%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU269+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:58:48 AM UTC 2026
% Result : Theorem 210.64s 210.98s
% Output : Proof 211.27s
% 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(d16_relat_2,axiom,
! [A] :
( relation(A)
=> ( transitive(A)
<=> is_transitive_in(A,relation_field(A)) ) ),
file('theBenchmark.p',d16_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(d8_relat_2,axiom,
! [A] :
( relation(A)
=> ! [B] :
( is_transitive_in(A,B)
<=> ! [C,D,E] :
( ( in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) )
=> in(ordered_pair(C,E),A) ) ) ),
file('theBenchmark.p',d8_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(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(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
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(t3_wellord2,conjecture,
! [A] : transitive(inclusion_relation(A)),
file('theBenchmark.p',t3_wellord2) ).
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(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_0,U_1] :
( ~ 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] :
( ( 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]) ).
fof(f_4_3,plain,
( ! [U_4] :
( one_to_one(U_4)
| ~ sP1(U_4) )
& ! [U_4] :
( function(U_4)
| ~ sP1(U_4) )
& ! [U_4] :
( relation(U_4)
| ~ sP1(U_4) )
& ! [U_4] :
( sP1(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP1(U_4)
| ~ function(U_4)
| ~ empty(U_4)
| ~ relation(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( relation(U_4)
| ~ sP1(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( function(U_4)
| ~ sP1(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_7,plain,
( one_to_one(U_4)
| ~ sP1(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
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]) ).
fof(f_5_3,plain,
! [U_5] :
( ordinal(U_5)
| ~ epsilon_connected(U_5)
| ~ epsilon_transitive(U_5) ),
inference(definitional_conversion,[status(esa)],[f_5_2]) ).
cnf(f_5_4,plain,
( ordinal(U_5)
| ~ epsilon_connected(U_5)
| ~ epsilon_transitive(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
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]) ).
fof(f_6_3,plain,
( ! [U_6] :
( ordinal(U_6)
| ~ sP2(U_6) )
& ! [U_6] :
( epsilon_connected(U_6)
| ~ sP2(U_6) )
& ! [U_6] :
( epsilon_transitive(U_6)
| ~ sP2(U_6) )
& ! [U_6] :
( sP2(U_6)
| ~ empty(U_6) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_6_2]) ).
cnf(f_6_4,plain,
( sP2(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( epsilon_transitive(U_6)
| ~ sP2(U_6) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( epsilon_connected(U_6)
| ~ sP2(U_6) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_7,plain,
( ordinal(U_6)
| ~ sP2(U_6) ),
inference(clausify,[status(thm)],[f_6_3]) ).
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]) ).
fof(f_7_3,plain,
! [U_8,U_7] : unordered_pair(U_8,U_7) = unordered_pair(U_7,U_8),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
unordered_pair(U_8,U_7) = unordered_pair(U_7,U_8),
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_10,U_9] : set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_9,U_10] : set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
set_union2(U_10,U_9) = set_union2(U_9,U_10),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A] :
( ( ( transitive(A)
| ~ is_transitive_in(A,relation_field(A)) )
& ( is_transitive_in(A,relation_field(A))
| ~ transitive(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d16_relat_2]) ).
fof(f_9_2,plain,
! [U_11] :
( ( ( transitive(U_11)
| ~ is_transitive_in(U_11,relation_field(U_11)) )
& ( is_transitive_in(U_11,relation_field(U_11))
| ~ transitive(U_11) ) )
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_11] :
( transitive(U_11)
| ~ is_transitive_in(U_11,relation_field(U_11))
| ~ sP3(U_11) )
& ! [U_11] :
( is_transitive_in(U_11,relation_field(U_11))
| ~ transitive(U_11)
| ~ sP3(U_11) )
& ! [U_11] :
( sP3(U_11)
| ~ relation(U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP3(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( is_transitive_in(U_11,relation_field(U_11))
| ~ transitive(U_11)
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( transitive(U_11)
| ~ is_transitive_in(U_11,relation_field(U_11))
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_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_10_2,plain,
! [U_17,U_16] :
( ( ( U_16 = inclusion_relation(U_17)
| ? [U_15,U_14] :
( ( ( ~ in(ordered_pair(U_15,U_14),U_16)
& subset(U_15,U_14) )
| ( ~ subset(U_15,U_14)
& in(ordered_pair(U_15,U_14),U_16) ) )
& in(U_14,U_17)
& in(U_15,U_17) )
| relation_field(U_16) != U_17 )
& ( ( ! [U_13,U_12] :
( ( ( in(ordered_pair(U_13,U_12),U_16)
| ~ subset(U_13,U_12) )
& ( subset(U_13,U_12)
| ~ in(ordered_pair(U_13,U_12),U_16) ) )
| ~ in(U_12,U_17)
| ~ in(U_13,U_17) )
& relation_field(U_16) = U_17 )
| U_16 != inclusion_relation(U_17) ) )
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_17,U_16] :
( ( ( U_16 = inclusion_relation(U_17)
| ? [U_14] :
( ( ( ~ in(ordered_pair(sK1(U_17,U_16),U_14),U_16)
& subset(sK1(U_17,U_16),U_14) )
| ( ~ subset(sK1(U_17,U_16),U_14)
& in(ordered_pair(sK1(U_17,U_16),U_14),U_16) ) )
& in(U_14,U_17)
& in(sK1(U_17,U_16),U_17) )
| relation_field(U_16) != U_17 )
& ( ( ! [U_13,U_12] :
( ( ( in(ordered_pair(U_13,U_12),U_16)
| ~ subset(U_13,U_12) )
& ( subset(U_13,U_12)
| ~ in(ordered_pair(U_13,U_12),U_16) ) )
| ~ in(U_12,U_17)
| ~ in(U_13,U_17) )
& relation_field(U_16) = U_17 )
| U_16 != inclusion_relation(U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_17,U_16))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_17,U_16] :
( ( ( U_16 = inclusion_relation(U_17)
| ( ( ( ~ in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
& subset(sK1(U_17,U_16),sK2(U_17,U_16)) )
| ( ~ subset(sK1(U_17,U_16),sK2(U_17,U_16))
& in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16) ) )
& in(sK2(U_17,U_16),U_17)
& in(sK1(U_17,U_16),U_17) )
| relation_field(U_16) != U_17 )
& ( ( ! [U_13,U_12] :
( ( ( in(ordered_pair(U_13,U_12),U_16)
| ~ subset(U_13,U_12) )
& ( subset(U_13,U_12)
| ~ in(ordered_pair(U_13,U_12),U_16) ) )
| ~ in(U_12,U_17)
| ~ in(U_13,U_17) )
& relation_field(U_16) = U_17 )
| U_16 != inclusion_relation(U_17) ) )
| ~ relation(U_16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_17,U_16))],[f_10_3]) ).
fof(f_10_5,plain,
( ! [U_16,U_17] :
( ~ in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| ~ sP7(U_16,U_17) )
& ! [U_16,U_17] :
( subset(sK1(U_17,U_16),sK2(U_17,U_16))
| ~ sP7(U_16,U_17) )
& ! [U_16,U_17] :
( ~ subset(sK1(U_17,U_16),sK2(U_17,U_16))
| ~ sP6(U_16,U_17) )
& ! [U_16,U_17] :
( in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| ~ sP6(U_16,U_17) )
& ! [U_16,U_17] :
( sP7(U_16,U_17)
| sP6(U_16,U_17)
| ~ sP8(U_16,U_17) )
& ! [U_16,U_17] :
( in(sK2(U_17,U_16),U_17)
| ~ sP8(U_16,U_17) )
& ! [U_16,U_17] :
( in(sK1(U_17,U_16),U_17)
| ~ sP8(U_16,U_17) )
& ! [U_12,U_13,U_16] :
( in(ordered_pair(U_13,U_12),U_16)
| ~ subset(U_13,U_12)
| ~ sP4(U_12,U_13,U_16) )
& ! [U_12,U_13,U_16] :
( subset(U_13,U_12)
| ~ in(ordered_pair(U_13,U_12),U_16)
| ~ sP4(U_12,U_13,U_16) )
& ! [U_12,U_13,U_16,U_17] :
( sP4(U_12,U_13,U_16)
| ~ in(U_12,U_17)
| ~ in(U_13,U_17)
| ~ sP5(U_12,U_13,U_16,U_17) )
& ! [U_12,U_13,U_16,U_17] :
( relation_field(U_16) = U_17
| ~ sP5(U_12,U_13,U_16,U_17) )
& ! [U_12,U_13,U_16,U_17] :
( U_16 = inclusion_relation(U_17)
| sP8(U_16,U_17)
| relation_field(U_16) != U_17
| ~ sP9(U_12,U_13,U_16,U_17) )
& ! [U_12,U_13,U_16,U_17] :
( sP5(U_12,U_13,U_16,U_17)
| U_16 != inclusion_relation(U_17)
| ~ sP9(U_12,U_13,U_16,U_17) )
& ! [U_12,U_13,U_16,U_17] :
( sP9(U_12,U_13,U_16,U_17)
| ~ relation(U_16) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4,sP5,sP6,sP7,sP8,sP9])],[f_10_4]) ).
cnf(f_10_6,plain,
( sP9(U_12,U_13,U_16,U_17)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_7,plain,
( sP5(U_12,U_13,U_16,U_17)
| U_16 != inclusion_relation(U_17)
| ~ sP9(U_12,U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_8,plain,
( U_16 = inclusion_relation(U_17)
| sP8(U_16,U_17)
| relation_field(U_16) != U_17
| ~ sP9(U_12,U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_9,plain,
( relation_field(U_16) = U_17
| ~ sP5(U_12,U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_10,plain,
( sP4(U_12,U_13,U_16)
| ~ in(U_12,U_17)
| ~ in(U_13,U_17)
| ~ sP5(U_12,U_13,U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_11,plain,
( subset(U_13,U_12)
| ~ in(ordered_pair(U_13,U_12),U_16)
| ~ sP4(U_12,U_13,U_16) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_12,plain,
( in(ordered_pair(U_13,U_12),U_16)
| ~ subset(U_13,U_12)
| ~ sP4(U_12,U_13,U_16) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_13,plain,
( in(sK1(U_17,U_16),U_17)
| ~ sP8(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_14,plain,
( in(sK2(U_17,U_16),U_17)
| ~ sP8(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_15,plain,
( sP7(U_16,U_17)
| sP6(U_16,U_17)
| ~ sP8(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_16,plain,
( in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| ~ sP6(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_17,plain,
( ~ subset(sK1(U_17,U_16),sK2(U_17,U_16))
| ~ sP6(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_18,plain,
( subset(sK1(U_17,U_16),sK2(U_17,U_16))
| ~ sP7(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
cnf(f_10_19,plain,
( ~ in(ordered_pair(sK1(U_17,U_16),sK2(U_17,U_16)),U_16)
| ~ sP7(U_16,U_17) ),
inference(clausify,[status(thm)],[f_10_5]) ).
fof(f_11_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_11_2,plain,
! [U_19,U_18] : ordered_pair(U_19,U_18) = unordered_pair(unordered_pair(U_19,U_18),singleton(U_19)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_18,U_19] : ordered_pair(U_19,U_18) = unordered_pair(unordered_pair(U_19,U_18),singleton(U_19)),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
ordered_pair(U_19,U_18) = unordered_pair(unordered_pair(U_19,U_18),singleton(U_19)),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_20] :
( relation_field(U_20) = set_union2(relation_dom(U_20),relation_rng(U_20))
| ~ relation(U_20) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_20] :
( relation_field(U_20) = set_union2(relation_dom(U_20),relation_rng(U_20))
| ~ relation(U_20) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( relation_field(U_20) = set_union2(relation_dom(U_20),relation_rng(U_20))
| ~ relation(U_20) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
( ! [B] :
( ( is_transitive_in(A,B)
| ? [C,D,E] :
( ~ in(ordered_pair(C,E),A)
& in(ordered_pair(D,E),A)
& in(ordered_pair(C,D),A)
& in(E,B)
& in(D,B)
& in(C,B) ) )
& ( ! [C,D,E] :
( in(ordered_pair(C,E),A)
| ~ in(ordered_pair(D,E),A)
| ~ in(ordered_pair(C,D),A)
| ~ in(E,B)
| ~ in(D,B)
| ~ in(C,B) )
| ~ is_transitive_in(A,B) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d8_relat_2]) ).
fof(f_13_2,plain,
! [U_28] :
( ! [U_27] :
( ( is_transitive_in(U_28,U_27)
| ? [U_26,U_25,U_24] :
( ~ in(ordered_pair(U_26,U_24),U_28)
& in(ordered_pair(U_25,U_24),U_28)
& in(ordered_pair(U_26,U_25),U_28)
& in(U_24,U_27)
& in(U_25,U_27)
& in(U_26,U_27) ) )
& ( ! [U_23,U_22,U_21] :
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_27)
| ~ in(U_22,U_27)
| ~ in(U_23,U_27) )
| ~ is_transitive_in(U_28,U_27) ) )
| ~ relation(U_28) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_28] :
( ( ! [U_30] :
( is_transitive_in(U_28,U_30)
| ? [U_26,U_25,U_24] :
( ~ in(ordered_pair(U_26,U_24),U_28)
& in(ordered_pair(U_25,U_24),U_28)
& in(ordered_pair(U_26,U_25),U_28)
& in(U_24,U_30)
& in(U_25,U_30)
& in(U_26,U_30) ) )
& ! [U_29] :
( ! [U_23,U_22,U_21] :
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_29)
| ~ in(U_22,U_29)
| ~ in(U_23,U_29) )
| ~ is_transitive_in(U_28,U_29) ) )
| ~ relation(U_28) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
fof(f_13_4,plain,
! [U_28] :
( ( ! [U_30] :
( is_transitive_in(U_28,U_30)
| ? [U_25,U_24] :
( ~ in(ordered_pair(sK3(U_28,U_30),U_24),U_28)
& in(ordered_pair(U_25,U_24),U_28)
& in(ordered_pair(sK3(U_28,U_30),U_25),U_28)
& in(U_24,U_30)
& in(U_25,U_30)
& in(sK3(U_28,U_30),U_30) ) )
& ! [U_29] :
( ! [U_23,U_22,U_21] :
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_29)
| ~ in(U_22,U_29)
| ~ in(U_23,U_29) )
| ~ is_transitive_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_13_3]) ).
fof(f_13_5,plain,
! [U_28] :
( ( ! [U_30] :
( is_transitive_in(U_28,U_30)
| ? [U_24] :
( ~ in(ordered_pair(sK3(U_28,U_30),U_24),U_28)
& in(ordered_pair(sK4(U_28,U_30),U_24),U_28)
& in(ordered_pair(sK3(U_28,U_30),sK4(U_28,U_30)),U_28)
& in(U_24,U_30)
& in(sK4(U_28,U_30),U_30)
& in(sK3(U_28,U_30),U_30) ) )
& ! [U_29] :
( ! [U_23,U_22,U_21] :
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_29)
| ~ in(U_22,U_29)
| ~ in(U_23,U_29) )
| ~ is_transitive_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_13_4]) ).
fof(f_13_6,plain,
! [U_28] :
( ( ! [U_30] :
( is_transitive_in(U_28,U_30)
| ( ~ in(ordered_pair(sK3(U_28,U_30),sK5(U_28,U_30)),U_28)
& in(ordered_pair(sK4(U_28,U_30),sK5(U_28,U_30)),U_28)
& in(ordered_pair(sK3(U_28,U_30),sK4(U_28,U_30)),U_28)
& in(sK5(U_28,U_30),U_30)
& in(sK4(U_28,U_30),U_30)
& in(sK3(U_28,U_30),U_30) ) )
& ! [U_29] :
( ! [U_23,U_22,U_21] :
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_29)
| ~ in(U_22,U_29)
| ~ in(U_23,U_29) )
| ~ is_transitive_in(U_28,U_29) ) )
| ~ relation(U_28) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_24,sK5(U_28,U_30))],[f_13_5]) ).
fof(f_13_7,plain,
( ! [U_28,U_30] :
( ~ in(ordered_pair(sK3(U_28,U_30),sK5(U_28,U_30)),U_28)
| ~ sP10(U_28,U_30) )
& ! [U_28,U_30] :
( in(ordered_pair(sK4(U_28,U_30),sK5(U_28,U_30)),U_28)
| ~ sP10(U_28,U_30) )
& ! [U_28,U_30] :
( in(ordered_pair(sK3(U_28,U_30),sK4(U_28,U_30)),U_28)
| ~ sP10(U_28,U_30) )
& ! [U_28,U_30] :
( in(sK5(U_28,U_30),U_30)
| ~ sP10(U_28,U_30) )
& ! [U_28,U_30] :
( in(sK4(U_28,U_30),U_30)
| ~ sP10(U_28,U_30) )
& ! [U_28,U_30] :
( in(sK3(U_28,U_30),U_30)
| ~ sP10(U_28,U_30) )
& ! [U_23,U_28,U_30,U_29,U_21,U_22] :
( is_transitive_in(U_28,U_30)
| sP10(U_28,U_30)
| ~ sP11(U_23,U_28,U_30,U_29,U_21,U_22) )
& ! [U_23,U_28,U_30,U_29,U_21,U_22] :
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_29)
| ~ in(U_22,U_29)
| ~ in(U_23,U_29)
| ~ is_transitive_in(U_28,U_29)
| ~ sP11(U_23,U_28,U_30,U_29,U_21,U_22) )
& ! [U_23,U_28,U_30,U_29,U_21,U_22] :
( sP11(U_23,U_28,U_30,U_29,U_21,U_22)
| ~ relation(U_28) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11])],[f_13_6]) ).
cnf(f_13_8,plain,
( sP11(U_23,U_28,U_30,U_29,U_21,U_22)
| ~ relation(U_28) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,plain,
( in(ordered_pair(U_23,U_21),U_28)
| ~ in(ordered_pair(U_22,U_21),U_28)
| ~ in(ordered_pair(U_23,U_22),U_28)
| ~ in(U_21,U_29)
| ~ in(U_22,U_29)
| ~ in(U_23,U_29)
| ~ is_transitive_in(U_28,U_29)
| ~ sP11(U_23,U_28,U_30,U_29,U_21,U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_10,plain,
( is_transitive_in(U_28,U_30)
| sP10(U_28,U_30)
| ~ sP11(U_23,U_28,U_30,U_29,U_21,U_22) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,plain,
( in(sK3(U_28,U_30),U_30)
| ~ sP10(U_28,U_30) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,plain,
( in(sK4(U_28,U_30),U_30)
| ~ sP10(U_28,U_30) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_13,plain,
( in(sK5(U_28,U_30),U_30)
| ~ sP10(U_28,U_30) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_14,plain,
( in(ordered_pair(sK3(U_28,U_30),sK4(U_28,U_30)),U_28)
| ~ sP10(U_28,U_30) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_15,plain,
( in(ordered_pair(sK4(U_28,U_30),sK5(U_28,U_30)),U_28)
| ~ sP10(U_28,U_30) ),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_16,plain,
( ~ in(ordered_pair(sK3(U_28,U_30),sK5(U_28,U_30)),U_28)
| ~ sP10(U_28,U_30) ),
inference(clausify,[status(thm)],[f_13_7]) ).
fof(f_14_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_relat_1]) ).
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,
! [A] : relation(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[dt_k1_wellord2]) ).
fof(f_16_2,plain,
! [U_31] : relation(inclusion_relation(U_31)),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_31] : relation(inclusion_relation(U_31)),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
relation(inclusion_relation(U_31)),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k1_xboole_0]) ).
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_k1_zfmisc_1]) ).
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_k2_relat_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,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_tarski]) ).
fof(f_20_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
$true,
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k2_xboole_0]) ).
fof(f_21_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,plain,
$true,
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k3_relat_1]) ).
fof(f_22_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,plain,
$true,
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_k4_tarski]) ).
fof(f_23_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_23_1]) ).
cnf(f_23_3,plain,
$true,
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
$true,
inference(fof_nnf,[status(thm)],[dt_m1_subset_1]) ).
fof(f_24_2,plain,
$true,
inference(definitional_conversion,[status(esa)],[f_24_1]) ).
cnf(f_24_3,plain,
$true,
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_25_2,plain,
! [U_33] :
? [U_32] : element(U_32,U_33),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_33] : element(sK6(U_33),U_33),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_32,sK6(U_33))],[f_25_2]) ).
fof(f_25_4,plain,
! [U_33] : element(sK6(U_33),U_33),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
element(sK6(U_33),U_33),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_26_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_26_1]) ).
cnf(f_26_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] : ~ empty(ordered_pair(A,B)),
inference(fof_nnf,[status(thm)],[fc1_zfmisc_1]) ).
fof(f_27_2,plain,
! [U_35,U_34] : ~ empty(ordered_pair(U_35,U_34)),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_34,U_35] : ~ empty(ordered_pair(U_35,U_34)),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
~ empty(ordered_pair(U_35,U_34)),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_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_28_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_28_1]) ).
cnf(f_28_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
cnf(f_28_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_29_2,plain,
! [U_37,U_36] :
( ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_37] :
( ! [U_36] : ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(miniscope,[status(thm)],[f_29_2]) ).
fof(f_29_4,plain,
! [U_36,U_37] :
( ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
( ~ empty(set_union2(U_37,U_36))
| empty(U_37) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_30_2,plain,
! [U_39,U_38] :
( ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_39] :
( ! [U_38] : ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(miniscope,[status(thm)],[f_30_2]) ).
fof(f_30_4,plain,
! [U_38,U_39] :
( ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
( ~ empty(set_union2(U_38,U_39))
| empty(U_39) ),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_31_2,plain,
! [U_41,U_40] : set_union2(U_41,U_41) = U_41,
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_41] : set_union2(U_41,U_41) = U_41,
inference(miniscope,[status(thm)],[f_31_2]) ).
fof(f_31_4,plain,
! [U_41] : set_union2(U_41,U_41) = U_41,
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
set_union2(U_41,U_41) = U_41,
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_32_2,plain,
? [U_42] :
( function(U_42)
& relation(U_42) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_42,sK7)],[f_32_2]) ).
fof(f_32_4,plain,
( function(sK7)
& relation(sK7) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
function(sK7),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_33_2,plain,
? [U_43] :
( ordinal(U_43)
& epsilon_connected(U_43)
& epsilon_transitive(U_43) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_43,sK8)],[f_33_2]) ).
fof(f_33_4,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
epsilon_transitive(sK8),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
epsilon_connected(sK8),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_7,plain,
ordinal(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_44] : empty(U_44),
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_44,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_45] :
( function(U_45)
& empty(U_45)
& relation(U_45) ),
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_45,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_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_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_46,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] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_37_2,plain,
? [U_47] : ~ empty(U_47),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
~ empty(sK12),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_47,sK12)],[f_37_2]) ).
fof(f_37_4,plain,
~ empty(sK12),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_38_2,plain,
? [U_48] :
( one_to_one(U_48)
& function(U_48)
& relation(U_48) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
( one_to_one(sK13)
& function(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_48,sK13)],[f_38_2]) ).
fof(f_38_4,plain,
( one_to_one(sK13)
& function(sK13)
& relation(sK13) ),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_6,plain,
function(sK13),
inference(clausify,[status(thm)],[f_38_4]) ).
cnf(f_38_7,plain,
one_to_one(sK13),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_39_2,plain,
? [U_49] :
( ordinal(U_49)
& epsilon_connected(U_49)
& epsilon_transitive(U_49)
& ~ empty(U_49) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14)
& ~ empty(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_49,sK14)],[f_39_2]) ).
fof(f_39_4,plain,
( ordinal(sK14)
& epsilon_connected(sK14)
& epsilon_transitive(sK14)
& ~ empty(sK14) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
~ empty(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
epsilon_transitive(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
epsilon_connected(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_8,plain,
ordinal(sK14),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_40_2,plain,
? [U_50] :
( function(U_50)
& relation_empty_yielding(U_50)
& relation(U_50) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
( function(sK15)
& relation_empty_yielding(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_50,sK15)],[f_40_2]) ).
fof(f_40_4,plain,
( function(sK15)
& relation_empty_yielding(sK15)
& relation(sK15) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
relation_empty_yielding(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
function(sK15),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_41_2,plain,
! [U_52,U_51] : subset(U_52,U_52),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_52] : subset(U_52,U_52),
inference(miniscope,[status(thm)],[f_41_2]) ).
fof(f_41_4,plain,
! [U_52] : subset(U_52,U_52),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
subset(U_52,U_52),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
! [A] : set_union2(A,empty_set) = A,
inference(fof_nnf,[status(thm)],[t1_boole]) ).
fof(f_42_2,plain,
! [U_53] : set_union2(U_53,empty_set) = U_53,
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_53] : set_union2(U_53,empty_set) = U_53,
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
set_union2(U_53,empty_set) = U_53,
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_43_2,plain,
! [U_55,U_54] :
( element(U_55,U_54)
| ~ in(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_55,U_54] :
( element(U_55,U_54)
| ~ in(U_55,U_54) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( element(U_55,U_54)
| ~ in(U_55,U_54) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_44_2,plain,
! [U_58,U_57,U_56] :
( subset(U_58,U_56)
| ~ subset(U_57,U_56)
| ~ subset(U_58,U_57) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_57,U_56,U_58] :
( subset(U_58,U_56)
| ~ subset(U_57,U_56)
| ~ subset(U_58,U_57) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( subset(U_58,U_56)
| ~ subset(U_57,U_56)
| ~ subset(U_58,U_57) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_45_2,plain,
! [U_60,U_59] :
( in(U_60,U_59)
| empty(U_59)
| ~ element(U_60,U_59) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_60,U_59] :
( in(U_60,U_59)
| empty(U_59)
| ~ element(U_60,U_59) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( in(U_60,U_59)
| empty(U_59)
| ~ element(U_60,U_59) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_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_46_2,plain,
! [U_62,U_61] :
( ( element(U_62,powerset(U_61))
| ~ subset(U_62,U_61) )
& ( subset(U_62,U_61)
| ~ element(U_62,powerset(U_61)) ) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_66,U_64] :
( element(U_66,powerset(U_64))
| ~ subset(U_66,U_64) )
& ! [U_65,U_63] :
( subset(U_65,U_63)
| ~ element(U_65,powerset(U_63)) ) ),
inference(miniscope,[status(thm)],[f_46_2]) ).
fof(f_46_4,plain,
( ! [U_66,U_64] :
( element(U_66,powerset(U_64))
| ~ subset(U_66,U_64) )
& ! [U_65,U_63] :
( subset(U_65,U_63)
| ~ element(U_65,powerset(U_63)) ) ),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
( subset(U_65,U_63)
| ~ element(U_65,powerset(U_63)) ),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
( element(U_66,powerset(U_64))
| ~ subset(U_66,U_64) ),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,negated_conjecture,
~ ! [A] : transitive(inclusion_relation(A)),
inference(negate,[status(cth)],[t3_wellord2]) ).
fof(f_47_2,negated_conjecture,
? [A] : ~ transitive(inclusion_relation(A)),
inference(fof_nnf,[status(thm)],[f_47_1]) ).
fof(f_47_3,negated_conjecture,
? [U_67] : ~ transitive(inclusion_relation(U_67)),
inference(variable_rename,[status(thm)],[f_47_2]) ).
fof(f_47_4,negated_conjecture,
~ transitive(inclusion_relation(sK16)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_67,sK16)],[f_47_3]) ).
fof(f_47_5,negated_conjecture,
~ transitive(inclusion_relation(sK16)),
inference(definitional_conversion,[status(esa)],[f_47_4]) ).
cnf(f_47_6,negated_conjecture,
~ transitive(inclusion_relation(sK16)),
inference(clausify,[status(thm)],[f_47_5]) ).
fof(f_48_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_48_2,plain,
! [U_70,U_69,U_68] :
( element(U_70,U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_68,U_69,U_70] :
( element(U_70,U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( element(U_70,U_68)
| ~ element(U_69,powerset(U_68))
| ~ in(U_70,U_69) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_49_2,plain,
! [U_73,U_72,U_71] :
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71))
| ~ in(U_73,U_72) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_73,U_72] :
( ! [U_71] :
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71)) )
| ~ in(U_73,U_72) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_72,U_73,U_71] :
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71))
| ~ in(U_73,U_72) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( ~ empty(U_71)
| ~ element(U_72,powerset(U_71))
| ~ in(U_73,U_72) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_50_2,plain,
! [U_74] :
( U_74 = empty_set
| ~ empty(U_74) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_74] :
( U_74 = empty_set
| ~ empty(U_74) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( U_74 = empty_set
| ~ empty(U_74) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_51_2,plain,
! [U_76,U_75] :
( ~ empty(U_75)
| ~ in(U_76,U_75) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_75,U_76] :
( ~ empty(U_75)
| ~ in(U_76,U_75) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( ~ empty(U_75)
| ~ in(U_76,U_75) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_52_2,plain,
! [U_78,U_77] :
( ~ empty(U_77)
| U_78 = U_77
| ~ empty(U_78) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_78] :
( ! [U_77] :
( ~ empty(U_77)
| U_78 = U_77 )
| ~ empty(U_78) ),
inference(miniscope,[status(thm)],[f_52_2]) ).
fof(f_52_4,plain,
! [U_77,U_78] :
( ~ empty(U_77)
| U_78 = U_77
| ~ empty(U_78) ),
inference(definitional_conversion,[status(esa)],[f_52_3]) ).
cnf(f_52_5,plain,
( ~ empty(U_77)
| U_78 = U_77
| ~ empty(U_78) ),
inference(clausify,[status(thm)],[f_52_4]) ).
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_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(f_20_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_20_3]) ).
cnf(f_21_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_21_3]) ).
cnf(f_22_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_22_3]) ).
cnf(f_23_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_23_3]) ).
cnf(f_24_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_24_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,
( 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,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( sK6(Eq_x_0) = sK6(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_19,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_20,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,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_27,axiom,
( transitive(Eq_y_0)
| ~ transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( is_transitive_in(Eq_y_0,Eq_y_1)
| ~ is_transitive_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(equality_32,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,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_40,axiom,
( sP8(Eq_y_0,Eq_y_1)
| ~ sP8(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_41,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP9(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_42,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_43,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| Eq_x_3 != Eq_y_3
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU269+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
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 23:43:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 210.64/210.98 % SZS status Theorem for theBenchmark
% 210.64/210.98 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------