%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU238+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:58:39 AM UTC 2026
% Result : Theorem 78.25s 78.57s
% Output : Proof 78.35s
% 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(antisymmetry_r2_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
=> ~ proper_subset(B,A) ),
file('theBenchmark.p',antisymmetry_r2_xboole_0) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(connectedness_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(B,A)
| ordinal_subset(A,B) ) ),
file('theBenchmark.p',connectedness_r1_ordinal1) ).
fof(d1_ordinal1,axiom,
! [A] : succ(A) = set_union2(A,singleton(A)),
file('theBenchmark.p',d1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [A,B] :
( proper_subset(A,B)
<=> ( A != B
& subset(A,B) ) ),
file('theBenchmark.p',d8_xboole_0) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc12_relat_1,axiom,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc12_relat_1) ).
fof(fc1_ordinal1,axiom,
! [A] : ~ empty(succ(A)),
file('theBenchmark.p',fc1_ordinal1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('theBenchmark.p',fc1_xboole_0) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc2_relat_1,axiom,
! [A,B] :
( ( relation(B)
& relation(A) )
=> relation(set_union2(A,B)) ),
file('theBenchmark.p',fc2_relat_1) ).
fof(fc2_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(A,B)) ),
file('theBenchmark.p',fc2_xboole_0) ).
fof(fc3_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) ) ),
file('theBenchmark.p',fc3_ordinal1) ).
fof(fc3_xboole_0,axiom,
! [A,B] :
( ~ empty(A)
=> ~ empty(set_union2(B,A)) ),
file('theBenchmark.p',fc3_xboole_0) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(idempotence_k2_xboole_0,axiom,
! [A,B] : set_union2(A,A) = A,
file('theBenchmark.p',idempotence_k2_xboole_0) ).
fof(irreflexivity_r2_xboole_0,axiom,
! [A,B] : ~ proper_subset(A,A),
file('theBenchmark.p',irreflexivity_r2_xboole_0) ).
fof(rc1_funct_1,axiom,
? [A] :
( function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal1) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_funct_1,axiom,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
file('theBenchmark.p',rc2_funct_1) ).
fof(rc2_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal1) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_funct_1,axiom,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc3_funct_1) ).
fof(rc3_ordinal1,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc3_ordinal1) ).
fof(rc3_relat_1,axiom,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc3_relat_1) ).
fof(rc4_funct_1,axiom,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
file('theBenchmark.p',rc4_funct_1) ).
fof(rc5_funct_1,axiom,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
file('theBenchmark.p',rc5_funct_1) ).
fof(redefinition_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ( ordinal_subset(A,B)
<=> subset(A,B) ) ),
file('theBenchmark.p',redefinition_r1_ordinal1) ).
fof(reflexivity_r1_ordinal1,axiom,
! [A,B] :
( ( ordinal(B)
& ordinal(A) )
=> ordinal_subset(A,A) ),
file('theBenchmark.p',reflexivity_r1_ordinal1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
fof(t10_ordinal1,axiom,
! [A] : in(A,succ(A)),
file('theBenchmark.p',t10_ordinal1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t21_ordinal1,axiom,
! [A] :
( epsilon_transitive(A)
=> ! [B] :
( ordinal(B)
=> ( proper_subset(A,B)
=> in(A,B) ) ) ),
file('theBenchmark.p',t21_ordinal1) ).
fof(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t33_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( ordinal(B)
=> ( in(A,B)
<=> ordinal_subset(succ(A),B) ) ) ),
file('theBenchmark.p',t33_ordinal1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t41_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( being_limit_ordinal(A)
<=> ! [B] :
( ordinal(B)
=> ( in(B,A)
=> in(succ(B),A) ) ) ) ),
file('theBenchmark.p',t41_ordinal1) ).
fof(t42_ordinal1,conjecture,
! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
file('theBenchmark.p',t42_ordinal1) ).
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]) ).
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,B] :
( ~ proper_subset(B,A)
| ~ proper_subset(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_xboole_0]) ).
fof(f_2_2,plain,
! [U_3,U_2] :
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
( ~ proper_subset(U_2,U_3)
| ~ proper_subset(U_3,U_2) ),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_3_2,plain,
! [U_4] :
( function(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( function(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_4_2,plain,
! [U_5] :
( ( epsilon_connected(U_5)
& epsilon_transitive(U_5) )
| ~ ordinal(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
cnf(f_4_3,plain,
( epsilon_transitive(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( epsilon_connected(U_5)
| ~ ordinal(U_5) ),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_5_2,plain,
! [U_6] :
( relation(U_6)
| ~ empty(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
cnf(f_5_3,plain,
( relation(U_6)
| ~ empty(U_6) ),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_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_6_2,plain,
! [U_7] :
( ( one_to_one(U_7)
& function(U_7)
& relation(U_7) )
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
cnf(f_6_3,plain,
( relation(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( function(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
cnf(f_6_5,plain,
( one_to_one(U_7)
| ~ function(U_7)
| ~ empty(U_7)
| ~ relation(U_7) ),
inference(clausify,[status(thm)],[f_6_2]) ).
fof(f_7_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_7_2,plain,
! [U_8] :
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ordinal(U_8)
| ~ epsilon_connected(U_8)
| ~ epsilon_transitive(U_8) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_8_2,plain,
! [U_9] :
( ( ordinal(U_9)
& epsilon_connected(U_9)
& epsilon_transitive(U_9) )
| ~ empty(U_9) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( epsilon_transitive(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( epsilon_connected(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( ordinal(U_9)
| ~ empty(U_9) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
inference(fof_nnf,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(f_9_2,plain,
! [U_11,U_10] : set_union2(U_11,U_10) = set_union2(U_10,U_11),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
set_union2(U_11,U_10) = set_union2(U_10,U_11),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_13,U_12] :
( ordinal_subset(U_12,U_13)
| ordinal_subset(U_13,U_12)
| ~ ordinal(U_12)
| ~ ordinal(U_13) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ordinal_subset(U_12,U_13)
| ordinal_subset(U_13,U_12)
| ~ ordinal(U_12)
| ~ ordinal(U_13) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [A] : succ(A) = set_union2(A,singleton(A)),
inference(fof_nnf,[status(thm)],[d1_ordinal1]) ).
fof(f_11_2,plain,
! [U_14] : succ(U_14) = set_union2(U_14,singleton(U_14)),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
succ(U_14) = set_union2(U_14,singleton(U_14)),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B] :
( ( proper_subset(A,B)
| A = B
| ~ subset(A,B) )
& ( ( A != B
& subset(A,B) )
| ~ proper_subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d8_xboole_0]) ).
fof(f_12_2,plain,
! [U_16,U_15] :
( ( proper_subset(U_16,U_15)
| U_16 = U_15
| ~ subset(U_16,U_15) )
& ( ( U_16 != U_15
& subset(U_16,U_15) )
| ~ proper_subset(U_16,U_15) ) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_20,U_18] :
( proper_subset(U_20,U_18)
| U_20 = U_18
| ~ subset(U_20,U_18) )
& ! [U_19,U_17] :
( ( U_19 != U_17
& subset(U_19,U_17) )
| ~ proper_subset(U_19,U_17) ) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( subset(U_19,U_17)
| ~ proper_subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( U_19 != U_17
| ~ proper_subset(U_19,U_17) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( proper_subset(U_20,U_18)
| U_20 = U_18
| ~ subset(U_20,U_18) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_13_2,plain,
! [U_22] :
? [U_21] : element(U_21,U_22),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_22] : element(sK1(U_22),U_22),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_21,sK1(U_22))],[f_13_2]) ).
cnf(f_13_4,plain,
element(sK1(U_22),U_22),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
cnf(f_14_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
cnf(f_14_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_14_1]) ).
fof(f_15_1,plain,
! [A] : ~ empty(succ(A)),
inference(fof_nnf,[status(thm)],[fc1_ordinal1]) ).
fof(f_15_2,plain,
! [U_23] : ~ empty(succ(U_23)),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
~ empty(succ(U_23)),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
cnf(f_16_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_1]) ).
fof(f_17_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_17_2,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_4,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_5,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_6,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_7,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_8,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
cnf(f_17_9,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_17_1]) ).
fof(f_18_1,plain,
! [A,B] :
( relation(set_union2(A,B))
| ~ relation(B)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc2_relat_1]) ).
fof(f_18_2,plain,
! [U_25,U_24] :
( relation(set_union2(U_25,U_24))
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( relation(set_union2(U_25,U_24))
| ~ relation(U_24)
| ~ relation(U_25) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,B] :
( ~ empty(set_union2(A,B))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc2_xboole_0]) ).
fof(f_19_2,plain,
! [U_27,U_26] :
( ~ empty(set_union2(U_27,U_26))
| empty(U_27) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_27] :
( ! [U_26] : ~ empty(set_union2(U_27,U_26))
| empty(U_27) ),
inference(miniscope,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
( ~ empty(set_union2(U_27,U_26))
| empty(U_27) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [A] :
( ( ordinal(succ(A))
& epsilon_connected(succ(A))
& epsilon_transitive(succ(A))
& ~ empty(succ(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc3_ordinal1]) ).
fof(f_20_2,plain,
! [U_28] :
( ( ordinal(succ(U_28))
& epsilon_connected(succ(U_28))
& epsilon_transitive(succ(U_28))
& ~ empty(succ(U_28)) )
| ~ ordinal(U_28) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
cnf(f_20_3,plain,
( ~ empty(succ(U_28))
| ~ ordinal(U_28) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( epsilon_transitive(succ(U_28))
| ~ ordinal(U_28) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_5,plain,
( epsilon_connected(succ(U_28))
| ~ ordinal(U_28) ),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_6,plain,
( ordinal(succ(U_28))
| ~ ordinal(U_28) ),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A,B] :
( ~ empty(set_union2(B,A))
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc3_xboole_0]) ).
fof(f_21_2,plain,
! [U_30,U_29] :
( ~ empty(set_union2(U_29,U_30))
| empty(U_30) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_30] :
( ! [U_29] : ~ empty(set_union2(U_29,U_30))
| empty(U_30) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
( ~ empty(set_union2(U_29,U_30))
| empty(U_30) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
cnf(f_22_2,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_22_1]) ).
fof(f_23_1,plain,
! [A,B] : set_union2(A,A) = A,
inference(fof_nnf,[status(thm)],[idempotence_k2_xboole_0]) ).
fof(f_23_2,plain,
! [U_32,U_31] : set_union2(U_32,U_32) = U_32,
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_32] : set_union2(U_32,U_32) = U_32,
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
set_union2(U_32,U_32) = U_32,
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [A,B] : ~ proper_subset(A,A),
inference(fof_nnf,[status(thm)],[irreflexivity_r2_xboole_0]) ).
fof(f_24_2,plain,
! [U_34,U_33] : ~ proper_subset(U_34,U_34),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_34] : ~ proper_subset(U_34,U_34),
inference(miniscope,[status(thm)],[f_24_2]) ).
cnf(f_24_4,plain,
~ proper_subset(U_34,U_34),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_25_2,plain,
? [U_35] :
( function(U_35)
& relation(U_35) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( function(sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_35,sK2)],[f_25_2]) ).
cnf(f_25_4,plain,
relation(sK2),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
function(sK2),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_26_2,plain,
? [U_36] :
( ordinal(U_36)
& epsilon_connected(U_36)
& epsilon_transitive(U_36) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ordinal(sK3)
& epsilon_connected(sK3)
& epsilon_transitive(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_36,sK3)],[f_26_2]) ).
cnf(f_26_4,plain,
epsilon_transitive(sK3),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_5,plain,
epsilon_connected(sK3),
inference(clausify,[status(thm)],[f_26_3]) ).
cnf(f_26_6,plain,
ordinal(sK3),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_27_2,plain,
? [U_37] :
( relation(U_37)
& empty(U_37) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( relation(sK4)
& empty(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_37,sK4)],[f_27_2]) ).
cnf(f_27_4,plain,
empty(sK4),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
relation(sK4),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_28_2,plain,
? [U_38] : empty(U_38),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
empty(sK5),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_38,sK5)],[f_28_2]) ).
cnf(f_28_4,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_29_2,plain,
? [U_39] :
( function(U_39)
& empty(U_39)
& relation(U_39) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( function(sK6)
& empty(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_39,sK6)],[f_29_2]) ).
cnf(f_29_4,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_29_3]) ).
cnf(f_29_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_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_30_2,plain,
? [U_40] :
( ordinal(U_40)
& epsilon_connected(U_40)
& epsilon_transitive(U_40)
& empty(U_40)
& one_to_one(U_40)
& function(U_40)
& relation(U_40) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7)
& empty(sK7)
& one_to_one(sK7)
& function(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_40,sK7)],[f_30_2]) ).
cnf(f_30_4,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
function(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
one_to_one(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_7,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_8,plain,
epsilon_transitive(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_9,plain,
epsilon_connected(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_10,plain,
ordinal(sK7),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_31_2,plain,
? [U_41] :
( relation(U_41)
& ~ empty(U_41) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( relation(sK8)
& ~ empty(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_41,sK8)],[f_31_2]) ).
cnf(f_31_4,plain,
~ empty(sK8),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_32_2,plain,
? [U_42] : ~ empty(U_42),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
~ empty(sK9),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_42,sK9)],[f_32_2]) ).
cnf(f_32_4,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_33_2,plain,
? [U_43] :
( one_to_one(U_43)
& function(U_43)
& relation(U_43) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( one_to_one(sK10)
& function(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_43,sK10)],[f_33_2]) ).
cnf(f_33_4,plain,
relation(sK10),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
function(sK10),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_6,plain,
one_to_one(sK10),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_34_2,plain,
? [U_44] :
( ordinal(U_44)
& epsilon_connected(U_44)
& epsilon_transitive(U_44)
& ~ empty(U_44) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ordinal(sK11)
& epsilon_connected(sK11)
& epsilon_transitive(sK11)
& ~ empty(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_44,sK11)],[f_34_2]) ).
cnf(f_34_4,plain,
~ empty(sK11),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
epsilon_transitive(sK11),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_6,plain,
epsilon_connected(sK11),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_7,plain,
ordinal(sK11),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_35_2,plain,
? [U_45] :
( relation_empty_yielding(U_45)
& relation(U_45) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( relation_empty_yielding(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_45,sK12)],[f_35_2]) ).
cnf(f_35_4,plain,
relation(sK12),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
relation_empty_yielding(sK12),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_36_2,plain,
? [U_46] :
( function(U_46)
& relation_empty_yielding(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( function(sK13)
& relation_empty_yielding(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_46,sK13)],[f_36_2]) ).
cnf(f_36_4,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_5,plain,
relation_empty_yielding(sK13),
inference(clausify,[status(thm)],[f_36_3]) ).
cnf(f_36_6,plain,
function(sK13),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_37_2,plain,
? [U_47] :
( function(U_47)
& relation_non_empty(U_47)
& relation(U_47) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( function(sK14)
& relation_non_empty(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_47,sK14)],[f_37_2]) ).
cnf(f_37_4,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_5,plain,
relation_non_empty(sK14),
inference(clausify,[status(thm)],[f_37_3]) ).
cnf(f_37_6,plain,
function(sK14),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_49,U_48] :
( ( ( ordinal_subset(U_49,U_48)
| ~ subset(U_49,U_48) )
& ( subset(U_49,U_48)
| ~ ordinal_subset(U_49,U_48) ) )
| ~ ordinal(U_48)
| ~ ordinal(U_49) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
cnf(f_38_3,plain,
( subset(U_49,U_48)
| ~ ordinal_subset(U_49,U_48)
| ~ ordinal(U_48)
| ~ ordinal(U_49) ),
inference(clausify,[status(thm)],[f_38_2]) ).
cnf(f_38_4,plain,
( ordinal_subset(U_49,U_48)
| ~ subset(U_49,U_48)
| ~ ordinal(U_48)
| ~ ordinal(U_49) ),
inference(clausify,[status(thm)],[f_38_2]) ).
fof(f_39_1,plain,
! [A,B] :
( ordinal_subset(A,A)
| ~ ordinal(B)
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1]) ).
fof(f_39_2,plain,
! [U_51,U_50] :
( ordinal_subset(U_51,U_51)
| ~ ordinal(U_50)
| ~ ordinal(U_51) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_51] :
( ! [U_50] : ~ ordinal(U_50)
| ~ ordinal(U_51)
| ordinal_subset(U_51,U_51) ),
inference(miniscope,[status(thm)],[f_39_2]) ).
cnf(f_39_4,plain,
( ~ ordinal(U_50)
| ~ ordinal(U_51)
| ordinal_subset(U_51,U_51) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_40_2,plain,
! [U_53,U_52] : subset(U_53,U_53),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_53] : subset(U_53,U_53),
inference(miniscope,[status(thm)],[f_40_2]) ).
cnf(f_40_4,plain,
subset(U_53,U_53),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [A] : in(A,succ(A)),
inference(fof_nnf,[status(thm)],[t10_ordinal1]) ).
fof(f_41_2,plain,
! [U_54] : in(U_54,succ(U_54)),
inference(variable_rename,[status(thm)],[f_41_1]) ).
cnf(f_41_3,plain,
in(U_54,succ(U_54)),
inference(clausify,[status(thm)],[f_41_2]) ).
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_55] : set_union2(U_55,empty_set) = U_55,
inference(variable_rename,[status(thm)],[f_42_1]) ).
cnf(f_42_3,plain,
set_union2(U_55,empty_set) = U_55,
inference(clausify,[status(thm)],[f_42_2]) ).
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_57,U_56] :
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
cnf(f_43_3,plain,
( element(U_57,U_56)
| ~ in(U_57,U_56) ),
inference(clausify,[status(thm)],[f_43_2]) ).
fof(f_44_1,plain,
! [A] :
( ! [B] :
( in(A,B)
| ~ proper_subset(A,B)
| ~ ordinal(B) )
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[t21_ordinal1]) ).
fof(f_44_2,plain,
! [U_59] :
( ! [U_58] :
( in(U_59,U_58)
| ~ proper_subset(U_59,U_58)
| ~ ordinal(U_58) )
| ~ epsilon_transitive(U_59) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
cnf(f_44_3,plain,
( in(U_59,U_58)
| ~ proper_subset(U_59,U_58)
| ~ ordinal(U_58)
| ~ epsilon_transitive(U_59) ),
inference(clausify,[status(thm)],[f_44_2]) ).
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_61,U_60] :
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
cnf(f_45_3,plain,
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(clausify,[status(thm)],[f_45_2]) ).
fof(f_46_1,plain,
! [A] :
( ! [B] :
( ( ( in(A,B)
| ~ ordinal_subset(succ(A),B) )
& ( ordinal_subset(succ(A),B)
| ~ in(A,B) ) )
| ~ ordinal(B) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t33_ordinal1]) ).
fof(f_46_2,plain,
! [U_63] :
( ! [U_62] :
( ( ( in(U_63,U_62)
| ~ ordinal_subset(succ(U_63),U_62) )
& ( ordinal_subset(succ(U_63),U_62)
| ~ in(U_63,U_62) ) )
| ~ ordinal(U_62) )
| ~ ordinal(U_63) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
cnf(f_46_3,plain,
( ordinal_subset(succ(U_63),U_62)
| ~ in(U_63,U_62)
| ~ ordinal(U_62)
| ~ ordinal(U_63) ),
inference(clausify,[status(thm)],[f_46_2]) ).
cnf(f_46_4,plain,
( in(U_63,U_62)
| ~ ordinal_subset(succ(U_63),U_62)
| ~ ordinal(U_62)
| ~ ordinal(U_63) ),
inference(clausify,[status(thm)],[f_46_2]) ).
fof(f_47_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_47_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_47_1]) ).
fof(f_47_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_47_2]) ).
cnf(f_47_4,plain,
( subset(U_68,U_66)
| ~ element(U_68,powerset(U_66)) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
( element(U_69,powerset(U_67))
| ~ subset(U_69,U_67) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [A] :
( ( ( being_limit_ordinal(A)
| ? [B] :
( ~ in(succ(B),A)
& in(B,A)
& ordinal(B) ) )
& ( ! [B] :
( in(succ(B),A)
| ~ in(B,A)
| ~ ordinal(B) )
| ~ being_limit_ordinal(A) ) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[t41_ordinal1]) ).
fof(f_48_2,plain,
! [U_72] :
( ( ( being_limit_ordinal(U_72)
| ? [U_71] :
( ~ in(succ(U_71),U_72)
& in(U_71,U_72)
& ordinal(U_71) ) )
& ( ! [U_70] :
( in(succ(U_70),U_72)
| ~ in(U_70,U_72)
| ~ ordinal(U_70) )
| ~ being_limit_ordinal(U_72) ) )
| ~ ordinal(U_72) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_72] :
( ( ( being_limit_ordinal(U_72)
| ( ~ in(succ(sK15(U_72)),U_72)
& in(sK15(U_72),U_72)
& ordinal(sK15(U_72)) ) )
& ( ! [U_70] :
( in(succ(U_70),U_72)
| ~ in(U_70,U_72)
| ~ ordinal(U_70) )
| ~ being_limit_ordinal(U_72) ) )
| ~ ordinal(U_72) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_71,sK15(U_72))],[f_48_2]) ).
cnf(f_48_4,plain,
( in(succ(U_70),U_72)
| ~ in(U_70,U_72)
| ~ ordinal(U_70)
| ~ being_limit_ordinal(U_72)
| ~ ordinal(U_72) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_5,plain,
( ordinal(sK15(U_72))
| being_limit_ordinal(U_72)
| ~ ordinal(U_72) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_6,plain,
( in(sK15(U_72),U_72)
| being_limit_ordinal(U_72)
| ~ ordinal(U_72) ),
inference(clausify,[status(thm)],[f_48_3]) ).
cnf(f_48_7,plain,
( ~ in(succ(sK15(U_72)),U_72)
| being_limit_ordinal(U_72)
| ~ ordinal(U_72) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,negated_conjecture,
~ ! [A] :
( ordinal(A)
=> ( ~ ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
& ~ ( ! [B] :
( ordinal(B)
=> A != succ(B) )
& ~ being_limit_ordinal(A) ) ) ),
inference(negate,[status(cth)],[t42_ordinal1]) ).
fof(f_49_2,negated_conjecture,
? [A] :
( ( ( being_limit_ordinal(A)
& ? [B] :
( A = succ(B)
& ordinal(B) ) )
| ( ! [B] :
( A != succ(B)
| ~ ordinal(B) )
& ~ being_limit_ordinal(A) ) )
& ordinal(A) ),
inference(fof_nnf,[status(thm)],[f_49_1]) ).
fof(f_49_3,negated_conjecture,
? [U_75] :
( ( ( being_limit_ordinal(U_75)
& ? [U_74] :
( U_75 = succ(U_74)
& ordinal(U_74) ) )
| ( ! [U_73] :
( U_75 != succ(U_73)
| ~ ordinal(U_73) )
& ~ being_limit_ordinal(U_75) ) )
& ordinal(U_75) ),
inference(variable_rename,[status(thm)],[f_49_2]) ).
fof(f_49_4,negated_conjecture,
( ( ( being_limit_ordinal(sK16)
& ? [U_74] :
( sK16 = succ(U_74)
& ordinal(U_74) ) )
| ( ! [U_73] :
( sK16 != succ(U_73)
| ~ ordinal(U_73) )
& ~ being_limit_ordinal(sK16) ) )
& ordinal(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_75,sK16)],[f_49_3]) ).
fof(f_49_5,negated_conjecture,
( ( ( being_limit_ordinal(sK16)
& sK16 = succ(sK17)
& ordinal(sK17) )
| ( ! [U_73] :
( sK16 != succ(U_73)
| ~ ordinal(U_73) )
& ~ being_limit_ordinal(sK16) ) )
& ordinal(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_74,sK17)],[f_49_4]) ).
cnf(f_49_6,negated_conjecture,
ordinal(sK16),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_7,negated_conjecture,
( ordinal(sK17)
| ~ being_limit_ordinal(sK16) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_8,negated_conjecture,
( sK16 = succ(sK17)
| ~ being_limit_ordinal(sK16) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_9,negated_conjecture,
( being_limit_ordinal(sK16)
| ~ being_limit_ordinal(sK16) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_10,negated_conjecture,
( ordinal(sK17)
| sK16 != succ(U_73)
| ~ ordinal(U_73) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_11,negated_conjecture,
( sK16 = succ(sK17)
| sK16 != succ(U_73)
| ~ ordinal(U_73) ),
inference(clausify,[status(thm)],[f_49_5]) ).
cnf(f_49_12,negated_conjecture,
( being_limit_ordinal(sK16)
| sK16 != succ(U_73)
| ~ ordinal(U_73) ),
inference(clausify,[status(thm)],[f_49_5]) ).
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_78,U_77,U_76] :
( element(U_78,U_76)
| ~ element(U_77,powerset(U_76))
| ~ in(U_78,U_77) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
cnf(f_50_3,plain,
( element(U_78,U_76)
| ~ element(U_77,powerset(U_76))
| ~ in(U_78,U_77) ),
inference(clausify,[status(thm)],[f_50_2]) ).
fof(f_51_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_51_2,plain,
! [U_81,U_80,U_79] :
( ~ empty(U_79)
| ~ element(U_80,powerset(U_79))
| ~ in(U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_81,U_80] :
( ! [U_79] :
( ~ empty(U_79)
| ~ element(U_80,powerset(U_79)) )
| ~ in(U_81,U_80) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
cnf(f_51_4,plain,
( ~ empty(U_79)
| ~ element(U_80,powerset(U_79))
| ~ in(U_81,U_80) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_52_2,plain,
! [U_82] :
( U_82 = empty_set
| ~ empty(U_82) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
cnf(f_52_3,plain,
( U_82 = empty_set
| ~ empty(U_82) ),
inference(clausify,[status(thm)],[f_52_2]) ).
fof(f_53_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_53_2,plain,
! [U_84,U_83] :
( ~ empty(U_83)
| ~ in(U_84,U_83) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
cnf(f_53_3,plain,
( ~ empty(U_83)
| ~ in(U_84,U_83) ),
inference(clausify,[status(thm)],[f_53_2]) ).
fof(f_54_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_54_2,plain,
! [U_86,U_85] :
( ~ empty(U_85)
| U_86 = U_85
| ~ empty(U_86) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_86] :
( ! [U_85] :
( ~ empty(U_85)
| U_86 = U_85 )
| ~ empty(U_86) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
cnf(f_54_4,plain,
( ~ empty(U_85)
| U_86 = U_85
| ~ empty(U_86) ),
inference(clausify,[status(thm)],[f_54_3]) ).
cnf(f_6_3_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_3]) ).
cnf(f_6_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_6_4]) ).
cnf(f_49_9_true,negated_conjecture,
$true,
inference(clause_is_true,[status(thm)],[f_49_9]) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( set_union2(Eq_x_0,Eq_x_1) = set_union2(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( succ(Eq_x_0) = succ(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( singleton(Eq_x_0) = singleton(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK15(Eq_x_0) = sK15(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,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_11,axiom,
( proper_subset(Eq_y_0,Eq_y_1)
| ~ proper_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_12,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_16,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,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_19,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_20,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_21,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_22,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_23,axiom,
( relation_non_empty(Eq_y_0)
| ~ relation_non_empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( being_limit_ordinal(Eq_y_0)
| ~ being_limit_ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU238+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 19 23:40:21 UTC 2026
% 0.10/0.37 % CPUTime :
% 78.25/78.57 % SZS status Theorem for theBenchmark
% 78.25/78.57 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------