%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU325+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 : n014.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 08:59:00 AM UTC 2026
% Result : Theorem 30.95s 31.30s
% Output : Proof 31.05s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
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(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(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(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ),
file('theBenchmark.p',cc1_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(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(d3_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> cast_as_carrier_subset(A) = the_carrier(A) ),
file('theBenchmark.p',d3_pre_topc) ).
fof(d4_tarski,axiom,
! [A,B] :
( B = union(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] :
( in(D,A)
& in(C,D) ) ) ),
file('theBenchmark.p',d4_tarski) ).
fof(d8_pre_topc,axiom,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ( is_a_cover_of_carrier(A,B)
<=> cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B) ) ) ),
file('theBenchmark.p',d8_pre_topc) ).
fof(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
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_k3_tarski,axiom,
$true,
file('theBenchmark.p',dt_k3_tarski) ).
fof(dt_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(union_of_subsets(A,B),powerset(A)) ),
file('theBenchmark.p',dt_k5_setfam_1) ).
fof(dt_l1_struct_0,axiom,
$true,
file('theBenchmark.p',dt_l1_struct_0) ).
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(existence_l1_struct_0,axiom,
? [A] : one_sorted_str(A),
file('theBenchmark.p',existence_l1_struct_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(the_carrier(A)) ),
file('theBenchmark.p',fc1_struct_0) ).
fof(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(fc2_pre_topc,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ~ empty(cast_as_carrier_subset(A)) ),
file('theBenchmark.p',fc2_pre_topc) ).
fof(fc6_membered,axiom,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc6_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(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(rc3_struct_0,axiom,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
file('theBenchmark.p',rc3_struct_0) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) ) ),
file('theBenchmark.p',rc5_struct_0) ).
fof(redefinition_k5_setfam_1,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> union_of_subsets(A,B) = union(B) ),
file('theBenchmark.p',redefinition_k5_setfam_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('theBenchmark.p',t5_subset) ).
fof(t5_tops_2,conjecture,
! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
file('theBenchmark.p',t5_tops_2) ).
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,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_2_2,plain,
! [U_3] :
( ! [U_2] :
( v1_xcmplx_0(U_2)
| ~ element(U_2,U_3) )
| ~ v1_membered(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_2] :
( v1_xcmplx_0(U_2)
| ~ element(U_2,U_3)
| ~ v1_membered(U_3) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( v1_xcmplx_0(U_2)
| ~ element(U_2,U_3)
| ~ v1_membered(U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_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_3_2,plain,
! [U_5] :
( ! [U_4] :
( ( v1_xreal_0(U_4)
& v1_xcmplx_0(U_4) )
| ~ element(U_4,U_5) )
| ~ v2_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_4] :
( v1_xreal_0(U_4)
| ~ sP0(U_4) )
& ! [U_4] :
( v1_xcmplx_0(U_4)
| ~ sP0(U_4) )
& ! [U_5,U_4] :
( sP0(U_4)
| ~ element(U_4,U_5)
| ~ v2_membered(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_4)
| ~ element(U_4,U_5)
| ~ v2_membered(U_5) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( v1_xcmplx_0(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( v1_xreal_0(U_4)
| ~ sP0(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_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_4_2,plain,
! [U_7] :
( ! [U_6] :
( ( v1_rat_1(U_6)
& v1_xreal_0(U_6)
& v1_xcmplx_0(U_6) )
| ~ element(U_6,U_7) )
| ~ v3_membered(U_7) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_6] :
( v1_rat_1(U_6)
| ~ sP1(U_6) )
& ! [U_6] :
( v1_xreal_0(U_6)
| ~ sP1(U_6) )
& ! [U_6] :
( v1_xcmplx_0(U_6)
| ~ sP1(U_6) )
& ! [U_6,U_7] :
( sP1(U_6)
| ~ element(U_6,U_7)
| ~ v3_membered(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP1(U_6)
| ~ element(U_6,U_7)
| ~ v3_membered(U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( v1_xcmplx_0(U_6)
| ~ sP1(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( v1_xreal_0(U_6)
| ~ sP1(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( v1_rat_1(U_6)
| ~ sP1(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_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_5_2,plain,
! [U_9] :
( ! [U_8] :
( ( v1_rat_1(U_8)
& v1_int_1(U_8)
& v1_xreal_0(U_8)
& v1_xcmplx_0(U_8) )
| ~ element(U_8,U_9) )
| ~ v4_membered(U_9) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_8] :
( v1_rat_1(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( v1_int_1(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( v1_xreal_0(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( v1_xcmplx_0(U_8)
| ~ sP2(U_8) )
& ! [U_9,U_8] :
( sP2(U_8)
| ~ element(U_8,U_9)
| ~ v4_membered(U_9) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP2(U_8)
| ~ element(U_8,U_9)
| ~ v4_membered(U_9) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( v1_xcmplx_0(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( v1_xreal_0(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( v1_int_1(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_8,plain,
( v1_rat_1(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_11] :
( ! [U_10] :
( ( v1_rat_1(U_10)
& v1_int_1(U_10)
& v1_xreal_0(U_10)
& natural(U_10)
& v1_xcmplx_0(U_10) )
| ~ element(U_10,U_11) )
| ~ v5_membered(U_11) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_10] :
( v1_rat_1(U_10)
| ~ sP3(U_10) )
& ! [U_10] :
( v1_int_1(U_10)
| ~ sP3(U_10) )
& ! [U_10] :
( v1_xreal_0(U_10)
| ~ sP3(U_10) )
& ! [U_10] :
( natural(U_10)
| ~ sP3(U_10) )
& ! [U_10] :
( v1_xcmplx_0(U_10)
| ~ sP3(U_10) )
& ! [U_10,U_11] :
( sP3(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP3(U_10)
| ~ element(U_10,U_11)
| ~ v5_membered(U_11) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( v1_xcmplx_0(U_10)
| ~ sP3(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( natural(U_10)
| ~ sP3(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( v1_xreal_0(U_10)
| ~ sP3(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_8,plain,
( v1_int_1(U_10)
| ~ sP3(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_9,plain,
( v1_rat_1(U_10)
| ~ sP3(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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_7_2,plain,
! [U_12] :
( ( v5_membered(U_12)
& v4_membered(U_12)
& v3_membered(U_12)
& v2_membered(U_12)
& v1_membered(U_12) )
| ~ empty(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_12] :
( v5_membered(U_12)
| ~ sP4(U_12) )
& ! [U_12] :
( v4_membered(U_12)
| ~ sP4(U_12) )
& ! [U_12] :
( v3_membered(U_12)
| ~ sP4(U_12) )
& ! [U_12] :
( v2_membered(U_12)
| ~ sP4(U_12) )
& ! [U_12] :
( v1_membered(U_12)
| ~ sP4(U_12) )
& ! [U_12] :
( sP4(U_12)
| ~ empty(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP4(U_12)
| ~ empty(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( v1_membered(U_12)
| ~ sP4(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( v2_membered(U_12)
| ~ sP4(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( v3_membered(U_12)
| ~ sP4(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
( v4_membered(U_12)
| ~ sP4(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_9,plain,
( v5_membered(U_12)
| ~ sP4(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_8_2,plain,
! [U_14] :
( ! [U_13] :
( v1_membered(U_13)
| ~ element(U_13,powerset(U_14)) )
| ~ v1_membered(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_13,U_14] :
( v1_membered(U_13)
| ~ element(U_13,powerset(U_14))
| ~ v1_membered(U_14) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( v1_membered(U_13)
| ~ element(U_13,powerset(U_14))
| ~ v1_membered(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_16] :
( ! [U_15] :
( ( v2_membered(U_15)
& v1_membered(U_15) )
| ~ element(U_15,powerset(U_16)) )
| ~ v2_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_15] :
( v2_membered(U_15)
| ~ sP5(U_15) )
& ! [U_15] :
( v1_membered(U_15)
| ~ sP5(U_15) )
& ! [U_16,U_15] :
( sP5(U_15)
| ~ element(U_15,powerset(U_16))
| ~ v2_membered(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP5(U_15)
| ~ element(U_15,powerset(U_16))
| ~ v2_membered(U_16) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( v1_membered(U_15)
| ~ sP5(U_15) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( v2_membered(U_15)
| ~ sP5(U_15) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_18] :
( ! [U_17] :
( ( v3_membered(U_17)
& v2_membered(U_17)
& v1_membered(U_17) )
| ~ element(U_17,powerset(U_18)) )
| ~ v3_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_17] :
( v3_membered(U_17)
| ~ sP6(U_17) )
& ! [U_17] :
( v2_membered(U_17)
| ~ sP6(U_17) )
& ! [U_17] :
( v1_membered(U_17)
| ~ sP6(U_17) )
& ! [U_18,U_17] :
( sP6(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v3_membered(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP6(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v3_membered(U_18) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( v1_membered(U_17)
| ~ sP6(U_17) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( v2_membered(U_17)
| ~ sP6(U_17) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( v3_membered(U_17)
| ~ sP6(U_17) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_20] :
( ! [U_19] :
( ( v4_membered(U_19)
& v3_membered(U_19)
& v2_membered(U_19)
& v1_membered(U_19) )
| ~ element(U_19,powerset(U_20)) )
| ~ v4_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_19] :
( v4_membered(U_19)
| ~ sP7(U_19) )
& ! [U_19] :
( v3_membered(U_19)
| ~ sP7(U_19) )
& ! [U_19] :
( v2_membered(U_19)
| ~ sP7(U_19) )
& ! [U_19] :
( v1_membered(U_19)
| ~ sP7(U_19) )
& ! [U_19,U_20] :
( sP7(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v4_membered(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP7(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v4_membered(U_20) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( v1_membered(U_19)
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( v2_membered(U_19)
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( v3_membered(U_19)
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_8,plain,
( v4_membered(U_19)
| ~ sP7(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_12_2,plain,
! [U_21] :
( v4_membered(U_21)
| ~ v5_membered(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_21] :
( v4_membered(U_21)
| ~ v5_membered(U_21) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( v4_membered(U_21)
| ~ v5_membered(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_2,plain,
! [U_23] :
( ! [U_22] :
( ( v5_membered(U_22)
& v4_membered(U_22)
& v3_membered(U_22)
& v2_membered(U_22)
& v1_membered(U_22) )
| ~ element(U_22,powerset(U_23)) )
| ~ v5_membered(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_22] :
( v5_membered(U_22)
| ~ sP8(U_22) )
& ! [U_22] :
( v4_membered(U_22)
| ~ sP8(U_22) )
& ! [U_22] :
( v3_membered(U_22)
| ~ sP8(U_22) )
& ! [U_22] :
( v2_membered(U_22)
| ~ sP8(U_22) )
& ! [U_22] :
( v1_membered(U_22)
| ~ sP8(U_22) )
& ! [U_23,U_22] :
( sP8(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_13_2]) ).
cnf(f_13_4,plain,
( sP8(U_22)
| ~ element(U_22,powerset(U_23))
| ~ v5_membered(U_23) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_5,plain,
( v1_membered(U_22)
| ~ sP8(U_22) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_6,plain,
( v2_membered(U_22)
| ~ sP8(U_22) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_7,plain,
( v3_membered(U_22)
| ~ sP8(U_22) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_8,plain,
( v4_membered(U_22)
| ~ sP8(U_22) ),
inference(clausify,[status(thm)],[f_13_3]) ).
cnf(f_13_9,plain,
( v5_membered(U_22)
| ~ sP8(U_22) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_14_2,plain,
! [U_24] :
( v3_membered(U_24)
| ~ v4_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_24] :
( v3_membered(U_24)
| ~ v4_membered(U_24) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( v3_membered(U_24)
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_15_2,plain,
! [U_25] :
( v2_membered(U_25)
| ~ v3_membered(U_25) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_25] :
( v2_membered(U_25)
| ~ v3_membered(U_25) ),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
( v2_membered(U_25)
| ~ v3_membered(U_25) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_16_2,plain,
! [U_26] :
( v1_membered(U_26)
| ~ v2_membered(U_26) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_26] :
( v1_membered(U_26)
| ~ v2_membered(U_26) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( v1_membered(U_26)
| ~ v2_membered(U_26) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( cast_as_carrier_subset(A) = the_carrier(A)
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d3_pre_topc]) ).
fof(f_17_2,plain,
! [U_27] :
( cast_as_carrier_subset(U_27) = the_carrier(U_27)
| ~ one_sorted_str(U_27) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_27] :
( cast_as_carrier_subset(U_27) = the_carrier(U_27)
| ~ one_sorted_str(U_27) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( cast_as_carrier_subset(U_27) = the_carrier(U_27)
| ~ one_sorted_str(U_27) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A,B] :
( ( B = union(A)
| ? [C] :
( ( ~ in(C,B)
& ? [D] :
( in(D,A)
& in(C,D) ) )
| ( ! [D] :
( ~ in(D,A)
| ~ in(C,D) )
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| ! [D] :
( ~ in(D,A)
| ~ in(C,D) ) )
& ( ? [D] :
( in(D,A)
& in(C,D) )
| ~ in(C,B) ) )
| B != union(A) ) ),
inference(fof_nnf,[status(thm)],[d4_tarski]) ).
fof(f_18_2,plain,
! [U_35,U_34] :
( ( U_34 = union(U_35)
| ? [U_33] :
( ( ~ in(U_33,U_34)
& ? [U_32] :
( in(U_32,U_35)
& in(U_33,U_32) ) )
| ( ! [U_31] :
( ~ in(U_31,U_35)
| ~ in(U_33,U_31) )
& in(U_33,U_34) ) ) )
& ( ! [U_30] :
( ( in(U_30,U_34)
| ! [U_29] :
( ~ in(U_29,U_35)
| ~ in(U_30,U_29) ) )
& ( ? [U_28] :
( in(U_28,U_35)
& in(U_30,U_28) )
| ~ in(U_30,U_34) ) )
| U_34 != union(U_35) ) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(U_39,U_32) ) )
| ? [U_38] :
( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(U_38,U_31) )
& in(U_38,U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ? [U_28] :
( in(U_28,U_42)
& in(U_36,U_28) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(miniscope,[status(thm)],[f_18_2]) ).
fof(f_18_4,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(U_39,U_32) ) )
| ? [U_38] :
( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(U_38,U_31) )
& in(U_38,U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK1(U_42,U_40,U_36),U_42)
& in(U_36,sK1(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_28,sK1(U_42,U_40,U_36))],[f_18_3]) ).
fof(f_18_5,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ? [U_39] :
( ~ in(U_39,U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(U_39,U_32) ) )
| ( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(sK2(U_43,U_41),U_31) )
& in(sK2(U_43,U_41),U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK1(U_42,U_40,U_36),U_42)
& in(U_36,sK1(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_38,sK2(U_43,U_41))],[f_18_4]) ).
fof(f_18_6,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ( ~ in(sK3(U_43,U_41),U_41)
& ? [U_32] :
( in(U_32,U_43)
& in(sK3(U_43,U_41),U_32) ) )
| ( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(sK2(U_43,U_41),U_31) )
& in(sK2(U_43,U_41),U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK1(U_42,U_40,U_36),U_42)
& in(U_36,sK1(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_39,sK3(U_43,U_41))],[f_18_5]) ).
fof(f_18_7,plain,
( ! [U_43,U_41] :
( U_41 = union(U_43)
| ( ~ in(sK3(U_43,U_41),U_41)
& in(sK4(U_43,U_41),U_43)
& in(sK3(U_43,U_41),sK4(U_43,U_41)) )
| ( ! [U_31] :
( ~ in(U_31,U_43)
| ~ in(sK2(U_43,U_41),U_31) )
& in(sK2(U_43,U_41),U_41) ) )
& ! [U_42,U_40] :
( ( ! [U_37] :
( in(U_37,U_40)
| ! [U_29] :
( ~ in(U_29,U_42)
| ~ in(U_37,U_29) ) )
& ! [U_36] :
( ( in(sK1(U_42,U_40,U_36),U_42)
& in(U_36,sK1(U_42,U_40,U_36)) )
| ~ in(U_36,U_40) ) )
| U_40 != union(U_42) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_32,sK4(U_43,U_41))],[f_18_6]) ).
fof(f_18_8,plain,
( ! [U_41,U_43] :
( ~ in(sK3(U_43,U_41),U_41)
| ~ sP12(U_41,U_43) )
& ! [U_41,U_43] :
( in(sK4(U_43,U_41),U_43)
| ~ sP12(U_41,U_43) )
& ! [U_41,U_43] :
( in(sK3(U_43,U_41),sK4(U_43,U_41))
| ~ sP12(U_41,U_43) )
& ! [U_41,U_43,U_31] :
( ~ in(U_31,U_43)
| ~ in(sK2(U_43,U_41),U_31)
| ~ sP11(U_41,U_43,U_31) )
& ! [U_41,U_43,U_31] :
( in(sK2(U_43,U_41),U_41)
| ~ sP11(U_41,U_43,U_31) )
& ! [U_36,U_40,U_42] :
( in(sK1(U_42,U_40,U_36),U_42)
| ~ sP9(U_36,U_40,U_42) )
& ! [U_36,U_40,U_42] :
( in(U_36,sK1(U_42,U_40,U_36))
| ~ sP9(U_36,U_40,U_42) )
& ! [U_29,U_36,U_37,U_40,U_42] :
( in(U_37,U_40)
| ~ in(U_29,U_42)
| ~ in(U_37,U_29)
| ~ sP10(U_29,U_36,U_37,U_40,U_42) )
& ! [U_29,U_36,U_37,U_40,U_42] :
( sP9(U_36,U_40,U_42)
| ~ in(U_36,U_40)
| ~ sP10(U_29,U_36,U_37,U_40,U_42) )
& ! [U_41,U_43,U_31] :
( U_41 = union(U_43)
| sP12(U_41,U_43)
| sP11(U_41,U_43,U_31) )
& ! [U_29,U_36,U_37,U_40,U_42] :
( sP10(U_29,U_36,U_37,U_40,U_42)
| U_40 != union(U_42) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10,sP11,sP12])],[f_18_7]) ).
cnf(f_18_9,plain,
( sP10(U_29,U_36,U_37,U_40,U_42)
| U_40 != union(U_42) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_10,plain,
( U_41 = union(U_43)
| sP12(U_41,U_43)
| sP11(U_41,U_43,U_31) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_11,plain,
( sP9(U_36,U_40,U_42)
| ~ in(U_36,U_40)
| ~ sP10(U_29,U_36,U_37,U_40,U_42) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_12,plain,
( in(U_37,U_40)
| ~ in(U_29,U_42)
| ~ in(U_37,U_29)
| ~ sP10(U_29,U_36,U_37,U_40,U_42) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_13,plain,
( in(U_36,sK1(U_42,U_40,U_36))
| ~ sP9(U_36,U_40,U_42) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_14,plain,
( in(sK1(U_42,U_40,U_36),U_42)
| ~ sP9(U_36,U_40,U_42) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_15,plain,
( in(sK2(U_43,U_41),U_41)
| ~ sP11(U_41,U_43,U_31) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_16,plain,
( ~ in(U_31,U_43)
| ~ in(sK2(U_43,U_41),U_31)
| ~ sP11(U_41,U_43,U_31) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_17,plain,
( in(sK3(U_43,U_41),sK4(U_43,U_41))
| ~ sP12(U_41,U_43) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_18,plain,
( in(sK4(U_43,U_41),U_43)
| ~ sP12(U_41,U_43) ),
inference(clausify,[status(thm)],[f_18_8]) ).
cnf(f_18_19,plain,
( ~ in(sK3(U_43,U_41),U_41)
| ~ sP12(U_41,U_43) ),
inference(clausify,[status(thm)],[f_18_8]) ).
fof(f_19_1,plain,
! [A] :
( ! [B] :
( ( ( is_a_cover_of_carrier(A,B)
| cast_as_carrier_subset(A) != union_of_subsets(the_carrier(A),B) )
& ( cast_as_carrier_subset(A) = union_of_subsets(the_carrier(A),B)
| ~ is_a_cover_of_carrier(A,B) ) )
| ~ element(B,powerset(powerset(the_carrier(A)))) )
| ~ one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[d8_pre_topc]) ).
fof(f_19_2,plain,
! [U_45] :
( ! [U_44] :
( ( ( is_a_cover_of_carrier(U_45,U_44)
| cast_as_carrier_subset(U_45) != union_of_subsets(the_carrier(U_45),U_44) )
& ( cast_as_carrier_subset(U_45) = union_of_subsets(the_carrier(U_45),U_44)
| ~ is_a_cover_of_carrier(U_45,U_44) ) )
| ~ element(U_44,powerset(powerset(the_carrier(U_45)))) )
| ~ one_sorted_str(U_45) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( ! [U_45,U_44] :
( is_a_cover_of_carrier(U_45,U_44)
| cast_as_carrier_subset(U_45) != union_of_subsets(the_carrier(U_45),U_44)
| ~ sP13(U_45,U_44) )
& ! [U_45,U_44] :
( cast_as_carrier_subset(U_45) = union_of_subsets(the_carrier(U_45),U_44)
| ~ is_a_cover_of_carrier(U_45,U_44)
| ~ sP13(U_45,U_44) )
& ! [U_45,U_44] :
( sP13(U_45,U_44)
| ~ element(U_44,powerset(powerset(the_carrier(U_45))))
| ~ one_sorted_str(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_19_2]) ).
cnf(f_19_4,plain,
( sP13(U_45,U_44)
| ~ element(U_44,powerset(powerset(the_carrier(U_45))))
| ~ one_sorted_str(U_45) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_5,plain,
( cast_as_carrier_subset(U_45) = union_of_subsets(the_carrier(U_45),U_44)
| ~ is_a_cover_of_carrier(U_45,U_44)
| ~ sP13(U_45,U_44) ),
inference(clausify,[status(thm)],[f_19_3]) ).
cnf(f_19_6,plain,
( is_a_cover_of_carrier(U_45,U_44)
| cast_as_carrier_subset(U_45) != union_of_subsets(the_carrier(U_45),U_44)
| ~ sP13(U_45,U_44) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_20_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
$true,
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_21_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
$true,
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_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_22_2,plain,
! [U_46] :
( element(cast_as_carrier_subset(U_46),powerset(the_carrier(U_46)))
| ~ one_sorted_str(U_46) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_46] :
( element(cast_as_carrier_subset(U_46),powerset(the_carrier(U_46)))
| ~ one_sorted_str(U_46) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( element(cast_as_carrier_subset(U_46),powerset(the_carrier(U_46)))
| ~ one_sorted_str(U_46) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_tarski]) ).
fof(f_23_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
$true,
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [A,B] :
( element(union_of_subsets(A,B),powerset(A))
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[dt_k5_setfam_1]) ).
fof(f_24_2,plain,
! [U_48,U_47] :
( element(union_of_subsets(U_48,U_47),powerset(U_48))
| ~ element(U_47,powerset(powerset(U_48))) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_47,U_48] :
( element(union_of_subsets(U_48,U_47),powerset(U_48))
| ~ element(U_47,powerset(powerset(U_48))) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( element(union_of_subsets(U_48,U_47),powerset(U_48))
| ~ element(U_47,powerset(powerset(U_48))) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_25_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_25_1]) ).
cnf(f_25_3,plain,
$true,
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_26_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_26_1]) ).
cnf(f_26_3,plain,
$true,
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_27_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_27_1]) ).
cnf(f_27_3,plain,
$true,
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_28_2,plain,
? [U_49] : one_sorted_str(U_49),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
one_sorted_str(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_49,sK5)],[f_28_2]) ).
fof(f_28_4,plain,
one_sorted_str(sK5),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
one_sorted_str(sK5),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_29_2,plain,
! [U_51] :
? [U_50] : element(U_50,U_51),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_51] : element(sK6(U_51),U_51),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_50,sK6(U_51))],[f_29_2]) ).
fof(f_29_4,plain,
! [U_51] : element(sK6(U_51),U_51),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
element(sK6(U_51),U_51),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A] :
( ~ empty(the_carrier(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc1_struct_0]) ).
fof(f_30_2,plain,
! [U_52] :
( ~ empty(the_carrier(U_52))
| ~ one_sorted_str(U_52)
| empty_carrier(U_52) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_52] :
( ~ empty(the_carrier(U_52))
| ~ one_sorted_str(U_52)
| empty_carrier(U_52) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( ~ empty(the_carrier(U_52))
| ~ one_sorted_str(U_52)
| empty_carrier(U_52) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_31_2,plain,
! [U_53] : ~ empty(powerset(U_53)),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_53] : ~ empty(powerset(U_53)),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
~ empty(powerset(U_53)),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A] :
( ~ empty(cast_as_carrier_subset(A))
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[fc2_pre_topc]) ).
fof(f_32_2,plain,
! [U_54] :
( ~ empty(cast_as_carrier_subset(U_54))
| ~ one_sorted_str(U_54)
| empty_carrier(U_54) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_54] :
( ~ empty(cast_as_carrier_subset(U_54))
| ~ one_sorted_str(U_54)
| empty_carrier(U_54) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ empty(cast_as_carrier_subset(U_54))
| ~ one_sorted_str(U_54)
| empty_carrier(U_54) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc6_membered]) ).
fof(f_33_2,plain,
( v5_membered(empty_set)
& v4_membered(empty_set)
& v3_membered(empty_set)
& v2_membered(empty_set)
& v1_membered(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_33_1]) ).
cnf(f_33_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
v1_membered(empty_set),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_5,plain,
v2_membered(empty_set),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_6,plain,
v3_membered(empty_set),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_7,plain,
v4_membered(empty_set),
inference(clausify,[status(thm)],[f_33_2]) ).
cnf(f_33_8,plain,
v5_membered(empty_set),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_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_34_2,plain,
? [U_55] :
( v5_membered(U_55)
& v4_membered(U_55)
& v3_membered(U_55)
& v2_membered(U_55)
& v1_membered(U_55)
& ~ empty(U_55) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( v5_membered(sK7)
& v4_membered(sK7)
& v3_membered(sK7)
& v2_membered(sK7)
& v1_membered(sK7)
& ~ empty(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_55,sK7)],[f_34_2]) ).
fof(f_34_4,plain,
( v5_membered(sK7)
& v4_membered(sK7)
& v3_membered(sK7)
& v2_membered(sK7)
& v1_membered(sK7)
& ~ empty(sK7) ),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
~ empty(sK7),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
v1_membered(sK7),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
v2_membered(sK7),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_8,plain,
v3_membered(sK7),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_9,plain,
v4_membered(sK7),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_10,plain,
v5_membered(sK7),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_35_2,plain,
! [U_57] :
( ? [U_56] :
( ~ empty(U_56)
& element(U_56,powerset(U_57)) )
| empty(U_57) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_57] :
( ( ~ empty(sK8(U_57))
& element(sK8(U_57),powerset(U_57)) )
| empty(U_57) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_56,sK8(U_57))],[f_35_2]) ).
fof(f_35_4,plain,
( ! [U_57] :
( ~ empty(sK8(U_57))
| ~ sP14(U_57) )
& ! [U_57] :
( element(sK8(U_57),powerset(U_57))
| ~ sP14(U_57) )
& ! [U_57] :
( sP14(U_57)
| empty(U_57) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_35_3]) ).
cnf(f_35_5,plain,
( sP14(U_57)
| empty(U_57) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
( element(sK8(U_57),powerset(U_57))
| ~ sP14(U_57) ),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
( ~ empty(sK8(U_57))
| ~ sP14(U_57) ),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_36_2,plain,
! [U_59] :
? [U_58] :
( empty(U_58)
& element(U_58,powerset(U_59)) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_59] :
( empty(sK9(U_59))
& element(sK9(U_59),powerset(U_59)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_58,sK9(U_59))],[f_36_2]) ).
fof(f_36_4,plain,
( ! [U_59] : empty(sK9(U_59))
& ! [U_59] : element(sK9(U_59),powerset(U_59)) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
element(sK9(U_59),powerset(U_59)),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
empty(sK9(U_59)),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
? [A] :
( ~ empty_carrier(A)
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[rc3_struct_0]) ).
fof(f_37_2,plain,
? [U_60] :
( ~ empty_carrier(U_60)
& one_sorted_str(U_60) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ~ empty_carrier(sK10)
& one_sorted_str(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_60,sK10)],[f_37_2]) ).
fof(f_37_4,plain,
( ~ empty_carrier(sK10)
& one_sorted_str(sK10) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
one_sorted_str(sK10),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
~ empty_carrier(sK10),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(the_carrier(A))) )
| ~ one_sorted_str(A)
| empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[rc5_struct_0]) ).
fof(f_38_2,plain,
! [U_62] :
( ? [U_61] :
( ~ empty(U_61)
& element(U_61,powerset(the_carrier(U_62))) )
| ~ one_sorted_str(U_62)
| empty_carrier(U_62) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_62] :
( ( ~ empty(sK11(U_62))
& element(sK11(U_62),powerset(the_carrier(U_62))) )
| ~ one_sorted_str(U_62)
| empty_carrier(U_62) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_61,sK11(U_62))],[f_38_2]) ).
fof(f_38_4,plain,
( ! [U_62] :
( ~ empty(sK11(U_62))
| ~ sP15(U_62) )
& ! [U_62] :
( element(sK11(U_62),powerset(the_carrier(U_62)))
| ~ sP15(U_62) )
& ! [U_62] :
( sP15(U_62)
| ~ one_sorted_str(U_62)
| empty_carrier(U_62) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_38_3]) ).
cnf(f_38_5,plain,
( sP15(U_62)
| ~ one_sorted_str(U_62)
| empty_carrier(U_62) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
( element(sK11(U_62),powerset(the_carrier(U_62)))
| ~ sP15(U_62) ),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
( ~ empty(sK11(U_62))
| ~ sP15(U_62) ),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
! [A,B] :
( union_of_subsets(A,B) = union(B)
| ~ element(B,powerset(powerset(A))) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_setfam_1]) ).
fof(f_39_2,plain,
! [U_64,U_63] :
( union_of_subsets(U_64,U_63) = union(U_63)
| ~ element(U_63,powerset(powerset(U_64))) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_63,U_64] :
( union_of_subsets(U_64,U_63) = union(U_63)
| ~ element(U_63,powerset(powerset(U_64))) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( union_of_subsets(U_64,U_63) = union(U_63)
| ~ element(U_63,powerset(powerset(U_64))) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_40_2,plain,
! [U_66,U_65] : subset(U_66,U_66),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_66] : subset(U_66,U_66),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
! [U_66] : subset(U_66,U_66),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
subset(U_66,U_66),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_41_2,plain,
! [U_68,U_67] :
( element(U_68,U_67)
| ~ in(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_68,U_67] :
( element(U_68,U_67)
| ~ in(U_68,U_67) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( element(U_68,U_67)
| ~ in(U_68,U_67) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_42_2,plain,
! [U_70,U_69] :
( in(U_70,U_69)
| empty(U_69)
| ~ element(U_70,U_69) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_70,U_69] :
( in(U_70,U_69)
| empty(U_69)
| ~ element(U_70,U_69) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( in(U_70,U_69)
| empty(U_69)
| ~ element(U_70,U_69) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A,B] :
( ( element(A,powerset(B))
| ~ subset(A,B) )
& ( subset(A,B)
| ~ element(A,powerset(B)) ) ),
inference(fof_nnf,[status(thm)],[t3_subset]) ).
fof(f_43_2,plain,
! [U_72,U_71] :
( ( element(U_72,powerset(U_71))
| ~ subset(U_72,U_71) )
& ( subset(U_72,U_71)
| ~ element(U_72,powerset(U_71)) ) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_76,U_74] :
( element(U_76,powerset(U_74))
| ~ subset(U_76,U_74) )
& ! [U_75,U_73] :
( subset(U_75,U_73)
| ~ element(U_75,powerset(U_73)) ) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
( ! [U_76,U_74] :
( element(U_76,powerset(U_74))
| ~ subset(U_76,U_74) )
& ! [U_75,U_73] :
( subset(U_75,U_73)
| ~ element(U_75,powerset(U_73)) ) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
( subset(U_75,U_73)
| ~ element(U_75,powerset(U_73)) ),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
( element(U_76,powerset(U_74))
| ~ subset(U_76,U_74) ),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_44_2,plain,
! [U_79,U_78,U_77] :
( element(U_79,U_77)
| ~ element(U_78,powerset(U_77))
| ~ in(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_78,U_77,U_79] :
( element(U_79,U_77)
| ~ element(U_78,powerset(U_77))
| ~ in(U_79,U_78) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( element(U_79,U_77)
| ~ element(U_78,powerset(U_77))
| ~ in(U_79,U_78) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_45_2,plain,
! [U_82,U_81,U_80] :
( ~ empty(U_80)
| ~ element(U_81,powerset(U_80))
| ~ in(U_82,U_81) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_82,U_81] :
( ! [U_80] :
( ~ empty(U_80)
| ~ element(U_81,powerset(U_80)) )
| ~ in(U_82,U_81) ),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_80,U_82,U_81] :
( ~ empty(U_80)
| ~ element(U_81,powerset(U_80))
| ~ in(U_82,U_81) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
( ~ empty(U_80)
| ~ element(U_81,powerset(U_80))
| ~ in(U_82,U_81) ),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,negated_conjecture,
~ ! [A] :
( ( one_sorted_str(A)
& ~ empty_carrier(A) )
=> ! [B] :
( element(B,powerset(powerset(the_carrier(A))))
=> ~ ( B = empty_set
& is_a_cover_of_carrier(A,B) ) ) ),
inference(negate,[status(cth)],[t5_tops_2]) ).
fof(f_46_2,negated_conjecture,
? [A] :
( ? [B] :
( B = empty_set
& is_a_cover_of_carrier(A,B)
& element(B,powerset(powerset(the_carrier(A)))) )
& one_sorted_str(A)
& ~ empty_carrier(A) ),
inference(fof_nnf,[status(thm)],[f_46_1]) ).
fof(f_46_3,negated_conjecture,
? [U_84] :
( ? [U_83] :
( U_83 = empty_set
& is_a_cover_of_carrier(U_84,U_83)
& element(U_83,powerset(powerset(the_carrier(U_84)))) )
& one_sorted_str(U_84)
& ~ empty_carrier(U_84) ),
inference(variable_rename,[status(thm)],[f_46_2]) ).
fof(f_46_4,negated_conjecture,
( ? [U_83] :
( U_83 = empty_set
& is_a_cover_of_carrier(sK12,U_83)
& element(U_83,powerset(powerset(the_carrier(sK12)))) )
& one_sorted_str(sK12)
& ~ empty_carrier(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_84,sK12)],[f_46_3]) ).
fof(f_46_5,negated_conjecture,
( sK13 = empty_set
& is_a_cover_of_carrier(sK12,sK13)
& element(sK13,powerset(powerset(the_carrier(sK12))))
& one_sorted_str(sK12)
& ~ empty_carrier(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_83,sK13)],[f_46_4]) ).
fof(f_46_6,negated_conjecture,
( sK13 = empty_set
& is_a_cover_of_carrier(sK12,sK13)
& element(sK13,powerset(powerset(the_carrier(sK12))))
& one_sorted_str(sK12)
& ~ empty_carrier(sK12) ),
inference(definitional_conversion,[status(esa)],[f_46_5]) ).
cnf(f_46_7,negated_conjecture,
~ empty_carrier(sK12),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_8,negated_conjecture,
one_sorted_str(sK12),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_9,negated_conjecture,
element(sK13,powerset(powerset(the_carrier(sK12)))),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_10,negated_conjecture,
is_a_cover_of_carrier(sK12,sK13),
inference(clausify,[status(thm)],[f_46_6]) ).
cnf(f_46_11,negated_conjecture,
sK13 = empty_set,
inference(clausify,[status(thm)],[f_46_6]) ).
fof(f_47_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_47_2,plain,
! [U_85] :
( U_85 = empty_set
| ~ empty(U_85) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_85] :
( U_85 = empty_set
| ~ empty(U_85) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( U_85 = empty_set
| ~ empty(U_85) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_48_2,plain,
! [U_87,U_86] :
( ~ empty(U_86)
| ~ in(U_87,U_86) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_87,U_86] :
( ~ empty(U_86)
| ~ in(U_87,U_86) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( ~ empty(U_86)
| ~ in(U_87,U_86) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_49_2,plain,
! [U_89,U_88] :
( ~ empty(U_88)
| U_89 = U_88
| ~ empty(U_89) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_89] :
( ! [U_88] :
( ~ empty(U_88)
| U_89 = U_88 )
| ~ empty(U_89) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_88,U_89] :
( ~ empty(U_88)
| U_89 = U_88
| ~ empty(U_89) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( ~ empty(U_88)
| U_89 = U_88
| ~ empty(U_89) ),
inference(clausify,[status(thm)],[f_49_4]) ).
cnf(f_20_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_3]) ).
cnf(f_21_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_3]) ).
cnf(f_23_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_3]) ).
cnf(f_25_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_3]) ).
cnf(f_26_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_26_3]) ).
cnf(f_27_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_27_3]) ).
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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,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_6,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( union(Eq_x_0) = union(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( union_of_subsets(Eq_x_0,Eq_x_1) = union_of_subsets(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK1(Eq_x_0,Eq_x_1,Eq_x_2) = sK1(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_10,axiom,
( sK2(Eq_x_0,Eq_x_1) = sK2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(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,
( sK4(Eq_x_0,Eq_x_1) = sK4(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,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_14,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,axiom,
( sK9(Eq_x_0) = sK9(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( sK11(Eq_x_0) = sK11(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_17,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_18,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,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_20,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_21,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_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,
( v1_rat_1(Eq_y_0)
| ~ v1_rat_1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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_27,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( one_sorted_str(Eq_y_0)
| ~ one_sorted_str(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( is_a_cover_of_carrier(Eq_y_0,Eq_y_1)
| ~ is_a_cover_of_carrier(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( empty_carrier(Eq_y_0)
| ~ empty_carrier(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,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_34,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_42,axiom,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_45,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_46,axiom,
( sP12(Eq_y_0,Eq_y_1)
| ~ sP12(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_47,axiom,
( sP13(Eq_y_0,Eq_y_1)
| ~ sP13(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_48,axiom,
( sP14(Eq_y_0)
| ~ sP14(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_49,axiom,
( sP15(Eq_y_0)
| ~ sP15(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
% 0.00/0.02 % Problem : SEU325+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
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 23:55:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 30.95/31.30 % SZS status Theorem for theBenchmark
% 30.95/31.30 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------