%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:58:57 AM UTC 2026
% Result : Theorem 171.43s 176.76s
% Output : Proof 172.16s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(s3_subset_1__e2_37_1_1__pre_topc,conjecture,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A) )
=> ? [C] :
( ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> in(set_difference(cast_as_carrier_subset(A),D),B) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ),
file('theBenchmark.p',s3_subset_1__e2_37_1_1__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(fc37_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_difference(A,B)) ),
file('theBenchmark.p',fc37_membered) ).
fof(fc38_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc38_membered) ).
fof(fc39_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc39_membered) ).
fof(fc40_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc40_membered) ).
fof(fc41_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_difference(A,B))
& v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) ) ),
file('theBenchmark.p',fc41_membered) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_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(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(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_k2_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('theBenchmark.p',dt_k2_pre_topc) ).
fof(dt_k4_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k4_xboole_0) ).
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(fc5_pre_topc,axiom,
! [A] :
( ( top_str(A)
& topological_space(A) )
=> closed_subset(cast_as_carrier_subset(A),A) ),
file('theBenchmark.p',fc5_pre_topc) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(s1_xboole_0__e2_37_1_1__pre_topc__1,axiom,
! [A,B] :
( ( element(B,powerset(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A) )
=> ? [C] :
! [D] :
( in(D,C)
<=> ( in(set_difference(cast_as_carrier_subset(A),D),B)
& in(D,powerset(the_carrier(A))) ) ) ),
file('theBenchmark.p',s1_xboole_0__e2_37_1_1__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(powerset(the_carrier(A))))
& top_str(A)
& topological_space(A) )
=> ? [C] :
( ! [D] :
( element(D,powerset(the_carrier(A)))
=> ( in(D,C)
<=> in(set_difference(cast_as_carrier_subset(A),D),B) ) )
& element(C,powerset(powerset(the_carrier(A)))) ) ),
inference(negate,[status(cth)],[s3_subset_1__e2_37_1_1__pre_topc]) ).
fof(f_1_2,negated_conjecture,
? [A,B] :
( ! [C] :
( ? [D] :
( ( ( ~ in(D,C)
& in(set_difference(cast_as_carrier_subset(A),D),B) )
| ( ~ in(set_difference(cast_as_carrier_subset(A),D),B)
& in(D,C) ) )
& element(D,powerset(the_carrier(A))) )
| ~ element(C,powerset(powerset(the_carrier(A)))) )
& element(B,powerset(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_3,U_2] :
( ! [U_1] :
( ? [U_0] :
( ( ( ~ in(U_0,U_1)
& in(set_difference(cast_as_carrier_subset(U_3),U_0),U_2) )
| ( ~ in(set_difference(cast_as_carrier_subset(U_3),U_0),U_2)
& in(U_0,U_1) ) )
& element(U_0,powerset(the_carrier(U_3))) )
| ~ element(U_1,powerset(powerset(the_carrier(U_3)))) )
& element(U_2,powerset(powerset(the_carrier(U_3))))
& top_str(U_3)
& topological_space(U_3) ),
inference(variable_rename,[status(thm)],[f_1_2]) ).
fof(f_1_4,negated_conjecture,
? [U_2] :
( ! [U_1] :
( ? [U_0] :
( ( ( ~ in(U_0,U_1)
& in(set_difference(cast_as_carrier_subset(sK1),U_0),U_2) )
| ( ~ in(set_difference(cast_as_carrier_subset(sK1),U_0),U_2)
& in(U_0,U_1) ) )
& element(U_0,powerset(the_carrier(sK1))) )
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) )
& element(U_2,powerset(powerset(the_carrier(sK1))))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_3,sK1)],[f_1_3]) ).
fof(f_1_5,negated_conjecture,
( ! [U_1] :
( ? [U_0] :
( ( ( ~ in(U_0,U_1)
& in(set_difference(cast_as_carrier_subset(sK1),U_0),sK2) )
| ( ~ in(set_difference(cast_as_carrier_subset(sK1),U_0),sK2)
& in(U_0,U_1) ) )
& element(U_0,powerset(the_carrier(sK1))) )
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) )
& element(sK2,powerset(powerset(the_carrier(sK1))))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_2,sK2)],[f_1_4]) ).
fof(f_1_6,negated_conjecture,
( ! [U_1] :
( ( ( ( ~ in(sK3(U_1),U_1)
& in(set_difference(cast_as_carrier_subset(sK1),sK3(U_1)),sK2) )
| ( ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(U_1)),sK2)
& in(sK3(U_1),U_1) ) )
& element(sK3(U_1),powerset(the_carrier(sK1))) )
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) )
& element(sK2,powerset(powerset(the_carrier(sK1))))
& top_str(sK1)
& topological_space(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_0,sK3(U_1))],[f_1_5]) ).
cnf(f_1_7,negated_conjecture,
topological_space(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_8,negated_conjecture,
top_str(sK1),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_9,negated_conjecture,
element(sK2,powerset(powerset(the_carrier(sK1)))),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_10,negated_conjecture,
( element(sK3(U_1),powerset(the_carrier(sK1)))
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_11,negated_conjecture,
( in(set_difference(cast_as_carrier_subset(sK1),sK3(U_1)),sK2)
| in(sK3(U_1),U_1)
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_12,negated_conjecture,
( ~ in(sK3(U_1),U_1)
| in(sK3(U_1),U_1)
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_13,negated_conjecture,
( in(set_difference(cast_as_carrier_subset(sK1),sK3(U_1)),sK2)
| ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(U_1)),sK2)
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_6]) ).
cnf(f_1_14,negated_conjecture,
( ~ in(sK3(U_1),U_1)
| ~ in(set_difference(cast_as_carrier_subset(sK1),sK3(U_1)),sK2)
| ~ element(U_1,powerset(powerset(the_carrier(sK1)))) ),
inference(clausify,[status(thm)],[f_1_6]) ).
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_4] :
( v4_membered(U_4)
| ~ v5_membered(U_4) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( v4_membered(U_4)
| ~ v5_membered(U_4) ),
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_5] :
( v3_membered(U_5)
| ~ v4_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( v3_membered(U_5)
| ~ v4_membered(U_5) ),
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_6] :
( v2_membered(U_6)
| ~ v3_membered(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( v2_membered(U_6)
| ~ v3_membered(U_6) ),
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_7] :
( v1_membered(U_7)
| ~ v2_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( v1_membered(U_7)
| ~ v2_membered(U_7) ),
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_8] :
( v5_membered(U_8)
& v4_membered(U_8)
& v3_membered(U_8)
& v2_membered(U_8)
& v1_membered(U_8)
& ~ empty(U_8) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( v5_membered(sK4)
& v4_membered(sK4)
& v3_membered(sK4)
& v2_membered(sK4)
& v1_membered(sK4)
& ~ empty(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_8,sK4)],[f_6_2]) ).
cnf(f_6_4,plain,
~ empty(sK4),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
v1_membered(sK4),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
v2_membered(sK4),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
v3_membered(sK4),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
v4_membered(sK4),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_9,plain,
v5_membered(sK4),
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_10] :
( ! [U_9] :
( v1_xcmplx_0(U_9)
| ~ element(U_9,U_10) )
| ~ v1_membered(U_10) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( v1_xcmplx_0(U_9)
| ~ element(U_9,U_10)
| ~ v1_membered(U_10) ),
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_12] :
( ! [U_11] :
( ( v1_xreal_0(U_11)
& v1_xcmplx_0(U_11) )
| ~ element(U_11,U_12) )
| ~ v2_membered(U_12) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( v1_xcmplx_0(U_11)
| ~ element(U_11,U_12)
| ~ v2_membered(U_12) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( v1_xreal_0(U_11)
| ~ element(U_11,U_12)
| ~ v2_membered(U_12) ),
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_14] :
( ! [U_13] :
( ( v1_rat_1(U_13)
& v1_xreal_0(U_13)
& v1_xcmplx_0(U_13) )
| ~ element(U_13,U_14) )
| ~ v3_membered(U_14) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( v1_xcmplx_0(U_13)
| ~ element(U_13,U_14)
| ~ v3_membered(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( v1_xreal_0(U_13)
| ~ element(U_13,U_14)
| ~ v3_membered(U_14) ),
inference(clausify,[status(thm)],[f_9_2]) ).
cnf(f_9_5,plain,
( v1_rat_1(U_13)
| ~ element(U_13,U_14)
| ~ v3_membered(U_14) ),
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_16] :
( ! [U_15] :
( ( v1_rat_1(U_15)
& v1_int_1(U_15)
& v1_xreal_0(U_15)
& v1_xcmplx_0(U_15) )
| ~ element(U_15,U_16) )
| ~ v4_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( v1_xcmplx_0(U_15)
| ~ element(U_15,U_16)
| ~ v4_membered(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( v1_xreal_0(U_15)
| ~ element(U_15,U_16)
| ~ v4_membered(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_5,plain,
( v1_int_1(U_15)
| ~ element(U_15,U_16)
| ~ v4_membered(U_16) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_6,plain,
( v1_rat_1(U_15)
| ~ element(U_15,U_16)
| ~ v4_membered(U_16) ),
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_18] :
( ! [U_17] :
( ( v1_rat_1(U_17)
& v1_int_1(U_17)
& v1_xreal_0(U_17)
& natural(U_17)
& v1_xcmplx_0(U_17) )
| ~ element(U_17,U_18) )
| ~ v5_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( v1_xcmplx_0(U_17)
| ~ element(U_17,U_18)
| ~ v5_membered(U_18) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( natural(U_17)
| ~ element(U_17,U_18)
| ~ v5_membered(U_18) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_5,plain,
( v1_xreal_0(U_17)
| ~ element(U_17,U_18)
| ~ v5_membered(U_18) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_6,plain,
( v1_int_1(U_17)
| ~ element(U_17,U_18)
| ~ v5_membered(U_18) ),
inference(clausify,[status(thm)],[f_11_2]) ).
cnf(f_11_7,plain,
( v1_rat_1(U_17)
| ~ element(U_17,U_18)
| ~ v5_membered(U_18) ),
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_20] :
( ! [U_19] :
( v1_membered(U_19)
| ~ element(U_19,powerset(U_20)) )
| ~ v1_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( v1_membered(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v1_membered(U_20) ),
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_22] :
( ! [U_21] :
( ( v2_membered(U_21)
& v1_membered(U_21) )
| ~ element(U_21,powerset(U_22)) )
| ~ v2_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( v1_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v2_membered(U_22) ),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( v2_membered(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v2_membered(U_22) ),
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_24] :
( ! [U_23] :
( ( v3_membered(U_23)
& v2_membered(U_23)
& v1_membered(U_23) )
| ~ element(U_23,powerset(U_24)) )
| ~ v3_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
( v1_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v3_membered(U_24) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( v2_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v3_membered(U_24) ),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
( v3_membered(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v3_membered(U_24) ),
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_26] :
( ! [U_25] :
( ( v4_membered(U_25)
& v3_membered(U_25)
& v2_membered(U_25)
& v1_membered(U_25) )
| ~ element(U_25,powerset(U_26)) )
| ~ v4_membered(U_26) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( v1_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v4_membered(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
( v2_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v4_membered(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_5,plain,
( v3_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v4_membered(U_26) ),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_6,plain,
( v4_membered(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v4_membered(U_26) ),
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_28] :
( ! [U_27] :
( ( v5_membered(U_27)
& v4_membered(U_27)
& v3_membered(U_27)
& v2_membered(U_27)
& v1_membered(U_27) )
| ~ element(U_27,powerset(U_28)) )
| ~ v5_membered(U_28) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( v1_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v5_membered(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( v2_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v5_membered(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_5,plain,
( v3_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v5_membered(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_6,plain,
( v4_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v5_membered(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
cnf(f_16_7,plain,
( v5_membered(U_27)
| ~ element(U_27,powerset(U_28))
| ~ v5_membered(U_28) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [A,B] :
( v1_membered(set_difference(A,B))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc37_membered]) ).
fof(f_17_2,plain,
! [U_30,U_29] :
( v1_membered(set_difference(U_30,U_29))
| ~ v1_membered(U_30) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_30] :
( ! [U_29] : v1_membered(set_difference(U_30,U_29))
| ~ v1_membered(U_30) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( v1_membered(set_difference(U_30,U_29))
| ~ v1_membered(U_30) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
( ( v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc38_membered]) ).
fof(f_18_2,plain,
! [U_32,U_31] :
( ( v2_membered(set_difference(U_32,U_31))
& v1_membered(set_difference(U_32,U_31)) )
| ~ v2_membered(U_32) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_32] :
( ( ! [U_34] : v2_membered(set_difference(U_32,U_34))
& ! [U_33] : v1_membered(set_difference(U_32,U_33)) )
| ~ v2_membered(U_32) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
cnf(f_18_4,plain,
( v1_membered(set_difference(U_32,U_33))
| ~ v2_membered(U_32) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( v2_membered(set_difference(U_32,U_34))
| ~ v2_membered(U_32) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( ( v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc39_membered]) ).
fof(f_19_2,plain,
! [U_36,U_35] :
( ( v3_membered(set_difference(U_36,U_35))
& v2_membered(set_difference(U_36,U_35))
& v1_membered(set_difference(U_36,U_35)) )
| ~ v3_membered(U_36) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_36] :
( ( ! [U_39] : v3_membered(set_difference(U_36,U_39))
& ! [U_38] : v2_membered(set_difference(U_36,U_38))
& ! [U_37] : v1_membered(set_difference(U_36,U_37)) )
| ~ v3_membered(U_36) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( v1_membered(set_difference(U_36,U_37))
| ~ v3_membered(U_36) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( v2_membered(set_difference(U_36,U_38))
| ~ v3_membered(U_36) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( v3_membered(set_difference(U_36,U_39))
| ~ v3_membered(U_36) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A,B] :
( ( v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc40_membered]) ).
fof(f_20_2,plain,
! [U_41,U_40] :
( ( v4_membered(set_difference(U_41,U_40))
& v3_membered(set_difference(U_41,U_40))
& v2_membered(set_difference(U_41,U_40))
& v1_membered(set_difference(U_41,U_40)) )
| ~ v4_membered(U_41) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_41] :
( ( ! [U_45] : v4_membered(set_difference(U_41,U_45))
& ! [U_44] : v3_membered(set_difference(U_41,U_44))
& ! [U_43] : v2_membered(set_difference(U_41,U_43))
& ! [U_42] : v1_membered(set_difference(U_41,U_42)) )
| ~ v4_membered(U_41) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( v1_membered(set_difference(U_41,U_42))
| ~ v4_membered(U_41) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( v2_membered(set_difference(U_41,U_43))
| ~ v4_membered(U_41) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( v3_membered(set_difference(U_41,U_44))
| ~ v4_membered(U_41) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( v4_membered(set_difference(U_41,U_45))
| ~ v4_membered(U_41) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,B] :
( ( v5_membered(set_difference(A,B))
& v4_membered(set_difference(A,B))
& v3_membered(set_difference(A,B))
& v2_membered(set_difference(A,B))
& v1_membered(set_difference(A,B)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc41_membered]) ).
fof(f_21_2,plain,
! [U_47,U_46] :
( ( v5_membered(set_difference(U_47,U_46))
& v4_membered(set_difference(U_47,U_46))
& v3_membered(set_difference(U_47,U_46))
& v2_membered(set_difference(U_47,U_46))
& v1_membered(set_difference(U_47,U_46)) )
| ~ v5_membered(U_47) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_47] :
( ( ! [U_52] : v5_membered(set_difference(U_47,U_52))
& ! [U_51] : v4_membered(set_difference(U_47,U_51))
& ! [U_50] : v3_membered(set_difference(U_47,U_50))
& ! [U_49] : v2_membered(set_difference(U_47,U_49))
& ! [U_48] : v1_membered(set_difference(U_47,U_48)) )
| ~ v5_membered(U_47) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( v1_membered(set_difference(U_47,U_48))
| ~ v5_membered(U_47) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
( v2_membered(set_difference(U_47,U_49))
| ~ v5_membered(U_47) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_6,plain,
( v3_membered(set_difference(U_47,U_50))
| ~ v5_membered(U_47) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_7,plain,
( v4_membered(set_difference(U_47,U_51))
| ~ v5_membered(U_47) ),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_8,plain,
( v5_membered(set_difference(U_47,U_52))
| ~ v5_membered(U_47) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
cnf(f_22_2,plain,
$true,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_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_23_2,plain,
! [U_54] :
( ? [U_53] :
( closed_subset(U_53,U_54)
& element(U_53,powerset(the_carrier(U_54))) )
| ~ top_str(U_54)
| ~ topological_space(U_54) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_54] :
( ( closed_subset(sK5(U_54),U_54)
& element(sK5(U_54),powerset(the_carrier(U_54))) )
| ~ top_str(U_54)
| ~ topological_space(U_54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_53,sK5(U_54))],[f_23_2]) ).
cnf(f_23_4,plain,
( element(sK5(U_54),powerset(the_carrier(U_54)))
| ~ top_str(U_54)
| ~ topological_space(U_54) ),
inference(clausify,[status(thm)],[f_23_3]) ).
cnf(f_23_5,plain,
( closed_subset(sK5(U_54),U_54)
| ~ top_str(U_54)
| ~ topological_space(U_54) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_24_2,plain,
! [U_56] :
( ? [U_55] :
( ~ empty(U_55)
& element(U_55,powerset(U_56)) )
| empty(U_56) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_56] :
( ( ~ empty(sK6(U_56))
& element(sK6(U_56),powerset(U_56)) )
| empty(U_56) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_55,sK6(U_56))],[f_24_2]) ).
cnf(f_24_4,plain,
( element(sK6(U_56),powerset(U_56))
| empty(U_56) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( ~ empty(sK6(U_56))
| empty(U_56) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_25_2,plain,
! [U_58] :
? [U_57] :
( empty(U_57)
& element(U_57,powerset(U_58)) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_58] :
( empty(sK7(U_58))
& element(sK7(U_58),powerset(U_58)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_57,sK7(U_58))],[f_25_2]) ).
cnf(f_25_4,plain,
element(sK7(U_58),powerset(U_58)),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
empty(sK7(U_58)),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_59] :
( ( v5_membered(U_59)
& v4_membered(U_59)
& v3_membered(U_59)
& v2_membered(U_59)
& v1_membered(U_59) )
| ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( v1_membered(U_59)
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( v2_membered(U_59)
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_5,plain,
( v3_membered(U_59)
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_6,plain,
( v4_membered(U_59)
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_7,plain,
( v5_membered(U_59)
| ~ empty(U_59) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_27_2,plain,
! [U_61,U_60] :
( ~ in(U_60,U_61)
| ~ in(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ~ in(U_60,U_61)
| ~ in(U_61,U_60) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_28_2,plain,
$true,
inference(clausify,[status(thm)],[f_28_1]) ).
fof(f_29_1,plain,
! [A] :
( element(cast_as_carrier_subset(A),powerset(the_carrier(A)))
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[dt_k2_pre_topc]) ).
fof(f_29_2,plain,
! [U_62] :
( element(cast_as_carrier_subset(U_62),powerset(the_carrier(U_62)))
| ~ one_sorted_str(U_62) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( element(cast_as_carrier_subset(U_62),powerset(the_carrier(U_62)))
| ~ one_sorted_str(U_62) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_xboole_0]) ).
cnf(f_30_2,plain,
$true,
inference(clausify,[status(thm)],[f_30_1]) ).
fof(f_31_1,plain,
! [A] :
( one_sorted_str(A)
| ~ top_str(A) ),
inference(fof_nnf,[status(thm)],[dt_l1_pre_topc]) ).
fof(f_31_2,plain,
! [U_63] :
( one_sorted_str(U_63)
| ~ top_str(U_63) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
( one_sorted_str(U_63)
| ~ top_str(U_63) ),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_32_2,plain,
$true,
inference(clausify,[status(thm)],[f_32_1]) ).
fof(f_33_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
cnf(f_33_2,plain,
$true,
inference(clausify,[status(thm)],[f_33_1]) ).
fof(f_34_1,plain,
! [A] :
( closed_subset(cast_as_carrier_subset(A),A)
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[fc5_pre_topc]) ).
fof(f_34_2,plain,
! [U_64] :
( closed_subset(cast_as_carrier_subset(U_64),U_64)
| ~ top_str(U_64)
| ~ topological_space(U_64) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( closed_subset(cast_as_carrier_subset(U_64),U_64)
| ~ top_str(U_64)
| ~ topological_space(U_64) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_35_2,plain,
! [U_65] : ~ empty(powerset(U_65)),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
~ empty(powerset(U_65)),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [A,B] :
( ? [C] :
! [D] :
( ( in(D,C)
| ~ in(set_difference(cast_as_carrier_subset(A),D),B)
| ~ in(D,powerset(the_carrier(A))) )
& ( ( in(set_difference(cast_as_carrier_subset(A),D),B)
& in(D,powerset(the_carrier(A))) )
| ~ in(D,C) ) )
| ~ element(B,powerset(powerset(the_carrier(A))))
| ~ top_str(A)
| ~ topological_space(A) ),
inference(fof_nnf,[status(thm)],[s1_xboole_0__e2_37_1_1__pre_topc__1]) ).
fof(f_36_2,plain,
! [U_69,U_68] :
( ? [U_67] :
! [U_66] :
( ( in(U_66,U_67)
| ~ in(set_difference(cast_as_carrier_subset(U_69),U_66),U_68)
| ~ in(U_66,powerset(the_carrier(U_69))) )
& ( ( in(set_difference(cast_as_carrier_subset(U_69),U_66),U_68)
& in(U_66,powerset(the_carrier(U_69))) )
| ~ in(U_66,U_67) ) )
| ~ element(U_68,powerset(powerset(the_carrier(U_69))))
| ~ top_str(U_69)
| ~ topological_space(U_69) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_69,U_68] :
( ? [U_67] :
( ! [U_71] :
( in(U_71,U_67)
| ~ in(set_difference(cast_as_carrier_subset(U_69),U_71),U_68)
| ~ in(U_71,powerset(the_carrier(U_69))) )
& ! [U_70] :
( ( in(set_difference(cast_as_carrier_subset(U_69),U_70),U_68)
& in(U_70,powerset(the_carrier(U_69))) )
| ~ in(U_70,U_67) ) )
| ~ element(U_68,powerset(powerset(the_carrier(U_69))))
| ~ top_str(U_69)
| ~ topological_space(U_69) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
fof(f_36_4,plain,
! [U_69,U_68] :
( ( ! [U_71] :
( in(U_71,sK8(U_69,U_68))
| ~ in(set_difference(cast_as_carrier_subset(U_69),U_71),U_68)
| ~ in(U_71,powerset(the_carrier(U_69))) )
& ! [U_70] :
( ( in(set_difference(cast_as_carrier_subset(U_69),U_70),U_68)
& in(U_70,powerset(the_carrier(U_69))) )
| ~ in(U_70,sK8(U_69,U_68)) ) )
| ~ element(U_68,powerset(powerset(the_carrier(U_69))))
| ~ top_str(U_69)
| ~ topological_space(U_69) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_67,sK8(U_69,U_68))],[f_36_3]) ).
cnf(f_36_5,plain,
( in(U_70,powerset(the_carrier(U_69)))
| ~ in(U_70,sK8(U_69,U_68))
| ~ element(U_68,powerset(powerset(the_carrier(U_69))))
| ~ top_str(U_69)
| ~ topological_space(U_69) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
( in(set_difference(cast_as_carrier_subset(U_69),U_70),U_68)
| ~ in(U_70,sK8(U_69,U_68))
| ~ element(U_68,powerset(powerset(the_carrier(U_69))))
| ~ top_str(U_69)
| ~ topological_space(U_69) ),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
( in(U_71,sK8(U_69,U_68))
| ~ in(set_difference(cast_as_carrier_subset(U_69),U_71),U_68)
| ~ in(U_71,powerset(the_carrier(U_69)))
| ~ element(U_68,powerset(powerset(the_carrier(U_69))))
| ~ top_str(U_69)
| ~ topological_space(U_69) ),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_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_37_2,plain,
! [U_73,U_72] :
( ( ( ( element(U_72,U_73)
| ~ empty(U_72) )
& ( empty(U_72)
| ~ element(U_72,U_73) ) )
| ~ empty(U_73) )
& ( ( ( element(U_72,U_73)
| ~ in(U_72,U_73) )
& ( in(U_72,U_73)
| ~ element(U_72,U_73) ) )
| empty(U_73) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_81] :
( ( ! [U_79] :
( element(U_79,U_81)
| ~ empty(U_79) )
& ! [U_78] :
( empty(U_78)
| ~ element(U_78,U_81) ) )
| ~ empty(U_81) )
& ! [U_80] :
( ( ! [U_77] :
( element(U_77,U_80)
| ~ in(U_77,U_80) )
& ! [U_76] :
( in(U_76,U_80)
| ~ element(U_76,U_80) ) )
| empty(U_80) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
cnf(f_37_4,plain,
( in(U_76,U_80)
| ~ element(U_76,U_80)
| empty(U_80) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
( element(U_77,U_80)
| ~ in(U_77,U_80)
| empty(U_80) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
( empty(U_78)
| ~ element(U_78,U_81)
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_7,plain,
( element(U_79,U_81)
| ~ empty(U_79)
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_38_2,plain,
$true,
inference(clausify,[status(thm)],[f_38_1]) ).
fof(f_39_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_39_2,plain,
! [U_83] :
? [U_82] : element(U_82,U_83),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_83] : element(sK9(U_83),U_83),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_82,sK9(U_83))],[f_39_2]) ).
cnf(f_39_4,plain,
element(sK9(U_83),U_83),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_40_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_40_1]) ).
fof(f_41_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_41_2,plain,
! [U_86,U_85] :
( element(U_86,powerset(U_85))
| ? [U_84] :
( ~ in(U_84,U_85)
& in(U_84,U_86) ) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_86,U_85] :
( element(U_86,powerset(U_85))
| ( ~ in(sK10(U_86,U_85),U_85)
& in(sK10(U_86,U_85),U_86) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_84,sK10(U_86,U_85))],[f_41_2]) ).
cnf(f_41_4,plain,
( in(sK10(U_86,U_85),U_86)
| element(U_86,powerset(U_85)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
( ~ in(sK10(U_86,U_85),U_85)
| element(U_86,powerset(U_85)) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_42_2,plain,
? [U_87] : empty(U_87),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_87,sK11)],[f_42_2]) ).
cnf(f_42_4,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_43_2,plain,
? [U_88] : ~ empty(U_88),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
~ empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_88,sK12)],[f_43_2]) ).
cnf(f_43_4,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_44_2,plain,
! [U_89] :
( U_89 = empty_set
| ~ empty(U_89) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( U_89 = empty_set
| ~ empty(U_89) ),
inference(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_45_2,plain,
! [U_91,U_90] :
( ~ empty(U_90)
| ~ in(U_91,U_90) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( ~ empty(U_90)
| ~ in(U_91,U_90) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_46_2,plain,
! [U_93,U_92] :
( ~ empty(U_92)
| U_93 = U_92
| ~ empty(U_93) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_93] :
( ! [U_92] :
( ~ empty(U_92)
| U_93 = U_92 )
| ~ empty(U_93) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( ~ empty(U_92)
| U_93 = U_92
| ~ empty(U_93) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_1_12_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_1_12]) ).
cnf(f_1_13_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_1_13]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_2]) ).
cnf(f_28_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_28_2]) ).
cnf(f_30_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_30_2]) ).
cnf(f_32_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_32_2]) ).
cnf(f_33_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_33_2]) ).
cnf(f_38_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_38_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,
( cast_as_carrier_subset(Eq_x_0) = cast_as_carrier_subset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( set_difference(Eq_x_0,Eq_x_1) = set_difference(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK7(Eq_x_0) = sK7(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(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,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,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_27,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_28,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_29,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,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_31,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 : SEU311+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.39 % Computer : n009.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Sat Sep 19 23:52:48 UTC 2026
% 0.09/5.39 % CPUTime :
% 171.43/176.76 % SZS status Theorem for theBenchmark
% 171.43/176.76 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------