%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU270+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:58:48 AM UTC 2026
% Result : Theorem 165.34s 170.66s
% Output : Proof 166.48s
% 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(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_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
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(d14_relat_2,axiom,
! [A] :
( relation(A)
=> ( connected(A)
<=> is_connected_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d14_relat_2) ).
fof(d1_wellord2,axiom,
! [A,B] :
( relation(B)
=> ( B = inclusion_relation(A)
<=> ( ! [C,D] :
( ( in(D,A)
& in(C,A) )
=> ( in(ordered_pair(C,D),B)
<=> subset(C,D) ) )
& relation_field(B) = A ) ) ),
file('theBenchmark.p',d1_wellord2) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(d6_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_connected_in(A,B)
<=> ! [C,D] :
~ ( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) ) ),
file('theBenchmark.p',d6_relat_2) ).
fof(dt_k1_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k1_relat_1) ).
fof(dt_k1_tarski,axiom,
$true,
file('theBenchmark.p',dt_k1_tarski) ).
fof(dt_k1_wellord2,axiom,
! [A] : relation(inclusion_relation(A)),
file('theBenchmark.p',dt_k1_wellord2) ).
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_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k2_relat_1) ).
fof(dt_k2_tarski,axiom,
$true,
file('theBenchmark.p',dt_k2_tarski) ).
fof(dt_k2_xboole_0,axiom,
$true,
file('theBenchmark.p',dt_k2_xboole_0) ).
fof(dt_k3_relat_1,axiom,
$true,
file('theBenchmark.p',dt_k3_relat_1) ).
fof(dt_k4_tarski,axiom,
$true,
file('theBenchmark.p',dt_k4_tarski) ).
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(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc1_zfmisc_1,axiom,
! [A,B] : ~ empty(ordered_pair(A,B)),
file('theBenchmark.p',fc1_zfmisc_1) ).
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_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
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_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_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(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(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(t23_ordinal1,axiom,
! [A,B] :
( ordinal(B)
=> ( in(A,B)
=> ordinal(A) ) ),
file('theBenchmark.p',t23_ordinal1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('theBenchmark.p',t4_subset) ).
fof(t4_wellord2,conjecture,
! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
file('theBenchmark.p',t4_wellord2) ).
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(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]) ).
cnf(f_1_3,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_2]) ).
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]) ).
cnf(f_2_3,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
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]) ).
cnf(f_3_3,plain,
( epsilon_transitive(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( epsilon_connected(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_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_4_2,plain,
! [U_4] :
( ( one_to_one(U_4)
& function(U_4)
& relation(U_4) )
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( relation(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_5,plain,
( one_to_one(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_5_2,plain,
! [U_5] :
( ordinal(U_5)
| ~ epsilon_connected(U_5)
| ~ epsilon_transitive(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( ordinal(U_5)
| ~ epsilon_connected(U_5)
| ~ epsilon_transitive(U_5) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_6_2,plain,
! [U_6] :
( ( ordinal(U_6)
& epsilon_connected(U_6)
& epsilon_transitive(U_6) )
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( epsilon_transitive(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( epsilon_connected(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( ordinal(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_tarski]) ).
fof(f_7_2,plain,
! [U_8,U_7] : unordered_pair(U_8,U_7) = unordered_pair(U_7,U_8),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
unordered_pair(U_8,U_7) = unordered_pair(U_7,U_8),
inference(clausify,[status(thm)],[f_7_2]) ).
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_10,U_9] : set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(clausify,[status(thm)],[f_8_2]) ).
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_12,U_11] :
( ordinal_subset(U_11,U_12)
| ordinal_subset(U_12,U_11)
| ~ ordinal(U_11)
| ~ ordinal(U_12) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ordinal_subset(U_11,U_12)
| ordinal_subset(U_12,U_11)
| ~ ordinal(U_11)
| ~ ordinal(U_12) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [A] :
( ( ( connected(A)
| ~ is_connected_in(A,relation_field(A)) )
& ( is_connected_in(A,relation_field(A))
| ~ connected(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d14_relat_2]) ).
fof(f_10_2,plain,
! [U_13] :
( ( ( connected(U_13)
| ~ is_connected_in(U_13,relation_field(U_13)) )
& ( is_connected_in(U_13,relation_field(U_13))
| ~ connected(U_13) ) )
| ~ relation(U_13) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( is_connected_in(U_13,relation_field(U_13))
| ~ connected(U_13)
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( connected(U_13)
| ~ is_connected_in(U_13,relation_field(U_13))
| ~ relation(U_13) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A,B] :
( ( ( B = inclusion_relation(A)
| ? [C,D] :
( ( ( ~ in(ordered_pair(C,D),B)
& subset(C,D) )
| ( ~ subset(C,D)
& in(ordered_pair(C,D),B) ) )
& in(D,A)
& in(C,A) )
| relation_field(B) != A )
& ( ( ! [C,D] :
( ( ( in(ordered_pair(C,D),B)
| ~ subset(C,D) )
& ( subset(C,D)
| ~ in(ordered_pair(C,D),B) ) )
| ~ in(D,A)
| ~ in(C,A) )
& relation_field(B) = A )
| B != inclusion_relation(A) ) )
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d1_wellord2]) ).
fof(f_11_2,plain,
! [U_19,U_18] :
( ( ( U_18 = inclusion_relation(U_19)
| ? [U_17,U_16] :
( ( ( ~ in(ordered_pair(U_17,U_16),U_18)
& subset(U_17,U_16) )
| ( ~ subset(U_17,U_16)
& in(ordered_pair(U_17,U_16),U_18) ) )
& in(U_16,U_19)
& in(U_17,U_19) )
| relation_field(U_18) != U_19 )
& ( ( ! [U_15,U_14] :
( ( ( in(ordered_pair(U_15,U_14),U_18)
| ~ subset(U_15,U_14) )
& ( subset(U_15,U_14)
| ~ in(ordered_pair(U_15,U_14),U_18) ) )
| ~ in(U_14,U_19)
| ~ in(U_15,U_19) )
& relation_field(U_18) = U_19 )
| U_18 != inclusion_relation(U_19) ) )
| ~ relation(U_18) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_19,U_18] :
( ( ( U_18 = inclusion_relation(U_19)
| ? [U_16] :
( ( ( ~ in(ordered_pair(sK1(U_19,U_18),U_16),U_18)
& subset(sK1(U_19,U_18),U_16) )
| ( ~ subset(sK1(U_19,U_18),U_16)
& in(ordered_pair(sK1(U_19,U_18),U_16),U_18) ) )
& in(U_16,U_19)
& in(sK1(U_19,U_18),U_19) )
| relation_field(U_18) != U_19 )
& ( ( ! [U_15,U_14] :
( ( ( in(ordered_pair(U_15,U_14),U_18)
| ~ subset(U_15,U_14) )
& ( subset(U_15,U_14)
| ~ in(ordered_pair(U_15,U_14),U_18) ) )
| ~ in(U_14,U_19)
| ~ in(U_15,U_19) )
& relation_field(U_18) = U_19 )
| U_18 != inclusion_relation(U_19) ) )
| ~ relation(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_17,sK1(U_19,U_18))],[f_11_2]) ).
fof(f_11_4,plain,
! [U_19,U_18] :
( ( ( U_18 = inclusion_relation(U_19)
| ( ( ( ~ in(ordered_pair(sK1(U_19,U_18),sK2(U_19,U_18)),U_18)
& subset(sK1(U_19,U_18),sK2(U_19,U_18)) )
| ( ~ subset(sK1(U_19,U_18),sK2(U_19,U_18))
& in(ordered_pair(sK1(U_19,U_18),sK2(U_19,U_18)),U_18) ) )
& in(sK2(U_19,U_18),U_19)
& in(sK1(U_19,U_18),U_19) )
| relation_field(U_18) != U_19 )
& ( ( ! [U_15,U_14] :
( ( ( in(ordered_pair(U_15,U_14),U_18)
| ~ subset(U_15,U_14) )
& ( subset(U_15,U_14)
| ~ in(ordered_pair(U_15,U_14),U_18) ) )
| ~ in(U_14,U_19)
| ~ in(U_15,U_19) )
& relation_field(U_18) = U_19 )
| U_18 != inclusion_relation(U_19) ) )
| ~ relation(U_18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_19,U_18))],[f_11_3]) ).
cnf(f_11_5,plain,
( relation_field(U_18) = U_19
| U_18 != inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_6,plain,
( subset(U_15,U_14)
| ~ in(ordered_pair(U_15,U_14),U_18)
| ~ in(U_14,U_19)
| ~ in(U_15,U_19)
| U_18 != inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_7,plain,
( in(ordered_pair(U_15,U_14),U_18)
| ~ subset(U_15,U_14)
| ~ in(U_14,U_19)
| ~ in(U_15,U_19)
| U_18 != inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_8,plain,
( in(sK1(U_19,U_18),U_19)
| relation_field(U_18) != U_19
| U_18 = inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_9,plain,
( in(sK2(U_19,U_18),U_19)
| relation_field(U_18) != U_19
| U_18 = inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_10,plain,
( subset(sK1(U_19,U_18),sK2(U_19,U_18))
| in(ordered_pair(sK1(U_19,U_18),sK2(U_19,U_18)),U_18)
| relation_field(U_18) != U_19
| U_18 = inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_11,plain,
( ~ in(ordered_pair(sK1(U_19,U_18),sK2(U_19,U_18)),U_18)
| in(ordered_pair(sK1(U_19,U_18),sK2(U_19,U_18)),U_18)
| relation_field(U_18) != U_19
| U_18 = inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_12,plain,
( subset(sK1(U_19,U_18),sK2(U_19,U_18))
| ~ subset(sK1(U_19,U_18),sK2(U_19,U_18))
| relation_field(U_18) != U_19
| U_18 = inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
cnf(f_11_13,plain,
( ~ in(ordered_pair(sK1(U_19,U_18),sK2(U_19,U_18)),U_18)
| ~ subset(sK1(U_19,U_18),sK2(U_19,U_18))
| relation_field(U_18) != U_19
| U_18 = inclusion_relation(U_19)
| ~ relation(U_18) ),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(fof_nnf,[status(thm)],[d5_tarski]) ).
fof(f_12_2,plain,
! [U_21,U_20] : ordered_pair(U_21,U_20) = unordered_pair(unordered_pair(U_21,U_20),singleton(U_21)),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
ordered_pair(U_21,U_20) = unordered_pair(unordered_pair(U_21,U_20),singleton(U_21)),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [A] :
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_1]) ).
fof(f_13_2,plain,
! [U_22] :
( relation_field(U_22) = set_union2(relation_dom(U_22),relation_rng(U_22))
| ~ relation(U_22) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
( relation_field(U_22) = set_union2(relation_dom(U_22),relation_rng(U_22))
| ~ relation(U_22) ),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [A] :
( ! [B] :
( ( is_connected_in(A,B)
| ? [C,D] :
( ~ in(ordered_pair(D,C),A)
& ~ in(ordered_pair(C,D),A)
& C != D
& in(D,B)
& in(C,B) ) )
& ( ! [C,D] :
( in(ordered_pair(D,C),A)
| in(ordered_pair(C,D),A)
| C = D
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_connected_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d6_relat_2]) ).
fof(f_14_2,plain,
! [U_28] :
( ! [U_27] :
( ( is_connected_in(U_28,U_27)
| ? [U_26,U_25] :
( ~ in(ordered_pair(U_25,U_26),U_28)
& ~ in(ordered_pair(U_26,U_25),U_28)
& U_26 != U_25
& in(U_25,U_27)
& in(U_26,U_27) ) )
& ( ! [U_24,U_23] :
( in(ordered_pair(U_23,U_24),U_28)
| in(ordered_pair(U_24,U_23),U_28)
| U_24 = U_23
| ~ in(U_23,U_27)
| ~ in(U_24,U_27) )
| ~ is_connected_in(U_28,U_27) ) )
| ~ relation(U_28) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_28] :
( ( ! [U_30] :
( is_connected_in(U_28,U_30)
| ? [U_26] :
( ? [U_25] :
( ~ in(ordered_pair(U_25,U_26),U_28)
& ~ in(ordered_pair(U_26,U_25),U_28)
& U_26 != U_25
& in(U_25,U_30) )
& in(U_26,U_30) ) )
& ! [U_29] :
( ! [U_24] :
( ! [U_23] :
( in(ordered_pair(U_23,U_24),U_28)
| in(ordered_pair(U_24,U_23),U_28)
| U_24 = U_23
| ~ in(U_23,U_29) )
| ~ in(U_24,U_29) )
| ~ is_connected_in(U_28,U_29) ) )
| ~ relation(U_28) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
fof(f_14_4,plain,
! [U_28] :
( ( ! [U_30] :
( is_connected_in(U_28,U_30)
| ( ? [U_25] :
( ~ in(ordered_pair(U_25,sK3(U_28,U_30)),U_28)
& ~ in(ordered_pair(sK3(U_28,U_30),U_25),U_28)
& sK3(U_28,U_30) != U_25
& in(U_25,U_30) )
& in(sK3(U_28,U_30),U_30) ) )
& ! [U_29] :
( ! [U_24] :
( ! [U_23] :
( in(ordered_pair(U_23,U_24),U_28)
| in(ordered_pair(U_24,U_23),U_28)
| U_24 = U_23
| ~ in(U_23,U_29) )
| ~ in(U_24,U_29) )
| ~ is_connected_in(U_28,U_29) ) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_26,sK3(U_28,U_30))],[f_14_3]) ).
fof(f_14_5,plain,
! [U_28] :
( ( ! [U_30] :
( is_connected_in(U_28,U_30)
| ( ~ in(ordered_pair(sK4(U_28,U_30),sK3(U_28,U_30)),U_28)
& ~ in(ordered_pair(sK3(U_28,U_30),sK4(U_28,U_30)),U_28)
& sK3(U_28,U_30) != sK4(U_28,U_30)
& in(sK4(U_28,U_30),U_30)
& in(sK3(U_28,U_30),U_30) ) )
& ! [U_29] :
( ! [U_24] :
( ! [U_23] :
( in(ordered_pair(U_23,U_24),U_28)
| in(ordered_pair(U_24,U_23),U_28)
| U_24 = U_23
| ~ in(U_23,U_29) )
| ~ in(U_24,U_29) )
| ~ is_connected_in(U_28,U_29) ) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_25,sK4(U_28,U_30))],[f_14_4]) ).
cnf(f_14_6,plain,
( in(ordered_pair(U_23,U_24),U_28)
| in(ordered_pair(U_24,U_23),U_28)
| U_24 = U_23
| ~ in(U_23,U_29)
| ~ in(U_24,U_29)
| ~ is_connected_in(U_28,U_29)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_7,plain,
( in(sK3(U_28,U_30),U_30)
| is_connected_in(U_28,U_30)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_8,plain,
( in(sK4(U_28,U_30),U_30)
| is_connected_in(U_28,U_30)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_9,plain,
( sK3(U_28,U_30) != sK4(U_28,U_30)
| is_connected_in(U_28,U_30)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_10,plain,
( ~ in(ordered_pair(sK3(U_28,U_30),sK4(U_28,U_30)),U_28)
| is_connected_in(U_28,U_30)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_14_5]) ).
cnf(f_14_11,plain,
( ~ in(ordered_pair(sK4(U_28,U_30),sK3(U_28,U_30)),U_28)
| is_connected_in(U_28,U_30)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_14_5]) ).
fof(f_15_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
cnf(f_15_2,plain,
$true,
inference(clausify,[status(thm)],[f_15_1]) ).
fof(f_16_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_tarski]) ).
cnf(f_16_2,plain,
$true,
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_1,plain,
! [A] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_17_2,plain,
! [U_31] : relation(inclusion_relation(U_31)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
relation(inclusion_relation(U_31)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
cnf(f_18_2,plain,
$true,
inference(clausify,[status(thm)],[f_18_1]) ).
fof(f_19_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_zfmisc_1]) ).
cnf(f_19_2,plain,
$true,
inference(clausify,[status(thm)],[f_19_1]) ).
fof(f_20_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_relat_1]) ).
cnf(f_20_2,plain,
$true,
inference(clausify,[status(thm)],[f_20_1]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
cnf(f_21_2,plain,
$true,
inference(clausify,[status(thm)],[f_21_1]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
cnf(f_22_2,plain,
$true,
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
cnf(f_23_2,plain,
$true,
inference(clausify,[status(thm)],[f_23_1]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
cnf(f_24_2,plain,
$true,
inference(clausify,[status(thm)],[f_24_1]) ).
fof(f_25_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
cnf(f_25_2,plain,
$true,
inference(clausify,[status(thm)],[f_25_1]) ).
fof(f_26_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_26_2,plain,
! [U_33] :
? [U_32] : element(U_32,U_33),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_33] : element(sK5(U_33),U_33),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_32,sK5(U_33))],[f_26_2]) ).
cnf(f_26_4,plain,
element(sK5(U_33),U_33),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_27_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_27_1]) ).
fof(f_28_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_28_2,plain,
! [U_35,U_34] : ~ empty(ordered_pair(U_35,U_34)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ empty(ordered_pair(U_35,U_34)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_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]) ).
cnf(f_29_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
cnf(f_29_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_29_1]) ).
fof(f_30_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_30_2,plain,
! [U_37,U_36] :
( ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_37] :
( ! [U_36] : ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
cnf(f_30_4,plain,
( ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_31_2,plain,
! [U_39,U_38] :
( ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_39] :
( ! [U_38] : ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_32_2,plain,
! [U_41,U_40] : set_union2(U_41,U_41) = U_41,
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_41] : set_union2(U_41,U_41) = U_41,
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
set_union2(U_41,U_41) = U_41,
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_33_2,plain,
? [U_42] :
( function(U_42)
& relation(U_42) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_42,sK6)],[f_33_2]) ).
cnf(f_33_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
function(sK6),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_34_2,plain,
? [U_43] :
( ordinal(U_43)
& epsilon_connected(U_43)
& epsilon_transitive(U_43) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_43,sK7)],[f_34_2]) ).
cnf(f_34_4,plain,
epsilon_transitive(sK7),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
epsilon_connected(sK7),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
ordinal(sK7),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_35_2,plain,
? [U_44] : empty(U_44),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
empty(sK8),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_44,sK8)],[f_35_2]) ).
cnf(f_35_4,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_36_2,plain,
? [U_45] :
( function(U_45)
& empty(U_45)
& relation(U_45) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( function(sK9)
& empty(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_45,sK9)],[f_36_2]) ).
cnf(f_36_4,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
function(sK9),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
? [U_46] :
( ordinal(U_46)
& epsilon_connected(U_46)
& epsilon_transitive(U_46)
& empty(U_46)
& one_to_one(U_46)
& function(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ordinal(sK10)
& epsilon_connected(sK10)
& epsilon_transitive(sK10)
& empty(sK10)
& one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_46,sK10)],[f_37_2]) ).
cnf(f_37_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_7,plain,
empty(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_8,plain,
epsilon_transitive(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_9,plain,
epsilon_connected(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_10,plain,
ordinal(sK10),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_38_2,plain,
? [U_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
~ empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_47,sK11)],[f_38_2]) ).
cnf(f_38_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_38_3]) ).
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_48] :
( one_to_one(U_48)
& function(U_48)
& relation(U_48) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_48,sK12)],[f_39_2]) ).
cnf(f_39_4,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_5,plain,
function(sK12),
inference(clausify,[status(thm)],[f_39_3]) ).
cnf(f_39_6,plain,
one_to_one(sK12),
inference(clausify,[status(thm)],[f_39_3]) ).
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_49] :
( ordinal(U_49)
& epsilon_connected(U_49)
& epsilon_transitive(U_49)
& ~ empty(U_49) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( ordinal(sK13)
& epsilon_connected(sK13)
& epsilon_transitive(sK13)
& ~ empty(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_49,sK13)],[f_40_2]) ).
cnf(f_40_4,plain,
~ empty(sK13),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_5,plain,
epsilon_transitive(sK13),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_6,plain,
epsilon_connected(sK13),
inference(clausify,[status(thm)],[f_40_3]) ).
cnf(f_40_7,plain,
ordinal(sK13),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_41_2,plain,
? [U_50] :
( function(U_50)
& relation_empty_yielding(U_50)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( function(sK14)
& relation_empty_yielding(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_50,sK14)],[f_41_2]) ).
cnf(f_41_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_5,plain,
relation_empty_yielding(sK14),
inference(clausify,[status(thm)],[f_41_3]) ).
cnf(f_41_6,plain,
function(sK14),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_52,U_51] :
( ( ( ordinal_subset(U_52,U_51)
| ~ subset(U_52,U_51) )
& ( subset(U_52,U_51)
| ~ ordinal_subset(U_52,U_51) ) )
| ~ ordinal(U_51)
| ~ ordinal(U_52) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
( subset(U_52,U_51)
| ~ ordinal_subset(U_52,U_51)
| ~ ordinal(U_51)
| ~ ordinal(U_52) ),
inference(clausify,[status(thm)],[f_42_2]) ).
cnf(f_42_4,plain,
( ordinal_subset(U_52,U_51)
| ~ subset(U_52,U_51)
| ~ ordinal(U_51)
| ~ ordinal(U_52) ),
inference(clausify,[status(thm)],[f_42_2]) ).
fof(f_43_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_43_2,plain,
! [U_54,U_53] :
( ordinal_subset(U_54,U_54)
| ~ ordinal(U_53)
| ~ ordinal(U_54) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_54] :
( ! [U_53] : ~ ordinal(U_53)
| ~ ordinal(U_54)
| ordinal_subset(U_54,U_54) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
cnf(f_43_4,plain,
( ~ ordinal(U_53)
| ~ ordinal(U_54)
| ordinal_subset(U_54,U_54) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_44_2,plain,
! [U_56,U_55] : subset(U_56,U_56),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_56] : subset(U_56,U_56),
inference(miniscope,[status(thm)],[f_44_2]) ).
cnf(f_44_4,plain,
subset(U_56,U_56),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_45_2,plain,
! [U_57] : set_union2(U_57,empty_set) = U_57,
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
set_union2(U_57,empty_set) = U_57,
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_46_2,plain,
! [U_59,U_58] :
( element(U_59,U_58)
| ~ in(U_59,U_58) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( element(U_59,U_58)
| ~ in(U_59,U_58) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_1,plain,
! [A,B] :
( ordinal(A)
| ~ in(A,B)
| ~ ordinal(B) ),
inference(fof_nnf,[status(thm)],[t23_ordinal1]) ).
fof(f_47_2,plain,
! [U_61,U_60] :
( ordinal(U_61)
| ~ in(U_61,U_60)
| ~ ordinal(U_60) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
cnf(f_47_3,plain,
( ordinal(U_61)
| ~ in(U_61,U_60)
| ~ ordinal(U_60) ),
inference(clausify,[status(thm)],[f_47_2]) ).
fof(f_48_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_48_2,plain,
! [U_63,U_62] :
( in(U_63,U_62)
| empty(U_62)
| ~ element(U_63,U_62) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
cnf(f_48_3,plain,
( in(U_63,U_62)
| empty(U_62)
| ~ element(U_63,U_62) ),
inference(clausify,[status(thm)],[f_48_2]) ).
fof(f_49_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_49_2,plain,
! [U_65,U_64] :
( ( element(U_65,powerset(U_64))
| ~ subset(U_65,U_64) )
& ( subset(U_65,U_64)
| ~ element(U_65,powerset(U_64)) ) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_69,U_67] :
( element(U_69,powerset(U_67))
| ~ subset(U_69,U_67) )
& ! [U_68,U_66] :
( subset(U_68,U_66)
| ~ element(U_68,powerset(U_66)) ) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
cnf(f_49_4,plain,
( subset(U_68,U_66)
| ~ element(U_68,powerset(U_66)) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( element(U_69,powerset(U_67))
| ~ subset(U_69,U_67) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_50_2,plain,
! [U_72,U_71,U_70] :
( element(U_72,U_70)
| ~ element(U_71,powerset(U_70))
| ~ in(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( element(U_72,U_70)
| ~ element(U_71,powerset(U_70))
| ~ in(U_72,U_71) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> connected(inclusion_relation(A)) ),
inference(negate,[status(cth)],[t4_wellord2]) ).
fof(f_51_2,negated_conjecture,
? [A] :
( ~ connected(inclusion_relation(A))
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[f_51_1]) ).
fof(f_51_3,negated_conjecture,
? [U_73] :
( ~ connected(inclusion_relation(U_73))
& ordinal(U_73) ),
inference(variable_rename,[status(thm)],[f_51_2]) ).
fof(f_51_4,negated_conjecture,
( ~ connected(inclusion_relation(sK15))
& ordinal(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_73,sK15)],[f_51_3]) ).
cnf(f_51_5,negated_conjecture,
ordinal(sK15),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,negated_conjecture,
~ connected(inclusion_relation(sK15)),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_52_2,plain,
! [U_76,U_75,U_74] :
( ~ empty(U_74)
| ~ element(U_75,powerset(U_74))
| ~ in(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_76,U_75] :
( ! [U_74] :
( ~ empty(U_74)
| ~ element(U_75,powerset(U_74)) )
| ~ in(U_76,U_75) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
cnf(f_52_4,plain,
( ~ empty(U_74)
| ~ element(U_75,powerset(U_74))
| ~ in(U_76,U_75) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_53_2,plain,
! [U_77] :
( U_77 = empty_set
| ~ empty(U_77) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( U_77 = empty_set
| ~ empty(U_77) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_54_2,plain,
! [U_79,U_78] :
( ~ empty(U_78)
| ~ in(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
cnf(f_54_3,plain,
( ~ empty(U_78)
| ~ in(U_79,U_78) ),
inference(clausify,[status(thm)],[f_54_2]) ).
fof(f_55_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_55_2,plain,
! [U_81,U_80] :
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_81] :
( ! [U_80] :
( ~ empty(U_80)
| U_81 = U_80 )
| ~ empty(U_81) ),
inference(miniscope,[status(thm)],[f_55_2]) ).
cnf(f_55_4,plain,
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_55_3]) ).
cnf(f_4_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_3]) ).
cnf(f_4_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_4_4]) ).
cnf(f_11_11_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_11]) ).
cnf(f_11_12_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_11_12]) ).
cnf(f_15_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_15_2]) ).
cnf(f_16_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_16_2]) ).
cnf(f_18_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_18_2]) ).
cnf(f_19_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_19_2]) ).
cnf(f_20_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_2]) ).
cnf(f_21_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_2]) ).
cnf(f_22_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_2]) ).
cnf(f_23_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_2]) ).
cnf(f_24_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_2]) ).
cnf(f_25_2_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_25_2]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( unordered_pair(Eq_x_0,Eq_x_1) = unordered_pair(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,
( 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_6,axiom,
( relation_field(Eq_x_0) = relation_field(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( inclusion_relation(Eq_x_0) = inclusion_relation(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( ordered_pair(Eq_x_0,Eq_x_1) = ordered_pair(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,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( relation_dom(Eq_x_0) = relation_dom(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_13,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_14,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_15,axiom,
( sK3(Eq_x_0,Eq_x_1) = sK3(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,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_17,axiom,
( sK5(Eq_x_0) = sK5(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( in(Eq_y_0,Eq_y_1)
| ~ in(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,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_26,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_27,axiom,
( connected(Eq_y_0)
| ~ connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( is_connected_in(Eq_y_0,Eq_y_1)
| ~ is_connected_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_29,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_30,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_31,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU270+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n019.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 19 23:44:14 UTC 2026
% 0.09/5.37 % CPUTime :
% 165.34/170.66 % SZS status Theorem for theBenchmark
% 165.34/170.66 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------