative_complement_sets(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & relative_complement_sets(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & relative_complement_sets(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & relative_complement_sets(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f6,type,f6: $i * $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f6,axiom,
% 0.21/0.41 f6(empty_set,empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f6(empty_set,empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,empty_set,empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(empty_set,empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,empty_set,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f6(empty_set,empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(empty_set,fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f6(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(fmb_$i_2,empty_set,empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,empty_set,empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,empty_set,empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(fmb_$i_2,empty_set,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f6(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f7,type,f7: $i * $i > $i).
% 0.21/0.41 tff(function_f7,axiom,
% 0.21/0.41 f7(empty_set,empty_set) = empty_set
% 0.21/0.41 & f7(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f7(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f7(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f8,type,f8: $i * $i > $i).
% 0.21/0.41 tff(function_f8,axiom,
% 0.21/0.41 f8(empty_set,empty_set) = empty_set
% 0.21/0.41 & f8(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f8(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f8(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f9,type,f9: $i * $i > $i).
% 0.21/0.41 tff(function_f9,axiom,
% 0.21/0.41 f9(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f9(empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f9(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f9(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_top_of_basis,type,top_of_basis: $i > $i).
% 0.21/0.41 tff(function_top_of_basis,axiom,
% 0.21/0.41 top_of_basis(empty_set) = empty_set
% 0.21/0.41 & top_of_basis(fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f10,type,f10: $i * $i * $i > $i).
% 0.21/0.41 tff(function_f10,axiom,
% 0.21/0.41 f10(empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f10(empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f10(empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f10(empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f10(fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f10(fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f10(fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f10(fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f11,type,f11: $i * $i > $i).
% 0.21/0.41 tff(function_f11,axiom,
% 0.21/0.41 f11(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f11(empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f11(fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f11(fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_subspace_topology,type,subspace_topology: $i * $i * $i > $i).
% 0.21/0.41 tff(function_subspace_topology,axiom,
% 0.21/0.41 subspace_topology(empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & subspace_topology(empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & subspace_topology(empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & subspace_topology(empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & subspace_topology(fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & subspace_topology(fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & subspace_topology(fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & subspace_topology(fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f12,type,f12: $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f12,axiom,
% 0.21/0.41 f12(empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f12(empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f12(empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f12(empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f12(empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f12(empty_set,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f12(empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f12(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f12(fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f12(fmb_$i_2,empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f12(fmb_$i_2,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f12(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f12(fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f12(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f12(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f12(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_interior,type,interior: $i * $i * $i > $i).
% 0.21/0.41 tff(function_interior,axiom,
% 0.21/0.41 interior(empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & interior(empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & interior(empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & interior(empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & interior(fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & interior(fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & interior(fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & interior(fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f13,type,f13: $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f13,axiom,
% 0.21/0.41 f13(empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f13(empty_set,empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f13(empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f13(empty_set,empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f13(empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f13(empty_set,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f13(empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f13(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f13(fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f13(fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f13(fmb_$i_2,empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f13(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f13(fmb_$i_2,fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f13(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f13(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f13(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_closure,type,closure: $i * $i * $i > $i).
% 0.21/0.41 tff(function_closure,axiom,
% 0.21/0.41 closure(empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & closure(empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & closure(empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & closure(empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & closure(fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & closure(fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & closure(fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & closure(fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f14,type,f14: $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f14,axiom,
% 0.21/0.41 f14(empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f14(empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f14(empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f14(empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f14(empty_set,fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f14(empty_set,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f14(empty_set,fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f14(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f14(fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f14(fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f14(fmb_$i_2,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f14(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f14(fmb_$i_2,fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f14(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f14(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f14(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f15,type,f15: $i * $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f15,axiom,
% 0.21/0.41 f15(empty_set,empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f15(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f15(fmb_$i_2,empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,empty_set,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f15(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f15(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f16,type,f16: $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f16,axiom,
% 0.21/0.41 f16(empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f16(empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f16(empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f16(empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f16(empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f16(empty_set,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f16(empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f16(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f16(fmb_$i_2,empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f16(fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f16(fmb_$i_2,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f16(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f16(fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f16(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f16(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f16(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_boundary,type,boundary: $i * $i * $i > $i).
% 0.21/0.41 tff(function_boundary,axiom,
% 0.21/0.41 boundary(empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & boundary(empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & boundary(empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & boundary(empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & boundary(fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & boundary(fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & boundary(fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & boundary(fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f17,type,f17: $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f17,axiom,
% 0.21/0.41 f17(empty_set,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f17(empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f17(empty_set,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f17(empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f17(empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f17(empty_set,fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f17(empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f17(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f17(fmb_$i_2,empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f17(fmb_$i_2,empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f17(fmb_$i_2,empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f17(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f17(fmb_$i_2,fmb_$i_2,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f17(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f17(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f17(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f18,type,f18: $i * $i * $i * $i > $i).
% 0.21/0.41 tff(function_f18,axiom,
% 0.21/0.41 f18(empty_set,empty_set,empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f18(empty_set,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(empty_set,empty_set,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f18(empty_set,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(empty_set,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f18(empty_set,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(empty_set,fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f18(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,empty_set,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f18(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set) = fmb_$i_2
% 0.21/0.41 & f18(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f19,type,f19: $i * $i > $i).
% 0.21/0.41 tff(function_f19,axiom,
% 0.21/0.41 f19(empty_set,empty_set) = empty_set
% 0.21/0.41 & f19(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f19(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f19(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f20,type,f20: $i * $i > $i).
% 0.21/0.41 tff(function_f20,axiom,
% 0.21/0.41 f20(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f20(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f20(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f20(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_union_of_sets,type,union_of_sets: $i * $i > $i).
% 0.21/0.41 tff(function_union_of_sets,axiom,
% 0.21/0.41 union_of_sets(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & union_of_sets(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & union_of_sets(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & union_of_sets(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f21,type,f21: $i * $i > $i).
% 0.21/0.41 tff(function_f21,axiom,
% 0.21/0.41 f21(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f21(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f21(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f21(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f22,type,f22: $i * $i > $i).
% 0.21/0.41 tff(function_f22,axiom,
% 0.21/0.41 f22(empty_set,empty_set) = empty_set
% 0.21/0.41 & f22(empty_set,fmb_$i_2) = empty_set
% 0.21/0.41 & f22(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f22(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f23,type,f23: $i * $i * $i > $i).
% 0.21/0.41 tff(function_f23,axiom,
% 0.21/0.41 f23(empty_set,empty_set,empty_set) = empty_set
% 0.21/0.41 & f23(empty_set,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f23(empty_set,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f23(empty_set,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f23(fmb_$i_2,empty_set,empty_set) = empty_set
% 0.21/0.41 & f23(fmb_$i_2,empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f23(fmb_$i_2,fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f23(fmb_$i_2,fmb_$i_2,fmb_$i_2) = fmb_$i_2
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_f24,type,f24: $i * $i > $i).
% 0.21/0.41 tff(function_f24,axiom,
% 0.21/0.41 f24(empty_set,empty_set) = fmb_$i_2
% 0.21/0.41 & f24(empty_set,fmb_$i_2) = fmb_$i_2
% 0.21/0.41 & f24(fmb_$i_2,empty_set) = empty_set
% 0.21/0.41 & f24(fmb_$i_2,fmb_$i_2) = empty_set
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_element_of_set,type,element_of_set: $i * $i > $o ).
% 0.21/0.41 tff(predicate_element_of_set,axiom,
% 0.21/0.41 element_of_set(empty_set,empty_set)
% 0.21/0.41 & ~element_of_set(empty_set,fmb_$i_2)
% 0.21/0.41 & element_of_set(fmb_$i_2,empty_set)
% 0.21/0.41 & ~element_of_set(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_element_of_collection,type,element_of_collection: $i * $i > $o ).
% 0.21/0.41 tff(predicate_element_of_collection,axiom,
% 0.21/0.41 ~element_of_collection(empty_set,empty_set)
% 0.21/0.41 & ~element_of_collection(empty_set,fmb_$i_2)
% 0.21/0.41 & element_of_collection(fmb_$i_2,empty_set)
% 0.21/0.41 & ~element_of_collection(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_topological_space,type,topological_space: $i * $i > $o ).
% 0.21/0.41 tff(predicate_topological_space,axiom,
% 0.21/0.41 ~topological_space(empty_set,empty_set)
% 0.21/0.41 & ~topological_space(empty_set,fmb_$i_2)
% 0.21/0.41 & ~topological_space(fmb_$i_2,empty_set)
% 0.21/0.41 & ~topological_space(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_equal_sets,type,equal_sets: $i * $i > $o ).
% 0.21/0.41 tff(predicate_equal_sets,axiom,
% 0.21/0.41 equal_sets(empty_set,empty_set)
% 0.21/0.41 & equal_sets(empty_set,fmb_$i_2)
% 0.21/0.41 & equal_sets(fmb_$i_2,empty_set)
% 0.21/0.41 & ~equal_sets(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_subset_collections,type,subset_collections: $i * $i > $o ).
% 0.21/0.41 tff(predicate_subset_collections,axiom,
% 0.21/0.41 subset_collections(empty_set,empty_set)
% 0.21/0.41 & subset_collections(empty_set,fmb_$i_2)
% 0.21/0.41 & subset_collections(fmb_$i_2,empty_set)
% 0.21/0.41 & ~subset_collections(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_open,type,open: $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_open,axiom,
% 0.21/0.41 ~open(empty_set,empty_set,empty_set)
% 0.21/0.41 & ~open(empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~open(empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~open(empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~open(fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~open(fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~open(fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~open(fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_closed,type,closed: $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_closed,axiom,
% 0.21/0.41 ~closed(empty_set,empty_set,empty_set)
% 0.21/0.41 & ~closed(empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~closed(empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~closed(empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~closed(fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~closed(fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~closed(fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~closed(fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_finer,type,finer: $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_finer,axiom,
% 0.21/0.41 ~finer(empty_set,empty_set,empty_set)
% 0.21/0.41 & ~finer(empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~finer(empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~finer(empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~finer(fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~finer(fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~finer(fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~finer(fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_basis,type,basis: $i * $i > $o ).
% 0.21/0.41 tff(predicate_basis,axiom,
% 0.21/0.41 basis(empty_set,empty_set)
% 0.21/0.41 & basis(empty_set,fmb_$i_2)
% 0.21/0.41 & ~basis(fmb_$i_2,empty_set)
% 0.21/0.41 & ~basis(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_subset_sets,type,subset_sets: $i * $i > $o ).
% 0.21/0.41 tff(predicate_subset_sets,axiom,
% 0.21/0.41 subset_sets(empty_set,empty_set)
% 0.21/0.41 & subset_sets(empty_set,fmb_$i_2)
% 0.21/0.41 & subset_sets(fmb_$i_2,empty_set)
% 0.21/0.41 & subset_sets(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_neighborhood,type,neighborhood: $i * $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_neighborhood,axiom,
% 0.21/0.41 ~neighborhood(empty_set,empty_set,empty_set,empty_set)
% 0.21/0.41 & ~neighborhood(empty_set,empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(empty_set,empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~neighborhood(empty_set,empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(empty_set,fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~neighborhood(empty_set,fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(empty_set,fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~neighborhood(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,empty_set,empty_set,empty_set)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~neighborhood(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_limit_point,type,limit_point: $i * $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_limit_point,axiom,
% 0.21/0.41 ~limit_point(empty_set,empty_set,empty_set,empty_set)
% 0.21/0.41 & ~limit_point(empty_set,empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~limit_point(empty_set,empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~limit_point(empty_set,empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~limit_point(empty_set,fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~limit_point(empty_set,fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~limit_point(empty_set,fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~limit_point(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~limit_point(fmb_$i_2,empty_set,empty_set,empty_set)
% 0.21/0.41 & ~limit_point(fmb_$i_2,empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~limit_point(fmb_$i_2,empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~limit_point(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~limit_point(fmb_$i_2,fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~limit_point(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~limit_point(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~limit_point(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_eq_p,type,eq_p: $i * $i > $o ).
% 0.21/0.41 tff(predicate_eq_p,axiom,
% 0.21/0.41 eq_p(empty_set,empty_set)
% 0.21/0.41 & eq_p(empty_set,fmb_$i_2)
% 0.21/0.41 & eq_p(fmb_$i_2,empty_set)
% 0.21/0.41 & eq_p(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_hausdorff,type,hausdorff: $i * $i > $o ).
% 0.21/0.41 tff(predicate_hausdorff,axiom,
% 0.21/0.41 ~hausdorff(empty_set,empty_set)
% 0.21/0.41 & ~hausdorff(empty_set,fmb_$i_2)
% 0.21/0.41 & ~hausdorff(fmb_$i_2,empty_set)
% 0.21/0.41 & ~hausdorff(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_disjoint_s,type,disjoint_s: $i * $i > $o ).
% 0.21/0.41 tff(predicate_disjoint_s,axiom,
% 0.21/0.41 ~disjoint_s(empty_set,empty_set)
% 0.21/0.41 & ~disjoint_s(empty_set,fmb_$i_2)
% 0.21/0.41 & ~disjoint_s(fmb_$i_2,empty_set)
% 0.21/0.41 & ~disjoint_s(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_separation,type,separation: $i * $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_separation,axiom,
% 0.21/0.41 ~separation(empty_set,empty_set,empty_set,empty_set)
% 0.21/0.41 & ~separation(empty_set,empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~separation(empty_set,empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~separation(empty_set,empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~separation(empty_set,fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~separation(empty_set,fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~separation(empty_set,fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~separation(empty_set,fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~separation(fmb_$i_2,empty_set,empty_set,empty_set)
% 0.21/0.41 & ~separation(fmb_$i_2,empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~separation(fmb_$i_2,empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~separation(fmb_$i_2,empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~separation(fmb_$i_2,fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~separation(fmb_$i_2,fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~separation(fmb_$i_2,fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~separation(fmb_$i_2,fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_connected_space,type,connected_space: $i * $i > $o ).
% 0.21/0.41 tff(predicate_connected_space,axiom,
% 0.21/0.41 ~connected_space(empty_set,empty_set)
% 0.21/0.41 & ~connected_space(empty_set,fmb_$i_2)
% 0.21/0.41 & ~connected_space(fmb_$i_2,empty_set)
% 0.21/0.41 & ~connected_space(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_connected_set,type,connected_set: $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_connected_set,axiom,
% 0.21/0.41 ~connected_set(empty_set,empty_set,empty_set)
% 0.21/0.41 & ~connected_set(empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~connected_set(empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~connected_set(empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~connected_set(fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~connected_set(fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~connected_set(fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~connected_set(fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_open_covering,type,open_covering: $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_open_covering,axiom,
% 0.21/0.41 ~open_covering(empty_set,empty_set,empty_set)
% 0.21/0.41 & ~open_covering(empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~open_covering(empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~open_covering(empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~open_covering(fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~open_covering(fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~open_covering(fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~open_covering(fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_compact_space,type,compact_space: $i * $i > $o ).
% 0.21/0.41 tff(predicate_compact_space,axiom,
% 0.21/0.41 ~compact_space(empty_set,empty_set)
% 0.21/0.41 & ~compact_space(empty_set,fmb_$i_2)
% 0.21/0.41 & ~compact_space(fmb_$i_2,empty_set)
% 0.21/0.41 & ~compact_space(fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_finite,type,finite: $i > $o ).
% 0.21/0.41 tff(predicate_finite,axiom,
% 0.21/0.41 ~finite(empty_set)
% 0.21/0.41 & ~finite(fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 tff(declare_compact_set,type,compact_set: $i * $i * $i > $o ).
% 0.21/0.41 tff(predicate_compact_set,axiom,
% 0.21/0.41 ~compact_set(empty_set,empty_set,empty_set)
% 0.21/0.41 & ~compact_set(empty_set,empty_set,fmb_$i_2)
% 0.21/0.41 & ~compact_set(empty_set,fmb_$i_2,empty_set)
% 0.21/0.41 & ~compact_set(empty_set,fmb_$i_2,fmb_$i_2)
% 0.21/0.41 & ~compact_set(fmb_$i_2,empty_set,empty_set)
% 0.21/0.41 & ~compact_set(fmb_$i_2,empty_set,fmb_$i_2)
% 0.21/0.41 & ~compact_set(fmb_$i_2,fmb_$i_2,empty_set)
% 0.21/0.41 & ~compact_set(fmb_$i_2,fmb_$i_2,fmb_$i_2)
% 0.21/0.41
% 0.21/0.41 ).
% 0.21/0.41
% 0.21/0.41 % SZS output end FiniteModel for theBenchmark
% 0.21/0.41 % (22198)------------------------------
% 0.21/0.41 % (22198)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41 % (22198)Termination reason: Satisfiable
% 0.21/0.41
% 0.21/0.41 % (22198)Memory used [KB]: 1200
% 0.21/0.41 % (22198)Time elapsed: 0.029 s
% 0.21/0.41 % (22198)Instructions burned: 54 (million)
% 0.21/0.41 % (22198)------------------------------
% 0.21/0.41 % (22198)------------------------------
% 0.21/0.41 % (22194)Success in time 0.048 s
%------------------------------------------------------------------------------