%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU236+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 : n016.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 08:58:38 AM UTC 2026
% Result : Theorem 216.16s 216.42s
% Output : Proof 216.79s
% 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(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d1_tarski,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('theBenchmark.p',d1_tarski) ).
fof(d2_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
<=> ! [B] :
( in(B,A)
=> subset(B,A) ) ),
file('theBenchmark.p',d2_ordinal1) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(dt_k1_ordinal1,axiom,
$true,
file('theBenchmark.p',dt_k1_ordinal1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
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_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_m1_subset_1,axiom,
$true,
file('theBenchmark.p',dt_m1_subset_1) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
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(t33_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
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(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(t8_xboole_1,axiom,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_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,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( epsilon_connected(U_3)
& epsilon_transitive(U_3) )
| ~ ordinal(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_3] :
( epsilon_connected(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( epsilon_transitive(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( sP0(U_3)
| ~ ordinal(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( epsilon_transitive(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( epsilon_connected(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_4_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_5_2,plain,
! [U_5] :
( ( one_to_one(U_5)
& function(U_5)
& relation(U_5) )
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_5] :
( one_to_one(U_5)
| ~ sP1(U_5) )
& ! [U_5] :
( function(U_5)
| ~ sP1(U_5) )
& ! [U_5] :
( relation(U_5)
| ~ sP1(U_5) )
& ! [U_5] :
( sP1(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP1(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( relation(U_5)
| ~ sP1(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( function(U_5)
| ~ sP1(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( one_to_one(U_5)
| ~ sP1(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_6_2,plain,
! [U_6] :
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_6] :
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_7_2,plain,
! [U_7] :
( ( ordinal(U_7)
& epsilon_connected(U_7)
& epsilon_transitive(U_7) )
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_7] :
( ordinal(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( epsilon_connected(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( epsilon_transitive(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( sP2(U_7)
| ~ empty(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP2(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( epsilon_transitive(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( epsilon_connected(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( ordinal(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_8_2,plain,
! [U_9,U_8] : set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_9,U_8] : set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
set_union2(U_9,U_8) = set_union2(U_8,U_9),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( ordinal_subset(B,A)
| ordinal_subset(A,B)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1]) ).
fof(f_9_2,plain,
! [U_11,U_10] :
( ordinal_subset(U_10,U_11)
| ordinal_subset(U_11,U_10)
| ~ ordinal(U_10)
| ~ ordinal(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_10,U_11] :
( ordinal_subset(U_10,U_11)
| ordinal_subset(U_11,U_10)
| ~ ordinal(U_10)
| ~ ordinal(U_11) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( ordinal_subset(U_10,U_11)
| ordinal_subset(U_11,U_10)
| ~ ordinal(U_10)
| ~ ordinal(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_10_2,plain,
! [U_12] : succ(U_12) = set_union2(U_12,singleton(U_12)),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_12] : succ(U_12) = set_union2(U_12,singleton(U_12)),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
succ(U_12) = set_union2(U_12,singleton(U_12)),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A,B] :
( ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
& C = A )
| ( C != A
& in(C,B) ) ) )
& ( ! [C] :
( ( in(C,B)
| C != A )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(fof_nnf,[status(thm)],[d1_tarski]) ).
fof(f_11_2,plain,
! [U_16,U_15] :
( ( U_15 = singleton(U_16)
| ? [U_14] :
( ( ~ in(U_14,U_15)
& U_14 = U_16 )
| ( U_14 != U_16
& in(U_14,U_15) ) ) )
& ( ! [U_13] :
( ( in(U_13,U_15)
| U_13 != U_16 )
& ( U_13 = U_16
| ~ in(U_13,U_15) ) )
| U_15 != singleton(U_16) ) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_24,U_22] :
( U_22 = singleton(U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& U_20 = U_24 )
| ? [U_19] :
( U_19 != U_24
& in(U_19,U_22) ) )
& ! [U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| U_18 != U_23 )
& ! [U_17] :
( U_17 = U_23
| ~ in(U_17,U_21) ) )
| U_21 != singleton(U_23) ) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
fof(f_11_4,plain,
( ! [U_24,U_22] :
( U_22 = singleton(U_24)
| ? [U_20] :
( ~ in(U_20,U_22)
& U_20 = U_24 )
| ( sK1(U_24,U_22) != U_24
& in(sK1(U_24,U_22),U_22) ) )
& ! [U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| U_18 != U_23 )
& ! [U_17] :
( U_17 = U_23
| ~ in(U_17,U_21) ) )
| U_21 != singleton(U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_19,sK1(U_24,U_22))],[f_11_3]) ).
fof(f_11_5,plain,
( ! [U_24,U_22] :
( U_22 = singleton(U_24)
| ( ~ in(sK2(U_24,U_22),U_22)
& sK2(U_24,U_22) = U_24 )
| ( sK1(U_24,U_22) != U_24
& in(sK1(U_24,U_22),U_22) ) )
& ! [U_23,U_21] :
( ( ! [U_18] :
( in(U_18,U_21)
| U_18 != U_23 )
& ! [U_17] :
( U_17 = U_23
| ~ in(U_17,U_21) ) )
| U_21 != singleton(U_23) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_20,sK2(U_24,U_22))],[f_11_4]) ).
fof(f_11_6,plain,
( ! [U_22,U_24] :
( ~ in(sK2(U_24,U_22),U_22)
| ~ sP5(U_22,U_24) )
& ! [U_22,U_24] :
( sK2(U_24,U_22) = U_24
| ~ sP5(U_22,U_24) )
& ! [U_22,U_24] :
( sK1(U_24,U_22) != U_24
| ~ sP4(U_22,U_24) )
& ! [U_22,U_24] :
( in(sK1(U_24,U_22),U_22)
| ~ sP4(U_22,U_24) )
& ! [U_23,U_17,U_18,U_21] :
( in(U_18,U_21)
| U_18 != U_23
| ~ sP3(U_23,U_17,U_18,U_21) )
& ! [U_23,U_17,U_18,U_21] :
( U_17 = U_23
| ~ in(U_17,U_21)
| ~ sP3(U_23,U_17,U_18,U_21) )
& ! [U_22,U_24] :
( U_22 = singleton(U_24)
| sP5(U_22,U_24)
| sP4(U_22,U_24) )
& ! [U_23,U_17,U_18,U_21] :
( sP3(U_23,U_17,U_18,U_21)
| U_21 != singleton(U_23) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4,sP5])],[f_11_5]) ).
cnf(f_11_7,plain,
( sP3(U_23,U_17,U_18,U_21)
| U_21 != singleton(U_23) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_8,plain,
( U_22 = singleton(U_24)
| sP5(U_22,U_24)
| sP4(U_22,U_24) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_9,plain,
( U_17 = U_23
| ~ in(U_17,U_21)
| ~ sP3(U_23,U_17,U_18,U_21) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_10,plain,
( in(U_18,U_21)
| U_18 != U_23
| ~ sP3(U_23,U_17,U_18,U_21) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_11,plain,
( in(sK1(U_24,U_22),U_22)
| ~ sP4(U_22,U_24) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_12,plain,
( sK1(U_24,U_22) != U_24
| ~ sP4(U_22,U_24) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_13,plain,
( sK2(U_24,U_22) = U_24
| ~ sP5(U_22,U_24) ),
inference(clausify,[status(thm)],[f_11_6]) ).
cnf(f_11_14,plain,
( ~ in(sK2(U_24,U_22),U_22)
| ~ sP5(U_22,U_24) ),
inference(clausify,[status(thm)],[f_11_6]) ).
fof(f_12_1,plain,
! [A] :
( ( epsilon_transitive(A)
| ? [B] :
( ~ subset(B,A)
& in(B,A) ) )
& ( ! [B] :
( subset(B,A)
| ~ in(B,A) )
| ~ epsilon_transitive(A) ) ),
inference(fof_nnf,[status(thm)],[d2_ordinal1]) ).
fof(f_12_2,plain,
! [U_27] :
( ( epsilon_transitive(U_27)
| ? [U_26] :
( ~ subset(U_26,U_27)
& in(U_26,U_27) ) )
& ( ! [U_25] :
( subset(U_25,U_27)
| ~ in(U_25,U_27) )
| ~ epsilon_transitive(U_27) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_29] :
( epsilon_transitive(U_29)
| ? [U_26] :
( ~ subset(U_26,U_29)
& in(U_26,U_29) ) )
& ! [U_28] :
( ! [U_25] :
( subset(U_25,U_28)
| ~ in(U_25,U_28) )
| ~ epsilon_transitive(U_28) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
fof(f_12_4,plain,
( ! [U_29] :
( epsilon_transitive(U_29)
| ( ~ subset(sK3(U_29),U_29)
& in(sK3(U_29),U_29) ) )
& ! [U_28] :
( ! [U_25] :
( subset(U_25,U_28)
| ~ in(U_25,U_28) )
| ~ epsilon_transitive(U_28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3(U_29))],[f_12_3]) ).
fof(f_12_5,plain,
( ! [U_29] :
( ~ subset(sK3(U_29),U_29)
| ~ sP6(U_29) )
& ! [U_29] :
( in(sK3(U_29),U_29)
| ~ sP6(U_29) )
& ! [U_29] :
( epsilon_transitive(U_29)
| sP6(U_29) )
& ! [U_28,U_25] :
( subset(U_25,U_28)
| ~ in(U_25,U_28)
| ~ epsilon_transitive(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_12_4]) ).
cnf(f_12_6,plain,
( subset(U_25,U_28)
| ~ in(U_25,U_28)
| ~ epsilon_transitive(U_28) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_7,plain,
( epsilon_transitive(U_29)
| sP6(U_29) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_8,plain,
( in(sK3(U_29),U_29)
| ~ sP6(U_29) ),
inference(clausify,[status(thm)],[f_12_5]) ).
cnf(f_12_9,plain,
( ~ subset(sK3(U_29),U_29)
| ~ sP6(U_29) ),
inference(clausify,[status(thm)],[f_12_5]) ).
fof(f_13_1,plain,
! [A,B] :
( ( subset(A,B)
| ? [C] :
( ~ in(C,B)
& in(C,A) ) )
& ( ! [C] :
( in(C,B)
| ~ in(C,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(f_13_2,plain,
! [U_33,U_32] :
( ( subset(U_33,U_32)
| ? [U_31] :
( ~ in(U_31,U_32)
& in(U_31,U_33) ) )
& ( ! [U_30] :
( in(U_30,U_32)
| ~ in(U_30,U_33) )
| ~ subset(U_33,U_32) ) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
( ! [U_37,U_35] :
( subset(U_37,U_35)
| ? [U_31] :
( ~ in(U_31,U_35)
& in(U_31,U_37) ) )
& ! [U_36,U_34] :
( ! [U_30] :
( in(U_30,U_34)
| ~ in(U_30,U_36) )
| ~ subset(U_36,U_34) ) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
( ! [U_37,U_35] :
( subset(U_37,U_35)
| ( ~ in(sK4(U_37,U_35),U_35)
& in(sK4(U_37,U_35),U_37) ) )
& ! [U_36,U_34] :
( ! [U_30] :
( in(U_30,U_34)
| ~ in(U_30,U_36) )
| ~ subset(U_36,U_34) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_31,sK4(U_37,U_35))],[f_13_3]) ).
fof(f_13_5,plain,
( ! [U_35,U_37] :
( ~ in(sK4(U_37,U_35),U_35)
| ~ sP7(U_35,U_37) )
& ! [U_35,U_37] :
( in(sK4(U_37,U_35),U_37)
| ~ sP7(U_35,U_37) )
& ! [U_35,U_37] :
( subset(U_37,U_35)
| sP7(U_35,U_37) )
& ! [U_36,U_34,U_30] :
( in(U_30,U_34)
| ~ in(U_30,U_36)
| ~ subset(U_36,U_34) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_13_4]) ).
cnf(f_13_6,plain,
( in(U_30,U_34)
| ~ in(U_30,U_36)
| ~ subset(U_36,U_34) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_7,plain,
( subset(U_37,U_35)
| sP7(U_35,U_37) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_8,plain,
( in(sK4(U_37,U_35),U_37)
| ~ sP7(U_35,U_37) ),
inference(clausify,[status(thm)],[f_13_5]) ).
cnf(f_13_9,plain,
( ~ in(sK4(U_37,U_35),U_35)
| ~ sP7(U_35,U_37) ),
inference(clausify,[status(thm)],[f_13_5]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_ordinal1]) ).
fof(f_14_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
$true,
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
fof(f_15_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
$true,
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
fof(f_16_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
$true,
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
fof(f_17_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
$true,
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_18_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
$true,
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_19_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
$true,
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_20_2,plain,
! [U_39] :
? [U_38] : element(U_38,U_39),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_39] : element(sK5(U_39),U_39),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5(U_39))],[f_20_2]) ).
fof(f_20_4,plain,
! [U_39] : element(sK5(U_39),U_39),
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
element(sK5(U_39),U_39),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_21_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_21_2]) ).
cnf(f_21_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_22_2,plain,
! [U_40] : ~ empty(succ(U_40)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_40] : ~ empty(succ(U_40)),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
~ empty(succ(U_40)),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_23_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(fof_nnf,[status(thm)],[fc2_ordinal1]) ).
fof(f_24_2,plain,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
cnf(f_24_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_25_2,plain,
! [U_42,U_41] :
( relation(set_union2(U_42,U_41))
| ~ relation(U_41)
| ~ relation(U_42) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_42,U_41] :
( relation(set_union2(U_42,U_41))
| ~ relation(U_41)
| ~ relation(U_42) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( relation(set_union2(U_42,U_41))
| ~ relation(U_41)
| ~ relation(U_42) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_26_2,plain,
! [U_44,U_43] :
( ~ empty(set_union2(U_44,U_43))
| empty(U_44) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_44] :
( ! [U_43] : ~ empty(set_union2(U_44,U_43))
| empty(U_44) ),
inference(miniscope,[status(thm)],[f_26_2]) ).
fof(f_26_4,plain,
! [U_43,U_44] :
( ~ empty(set_union2(U_44,U_43))
| empty(U_44) ),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
( ~ empty(set_union2(U_44,U_43))
| empty(U_44) ),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc3_ordinal1]) ).
fof(f_27_2,plain,
! [U_45] :
( ( ordinal(succ(U_45))
& epsilon_connected(succ(U_45))
& epsilon_transitive(succ(U_45))
& ~ empty(succ(U_45)) )
| ~ ordinal(U_45) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_45] :
( ordinal(succ(U_45))
| ~ sP8(U_45) )
& ! [U_45] :
( epsilon_connected(succ(U_45))
| ~ sP8(U_45) )
& ! [U_45] :
( epsilon_transitive(succ(U_45))
| ~ sP8(U_45) )
& ! [U_45] :
( ~ empty(succ(U_45))
| ~ sP8(U_45) )
& ! [U_45] :
( sP8(U_45)
| ~ ordinal(U_45) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP8(U_45)
| ~ ordinal(U_45) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( ~ empty(succ(U_45))
| ~ sP8(U_45) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( epsilon_transitive(succ(U_45))
| ~ sP8(U_45) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_7,plain,
( epsilon_connected(succ(U_45))
| ~ sP8(U_45) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_8,plain,
( ordinal(succ(U_45))
| ~ sP8(U_45) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_28_2,plain,
! [U_47,U_46] :
( ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_47] :
( ! [U_46] : ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(miniscope,[status(thm)],[f_28_2]) ).
fof(f_28_4,plain,
! [U_47,U_46] :
( ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
( ~ empty(set_union2(U_46,U_47))
| empty(U_47) ),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_29_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_29_1]) ).
cnf(f_29_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_30_2,plain,
! [U_49,U_48] : set_union2(U_49,U_49) = U_49,
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_49] : set_union2(U_49,U_49) = U_49,
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_49] : set_union2(U_49,U_49) = U_49,
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
set_union2(U_49,U_49) = U_49,
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_31_2,plain,
? [U_50] :
( function(U_50)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_50,sK6)],[f_31_2]) ).
fof(f_31_4,plain,
( function(sK6)
& relation(sK6) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_32_2,plain,
? [U_51] :
( ordinal(U_51)
& epsilon_connected(U_51)
& epsilon_transitive(U_51) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_51,sK7)],[f_32_2]) ).
fof(f_32_4,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
epsilon_transitive(sK7),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
epsilon_connected(sK7),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
ordinal(sK7),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_33_2,plain,
? [U_52] :
( relation(U_52)
& empty(U_52) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( relation(sK8)
& empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_52,sK8)],[f_33_2]) ).
fof(f_33_4,plain,
( relation(sK8)
& empty(sK8) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_34_2,plain,
? [U_53] : empty(U_53),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_53,sK9)],[f_34_2]) ).
fof(f_34_4,plain,
empty(sK9),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_35_2,plain,
? [U_54] :
( function(U_54)
& empty(U_54)
& relation(U_54) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_54,sK10)],[f_35_2]) ).
fof(f_35_4,plain,
( function(sK10)
& empty(sK10)
& relation(sK10) ),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
function(sK10),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal1]) ).
fof(f_36_2,plain,
? [U_55] :
( ordinal(U_55)
& epsilon_connected(U_55)
& epsilon_transitive(U_55)
& empty(U_55)
& one_to_one(U_55)
& function(U_55)
& relation(U_55) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& empty(sK11)
& one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_55,sK11)],[f_36_2]) ).
fof(f_36_4,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& empty(sK11)
& one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
function(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_7,plain,
one_to_one(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_8,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_9,plain,
epsilon_transitive(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_10,plain,
epsilon_connected(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_11,plain,
ordinal(sK11),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_37_2,plain,
? [U_56] :
( relation(U_56)
& ~ empty(U_56) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_56,sK12)],[f_37_2]) ).
fof(f_37_4,plain,
( relation(sK12)
& ~ empty(sK12) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_38_2,plain,
? [U_57] : ~ empty(U_57),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
~ empty(sK13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_57,sK13)],[f_38_2]) ).
fof(f_38_4,plain,
~ empty(sK13),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_39_2,plain,
? [U_58] :
( one_to_one(U_58)
& function(U_58)
& relation(U_58) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( one_to_one(sK14)
& function(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_58,sK14)],[f_39_2]) ).
fof(f_39_4,plain,
( one_to_one(sK14)
& function(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
function(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
one_to_one(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_40_2,plain,
? [U_59] :
( ordinal(U_59)
& epsilon_connected(U_59)
& epsilon_transitive(U_59)
& ~ empty(U_59) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15)
& ~ empty(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_59,sK15)],[f_40_2]) ).
fof(f_40_4,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15)
& ~ empty(sK15) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
~ empty(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
epsilon_transitive(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
epsilon_connected(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_8,plain,
ordinal(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_41_2,plain,
? [U_60] :
( relation_empty_yielding(U_60)
& relation(U_60) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( relation_empty_yielding(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_60,sK16)],[f_41_2]) ).
fof(f_41_4,plain,
( relation_empty_yielding(sK16)
& relation(sK16) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
relation_empty_yielding(sK16),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_42_2,plain,
? [U_61] :
( function(U_61)
& relation_empty_yielding(U_61)
& relation(U_61) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( function(sK17)
& relation_empty_yielding(sK17)
& relation(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_61,sK17)],[f_42_2]) ).
fof(f_42_4,plain,
( function(sK17)
& relation_empty_yielding(sK17)
& relation(sK17) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
relation(sK17),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
relation_empty_yielding(sK17),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,plain,
function(sK17),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
! [A,B] :
( ( ( ordinal_subset(A,B)
| ~ subset(A,B) )
& ( subset(A,B)
| ~ ordinal_subset(A,B) ) )
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1]) ).
fof(f_43_2,plain,
! [U_63,U_62] :
( ( ( ordinal_subset(U_63,U_62)
| ~ subset(U_63,U_62) )
& ( subset(U_63,U_62)
| ~ ordinal_subset(U_63,U_62) ) )
| ~ ordinal(U_62)
| ~ ordinal(U_63) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( ! [U_63,U_62] :
( ordinal_subset(U_63,U_62)
| ~ subset(U_63,U_62)
| ~ sP9(U_63,U_62) )
& ! [U_63,U_62] :
( subset(U_63,U_62)
| ~ ordinal_subset(U_63,U_62)
| ~ sP9(U_63,U_62) )
& ! [U_63,U_62] :
( sP9(U_63,U_62)
| ~ ordinal(U_62)
| ~ ordinal(U_63) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_43_2]) ).
cnf(f_43_4,plain,
( sP9(U_63,U_62)
| ~ ordinal(U_62)
| ~ ordinal(U_63) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_5,plain,
( subset(U_63,U_62)
| ~ ordinal_subset(U_63,U_62)
| ~ sP9(U_63,U_62) ),
inference(clausify,[status(thm)],[f_43_3]) ).
cnf(f_43_6,plain,
( ordinal_subset(U_63,U_62)
| ~ subset(U_63,U_62)
| ~ sP9(U_63,U_62) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_44_2,plain,
! [U_65,U_64] :
( ordinal_subset(U_65,U_65)
| ~ ordinal(U_64)
| ~ ordinal(U_65) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_65] :
( ! [U_64] : ~ ordinal(U_64)
| ~ ordinal(U_65)
| ordinal_subset(U_65,U_65) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
! [U_65,U_64] :
( ~ ordinal(U_64)
| ~ ordinal(U_65)
| ordinal_subset(U_65,U_65) ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
( ~ ordinal(U_64)
| ~ ordinal(U_65)
| ordinal_subset(U_65,U_65) ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_45_2,plain,
! [U_67,U_66] : subset(U_67,U_67),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_67] : subset(U_67,U_67),
inference(miniscope,[status(thm)],[f_45_2]) ).
fof(f_45_4,plain,
! [U_67] : subset(U_67,U_67),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
subset(U_67,U_67),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_46_2,plain,
! [U_68] : in(U_68,succ(U_68)),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_68] : in(U_68,succ(U_68)),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
in(U_68,succ(U_68)),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_47_2,plain,
! [U_69] : set_union2(U_69,empty_set) = U_69,
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_69] : set_union2(U_69,empty_set) = U_69,
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
set_union2(U_69,empty_set) = U_69,
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_48_2,plain,
! [U_71,U_70] :
( element(U_71,U_70)
| ~ in(U_71,U_70) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_71,U_70] :
( element(U_71,U_70)
| ~ in(U_71,U_70) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( element(U_71,U_70)
| ~ in(U_71,U_70) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_49_2,plain,
! [U_73,U_72] :
( in(U_73,U_72)
| empty(U_72)
| ~ element(U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_73,U_72] :
( in(U_73,U_72)
| empty(U_72)
| ~ element(U_73,U_72) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( in(U_73,U_72)
| empty(U_72)
| ~ element(U_73,U_72) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
inference(negate,[status(cth)],[t33_ordinal1]) ).
fof(f_50_2,negated_conjecture,
? [A] :
( ? [B] :
( ( ( ~ in(A,B)
& ordinal_subset(succ(A),B) )
| ( ~ ordinal_subset(succ(A),B)
& in(A,B) ) )
& ordinal(B) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[f_50_1]) ).
fof(f_50_3,negated_conjecture,
? [U_75] :
( ? [U_74] :
( ( ( ~ in(U_75,U_74)
& ordinal_subset(succ(U_75),U_74) )
| ( ~ ordinal_subset(succ(U_75),U_74)
& in(U_75,U_74) ) )
& ordinal(U_74) )
& ordinal(U_75) ),
inference(variable_rename,[status(thm)],[f_50_2]) ).
fof(f_50_4,negated_conjecture,
( ? [U_74] :
( ( ( ~ in(sK18,U_74)
& ordinal_subset(succ(sK18),U_74) )
| ( ~ ordinal_subset(succ(sK18),U_74)
& in(sK18,U_74) ) )
& ordinal(U_74) )
& ordinal(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_75,sK18)],[f_50_3]) ).
fof(f_50_5,negated_conjecture,
( ( ( ~ in(sK18,sK19)
& ordinal_subset(succ(sK18),sK19) )
| ( ~ ordinal_subset(succ(sK18),sK19)
& in(sK18,sK19) ) )
& ordinal(sK19)
& ordinal(sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_74,sK19)],[f_50_4]) ).
fof(f_50_6,negated_conjecture,
( ( ~ in(sK18,sK19)
| ~ sP11 )
& ( ordinal_subset(succ(sK18),sK19)
| ~ sP11 )
& ( ~ ordinal_subset(succ(sK18),sK19)
| ~ sP10 )
& ( in(sK18,sK19)
| ~ sP10 )
& ( sP11
| sP10 )
& ordinal(sK19)
& ordinal(sK18) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11])],[f_50_5]) ).
cnf(f_50_7,negated_conjecture,
ordinal(sK18),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_8,negated_conjecture,
ordinal(sK19),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_9,negated_conjecture,
( sP11
| sP10 ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_10,negated_conjecture,
( in(sK18,sK19)
| ~ sP10 ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_11,negated_conjecture,
( ~ ordinal_subset(succ(sK18),sK19)
| ~ sP10 ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_12,negated_conjecture,
( ordinal_subset(succ(sK18),sK19)
| ~ sP11 ),
inference(clausify,[status(thm)],[f_50_6]) ).
cnf(f_50_13,negated_conjecture,
( ~ in(sK18,sK19)
| ~ sP11 ),
inference(clausify,[status(thm)],[f_50_6]) ).
fof(f_51_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_51_2,plain,
! [U_77,U_76] :
( ( element(U_77,powerset(U_76))
| ~ subset(U_77,U_76) )
& ( subset(U_77,U_76)
| ~ element(U_77,powerset(U_76)) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_81,U_79] :
( element(U_81,powerset(U_79))
| ~ subset(U_81,U_79) )
& ! [U_80,U_78] :
( subset(U_80,U_78)
| ~ element(U_80,powerset(U_78)) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_81,U_79] :
( element(U_81,powerset(U_79))
| ~ subset(U_81,U_79) )
& ! [U_80,U_78] :
( subset(U_80,U_78)
| ~ element(U_80,powerset(U_78)) ) ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
( subset(U_80,U_78)
| ~ element(U_80,powerset(U_78)) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
( element(U_81,powerset(U_79))
| ~ subset(U_81,U_79) ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_52_2,plain,
! [U_84,U_83,U_82] :
( element(U_84,U_82)
| ~ element(U_83,powerset(U_82))
| ~ in(U_84,U_83) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_82,U_83,U_84] :
( element(U_84,U_82)
| ~ element(U_83,powerset(U_82))
| ~ in(U_84,U_83) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( element(U_84,U_82)
| ~ element(U_83,powerset(U_82))
| ~ in(U_84,U_83) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_53_2,plain,
! [U_87,U_86,U_85] :
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85))
| ~ in(U_87,U_86) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_87,U_86] :
( ! [U_85] :
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85)) )
| ~ in(U_87,U_86) ),
inference(miniscope,[status(thm)],[f_53_2]) ).
fof(f_53_4,plain,
! [U_85,U_87,U_86] :
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85))
| ~ in(U_87,U_86) ),
inference(definitional_conversion,[status(esa)],[f_53_3]) ).
cnf(f_53_5,plain,
( ~ empty(U_85)
| ~ element(U_86,powerset(U_85))
| ~ in(U_87,U_86) ),
inference(clausify,[status(thm)],[f_53_4]) ).
fof(f_54_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_54_2,plain,
! [U_88] :
( U_88 = empty_set
| ~ empty(U_88) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_88] :
( U_88 = empty_set
| ~ empty(U_88) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( U_88 = empty_set
| ~ empty(U_88) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_55_2,plain,
! [U_90,U_89] :
( ~ empty(U_89)
| ~ in(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_89,U_90] :
( ~ empty(U_89)
| ~ in(U_90,U_89) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( ~ empty(U_89)
| ~ in(U_90,U_89) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_56_2,plain,
! [U_92,U_91] :
( ~ empty(U_91)
| U_92 = U_91
| ~ empty(U_92) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_92] :
( ! [U_91] :
( ~ empty(U_91)
| U_92 = U_91 )
| ~ empty(U_92) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
! [U_91,U_92] :
( ~ empty(U_91)
| U_92 = U_91
| ~ empty(U_92) ),
inference(definitional_conversion,[status(esa)],[f_56_3]) ).
cnf(f_56_5,plain,
( ~ empty(U_91)
| U_92 = U_91
| ~ empty(U_92) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_1,plain,
! [A,B,C] :
( subset(set_union2(A,C),B)
| ~ subset(C,B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1]) ).
fof(f_57_2,plain,
! [U_95,U_94,U_93] :
( subset(set_union2(U_95,U_93),U_94)
| ~ subset(U_93,U_94)
| ~ subset(U_95,U_94) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_94,U_93,U_95] :
( subset(set_union2(U_95,U_93),U_94)
| ~ subset(U_93,U_94)
| ~ subset(U_95,U_94) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( subset(set_union2(U_95,U_93),U_94)
| ~ subset(U_93,U_94)
| ~ subset(U_95,U_94) ),
inference(clausify,[status(thm)],[f_57_3]) ).
cnf(f_14_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_14_3]) ).
cnf(f_15_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_3]) ).
cnf(f_16_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_3]) ).
cnf(f_17_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_17_3]) ).
cnf(f_18_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_3]) ).
cnf(f_19_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_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,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK1(Eq_x_0,Eq_x_1) = sK1(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,
( 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_10,axiom,
( sK3(Eq_x_0) = sK3(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,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_12,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( one_to_one(Eq_y_0)
| ~ one_to_one(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( ordinal_subset(Eq_y_0,Eq_y_1)
| ~ ordinal_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_22,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_23,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_24,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(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_29,axiom,
( sP4(Eq_y_0,Eq_y_1)
| ~ sP4(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_30,axiom,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP7(Eq_y_0,Eq_y_1)
| ~ sP7(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| 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 : SEU236+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
% 0.08/0.34 % Computer : n016.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 19 23:43:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 216.16/216.42 % SZS status Theorem for theBenchmark
% 216.16/216.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------