%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU307+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 : n010.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 35.35s 35.67s
% Output : Proof 35.45s
% 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(dt_k1_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k1_xboole_0) ).
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(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(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(fc27_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_intersection2(A,B)) ),
file('theBenchmark.p',fc27_membered) ).
fof(fc28_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(set_intersection2(B,A)) ),
file('theBenchmark.p',fc28_membered) ).
fof(fc29_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc29_membered) ).
fof(fc30_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc30_membered) ).
fof(fc31_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc31_membered) ).
fof(fc32_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc32_membered) ).
fof(fc33_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc33_membered) ).
fof(fc34_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc34_membered) ).
fof(fc35_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_intersection2(A,B))
& v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) ) ),
file('theBenchmark.p',fc35_membered) ).
fof(fc36_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v5_membered(set_intersection2(B,A))
& v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) ) ),
file('theBenchmark.p',fc36_membered) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
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(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(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
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(commutativity_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('theBenchmark.p',commutativity_k3_xboole_0) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('theBenchmark.p',idempotence_k3_xboole_0) ).
fof(commutativity_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = subset_intersection2(A,C,B) ),
file('theBenchmark.p',commutativity_k5_subset_1) ).
fof(idempotence_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,B) = B ),
file('theBenchmark.p',idempotence_k5_subset_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
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(redefinition_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> subset_intersection2(A,B,C) = set_intersection2(B,C) ),
file('theBenchmark.p',redefinition_k5_subset_1) ).
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_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k3_xboole_0) ).
fof(dt_k5_subset_1,axiom,
! [A,B,C] :
( ( element(C,powerset(A))
& element(B,powerset(A)) )
=> element(subset_intersection2(A,B,C),powerset(A)) ),
file('theBenchmark.p',dt_k5_subset_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(fc1_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
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(t15_pre_topc,conjecture,
! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
file('theBenchmark.p',t15_pre_topc) ).
fof(t28_xboole_1,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('theBenchmark.p',t28_xboole_1) ).
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,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_2_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
$true,
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( v4_membered(A)
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[cc1_membered]) ).
fof(f_3_2,plain,
! [U_2] :
( v4_membered(U_2)
| ~ v5_membered(U_2) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_2] :
( v4_membered(U_2)
| ~ v5_membered(U_2) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( v4_membered(U_2)
| ~ v5_membered(U_2) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( v3_membered(A)
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[cc2_membered]) ).
fof(f_4_2,plain,
! [U_3] :
( v3_membered(U_3)
| ~ v4_membered(U_3) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_3] :
( v3_membered(U_3)
| ~ v4_membered(U_3) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( v3_membered(U_3)
| ~ v4_membered(U_3) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( v2_membered(A)
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[cc3_membered]) ).
fof(f_5_2,plain,
! [U_4] :
( v2_membered(U_4)
| ~ v3_membered(U_4) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_4] :
( v2_membered(U_4)
| ~ v3_membered(U_4) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( v2_membered(U_4)
| ~ v3_membered(U_4) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( v1_membered(A)
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[cc4_membered]) ).
fof(f_6_2,plain,
! [U_5] :
( v1_membered(U_5)
| ~ v2_membered(U_5) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_5] :
( v1_membered(U_5)
| ~ v2_membered(U_5) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( v1_membered(U_5)
| ~ v2_membered(U_5) ),
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)],[rc1_membered]) ).
fof(f_7_2,plain,
? [U_6] :
( v5_membered(U_6)
& v4_membered(U_6)
& v3_membered(U_6)
& v2_membered(U_6)
& v1_membered(U_6)
& ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( v5_membered(sK1)
& v4_membered(sK1)
& v3_membered(sK1)
& v2_membered(sK1)
& v1_membered(sK1)
& ~ empty(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_6,sK1)],[f_7_2]) ).
fof(f_7_4,plain,
( v5_membered(sK1)
& v4_membered(sK1)
& v3_membered(sK1)
& v2_membered(sK1)
& v1_membered(sK1)
& ~ empty(sK1) ),
inference(definitional_conversion,[status(esa)],[f_7_3]) ).
cnf(f_7_5,plain,
~ empty(sK1),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_6,plain,
v1_membered(sK1),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_7,plain,
v2_membered(sK1),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_8,plain,
v3_membered(sK1),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_9,plain,
v4_membered(sK1),
inference(clausify,[status(thm)],[f_7_4]) ).
cnf(f_7_10,plain,
v5_membered(sK1),
inference(clausify,[status(thm)],[f_7_4]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( v1_xcmplx_0(B)
| ~ element(B,A) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc10_membered]) ).
fof(f_8_2,plain,
! [U_8] :
( ! [U_7] :
( v1_xcmplx_0(U_7)
| ~ element(U_7,U_8) )
| ~ v1_membered(U_8) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_7,U_8] :
( v1_xcmplx_0(U_7)
| ~ element(U_7,U_8)
| ~ v1_membered(U_8) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( v1_xcmplx_0(U_7)
| ~ element(U_7,U_8)
| ~ v1_membered(U_8) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_10] :
( ! [U_9] :
( ( v1_xreal_0(U_9)
& v1_xcmplx_0(U_9) )
| ~ element(U_9,U_10) )
| ~ v2_membered(U_10) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_9] :
( v1_xreal_0(U_9)
| ~ sP0(U_9) )
& ! [U_9] :
( v1_xcmplx_0(U_9)
| ~ sP0(U_9) )
& ! [U_10,U_9] :
( sP0(U_9)
| ~ element(U_9,U_10)
| ~ v2_membered(U_10) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP0(U_9)
| ~ element(U_9,U_10)
| ~ v2_membered(U_10) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( v1_xcmplx_0(U_9)
| ~ sP0(U_9) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( v1_xreal_0(U_9)
| ~ sP0(U_9) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_12] :
( ! [U_11] :
( ( v1_rat_1(U_11)
& v1_xreal_0(U_11)
& v1_xcmplx_0(U_11) )
| ~ element(U_11,U_12) )
| ~ v3_membered(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_11] :
( v1_rat_1(U_11)
| ~ sP1(U_11) )
& ! [U_11] :
( v1_xreal_0(U_11)
| ~ sP1(U_11) )
& ! [U_11] :
( v1_xcmplx_0(U_11)
| ~ sP1(U_11) )
& ! [U_12,U_11] :
( sP1(U_11)
| ~ element(U_11,U_12)
| ~ v3_membered(U_12) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_10_2]) ).
cnf(f_10_4,plain,
( sP1(U_11)
| ~ element(U_11,U_12)
| ~ v3_membered(U_12) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( v1_xcmplx_0(U_11)
| ~ sP1(U_11) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( v1_xreal_0(U_11)
| ~ sP1(U_11) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( v1_rat_1(U_11)
| ~ sP1(U_11) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_14] :
( ! [U_13] :
( ( v1_rat_1(U_13)
& v1_int_1(U_13)
& v1_xreal_0(U_13)
& v1_xcmplx_0(U_13) )
| ~ element(U_13,U_14) )
| ~ v4_membered(U_14) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_13] :
( v1_rat_1(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( v1_int_1(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( v1_xreal_0(U_13)
| ~ sP2(U_13) )
& ! [U_13] :
( v1_xcmplx_0(U_13)
| ~ sP2(U_13) )
& ! [U_14,U_13] :
( sP2(U_13)
| ~ element(U_13,U_14)
| ~ v4_membered(U_14) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP2(U_13)
| ~ element(U_13,U_14)
| ~ v4_membered(U_14) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( v1_xcmplx_0(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( v1_xreal_0(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( v1_int_1(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_8,plain,
( v1_rat_1(U_13)
| ~ sP2(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_16] :
( ! [U_15] :
( ( v1_rat_1(U_15)
& v1_int_1(U_15)
& v1_xreal_0(U_15)
& natural(U_15)
& v1_xcmplx_0(U_15) )
| ~ element(U_15,U_16) )
| ~ v5_membered(U_16) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_15] :
( v1_rat_1(U_15)
| ~ sP3(U_15) )
& ! [U_15] :
( v1_int_1(U_15)
| ~ sP3(U_15) )
& ! [U_15] :
( v1_xreal_0(U_15)
| ~ sP3(U_15) )
& ! [U_15] :
( natural(U_15)
| ~ sP3(U_15) )
& ! [U_15] :
( v1_xcmplx_0(U_15)
| ~ sP3(U_15) )
& ! [U_16,U_15] :
( sP3(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP3(U_15)
| ~ element(U_15,U_16)
| ~ v5_membered(U_16) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( v1_xcmplx_0(U_15)
| ~ sP3(U_15) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( natural(U_15)
| ~ sP3(U_15) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
( v1_xreal_0(U_15)
| ~ sP3(U_15) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_8,plain,
( v1_int_1(U_15)
| ~ sP3(U_15) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_9,plain,
( v1_rat_1(U_15)
| ~ sP3(U_15) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_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_13_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_13_1]) ).
cnf(f_13_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
v1_membered(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_5,plain,
v2_membered(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_6,plain,
v3_membered(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_7,plain,
v4_membered(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
cnf(f_13_8,plain,
v5_membered(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( v1_membered(B)
| ~ element(B,powerset(A)) )
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[cc16_membered]) ).
fof(f_14_2,plain,
! [U_18] :
( ! [U_17] :
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18)) )
| ~ v1_membered(U_18) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_18,U_17] :
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v1_membered(U_18) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( v1_membered(U_17)
| ~ element(U_17,powerset(U_18))
| ~ v1_membered(U_18) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_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_15_2,plain,
! [U_20] :
( ! [U_19] :
( ( v2_membered(U_19)
& v1_membered(U_19) )
| ~ element(U_19,powerset(U_20)) )
| ~ v2_membered(U_20) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_19] :
( v2_membered(U_19)
| ~ sP4(U_19) )
& ! [U_19] :
( v1_membered(U_19)
| ~ sP4(U_19) )
& ! [U_20,U_19] :
( sP4(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v2_membered(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_15_2]) ).
cnf(f_15_4,plain,
( sP4(U_19)
| ~ element(U_19,powerset(U_20))
| ~ v2_membered(U_20) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
( v1_membered(U_19)
| ~ sP4(U_19) ),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_6,plain,
( v2_membered(U_19)
| ~ sP4(U_19) ),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_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_16_2,plain,
! [U_22] :
( ! [U_21] :
( ( v3_membered(U_21)
& v2_membered(U_21)
& v1_membered(U_21) )
| ~ element(U_21,powerset(U_22)) )
| ~ v3_membered(U_22) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_21] :
( v3_membered(U_21)
| ~ sP5(U_21) )
& ! [U_21] :
( v2_membered(U_21)
| ~ sP5(U_21) )
& ! [U_21] :
( v1_membered(U_21)
| ~ sP5(U_21) )
& ! [U_21,U_22] :
( sP5(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_16_2]) ).
cnf(f_16_4,plain,
( sP5(U_21)
| ~ element(U_21,powerset(U_22))
| ~ v3_membered(U_22) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( v1_membered(U_21)
| ~ sP5(U_21) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( v2_membered(U_21)
| ~ sP5(U_21) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_7,plain,
( v3_membered(U_21)
| ~ sP5(U_21) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_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_17_2,plain,
! [U_24] :
( ! [U_23] :
( ( v4_membered(U_23)
& v3_membered(U_23)
& v2_membered(U_23)
& v1_membered(U_23) )
| ~ element(U_23,powerset(U_24)) )
| ~ v4_membered(U_24) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
( ! [U_23] :
( v4_membered(U_23)
| ~ sP6(U_23) )
& ! [U_23] :
( v3_membered(U_23)
| ~ sP6(U_23) )
& ! [U_23] :
( v2_membered(U_23)
| ~ sP6(U_23) )
& ! [U_23] :
( v1_membered(U_23)
| ~ sP6(U_23) )
& ! [U_23,U_24] :
( sP6(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_17_2]) ).
cnf(f_17_4,plain,
( sP6(U_23)
| ~ element(U_23,powerset(U_24))
| ~ v4_membered(U_24) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( v1_membered(U_23)
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( v2_membered(U_23)
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_7,plain,
( v3_membered(U_23)
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_8,plain,
( v4_membered(U_23)
| ~ sP6(U_23) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_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_18_2,plain,
! [U_26] :
( ! [U_25] :
( ( v5_membered(U_25)
& v4_membered(U_25)
& v3_membered(U_25)
& v2_membered(U_25)
& v1_membered(U_25) )
| ~ element(U_25,powerset(U_26)) )
| ~ v5_membered(U_26) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_25] :
( v5_membered(U_25)
| ~ sP7(U_25) )
& ! [U_25] :
( v4_membered(U_25)
| ~ sP7(U_25) )
& ! [U_25] :
( v3_membered(U_25)
| ~ sP7(U_25) )
& ! [U_25] :
( v2_membered(U_25)
| ~ sP7(U_25) )
& ! [U_25] :
( v1_membered(U_25)
| ~ sP7(U_25) )
& ! [U_25,U_26] :
( sP7(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_18_2]) ).
cnf(f_18_4,plain,
( sP7(U_25)
| ~ element(U_25,powerset(U_26))
| ~ v5_membered(U_26) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( v1_membered(U_25)
| ~ sP7(U_25) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( v2_membered(U_25)
| ~ sP7(U_25) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_7,plain,
( v3_membered(U_25)
| ~ sP7(U_25) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_8,plain,
( v4_membered(U_25)
| ~ sP7(U_25) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_9,plain,
( v5_membered(U_25)
| ~ sP7(U_25) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
! [A,B] :
( v1_membered(set_intersection2(A,B))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc27_membered]) ).
fof(f_19_2,plain,
! [U_28,U_27] :
( v1_membered(set_intersection2(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_28] :
( ! [U_27] : v1_membered(set_intersection2(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
fof(f_19_4,plain,
! [U_28,U_27] :
( v1_membered(set_intersection2(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
( v1_membered(set_intersection2(U_28,U_27))
| ~ v1_membered(U_28) ),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
! [A,B] :
( v1_membered(set_intersection2(B,A))
| ~ v1_membered(A) ),
inference(fof_nnf,[status(thm)],[fc28_membered]) ).
fof(f_20_2,plain,
! [U_30,U_29] :
( v1_membered(set_intersection2(U_29,U_30))
| ~ v1_membered(U_30) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_30] :
( ! [U_29] : v1_membered(set_intersection2(U_29,U_30))
| ~ v1_membered(U_30) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
fof(f_20_4,plain,
! [U_30,U_29] :
( v1_membered(set_intersection2(U_29,U_30))
| ~ v1_membered(U_30) ),
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
( v1_membered(set_intersection2(U_29,U_30))
| ~ v1_membered(U_30) ),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
! [A,B] :
( ( v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc29_membered]) ).
fof(f_21_2,plain,
! [U_32,U_31] :
( ( v2_membered(set_intersection2(U_32,U_31))
& v1_membered(set_intersection2(U_32,U_31)) )
| ~ v2_membered(U_32) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_32] :
( ( ! [U_34] : v2_membered(set_intersection2(U_32,U_34))
& ! [U_33] : v1_membered(set_intersection2(U_32,U_33)) )
| ~ v2_membered(U_32) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_32,U_33,U_34] :
( v2_membered(set_intersection2(U_32,U_34))
| ~ sP8(U_32,U_33,U_34) )
& ! [U_32,U_33,U_34] :
( v1_membered(set_intersection2(U_32,U_33))
| ~ sP8(U_32,U_33,U_34) )
& ! [U_32,U_33,U_34] :
( sP8(U_32,U_33,U_34)
| ~ v2_membered(U_32) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_21_3]) ).
cnf(f_21_5,plain,
( sP8(U_32,U_33,U_34)
| ~ v2_membered(U_32) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( v1_membered(set_intersection2(U_32,U_33))
| ~ sP8(U_32,U_33,U_34) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( v2_membered(set_intersection2(U_32,U_34))
| ~ sP8(U_32,U_33,U_34) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
! [A,B] :
( ( v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v2_membered(A) ),
inference(fof_nnf,[status(thm)],[fc30_membered]) ).
fof(f_22_2,plain,
! [U_36,U_35] :
( ( v2_membered(set_intersection2(U_35,U_36))
& v1_membered(set_intersection2(U_35,U_36)) )
| ~ v2_membered(U_36) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_36] :
( ( ! [U_38] : v2_membered(set_intersection2(U_38,U_36))
& ! [U_37] : v1_membered(set_intersection2(U_37,U_36)) )
| ~ v2_membered(U_36) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
fof(f_22_4,plain,
( ! [U_36,U_37,U_38] :
( v2_membered(set_intersection2(U_38,U_36))
| ~ sP9(U_36,U_37,U_38) )
& ! [U_36,U_37,U_38] :
( v1_membered(set_intersection2(U_37,U_36))
| ~ sP9(U_36,U_37,U_38) )
& ! [U_36,U_37,U_38] :
( sP9(U_36,U_37,U_38)
| ~ v2_membered(U_36) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_22_3]) ).
cnf(f_22_5,plain,
( sP9(U_36,U_37,U_38)
| ~ v2_membered(U_36) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
( v1_membered(set_intersection2(U_37,U_36))
| ~ sP9(U_36,U_37,U_38) ),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
( v2_membered(set_intersection2(U_38,U_36))
| ~ sP9(U_36,U_37,U_38) ),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
! [A,B] :
( ( v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc31_membered]) ).
fof(f_23_2,plain,
! [U_40,U_39] :
( ( v3_membered(set_intersection2(U_40,U_39))
& v2_membered(set_intersection2(U_40,U_39))
& v1_membered(set_intersection2(U_40,U_39)) )
| ~ v3_membered(U_40) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_40] :
( ( ! [U_43] : v3_membered(set_intersection2(U_40,U_43))
& ! [U_42] : v2_membered(set_intersection2(U_40,U_42))
& ! [U_41] : v1_membered(set_intersection2(U_40,U_41)) )
| ~ v3_membered(U_40) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
fof(f_23_4,plain,
( ! [U_41,U_40,U_42,U_43] :
( v3_membered(set_intersection2(U_40,U_43))
| ~ sP10(U_41,U_40,U_42,U_43) )
& ! [U_41,U_40,U_42,U_43] :
( v2_membered(set_intersection2(U_40,U_42))
| ~ sP10(U_41,U_40,U_42,U_43) )
& ! [U_41,U_40,U_42,U_43] :
( v1_membered(set_intersection2(U_40,U_41))
| ~ sP10(U_41,U_40,U_42,U_43) )
& ! [U_41,U_40,U_42,U_43] :
( sP10(U_41,U_40,U_42,U_43)
| ~ v3_membered(U_40) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_23_3]) ).
cnf(f_23_5,plain,
( sP10(U_41,U_40,U_42,U_43)
| ~ v3_membered(U_40) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
( v1_membered(set_intersection2(U_40,U_41))
| ~ sP10(U_41,U_40,U_42,U_43) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
( v2_membered(set_intersection2(U_40,U_42))
| ~ sP10(U_41,U_40,U_42,U_43) ),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_8,plain,
( v3_membered(set_intersection2(U_40,U_43))
| ~ sP10(U_41,U_40,U_42,U_43) ),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
! [A,B] :
( ( v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v3_membered(A) ),
inference(fof_nnf,[status(thm)],[fc32_membered]) ).
fof(f_24_2,plain,
! [U_45,U_44] :
( ( v3_membered(set_intersection2(U_44,U_45))
& v2_membered(set_intersection2(U_44,U_45))
& v1_membered(set_intersection2(U_44,U_45)) )
| ~ v3_membered(U_45) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_45] :
( ( ! [U_48] : v3_membered(set_intersection2(U_48,U_45))
& ! [U_47] : v2_membered(set_intersection2(U_47,U_45))
& ! [U_46] : v1_membered(set_intersection2(U_46,U_45)) )
| ~ v3_membered(U_45) ),
inference(miniscope,[status(thm)],[f_24_2]) ).
fof(f_24_4,plain,
( ! [U_46,U_45,U_47,U_48] :
( v3_membered(set_intersection2(U_48,U_45))
| ~ sP11(U_46,U_45,U_47,U_48) )
& ! [U_46,U_45,U_47,U_48] :
( v2_membered(set_intersection2(U_47,U_45))
| ~ sP11(U_46,U_45,U_47,U_48) )
& ! [U_46,U_45,U_47,U_48] :
( v1_membered(set_intersection2(U_46,U_45))
| ~ sP11(U_46,U_45,U_47,U_48) )
& ! [U_46,U_45,U_47,U_48] :
( sP11(U_46,U_45,U_47,U_48)
| ~ v3_membered(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_24_3]) ).
cnf(f_24_5,plain,
( sP11(U_46,U_45,U_47,U_48)
| ~ v3_membered(U_45) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
( v1_membered(set_intersection2(U_46,U_45))
| ~ sP11(U_46,U_45,U_47,U_48) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
( v2_membered(set_intersection2(U_47,U_45))
| ~ sP11(U_46,U_45,U_47,U_48) ),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_8,plain,
( v3_membered(set_intersection2(U_48,U_45))
| ~ sP11(U_46,U_45,U_47,U_48) ),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
! [A,B] :
( ( v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc33_membered]) ).
fof(f_25_2,plain,
! [U_50,U_49] :
( ( v4_membered(set_intersection2(U_50,U_49))
& v3_membered(set_intersection2(U_50,U_49))
& v2_membered(set_intersection2(U_50,U_49))
& v1_membered(set_intersection2(U_50,U_49)) )
| ~ v4_membered(U_50) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_50] :
( ( ! [U_54] : v4_membered(set_intersection2(U_50,U_54))
& ! [U_53] : v3_membered(set_intersection2(U_50,U_53))
& ! [U_52] : v2_membered(set_intersection2(U_50,U_52))
& ! [U_51] : v1_membered(set_intersection2(U_50,U_51)) )
| ~ v4_membered(U_50) ),
inference(miniscope,[status(thm)],[f_25_2]) ).
fof(f_25_4,plain,
( ! [U_50,U_51,U_52,U_53,U_54] :
( v4_membered(set_intersection2(U_50,U_54))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) )
& ! [U_50,U_51,U_52,U_53,U_54] :
( v3_membered(set_intersection2(U_50,U_53))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) )
& ! [U_50,U_51,U_52,U_53,U_54] :
( v2_membered(set_intersection2(U_50,U_52))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) )
& ! [U_50,U_51,U_52,U_53,U_54] :
( v1_membered(set_intersection2(U_50,U_51))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) )
& ! [U_50,U_51,U_52,U_53,U_54] :
( sP12(U_50,U_51,U_52,U_53,U_54)
| ~ v4_membered(U_50) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_25_3]) ).
cnf(f_25_5,plain,
( sP12(U_50,U_51,U_52,U_53,U_54)
| ~ v4_membered(U_50) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
( v1_membered(set_intersection2(U_50,U_51))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_7,plain,
( v2_membered(set_intersection2(U_50,U_52))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_8,plain,
( v3_membered(set_intersection2(U_50,U_53))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) ),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_9,plain,
( v4_membered(set_intersection2(U_50,U_54))
| ~ sP12(U_50,U_51,U_52,U_53,U_54) ),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
! [A,B] :
( ( v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v4_membered(A) ),
inference(fof_nnf,[status(thm)],[fc34_membered]) ).
fof(f_26_2,plain,
! [U_56,U_55] :
( ( v4_membered(set_intersection2(U_55,U_56))
& v3_membered(set_intersection2(U_55,U_56))
& v2_membered(set_intersection2(U_55,U_56))
& v1_membered(set_intersection2(U_55,U_56)) )
| ~ v4_membered(U_56) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_56] :
( ( ! [U_60] : v4_membered(set_intersection2(U_60,U_56))
& ! [U_59] : v3_membered(set_intersection2(U_59,U_56))
& ! [U_58] : v2_membered(set_intersection2(U_58,U_56))
& ! [U_57] : v1_membered(set_intersection2(U_57,U_56)) )
| ~ v4_membered(U_56) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
( ! [U_56,U_58,U_57,U_59,U_60] :
( v4_membered(set_intersection2(U_60,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) )
& ! [U_56,U_58,U_57,U_59,U_60] :
( v3_membered(set_intersection2(U_59,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) )
& ! [U_56,U_58,U_57,U_59,U_60] :
( v2_membered(set_intersection2(U_58,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) )
& ! [U_56,U_58,U_57,U_59,U_60] :
( v1_membered(set_intersection2(U_57,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) )
& ! [U_56,U_58,U_57,U_59,U_60] :
( sP13(U_56,U_58,U_57,U_59,U_60)
| ~ v4_membered(U_56) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_26_3]) ).
cnf(f_26_5,plain,
( sP13(U_56,U_58,U_57,U_59,U_60)
| ~ v4_membered(U_56) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
( v1_membered(set_intersection2(U_57,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
( v2_membered(set_intersection2(U_58,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_8,plain,
( v3_membered(set_intersection2(U_59,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) ),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_9,plain,
( v4_membered(set_intersection2(U_60,U_56))
| ~ sP13(U_56,U_58,U_57,U_59,U_60) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
! [A,B] :
( ( v5_membered(set_intersection2(A,B))
& v4_membered(set_intersection2(A,B))
& v3_membered(set_intersection2(A,B))
& v2_membered(set_intersection2(A,B))
& v1_membered(set_intersection2(A,B)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc35_membered]) ).
fof(f_27_2,plain,
! [U_62,U_61] :
( ( v5_membered(set_intersection2(U_62,U_61))
& v4_membered(set_intersection2(U_62,U_61))
& v3_membered(set_intersection2(U_62,U_61))
& v2_membered(set_intersection2(U_62,U_61))
& v1_membered(set_intersection2(U_62,U_61)) )
| ~ v5_membered(U_62) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_62] :
( ( ! [U_67] : v5_membered(set_intersection2(U_62,U_67))
& ! [U_66] : v4_membered(set_intersection2(U_62,U_66))
& ! [U_65] : v3_membered(set_intersection2(U_62,U_65))
& ! [U_64] : v2_membered(set_intersection2(U_62,U_64))
& ! [U_63] : v1_membered(set_intersection2(U_62,U_63)) )
| ~ v5_membered(U_62) ),
inference(miniscope,[status(thm)],[f_27_2]) ).
fof(f_27_4,plain,
( ! [U_62,U_64,U_63,U_65,U_66,U_67] :
( v5_membered(set_intersection2(U_62,U_67))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) )
& ! [U_62,U_64,U_63,U_65,U_66,U_67] :
( v4_membered(set_intersection2(U_62,U_66))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) )
& ! [U_62,U_64,U_63,U_65,U_66,U_67] :
( v3_membered(set_intersection2(U_62,U_65))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) )
& ! [U_62,U_64,U_63,U_65,U_66,U_67] :
( v2_membered(set_intersection2(U_62,U_64))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) )
& ! [U_62,U_64,U_63,U_65,U_66,U_67] :
( v1_membered(set_intersection2(U_62,U_63))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) )
& ! [U_62,U_64,U_63,U_65,U_66,U_67] :
( sP14(U_62,U_64,U_63,U_65,U_66,U_67)
| ~ v5_membered(U_62) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_27_3]) ).
cnf(f_27_5,plain,
( sP14(U_62,U_64,U_63,U_65,U_66,U_67)
| ~ v5_membered(U_62) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
( v1_membered(set_intersection2(U_62,U_63))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
( v2_membered(set_intersection2(U_62,U_64))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_8,plain,
( v3_membered(set_intersection2(U_62,U_65))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_9,plain,
( v4_membered(set_intersection2(U_62,U_66))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_10,plain,
( v5_membered(set_intersection2(U_62,U_67))
| ~ sP14(U_62,U_64,U_63,U_65,U_66,U_67) ),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
! [A,B] :
( ( v5_membered(set_intersection2(B,A))
& v4_membered(set_intersection2(B,A))
& v3_membered(set_intersection2(B,A))
& v2_membered(set_intersection2(B,A))
& v1_membered(set_intersection2(B,A)) )
| ~ v5_membered(A) ),
inference(fof_nnf,[status(thm)],[fc36_membered]) ).
fof(f_28_2,plain,
! [U_69,U_68] :
( ( v5_membered(set_intersection2(U_68,U_69))
& v4_membered(set_intersection2(U_68,U_69))
& v3_membered(set_intersection2(U_68,U_69))
& v2_membered(set_intersection2(U_68,U_69))
& v1_membered(set_intersection2(U_68,U_69)) )
| ~ v5_membered(U_69) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_69] :
( ( ! [U_74] : v5_membered(set_intersection2(U_74,U_69))
& ! [U_73] : v4_membered(set_intersection2(U_73,U_69))
& ! [U_72] : v3_membered(set_intersection2(U_72,U_69))
& ! [U_71] : v2_membered(set_intersection2(U_71,U_69))
& ! [U_70] : v1_membered(set_intersection2(U_70,U_69)) )
| ~ v5_membered(U_69) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
( ! [U_71,U_72,U_69,U_73,U_70,U_74] :
( v5_membered(set_intersection2(U_74,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) )
& ! [U_71,U_72,U_69,U_73,U_70,U_74] :
( v4_membered(set_intersection2(U_73,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) )
& ! [U_71,U_72,U_69,U_73,U_70,U_74] :
( v3_membered(set_intersection2(U_72,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) )
& ! [U_71,U_72,U_69,U_73,U_70,U_74] :
( v2_membered(set_intersection2(U_71,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) )
& ! [U_71,U_72,U_69,U_73,U_70,U_74] :
( v1_membered(set_intersection2(U_70,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) )
& ! [U_71,U_72,U_69,U_73,U_70,U_74] :
( sP15(U_71,U_72,U_69,U_73,U_70,U_74)
| ~ v5_membered(U_69) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_28_3]) ).
cnf(f_28_5,plain,
( sP15(U_71,U_72,U_69,U_73,U_70,U_74)
| ~ v5_membered(U_69) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
( v1_membered(set_intersection2(U_70,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_7,plain,
( v2_membered(set_intersection2(U_71,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_8,plain,
( v3_membered(set_intersection2(U_72,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_9,plain,
( v4_membered(set_intersection2(U_73,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) ),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_10,plain,
( v5_membered(set_intersection2(U_74,U_69))
| ~ sP15(U_71,U_72,U_69,U_73,U_70,U_74) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_29_2,plain,
! [U_76,U_75] :
( element(U_76,U_75)
| ~ in(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_76,U_75] :
( element(U_76,U_75)
| ~ in(U_76,U_75) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( element(U_76,U_75)
| ~ in(U_76,U_75) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [A] : set_intersection2(A,empty_set) = empty_set,
inference(fof_nnf,[status(thm)],[t2_boole]) ).
fof(f_30_2,plain,
! [U_77] : set_intersection2(U_77,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_77] : set_intersection2(U_77,empty_set) = empty_set,
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
set_intersection2(U_77,empty_set) = empty_set,
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_31_2,plain,
! [U_80,U_79,U_78] :
( element(U_80,U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_78,U_79,U_80] :
( element(U_80,U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( element(U_80,U_78)
| ~ element(U_79,powerset(U_78))
| ~ in(U_80,U_79) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_32_2,plain,
! [U_83,U_82,U_81] :
( ~ empty(U_81)
| ~ element(U_82,powerset(U_81))
| ~ in(U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_83,U_82] :
( ! [U_81] :
( ~ empty(U_81)
| ~ element(U_82,powerset(U_81)) )
| ~ in(U_83,U_82) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
fof(f_32_4,plain,
! [U_82,U_81,U_83] :
( ~ empty(U_81)
| ~ element(U_82,powerset(U_81))
| ~ in(U_83,U_82) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
( ~ empty(U_81)
| ~ element(U_82,powerset(U_81))
| ~ in(U_83,U_82) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_33_2,plain,
! [U_85] :
( ? [U_84] :
( ~ empty(U_84)
& element(U_84,powerset(U_85)) )
| empty(U_85) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_85] :
( ( ~ empty(sK2(U_85))
& element(sK2(U_85),powerset(U_85)) )
| empty(U_85) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_84,sK2(U_85))],[f_33_2]) ).
fof(f_33_4,plain,
( ! [U_85] :
( ~ empty(sK2(U_85))
| ~ sP16(U_85) )
& ! [U_85] :
( element(sK2(U_85),powerset(U_85))
| ~ sP16(U_85) )
& ! [U_85] :
( sP16(U_85)
| empty(U_85) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_33_3]) ).
cnf(f_33_5,plain,
( sP16(U_85)
| empty(U_85) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
( element(sK2(U_85),powerset(U_85))
| ~ sP16(U_85) ),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_7,plain,
( ~ empty(sK2(U_85))
| ~ sP16(U_85) ),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_34_2,plain,
! [U_87] :
? [U_86] :
( empty(U_86)
& element(U_86,powerset(U_87)) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_87] :
( empty(sK3(U_87))
& element(sK3(U_87),powerset(U_87)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_86,sK3(U_87))],[f_34_2]) ).
fof(f_34_4,plain,
( ! [U_87] : empty(sK3(U_87))
& ! [U_87] : element(sK3(U_87),powerset(U_87)) ),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
element(sK3(U_87),powerset(U_87)),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
empty(sK3(U_87)),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_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_35_2,plain,
! [U_88] :
( ( v5_membered(U_88)
& v4_membered(U_88)
& v3_membered(U_88)
& v2_membered(U_88)
& v1_membered(U_88) )
| ~ empty(U_88) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_88] :
( v5_membered(U_88)
| ~ sP17(U_88) )
& ! [U_88] :
( v4_membered(U_88)
| ~ sP17(U_88) )
& ! [U_88] :
( v3_membered(U_88)
| ~ sP17(U_88) )
& ! [U_88] :
( v2_membered(U_88)
| ~ sP17(U_88) )
& ! [U_88] :
( v1_membered(U_88)
| ~ sP17(U_88) )
& ! [U_88] :
( sP17(U_88)
| ~ empty(U_88) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_35_2]) ).
cnf(f_35_4,plain,
( sP17(U_88)
| ~ empty(U_88) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( v1_membered(U_88)
| ~ sP17(U_88) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_6,plain,
( v2_membered(U_88)
| ~ sP17(U_88) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_7,plain,
( v3_membered(U_88)
| ~ sP17(U_88) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_8,plain,
( v4_membered(U_88)
| ~ sP17(U_88) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_9,plain,
( v5_membered(U_88)
| ~ sP17(U_88) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_36_2,plain,
! [U_90,U_89] :
( in(U_90,U_89)
| empty(U_89)
| ~ element(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_90,U_89] :
( in(U_90,U_89)
| empty(U_89)
| ~ element(U_90,U_89) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( in(U_90,U_89)
| empty(U_89)
| ~ element(U_90,U_89) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_37_2,plain,
! [U_91] :
( U_91 = empty_set
| ~ empty(U_91) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_91] :
( U_91 = empty_set
| ~ empty(U_91) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( U_91 = empty_set
| ~ empty(U_91) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_38_2,plain,
! [U_93,U_92] :
( ~ empty(U_92)
| ~ in(U_93,U_92) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_93,U_92] :
( ~ empty(U_92)
| ~ in(U_93,U_92) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( ~ empty(U_92)
| ~ in(U_93,U_92) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_39_2,plain,
! [U_95,U_94] :
( ~ empty(U_94)
| U_95 = U_94
| ~ empty(U_95) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_95] :
( ! [U_94] :
( ~ empty(U_94)
| U_95 = U_94 )
| ~ empty(U_95) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
fof(f_39_4,plain,
! [U_94,U_95] :
( ~ empty(U_94)
| U_95 = U_94
| ~ empty(U_95) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
( ~ empty(U_94)
| U_95 = U_94
| ~ empty(U_95) ),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(f_40_2,plain,
! [U_97,U_96] : set_intersection2(U_97,U_96) = set_intersection2(U_96,U_97),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_97,U_96] : set_intersection2(U_97,U_96) = set_intersection2(U_96,U_97),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
set_intersection2(U_97,U_96) = set_intersection2(U_96,U_97),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A,B] : set_intersection2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k3_xboole_0]) ).
fof(f_41_2,plain,
! [U_99,U_98] : set_intersection2(U_99,U_99) = U_99,
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_99] : set_intersection2(U_99,U_99) = U_99,
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
! [U_99] : set_intersection2(U_99,U_99) = U_99,
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
set_intersection2(U_99,U_99) = U_99,
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [A,B,C] :
( subset_intersection2(A,B,C) = subset_intersection2(A,C,B)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[commutativity_k5_subset_1]) ).
fof(f_42_2,plain,
! [U_102,U_101,U_100] :
( subset_intersection2(U_102,U_101,U_100) = subset_intersection2(U_102,U_100,U_101)
| ~ element(U_100,powerset(U_102))
| ~ element(U_101,powerset(U_102)) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_100,U_101,U_102] :
( subset_intersection2(U_102,U_101,U_100) = subset_intersection2(U_102,U_100,U_101)
| ~ element(U_100,powerset(U_102))
| ~ element(U_101,powerset(U_102)) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( subset_intersection2(U_102,U_101,U_100) = subset_intersection2(U_102,U_100,U_101)
| ~ element(U_100,powerset(U_102))
| ~ element(U_101,powerset(U_102)) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A,B,C] :
( subset_intersection2(A,B,B) = B
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[idempotence_k5_subset_1]) ).
fof(f_43_2,plain,
! [U_105,U_104,U_103] :
( subset_intersection2(U_105,U_104,U_104) = U_104
| ~ element(U_103,powerset(U_105))
| ~ element(U_104,powerset(U_105)) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_105,U_104] :
( ! [U_103] : ~ element(U_103,powerset(U_105))
| ~ element(U_104,powerset(U_105))
| subset_intersection2(U_105,U_104,U_104) = U_104 ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_105,U_104,U_103] :
( ~ element(U_103,powerset(U_105))
| ~ element(U_104,powerset(U_105))
| subset_intersection2(U_105,U_104,U_104) = U_104 ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
( ~ element(U_103,powerset(U_105))
| ~ element(U_104,powerset(U_105))
| subset_intersection2(U_105,U_104,U_104) = U_104 ),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_44_2,plain,
! [U_107,U_106] : subset(U_107,U_107),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_107] : subset(U_107,U_107),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
! [U_107] : subset(U_107,U_107),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
subset(U_107,U_107),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
? [A] : one_sorted_str(A),
inference(fof_nnf,[status(thm)],[existence_l1_struct_0]) ).
fof(f_45_2,plain,
? [U_108] : one_sorted_str(U_108),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
one_sorted_str(sK4),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_108,sK4)],[f_45_2]) ).
fof(f_45_4,plain,
one_sorted_str(sK4),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
one_sorted_str(sK4),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_46_2,plain,
! [U_110] :
? [U_109] : element(U_109,U_110),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_110] : element(sK5(U_110),U_110),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_109,sK5(U_110))],[f_46_2]) ).
fof(f_46_4,plain,
! [U_110] : element(sK5(U_110),U_110),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
element(sK5(U_110),U_110),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
! [A,B,C] :
( subset_intersection2(A,B,C) = set_intersection2(B,C)
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[redefinition_k5_subset_1]) ).
fof(f_47_2,plain,
! [U_113,U_112,U_111] :
( subset_intersection2(U_113,U_112,U_111) = set_intersection2(U_112,U_111)
| ~ element(U_111,powerset(U_113))
| ~ element(U_112,powerset(U_113)) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_111,U_112,U_113] :
( subset_intersection2(U_113,U_112,U_111) = set_intersection2(U_112,U_111)
| ~ element(U_111,powerset(U_113))
| ~ element(U_112,powerset(U_113)) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( subset_intersection2(U_113,U_112,U_111) = set_intersection2(U_112,U_111)
| ~ element(U_111,powerset(U_113))
| ~ element(U_112,powerset(U_113)) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_48_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_48_1]) ).
cnf(f_48_3,plain,
$true,
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_114] :
( element(cast_as_carrier_subset(U_114),powerset(the_carrier(U_114)))
| ~ one_sorted_str(U_114) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_114] :
( element(cast_as_carrier_subset(U_114),powerset(the_carrier(U_114)))
| ~ one_sorted_str(U_114) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( element(cast_as_carrier_subset(U_114),powerset(the_carrier(U_114)))
| ~ one_sorted_str(U_114) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_xboole_0]) ).
fof(f_50_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_50_1]) ).
cnf(f_50_3,plain,
$true,
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C] :
( element(subset_intersection2(A,B,C),powerset(A))
| ~ element(C,powerset(A))
| ~ element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[dt_k5_subset_1]) ).
fof(f_51_2,plain,
! [U_117,U_116,U_115] :
( element(subset_intersection2(U_117,U_116,U_115),powerset(U_117))
| ~ element(U_115,powerset(U_117))
| ~ element(U_116,powerset(U_117)) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_116,U_115,U_117] :
( element(subset_intersection2(U_117,U_116,U_115),powerset(U_117))
| ~ element(U_115,powerset(U_117))
| ~ element(U_116,powerset(U_117)) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( element(subset_intersection2(U_117,U_116,U_115),powerset(U_117))
| ~ element(U_115,powerset(U_117))
| ~ element(U_116,powerset(U_117)) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_l1_struct_0]) ).
fof(f_52_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_52_1]) ).
cnf(f_52_3,plain,
$true,
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_53_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_53_1]) ).
cnf(f_53_3,plain,
$true,
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_u1_struct_0]) ).
fof(f_54_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_54_1]) ).
cnf(f_54_3,plain,
$true,
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_55_2,plain,
! [U_118] : ~ empty(powerset(U_118)),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_118] : ~ empty(powerset(U_118)),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
~ empty(powerset(U_118)),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
! [U_120,U_119] :
( ( element(U_120,powerset(U_119))
| ~ subset(U_120,U_119) )
& ( subset(U_120,U_119)
| ~ element(U_120,powerset(U_119)) ) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
( ! [U_124,U_122] :
( element(U_124,powerset(U_122))
| ~ subset(U_124,U_122) )
& ! [U_123,U_121] :
( subset(U_123,U_121)
| ~ element(U_123,powerset(U_121)) ) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
( ! [U_124,U_122] :
( element(U_124,powerset(U_122))
| ~ subset(U_124,U_122) )
& ! [U_123,U_121] :
( subset(U_123,U_121)
| ~ element(U_123,powerset(U_121)) ) ),
inference(definitional_conversion,[status(esa)],[f_56_3]) ).
cnf(f_56_5,plain,
( subset(U_123,U_121)
| ~ element(U_123,powerset(U_121)) ),
inference(clausify,[status(thm)],[f_56_4]) ).
cnf(f_56_6,plain,
( element(U_124,powerset(U_122))
| ~ subset(U_124,U_122) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_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_57_2,plain,
! [U_125] :
( cast_as_carrier_subset(U_125) = the_carrier(U_125)
| ~ one_sorted_str(U_125) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_125] :
( cast_as_carrier_subset(U_125) = the_carrier(U_125)
| ~ one_sorted_str(U_125) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( cast_as_carrier_subset(U_125) = the_carrier(U_125)
| ~ one_sorted_str(U_125) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,negated_conjecture,
~ ! [A] :
( one_sorted_str(A)
=> ! [B] :
( element(B,powerset(the_carrier(A)))
=> subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) = B ) ),
inference(negate,[status(cth)],[t15_pre_topc]) ).
fof(f_58_2,negated_conjecture,
? [A] :
( ? [B] :
( subset_intersection2(the_carrier(A),B,cast_as_carrier_subset(A)) != B
& element(B,powerset(the_carrier(A))) )
& one_sorted_str(A) ),
inference(fof_nnf,[status(thm)],[f_58_1]) ).
fof(f_58_3,negated_conjecture,
? [U_127] :
( ? [U_126] :
( subset_intersection2(the_carrier(U_127),U_126,cast_as_carrier_subset(U_127)) != U_126
& element(U_126,powerset(the_carrier(U_127))) )
& one_sorted_str(U_127) ),
inference(variable_rename,[status(thm)],[f_58_2]) ).
fof(f_58_4,negated_conjecture,
( ? [U_126] :
( subset_intersection2(the_carrier(sK6),U_126,cast_as_carrier_subset(sK6)) != U_126
& element(U_126,powerset(the_carrier(sK6))) )
& one_sorted_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_127,sK6)],[f_58_3]) ).
fof(f_58_5,negated_conjecture,
( subset_intersection2(the_carrier(sK6),sK7,cast_as_carrier_subset(sK6)) != sK7
& element(sK7,powerset(the_carrier(sK6)))
& one_sorted_str(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_126,sK7)],[f_58_4]) ).
fof(f_58_6,negated_conjecture,
( subset_intersection2(the_carrier(sK6),sK7,cast_as_carrier_subset(sK6)) != sK7
& element(sK7,powerset(the_carrier(sK6)))
& one_sorted_str(sK6) ),
inference(definitional_conversion,[status(esa)],[f_58_5]) ).
cnf(f_58_7,negated_conjecture,
one_sorted_str(sK6),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_8,negated_conjecture,
element(sK7,powerset(the_carrier(sK6))),
inference(clausify,[status(thm)],[f_58_6]) ).
cnf(f_58_9,negated_conjecture,
subset_intersection2(the_carrier(sK6),sK7,cast_as_carrier_subset(sK6)) != sK7,
inference(clausify,[status(thm)],[f_58_6]) ).
fof(f_59_1,plain,
! [A,B] :
( set_intersection2(A,B) = A
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t28_xboole_1]) ).
fof(f_59_2,plain,
! [U_129,U_128] :
( set_intersection2(U_129,U_128) = U_129
| ~ subset(U_129,U_128) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_129,U_128] :
( set_intersection2(U_129,U_128) = U_129
| ~ subset(U_129,U_128) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( set_intersection2(U_129,U_128) = U_129
| ~ subset(U_129,U_128) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_2_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_2_3]) ).
cnf(f_48_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_48_3]) ).
cnf(f_50_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_50_3]) ).
cnf(f_52_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_52_3]) ).
cnf(f_53_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_53_3]) ).
cnf(f_54_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_54_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,
( set_intersection2(Eq_x_0,Eq_x_1) = set_intersection2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( subset_intersection2(Eq_x_0,Eq_x_1,Eq_x_2) = subset_intersection2(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_7,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_8,axiom,
( the_carrier(Eq_x_0) = the_carrier(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,axiom,
( v5_membered(Eq_y_0)
| ~ v5_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( v4_membered(Eq_y_0)
| ~ v4_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( v3_membered(Eq_y_0)
| ~ v3_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( v2_membered(Eq_y_0)
| ~ v2_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( v1_membered(Eq_y_0)
| ~ v1_membered(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( empty(Eq_y_0)
| ~ empty(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,
( v1_xreal_0(Eq_y_0)
| ~ v1_xreal_0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_23,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_24,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,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_27,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_29,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(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_36,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_37,axiom,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| 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_38,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| 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_39,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP12(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_40,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP13(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_41,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_42,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| 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_43,axiom,
( sP16(Eq_y_0)
| ~ sP16(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_44,axiom,
( sP17(Eq_y_0)
| ~ sP17(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 : SEU307+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
% 0.08/0.37 % Computer : n010.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 19 23:52:09 UTC 2026
% 0.08/0.37 % CPUTime :
% 35.35/35.67 % SZS status Theorem for theBenchmark
% 35.35/35.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------