%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:58 AM UTC 2026
% Result : Theorem 265.18s 265.50s
% Output : Proof 267.54s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(s3_subset_1__e1_40__pre_topc,conjecture,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> ? [C] :
( ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) ) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ),
file('theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).
fof(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ),
file('theBenchmark.p',cc1_membered) ).
fof(cc2_membered,axiom,
! [A] :
( v4_membered(A)
=> v3_membered(A) ),
file('theBenchmark.p',cc2_membered) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ),
file('theBenchmark.p',cc3_membered) ).
fof(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ),
file('theBenchmark.p',cc4_membered) ).
fof(rc1_membered,axiom,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_membered) ).
fof(cc10_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( element(B,A)
=> v1_xcmplx_0(B) ) ),
file('theBenchmark.p',cc10_membered) ).
fof(cc11_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc11_membered) ).
fof(cc12_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc12_membered) ).
fof(cc13_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc13_membered) ).
fof(cc14_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( element(B,A)
=> ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& natural(B)
& v1_xcmplx_0(B) ) ) ),
file('theBenchmark.p',cc14_membered) ).
fof(cc16_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> v1_membered(B) ) ),
file('theBenchmark.p',cc16_membered) ).
fof(cc17_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc17_membered) ).
fof(cc18_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc18_membered) ).
fof(cc19_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc19_membered) ).
fof(cc20_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( element(B,powerset(A))
=> ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) ) ) ),
file('theBenchmark.p',cc20_membered) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(cc15_membered,axiom,
! [A] :
( empty(A)
=> ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) ) ),
file('theBenchmark.p',cc15_membered) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(dt_k1_zfmisc_1,axiom,
$true,
file('theBenchmark.p',dt_k1_zfmisc_1) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( top_str(A)
=> one_sorted_str(A) ),
file('theBenchmark.p',dt_l1_pre_topc) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(dt_u1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_u1_struct_0) ).
fof(rc6_pre_topc,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> ? [B] :
( closed_subset(B,A)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc6_pre_topc) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(s1_xboole_0__e1_40__pre_topc__1,axiom,
! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) )
& in(D,powerset(the_carrier(A))) ) ) ),
file('theBenchmark.p',s1_xboole_0__e1_40__pre_topc__1) ).
fof(d2_subset_1,axiom,
! [A,B] :
( ( empty(A)
=> ( element(B,A)
<=> empty(B) ) )
& ( ~ empty(A)
=> ( element(B,A)
<=> in(B,A) ) ) ),
file('theBenchmark.p',d2_subset_1) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(l71_subset_1,axiom,
! [A,B] :
( ! [C] :
( in(C,A)
=> in(C,B) )
=> element(A,powerset(B)) ),
file('theBenchmark.p',l71_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(t6_boole,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('theBenchmark.p',t6_boole) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('theBenchmark.p',t7_boole) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
fof(f_1_1,negated_conjecture,
~ ! [A,B] :
( ( element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) )
=> ? [C] :
( ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) ) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ),
inference(negate,[status(cth)],[s3_subset_1__e1_40__pre_topc]) ).
fof(f_1_2,negated_conjecture,
? [A,B] :
( ! [C] :
( ? [D] :
( ( ( ~ in(D,C)
& ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) ) )
| ( ! [E] :
( ~ subset(B,D)
| ~ closed_subset(E,A)
| E != D
| ~ element(E,powerset(the_carrier(A))) )
& in(D,C) ) )
& element(D,powerset(the_carrier(A))) )
| ~ element(C,powerset(powerset(the_carrier(A)))) )
& element(B,powerset(the_carrier(A)))
& top_str(A)
& topological_space(A) ),
inference(fof_nnf,[status(thm)],[f_1_1]) ).
fof(f_1_3,negated_conjecture,
? [U_5,U_4] :
( ! [U_3] :
( ? [U_2] :
( ( ( ~ in(U_2,U_3)
& ? [U_1] :
( subset(U_4,U_2)
& closed_subset(U_1,U_5)
& U_1 = U_2
& element(U_1,powerset(the_carrier(U_5))) ) )
| ( ! [U_0] :
( ~ subset(U_4,U_2)
| ~ closed_subset(U_0,U_5)
| U_0 != U_2
| ~ element(U_0,powerset(the_carrier(U_5))) )
& in(U_2,U_3) ) )
& element(U_2,powerset(the_carrier(U_5))) )
| ~ element(U_3,powerset(powerset(the_carrier(U_5)))) )
& element(U_4,powerset(the_carrier(U_5)))
& top_str(U_5)
& topological_space(U_5) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
? [U_5,U_4] :
( ! [U_3] :
( ? [U_2] :
( ( ( ~ in(U_2,U_3)
& ? [U_1] :
( closed_subset(U_1,U_5)
& U_1 = U_2
& element(U_1,powerset(the_carrier(U_5))) )
& subset(U_4,U_2) )
| ( ( ! [U_0] :
( ~ closed_subset(U_0,U_5)
| U_0 != U_2
| ~ element(U_0,powerset(the_carrier(U_5))) )
| ~ subset(U_4,U_2) )
& in(U_2,U_3) ) )
& element(U_2,powerset(the_carrier(U_5))) )
| ~ element(U_3,powerset(powerset(the_carrier(U_5)))) )
& element(U_4,powerset(the_carrier(U_5)))
& top_str(U_5)
& topological_space(U_5) ),
inference(miniscope,[status(thm)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
? [U_4] :
( ! [U_3] :
( ? [U_2] :
( ( ( ~ in(U_2,U_3)
& ? [U_1] :
( closed_subset(U_1,sK1)
& U_1 = U_2
& element(U_1,powerset(the_carrier(sK1))) )
& subset(U_4,U_2) )
| ( ( ! [U_0] :
( ~ closed_subset(U_0,sK1)
| U_0 != U_2
| ~ element(U_0,powerset(the_carrier(sK1))) )
| ~ subset(U_4,U_2) )
& in(U_2,U_3) ) )
& element(U_2,powerset(the_carrier(sK1))) )
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) )
& element(U_4,powerset(the_carrier(sK1)))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_5,sK1)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ! [U_3] :
( ? [U_2] :
( ( ( ~ in(U_2,U_3)
& ? [U_1] :
( closed_subset(U_1,sK1)
& U_1 = U_2
& element(U_1,powerset(the_carrier(sK1))) )
& subset(sK2,U_2) )
| ( ( ! [U_0] :
( ~ closed_subset(U_0,sK1)
| U_0 != U_2
| ~ element(U_0,powerset(the_carrier(sK1))) )
| ~ subset(sK2,U_2) )
& in(U_2,U_3) ) )
& element(U_2,powerset(the_carrier(sK1))) )
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) )
& element(sK2,powerset(the_carrier(sK1)))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_4,sK2)],[f_1_5]) ).
fof(f_1_7,negated_conjecture,
( ! [U_3] :
( ( ( ( ~ in(sK3(U_3),U_3)
& ? [U_1] :
( closed_subset(U_1,sK1)
& U_1 = sK3(U_3)
& element(U_1,powerset(the_carrier(sK1))) )
& subset(sK2,sK3(U_3)) )
| ( ( ! [U_0] :
( ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1))) )
| ~ subset(sK2,sK3(U_3)) )
& in(sK3(U_3),U_3) ) )
& element(sK3(U_3),powerset(the_carrier(sK1))) )
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) )
& element(sK2,powerset(the_carrier(sK1)))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_2,sK3(U_3))],[f_1_6]) ).
fof(f_1_8,negated_conjecture,
( ! [U_3] :
( ( ( ( ~ in(sK3(U_3),U_3)
& closed_subset(sK4(U_3),sK1)
& sK4(U_3) = sK3(U_3)
& element(sK4(U_3),powerset(the_carrier(sK1)))
& subset(sK2,sK3(U_3)) )
| ( ( ! [U_0] :
( ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1))) )
| ~ subset(sK2,sK3(U_3)) )
& in(sK3(U_3),U_3) ) )
& element(sK3(U_3),powerset(the_carrier(sK1))) )
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) )
& element(sK2,powerset(the_carrier(sK1)))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_1,sK4(U_3))],[f_1_7]) ).
cnf(f_1_9,negated_conjecture,
topological_space(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_10,negated_conjecture,
top_str(sK1),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_11,negated_conjecture,
element(sK2,powerset(the_carrier(sK1))),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_12,negated_conjecture,
( element(sK3(U_3),powerset(the_carrier(sK1)))
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_13,negated_conjecture,
( subset(sK2,sK3(U_3))
| in(sK3(U_3),U_3)
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_14,negated_conjecture,
( element(sK4(U_3),powerset(the_carrier(sK1)))
| in(sK3(U_3),U_3)
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_15,negated_conjecture,
( sK4(U_3) = sK3(U_3)
| in(sK3(U_3),U_3)
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_16,negated_conjecture,
( closed_subset(sK4(U_3),sK1)
| in(sK3(U_3),U_3)
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_17,negated_conjecture,
( ~ in(sK3(U_3),U_3)
| in(sK3(U_3),U_3)
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_18,negated_conjecture,
( subset(sK2,sK3(U_3))
| ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1)))
| ~ subset(sK2,sK3(U_3))
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_19,negated_conjecture,
( element(sK4(U_3),powerset(the_carrier(sK1)))
| ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1)))
| ~ subset(sK2,sK3(U_3))
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_20,negated_conjecture,
( sK4(U_3) = sK3(U_3)
| ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1)))
| ~ subset(sK2,sK3(U_3))
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_21,negated_conjecture,
( closed_subset(sK4(U_3),sK1)
| ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1)))
| ~ subset(sK2,sK3(U_3))
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
cnf(f_1_22,negated_conjecture,
( ~ in(sK3(U_3),U_3)
| ~ closed_subset(U_0,sK1)
| U_0 != sK3(U_3)
| ~ element(U_0,powerset(the_carrier(sK1)))
| ~ subset(sK2,sK3(U_3))
| ~ element(U_3,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_8]) ).
fof(f_2_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_2_2,plain,
! [U_6] :
( v4_membered(U_6)
| ~ v5_membered(U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( v4_membered(U_6)
| ~ v5_membered(U_6) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_3_2,plain,
! [U_7] :
( v3_membered(U_7)
| ~ v4_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v3_membered(U_7)
| ~ v4_membered(U_7) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_4_2,plain,
! [U_8] :
( v2_membered(U_8)
| ~ v3_membered(U_8) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v2_membered(U_8)
| ~ v3_membered(U_8) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_5_2,plain,
! [U_9] :
( v1_membered(U_9)
| ~ v2_membered(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_membered(U_9)
| ~ v2_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
? [A] :
( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_membered]) ).
fof(f_6_2,plain,
? [U_10] :
( v5_membered(U_10)
& v4_membered(U_10)
& v3_membered(U_10)
& v2_membered(U_10)
& v1_membered(U_10)
& ~ empty(U_10) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( v5_membered(sK5)
& v4_membered(sK5)
& v3_membered(sK5)
& v2_membered(sK5)
& v1_membered(sK5)
& ~ empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_10,sK5)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
v1_membered(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
v2_membered(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
v3_membered(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
v4_membered(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_9,plain,
v5_membered(sK5),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_7_2,plain,
! [U_12] :
( ! [U_11] :
( v1_xcmplx_0(U_11)
| ~ element(U_11,U_12) )
| ~ v1_membered(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_xcmplx_0(U_11)
| ~ element(U_11,U_12)
| ~ v1_membered(U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( ( v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc11_membered]) ).
fof(f_8_2,plain,
! [U_14] :
( ! [U_13] :
( ( v1_xreal_0(U_13)
& v1_xcmplx_0(U_13) )
| ~ element(U_13,U_14) )
| ~ v2_membered(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v1_xcmplx_0(U_13)
| ~ element(U_13,U_14)
| ~ v2_membered(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( v1_xreal_0(U_13)
| ~ element(U_13,U_14)
| ~ v2_membered(U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc12_membered]) ).
fof(f_9_2,plain,
! [U_16] :
( ! [U_15] :
( ( v1_rat_1(U_15)
& v1_xreal_0(U_15)
& v1_xcmplx_0(U_15) )
| ~ element(U_15,U_16) )
| ~ v3_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_xcmplx_0(U_15)
| ~ element(U_15,U_16)
| ~ v3_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( v1_xreal_0(U_15)
| ~ element(U_15,U_16)
| ~ v3_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_5,plain,
( v1_rat_1(U_15)
| ~ element(U_15,U_16)
| ~ v3_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc13_membered]) ).
fof(f_10_2,plain,
! [U_18] :
( ! [U_17] :
( ( v1_rat_1(U_17)
& v1_int_1(U_17)
& v1_xreal_0(U_17)
& v1_xcmplx_0(U_17) )
| ~ element(U_17,U_18) )
| ~ v4_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_xcmplx_0(U_17)
| ~ element(U_17,U_18)
| ~ v4_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v1_xreal_0(U_17)
| ~ element(U_17,U_18)
| ~ v4_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v1_int_1(U_17)
| ~ element(U_17,U_18)
| ~ v4_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_6,plain,
( v1_rat_1(U_17)
| ~ element(U_17,U_18)
| ~ v4_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] :
( ! [B] :
( ( v1_rat_1(B)
& v1_int_1(B)
& v1_xreal_0(B)
& natural(B)
& v1_xcmplx_0(B) )
| ~ element(B,A) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc14_membered]) ).
fof(f_11_2,plain,
! [U_20] :
( ! [U_19] :
( ( v1_rat_1(U_19)
& v1_int_1(U_19)
& v1_xreal_0(U_19)
& natural(U_19)
& v1_xcmplx_0(U_19) )
| ~ element(U_19,U_20) )
| ~ v5_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_xcmplx_0(U_19)
| ~ element(U_19,U_20)
| ~ v5_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( natural(U_19)
| ~ element(U_19,U_20)
| ~ v5_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v1_xreal_0(U_19)
| ~ element(U_19,U_20)
| ~ v5_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_6,plain,
( v1_int_1(U_19)
| ~ element(U_19,U_20)
| ~ v5_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_7,plain,
( v1_rat_1(U_19)
| ~ element(U_19,U_20)
| ~ v5_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_12_2,plain,
! [U_22] :
( ! [U_21] :
( v1_membered(U_21)
| ~ element(U_21,powerset(U_22)) )
| ~ v1_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v1_membered(U_22) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( ! [B] :
( ( v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc17_membered]) ).
fof(f_13_2,plain,
! [U_24] :
( ! [U_23] :
( ( v2_membered(U_23)
& v1_membered(U_23) )
| ~ element(U_23,powerset(U_24)) )
| ~ v2_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( v1_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v2_membered(U_24) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( v2_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v2_membered(U_24) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( ( v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc18_membered]) ).
fof(f_14_2,plain,
! [U_26] :
( ! [U_25] :
( ( v3_membered(U_25)
& v2_membered(U_25)
& v1_membered(U_25) )
| ~ element(U_25,powerset(U_26)) )
| ~ v3_membered(U_26) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v1_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v3_membered(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( v2_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v3_membered(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( v3_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v3_membered(U_26) ),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] :
( ! [B] :
( ( v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc19_membered]) ).
fof(f_15_2,plain,
! [U_28] :
( ! [U_27] :
( ( v4_membered(U_27)
& v3_membered(U_27)
& v2_membered(U_27)
& v1_membered(U_27) )
| ~ element(U_27,powerset(U_28)) )
| ~ v4_membered(U_28) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( v1_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v4_membered(U_28) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( v2_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v4_membered(U_28) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_5,plain,
( v3_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v4_membered(U_28) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_6,plain,
( v4_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v4_membered(U_28) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( ! [B] :
( ( v5_membered(B)
& v4_membered(B)
& v3_membered(B)
& v2_membered(B)
& v1_membered(B) )
| ~ element(B,powerset(A)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc20_membered]) ).
fof(f_16_2,plain,
! [U_30] :
( ! [U_29] :
( ( v5_membered(U_29)
& v4_membered(U_29)
& v3_membered(U_29)
& v2_membered(U_29)
& v1_membered(U_29) )
| ~ element(U_29,powerset(U_30)) )
| ~ v5_membered(U_30) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( v1_membered(U_29)
| ~ element(U_29,powerset(U_30))
| ~ v5_membered(U_30) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( v2_membered(U_29)
| ~ element(U_29,powerset(U_30))
| ~ v5_membered(U_30) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_5,plain,
( v3_membered(U_29)
| ~ element(U_29,powerset(U_30))
| ~ v5_membered(U_30) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_6,plain,
( v4_membered(U_29)
| ~ element(U_29,powerset(U_30))
| ~ v5_membered(U_30) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_7,plain,
( v5_membered(U_29)
| ~ element(U_29,powerset(U_30))
| ~ v5_membered(U_30) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_17_2,plain,
$true,
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_18_2,plain,
! [U_32] :
( ? [U_31] :
( ~ empty(U_31)
& element(U_31,powerset(U_32)) )
| empty(U_32) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_32] :
( ( ~ empty(sK6(U_32))
& element(sK6(U_32),powerset(U_32)) )
| empty(U_32) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_31,sK6(U_32))],[f_18_2]) ).
cnf(f_18_4,plain,
( element(sK6(U_32),powerset(U_32))
| empty(U_32) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( ~ empty(sK6(U_32))
| empty(U_32) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_19_2,plain,
! [U_34] :
? [U_33] :
( empty(U_33)
& element(U_33,powerset(U_34)) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_34] :
( empty(sK7(U_34))
& element(sK7(U_34),powerset(U_34)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_33,sK7(U_34))],[f_19_2]) ).
cnf(f_19_4,plain,
element(sK7(U_34),powerset(U_34)),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
empty(sK7(U_34)),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ( v5_membered(A)
& v4_membered(A)
& v3_membered(A)
& v2_membered(A)
& v1_membered(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc15_membered]) ).
fof(f_20_2,plain,
! [U_35] :
( ( v5_membered(U_35)
& v4_membered(U_35)
& v3_membered(U_35)
& v2_membered(U_35)
& v1_membered(U_35) )
| ~ empty(U_35) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( v1_membered(U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( v2_membered(U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_5,plain,
( v3_membered(U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_6,plain,
( v4_membered(U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_7,plain,
( v5_membered(U_35)
| ~ empty(U_35) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_21_2,plain,
! [U_37,U_36] : subset(U_37,U_37),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_37] : subset(U_37,U_37),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
subset(U_37,U_37),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_22_2,plain,
! [U_39,U_38] :
( ~ in(U_38,U_39)
| ~ in(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( ~ in(U_38,U_39)
| ~ in(U_39,U_38) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_23_2,plain,
$true,
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_pre_topc]) ).
fof(f_24_2,plain,
! [U_40] :
( one_sorted_str(U_40)
| ~ top_str(U_40) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( one_sorted_str(U_40)
| ~ top_str(U_40) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_26_2,plain,
$true,
inference(clausify,[status(thm)],[f_26_1]) ).
fof(f_27_1,plain,
! [A] :
( ? [B] :
( closed_subset(B,A)
& element(B,powerset(the_carrier(A))) )
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[rc6_pre_topc]) ).
fof(f_27_2,plain,
! [U_42] :
( ? [U_41] :
( closed_subset(U_41,U_42)
& element(U_41,powerset(the_carrier(U_42))) )
| ~ top_str(U_42)
| ~ topological_space(U_42) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_42] :
( ( closed_subset(sK8(U_42),U_42)
& element(sK8(U_42),powerset(the_carrier(U_42))) )
| ~ top_str(U_42)
| ~ topological_space(U_42) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8(U_42))],[f_27_2]) ).
cnf(f_27_4,plain,
( element(sK8(U_42),powerset(the_carrier(U_42)))
| ~ top_str(U_42)
| ~ topological_space(U_42) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( closed_subset(sK8(U_42),U_42)
| ~ top_str(U_42)
| ~ topological_space(U_42) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_28_2,plain,
! [U_43] : ~ empty(powerset(U_43)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ empty(powerset(U_43)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ! [E] :
( ~ subset(B,D)
| ~ closed_subset(E,A)
| E != D
| ~ element(E,powerset(the_carrier(A))) )
| ~ in(D,powerset(the_carrier(A))) )
& ( ( ? [E] :
( subset(B,D)
& closed_subset(E,A)
& E = D
& element(E,powerset(the_carrier(A))) )
& in(D,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ element(B,powerset(the_carrier(A)))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e1_40__pre_topc__1]) ).
fof(f_29_2,plain,
! [U_49,U_48] :
( ? [U_47] :
! [U_46] :
( ( in(U_46,U_47)
| ! [U_45] :
( ~ subset(U_48,U_46)
| ~ closed_subset(U_45,U_49)
| U_45 != U_46
| ~ element(U_45,powerset(the_carrier(U_49))) )
| ~ in(U_46,powerset(the_carrier(U_49))) )
& ( ( ? [U_44] :
( subset(U_48,U_46)
& closed_subset(U_44,U_49)
& U_44 = U_46
& element(U_44,powerset(the_carrier(U_49))) )
& in(U_46,powerset(the_carrier(U_49))) )
| ~ in(U_46,U_47) ) )
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_49,U_48] :
( ? [U_47] :
( ! [U_51] :
( in(U_51,U_47)
| ! [U_45] :
( ~ closed_subset(U_45,U_49)
| U_45 != U_51
| ~ element(U_45,powerset(the_carrier(U_49))) )
| ~ subset(U_48,U_51)
| ~ in(U_51,powerset(the_carrier(U_49))) )
& ! [U_50] :
( ( ? [U_44] :
( closed_subset(U_44,U_49)
& U_44 = U_50
& element(U_44,powerset(the_carrier(U_49))) )
& subset(U_48,U_50)
& in(U_50,powerset(the_carrier(U_49))) )
| ~ in(U_50,U_47) ) )
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_49,U_48] :
( ( ! [U_51] :
( in(U_51,sK9(U_49,U_48))
| ! [U_45] :
( ~ closed_subset(U_45,U_49)
| U_45 != U_51
| ~ element(U_45,powerset(the_carrier(U_49))) )
| ~ subset(U_48,U_51)
| ~ in(U_51,powerset(the_carrier(U_49))) )
& ! [U_50] :
( ( ? [U_44] :
( closed_subset(U_44,U_49)
& U_44 = U_50
& element(U_44,powerset(the_carrier(U_49))) )
& subset(U_48,U_50)
& in(U_50,powerset(the_carrier(U_49))) )
| ~ in(U_50,sK9(U_49,U_48)) ) )
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_47,sK9(U_49,U_48))],[f_29_3]) ).
fof(f_29_5,plain,
! [U_49,U_48] :
( ( ! [U_51] :
( in(U_51,sK9(U_49,U_48))
| ! [U_45] :
( ~ closed_subset(U_45,U_49)
| U_45 != U_51
| ~ element(U_45,powerset(the_carrier(U_49))) )
| ~ subset(U_48,U_51)
| ~ in(U_51,powerset(the_carrier(U_49))) )
& ! [U_50] :
( ( closed_subset(sK10(U_49,U_48,U_50),U_49)
& sK10(U_49,U_48,U_50) = U_50
& element(sK10(U_49,U_48,U_50),powerset(the_carrier(U_49)))
& subset(U_48,U_50)
& in(U_50,powerset(the_carrier(U_49))) )
| ~ in(U_50,sK9(U_49,U_48)) ) )
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_44,sK10(U_49,U_48,U_50))],[f_29_4]) ).
cnf(f_29_6,plain,
( in(U_50,powerset(the_carrier(U_49)))
| ~ in(U_50,sK9(U_49,U_48))
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_7,plain,
( subset(U_48,U_50)
| ~ in(U_50,sK9(U_49,U_48))
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_8,plain,
( element(sK10(U_49,U_48,U_50),powerset(the_carrier(U_49)))
| ~ in(U_50,sK9(U_49,U_48))
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_9,plain,
( sK10(U_49,U_48,U_50) = U_50
| ~ in(U_50,sK9(U_49,U_48))
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_10,plain,
( closed_subset(sK10(U_49,U_48,U_50),U_49)
| ~ in(U_50,sK9(U_49,U_48))
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(clausify,[status(thm)],[f_29_5]) ).
cnf(f_29_11,plain,
( in(U_51,sK9(U_49,U_48))
| ~ closed_subset(U_45,U_49)
| U_45 != U_51
| ~ element(U_45,powerset(the_carrier(U_49)))
| ~ subset(U_48,U_51)
| ~ in(U_51,powerset(the_carrier(U_49)))
| ~ element(U_48,powerset(the_carrier(U_49)))
| ~ top_str(U_49)
| ~ topological_space(U_49) ),
inference(clausify,[status(thm)],[f_29_5]) ).
fof(f_30_1,plain,
! [A,B] :
( ( ( ( element(B,A)
| ~ empty(B) )
& ( empty(B)
| ~ element(B,A) ) )
| ~ empty(A) )
& ( ( ( element(B,A)
| ~ in(B,A) )
& ( in(B,A)
| ~ element(B,A) ) )
| empty(A) ) ),
inference(fof_nnf,[status(thm)],[d2_subset_1]) ).
fof(f_30_2,plain,
! [U_53,U_52] :
( ( ( ( element(U_52,U_53)
| ~ empty(U_52) )
& ( empty(U_52)
| ~ element(U_52,U_53) ) )
| ~ empty(U_53) )
& ( ( ( element(U_52,U_53)
| ~ in(U_52,U_53) )
& ( in(U_52,U_53)
| ~ element(U_52,U_53) ) )
| empty(U_53) ) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_61] :
( ( ! [U_59] :
( element(U_59,U_61)
| ~ empty(U_59) )
& ! [U_58] :
( empty(U_58)
| ~ element(U_58,U_61) ) )
| ~ empty(U_61) )
& ! [U_60] :
( ( ! [U_57] :
( element(U_57,U_60)
| ~ in(U_57,U_60) )
& ! [U_56] :
( in(U_56,U_60)
| ~ element(U_56,U_60) ) )
| empty(U_60) ) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
( in(U_56,U_60)
| ~ element(U_56,U_60)
| empty(U_60) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( element(U_57,U_60)
| ~ in(U_57,U_60)
| empty(U_60) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
( empty(U_58)
| ~ element(U_58,U_61)
| ~ empty(U_61) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_7,plain,
( element(U_59,U_61)
| ~ empty(U_59)
| ~ empty(U_61) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_31_2,plain,
$true,
inference(clausify,[status(thm)],[f_31_1]) ).
fof(f_32_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_32_2,plain,
! [U_63] :
? [U_62] : element(U_62,U_63),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_63] : element(sK11(U_63),U_63),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_62,sK11(U_63))],[f_32_2]) ).
cnf(f_32_4,plain,
element(sK11(U_63),U_63),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_33_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
! [A,B] :
( element(A,powerset(B))
| ? [C] :
( ~ in(C,B)
& in(C,A) ) ),
inference(fof_nnf,[status(thm)],[l71_subset_1]) ).
fof(f_34_2,plain,
! [U_66,U_65] :
( element(U_66,powerset(U_65))
| ? [U_64] :
( ~ in(U_64,U_65)
& in(U_64,U_66) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_66,U_65] :
( element(U_66,powerset(U_65))
| ( ~ in(sK12(U_66,U_65),U_65)
& in(sK12(U_66,U_65),U_66) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_64,sK12(U_66,U_65))],[f_34_2]) ).
cnf(f_34_4,plain,
( in(sK12(U_66,U_65),U_66)
| element(U_66,powerset(U_65)) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( ~ in(sK12(U_66,U_65),U_65)
| element(U_66,powerset(U_65)) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_35_2,plain,
? [U_67] : empty(U_67),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_67,sK13)],[f_35_2]) ).
cnf(f_35_4,plain,
empty(sK13),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_36_2,plain,
? [U_68] : ~ empty(U_68),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
~ empty(sK14),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_68,sK14)],[f_36_2]) ).
cnf(f_36_4,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_69] :
( U_69 = empty_set
| ~ empty(U_69) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
cnf(f_37_3,plain,
( U_69 = empty_set
| ~ empty(U_69) ),
inference(clausify,[status(thm)],[f_37_2]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_71,U_70] :
( ~ empty(U_70)
| ~ in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( ~ empty(U_70)
| ~ in(U_71,U_70) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_73,U_72] :
( ~ empty(U_72)
| U_73 = U_72
| ~ empty(U_73) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_73] :
( ! [U_72] :
( ~ empty(U_72)
| U_73 = U_72 )
| ~ empty(U_73) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ empty(U_72)
| U_73 = U_72
| ~ empty(U_73) ),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_1_17_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_1_17]) ).
cnf(f_1_18_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_1_18]) ).
cnf(f_17_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_2]) ).
cnf(f_23_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(f_26_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_2]) ).
cnf(f_31_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_31_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK4(Eq_x_0) = sK4(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK10(Eq_x_0,Eq_x_1,Eq_x_2) = sK10(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK12(Eq_x_0,Eq_x_1) = sK12(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( topological_space(Eq_y_0)
| ~ topological_space(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( top_str(Eq_y_0)
| ~ top_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( closed_subset(Eq_y_0,Eq_y_1)
| ~ closed_subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( subset(Eq_y_0,Eq_y_1)
| ~ subset(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( v1_xcmplx_0(Eq_y_0)
| ~ v1_xcmplx_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( v1_xreal_0(Eq_y_0)
| ~ v1_xreal_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( v1_rat_1(Eq_y_0)
| ~ v1_rat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( v1_int_1(Eq_y_0)
| ~ v1_int_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU315+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 19 23:53:03 UTC 2026
% 0.10/0.36 % CPUTime :
% 265.18/265.50 % SZS status Theorem for theBenchmark
% 265.18/265.50 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------