%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n004.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 08:52:11 AM UTC 2026
% Result : Theorem 30.65s 31.00s
% Output : Proof 30.65s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('theBenchmark.p',antisymmetry_r2_hidden) ).
fof(cc1_funct_1,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('theBenchmark.p',cc1_funct_1) ).
fof(cc1_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [A] :
( empty(A)
=> relation(A) ),
file('theBenchmark.p',cc1_relat_1) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( function(A)
& empty(A)
& relation(A) )
=> ( one_to_one(A)
& function(A)
& relation(A) ) ),
file('theBenchmark.p',cc2_funct_1) ).
fof(cc2_ordinal1,axiom,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
=> ordinal(A) ),
file('theBenchmark.p',cc2_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(d8_ordinal1,axiom,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
=> ( transfinite_sequence_of(B,A)
<=> subset(relation_rng(B),A) ) ),
file('theBenchmark.p',d8_ordinal1) ).
fof(dt_m1_ordinal1,axiom,
! [A,B] :
( transfinite_sequence_of(B,A)
=> ( transfinite_sequence(B)
& function(B)
& relation(B) ) ),
file('theBenchmark.p',dt_m1_ordinal1) ).
fof(existence_m1_ordinal1,axiom,
! [A] :
? [B] : transfinite_sequence_of(B,A),
file('theBenchmark.p',existence_m1_ordinal1) ).
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_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(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc6_funct_1,axiom,
! [A] :
( ( function(A)
& relation_non_empty(A)
& relation(A) )
=> with_non_empty_elements(relation_rng(A)) ),
file('theBenchmark.p',fc6_funct_1) ).
fof(fc6_relat_1,axiom,
! [A] :
( ( relation(A)
& ~ empty(A) )
=> ~ empty(relation_rng(A)) ),
file('theBenchmark.p',fc6_relat_1) ).
fof(fc8_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_rng(A))
& empty(relation_rng(A)) ) ),
file('theBenchmark.p',fc8_relat_1) ).
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(rc4_ordinal1,axiom,
? [A] :
( transfinite_sequence(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc4_ordinal1) ).
fof(rc5_funct_1,axiom,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
file('theBenchmark.p',rc5_funct_1) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : subset(A,A),
file('theBenchmark.p',reflexivity_r1_tarski) ).
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(t47_ordinal1,conjecture,
! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
file('theBenchmark.p',t47_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]) ).
fof(f_1_3,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(definitional_conversion,[status(esa)],[f_1_2]) ).
cnf(f_1_4,plain,
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_2_2,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_2] :
( function(U_2)
| ~ empty(U_2) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( function(U_2)
| ~ empty(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_3_2,plain,
! [U_3] :
( ( epsilon_connected(U_3)
& epsilon_transitive(U_3) )
| ~ ordinal(U_3) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_3] :
( epsilon_connected(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( epsilon_transitive(U_3)
| ~ sP0(U_3) )
& ! [U_3] :
( sP0(U_3)
| ~ ordinal(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_2]) ).
cnf(f_3_4,plain,
( sP0(U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( epsilon_transitive(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_6,plain,
( epsilon_connected(U_3)
| ~ sP0(U_3) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_4_2,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_4] :
( relation(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( relation(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ( one_to_one(A)
& function(A)
& relation(A) )
| ~ function(A)
| ~ empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[cc2_funct_1]) ).
fof(f_5_2,plain,
! [U_5] :
( ( one_to_one(U_5)
& function(U_5)
& relation(U_5) )
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_5] :
( one_to_one(U_5)
| ~ sP1(U_5) )
& ! [U_5] :
( function(U_5)
| ~ sP1(U_5) )
& ! [U_5] :
( relation(U_5)
| ~ sP1(U_5) )
& ! [U_5] :
( sP1(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP1(U_5)
| ~ function(U_5)
| ~ empty(U_5)
| ~ relation(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( relation(U_5)
| ~ sP1(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( function(U_5)
| ~ sP1(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_7,plain,
( one_to_one(U_5)
| ~ sP1(U_5) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_6_2,plain,
! [U_6] :
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_6] :
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( ordinal(U_6)
| ~ epsilon_connected(U_6)
| ~ epsilon_transitive(U_6) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_7_2,plain,
! [U_7] :
( ( ordinal(U_7)
& epsilon_connected(U_7)
& epsilon_transitive(U_7) )
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_7] :
( ordinal(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( epsilon_connected(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( epsilon_transitive(U_7)
| ~ sP2(U_7) )
& ! [U_7] :
( sP2(U_7)
| ~ empty(U_7) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP2(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( epsilon_transitive(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( epsilon_connected(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( ordinal(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B] :
( ( ( transfinite_sequence_of(B,A)
| ~ subset(relation_rng(B),A) )
& ( subset(relation_rng(B),A)
| ~ transfinite_sequence_of(B,A) ) )
| ~ transfinite_sequence(B)
| ~ function(B)
| ~ relation(B) ),
inference(fof_nnf,[status(thm)],[d8_ordinal1]) ).
fof(f_8_2,plain,
! [U_9,U_8] :
( ( ( transfinite_sequence_of(U_8,U_9)
| ~ subset(relation_rng(U_8),U_9) )
& ( subset(relation_rng(U_8),U_9)
| ~ transfinite_sequence_of(U_8,U_9) ) )
| ~ transfinite_sequence(U_8)
| ~ function(U_8)
| ~ relation(U_8) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_8,U_9] :
( transfinite_sequence_of(U_8,U_9)
| ~ subset(relation_rng(U_8),U_9)
| ~ sP3(U_8,U_9) )
& ! [U_8,U_9] :
( subset(relation_rng(U_8),U_9)
| ~ transfinite_sequence_of(U_8,U_9)
| ~ sP3(U_8,U_9) )
& ! [U_8,U_9] :
( sP3(U_8,U_9)
| ~ transfinite_sequence(U_8)
| ~ function(U_8)
| ~ relation(U_8) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_8_2]) ).
cnf(f_8_4,plain,
( sP3(U_8,U_9)
| ~ transfinite_sequence(U_8)
| ~ function(U_8)
| ~ relation(U_8) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( subset(relation_rng(U_8),U_9)
| ~ transfinite_sequence_of(U_8,U_9)
| ~ sP3(U_8,U_9) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( transfinite_sequence_of(U_8,U_9)
| ~ subset(relation_rng(U_8),U_9)
| ~ sP3(U_8,U_9) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [A,B] :
( ( transfinite_sequence(B)
& function(B)
& relation(B) )
| ~ transfinite_sequence_of(B,A) ),
inference(fof_nnf,[status(thm)],[dt_m1_ordinal1]) ).
fof(f_9_2,plain,
! [U_11,U_10] :
( ( transfinite_sequence(U_10)
& function(U_10)
& relation(U_10) )
| ~ transfinite_sequence_of(U_10,U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_10] :
( transfinite_sequence(U_10)
| ~ sP4(U_10) )
& ! [U_10] :
( function(U_10)
| ~ sP4(U_10) )
& ! [U_10] :
( relation(U_10)
| ~ sP4(U_10) )
& ! [U_11,U_10] :
( sP4(U_10)
| ~ transfinite_sequence_of(U_10,U_11) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP4(U_10)
| ~ transfinite_sequence_of(U_10,U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( relation(U_10)
| ~ sP4(U_10) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( function(U_10)
| ~ sP4(U_10) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( transfinite_sequence(U_10)
| ~ sP4(U_10) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
? [B] : transfinite_sequence_of(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_ordinal1]) ).
fof(f_10_2,plain,
! [U_13] :
? [U_12] : transfinite_sequence_of(U_12,U_13),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_13] : transfinite_sequence_of(sK1(U_13),U_13),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_12,sK1(U_13))],[f_10_2]) ).
fof(f_10_4,plain,
! [U_13] : transfinite_sequence_of(sK1(U_13),U_13),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
transfinite_sequence_of(sK1(U_13),U_13),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_11_2,plain,
! [U_15] :
? [U_14] : element(U_14,U_15),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_15] : element(sK2(U_15),U_15),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_14,sK2(U_15))],[f_11_2]) ).
fof(f_11_4,plain,
! [U_15] : element(sK2(U_15),U_15),
inference(definitional_conversion,[status(esa)],[f_11_3]) ).
cnf(f_11_5,plain,
element(sK2(U_15),U_15),
inference(clausify,[status(thm)],[f_11_4]) ).
fof(f_12_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_12_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_12_1]) ).
cnf(f_12_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_12_2]) ).
cnf(f_12_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_13_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_13_1]) ).
cnf(f_13_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_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_14_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_14_1]) ).
cnf(f_14_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_15_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [A] :
( with_non_empty_elements(relation_rng(A))
| ~ function(A)
| ~ relation_non_empty(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[fc6_funct_1]) ).
fof(f_16_2,plain,
! [U_16] :
( with_non_empty_elements(relation_rng(U_16))
| ~ function(U_16)
| ~ relation_non_empty(U_16)
| ~ relation(U_16) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_16] :
( with_non_empty_elements(relation_rng(U_16))
| ~ function(U_16)
| ~ relation_non_empty(U_16)
| ~ relation(U_16) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( with_non_empty_elements(relation_rng(U_16))
| ~ function(U_16)
| ~ relation_non_empty(U_16)
| ~ relation(U_16) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [A] :
( ~ empty(relation_rng(A))
| ~ relation(A)
| empty(A) ),
inference(fof_nnf,[status(thm)],[fc6_relat_1]) ).
fof(f_17_2,plain,
! [U_17] :
( ~ empty(relation_rng(U_17))
| ~ relation(U_17)
| empty(U_17) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_17] :
( ~ empty(relation_rng(U_17))
| ~ relation(U_17)
| empty(U_17) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( ~ empty(relation_rng(U_17))
| ~ relation(U_17)
| empty(U_17) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_18_2,plain,
! [U_18] :
( ( relation(relation_rng(U_18))
& empty(relation_rng(U_18)) )
| ~ empty(U_18) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_18] :
( relation(relation_rng(U_18))
| ~ sP5(U_18) )
& ! [U_18] :
( empty(relation_rng(U_18))
| ~ sP5(U_18) )
& ! [U_18] :
( sP5(U_18)
| ~ empty(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_18_2]) ).
cnf(f_18_4,plain,
( sP5(U_18)
| ~ empty(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( empty(relation_rng(U_18))
| ~ sP5(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( relation(relation_rng(U_18))
| ~ sP5(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_19_2,plain,
? [U_19] :
( function(U_19)
& relation(U_19) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
( function(sK3)
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_19,sK3)],[f_19_2]) ).
fof(f_19_4,plain,
( function(sK3)
& relation(sK3) ),
inference(definitional_conversion,[status(esa)],[f_19_3]) ).
cnf(f_19_5,plain,
relation(sK3),
inference(clausify,[status(thm)],[f_19_4]) ).
cnf(f_19_6,plain,
function(sK3),
inference(clausify,[status(thm)],[f_19_4]) ).
fof(f_20_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal1]) ).
fof(f_20_2,plain,
? [U_20] :
( ordinal(U_20)
& epsilon_connected(U_20)
& epsilon_transitive(U_20) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ordinal(sK4)
& epsilon_connected(sK4)
& epsilon_transitive(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_20,sK4)],[f_20_2]) ).
fof(f_20_4,plain,
( ordinal(sK4)
& epsilon_connected(sK4)
& epsilon_transitive(sK4) ),
inference(definitional_conversion,[status(esa)],[f_20_3]) ).
cnf(f_20_5,plain,
epsilon_transitive(sK4),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_6,plain,
epsilon_connected(sK4),
inference(clausify,[status(thm)],[f_20_4]) ).
cnf(f_20_7,plain,
ordinal(sK4),
inference(clausify,[status(thm)],[f_20_4]) ).
fof(f_21_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_21_2,plain,
? [U_21] :
( relation(U_21)
& empty(U_21) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( relation(sK5)
& empty(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_21,sK5)],[f_21_2]) ).
fof(f_21_4,plain,
( relation(sK5)
& empty(sK5) ),
inference(definitional_conversion,[status(esa)],[f_21_3]) ).
cnf(f_21_5,plain,
empty(sK5),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_22_2,plain,
? [U_22] : empty(U_22),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
empty(sK6),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_22,sK6)],[f_22_2]) ).
fof(f_22_4,plain,
empty(sK6),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
empty(sK6),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_23_2,plain,
? [U_23] :
( function(U_23)
& empty(U_23)
& relation(U_23) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( function(sK7)
& empty(sK7)
& relation(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_23,sK7)],[f_23_2]) ).
fof(f_23_4,plain,
( function(sK7)
& empty(sK7)
& relation(sK7) ),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,plain,
relation(sK7),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
empty(sK7),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_7,plain,
function(sK7),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_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_24_2,plain,
? [U_24] :
( ordinal(U_24)
& epsilon_connected(U_24)
& epsilon_transitive(U_24)
& empty(U_24)
& one_to_one(U_24)
& function(U_24)
& relation(U_24) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8)
& empty(sK8)
& one_to_one(sK8)
& function(sK8)
& relation(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_24,sK8)],[f_24_2]) ).
fof(f_24_4,plain,
( ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8)
& empty(sK8)
& one_to_one(sK8)
& function(sK8)
& relation(sK8) ),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
function(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
one_to_one(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_8,plain,
empty(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_9,plain,
epsilon_transitive(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_10,plain,
epsilon_connected(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_11,plain,
ordinal(sK8),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_25_2,plain,
? [U_25] :
( relation(U_25)
& ~ empty(U_25) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_25,sK9)],[f_25_2]) ).
fof(f_25_4,plain,
( relation(sK9)
& ~ empty(sK9) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
~ empty(sK9),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_25_4]) ).
fof(f_26_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_26_2,plain,
? [U_26] : ~ empty(U_26),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
~ empty(sK10),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_26,sK10)],[f_26_2]) ).
fof(f_26_4,plain,
~ empty(sK10),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
~ empty(sK10),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_27_2,plain,
? [U_27] :
( one_to_one(U_27)
& function(U_27)
& relation(U_27) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_27,sK11)],[f_27_2]) ).
fof(f_27_4,plain,
( one_to_one(sK11)
& function(sK11)
& relation(sK11) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
relation(sK11),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
function(sK11),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
one_to_one(sK11),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_28_2,plain,
? [U_28] :
( ordinal(U_28)
& epsilon_connected(U_28)
& epsilon_transitive(U_28)
& ~ empty(U_28) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_28,sK12)],[f_28_2]) ).
fof(f_28_4,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
epsilon_transitive(sK12),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_7,plain,
epsilon_connected(sK12),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_8,plain,
ordinal(sK12),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_29_2,plain,
? [U_29] :
( relation_empty_yielding(U_29)
& relation(U_29) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
( relation_empty_yielding(sK13)
& relation(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_29,sK13)],[f_29_2]) ).
fof(f_29_4,plain,
( relation_empty_yielding(sK13)
& relation(sK13) ),
inference(definitional_conversion,[status(esa)],[f_29_3]) ).
cnf(f_29_5,plain,
relation(sK13),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
relation_empty_yielding(sK13),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_30_2,plain,
? [U_30] :
( function(U_30)
& relation_empty_yielding(U_30)
& relation(U_30) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( function(sK14)
& relation_empty_yielding(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_30,sK14)],[f_30_2]) ).
fof(f_30_4,plain,
( function(sK14)
& relation_empty_yielding(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_6,plain,
relation_empty_yielding(sK14),
inference(clausify,[status(thm)],[f_30_4]) ).
cnf(f_30_7,plain,
function(sK14),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
? [A] :
( transfinite_sequence(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_ordinal1]) ).
fof(f_31_2,plain,
? [U_31] :
( transfinite_sequence(U_31)
& function(U_31)
& relation(U_31) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( transfinite_sequence(sK15)
& function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_31,sK15)],[f_31_2]) ).
fof(f_31_4,plain,
( transfinite_sequence(sK15)
& function(sK15)
& relation(sK15) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
function(sK15),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
transfinite_sequence(sK15),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_32_2,plain,
? [U_32] :
( function(U_32)
& relation_non_empty(U_32)
& relation(U_32) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( function(sK16)
& relation_non_empty(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_32,sK16)],[f_32_2]) ).
fof(f_32_4,plain,
( function(sK16)
& relation_non_empty(sK16)
& relation(sK16) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
relation_non_empty(sK16),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
function(sK16),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_33_2,plain,
! [U_34,U_33] : subset(U_34,U_34),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_34] : subset(U_34,U_34),
inference(miniscope,[status(thm)],[f_33_2]) ).
fof(f_33_4,plain,
! [U_34] : subset(U_34,U_34),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
subset(U_34,U_34),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_34_2,plain,
! [U_36,U_35] :
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_36,U_35] :
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( element(U_36,U_35)
| ~ in(U_36,U_35) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [A,B,C] :
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t1_xboole_1]) ).
fof(f_35_2,plain,
! [U_39,U_38,U_37] :
( subset(U_39,U_37)
| ~ subset(U_38,U_37)
| ~ subset(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_38,U_37,U_39] :
( subset(U_39,U_37)
| ~ subset(U_38,U_37)
| ~ subset(U_39,U_38) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( subset(U_39,U_37)
| ~ subset(U_38,U_37)
| ~ subset(U_39,U_38) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_36_2,plain,
! [U_41,U_40] :
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_41,U_40] :
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( in(U_41,U_40)
| empty(U_40)
| ~ element(U_41,U_40) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_43,U_42] :
( ( element(U_43,powerset(U_42))
| ~ subset(U_43,U_42) )
& ( subset(U_43,U_42)
| ~ element(U_43,powerset(U_42)) ) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
( ! [U_47,U_45] :
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) )
& ! [U_46,U_44] :
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ) ),
inference(miniscope,[status(thm)],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_47,U_45] :
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) )
& ! [U_46,U_44] :
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
( subset(U_46,U_44)
| ~ element(U_46,powerset(U_44)) ),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
( element(U_47,powerset(U_45))
| ~ subset(U_47,U_45) ),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> ! [C] :
( transfinite_sequence_of(C,A)
=> transfinite_sequence_of(C,B) ) ),
inference(negate,[status(cth)],[t47_ordinal1]) ).
fof(f_38_2,negated_conjecture,
? [A,B] :
( ? [C] :
( ~ transfinite_sequence_of(C,B)
& transfinite_sequence_of(C,A) )
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[f_38_1]) ).
fof(f_38_3,negated_conjecture,
? [U_50,U_49] :
( ? [U_48] :
( ~ transfinite_sequence_of(U_48,U_49)
& transfinite_sequence_of(U_48,U_50) )
& subset(U_50,U_49) ),
inference(variable_rename,[status(thm)],[f_38_2]) ).
fof(f_38_4,negated_conjecture,
? [U_49] :
( ? [U_48] :
( ~ transfinite_sequence_of(U_48,U_49)
& transfinite_sequence_of(U_48,sK17) )
& subset(sK17,U_49) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_50,sK17)],[f_38_3]) ).
fof(f_38_5,negated_conjecture,
( ? [U_48] :
( ~ transfinite_sequence_of(U_48,sK18)
& transfinite_sequence_of(U_48,sK17) )
& subset(sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_49,sK18)],[f_38_4]) ).
fof(f_38_6,negated_conjecture,
( ~ transfinite_sequence_of(sK19,sK18)
& transfinite_sequence_of(sK19,sK17)
& subset(sK17,sK18) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_48,sK19)],[f_38_5]) ).
fof(f_38_7,negated_conjecture,
( ~ transfinite_sequence_of(sK19,sK18)
& transfinite_sequence_of(sK19,sK17)
& subset(sK17,sK18) ),
inference(definitional_conversion,[status(esa)],[f_38_6]) ).
cnf(f_38_8,negated_conjecture,
subset(sK17,sK18),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_9,negated_conjecture,
transfinite_sequence_of(sK19,sK17),
inference(clausify,[status(thm)],[f_38_7]) ).
cnf(f_38_10,negated_conjecture,
~ transfinite_sequence_of(sK19,sK18),
inference(clausify,[status(thm)],[f_38_7]) ).
fof(f_39_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_39_2,plain,
! [U_53,U_52,U_51] :
( element(U_53,U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_51,U_53,U_52] :
( element(U_53,U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( element(U_53,U_51)
| ~ element(U_52,powerset(U_51))
| ~ in(U_53,U_52) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_40_2,plain,
! [U_56,U_55,U_54] :
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54))
| ~ in(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_56,U_55] :
( ! [U_54] :
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54)) )
| ~ in(U_56,U_55) ),
inference(miniscope,[status(thm)],[f_40_2]) ).
fof(f_40_4,plain,
! [U_54,U_56,U_55] :
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54))
| ~ in(U_56,U_55) ),
inference(definitional_conversion,[status(esa)],[f_40_3]) ).
cnf(f_40_5,plain,
( ~ empty(U_54)
| ~ element(U_55,powerset(U_54))
| ~ in(U_56,U_55) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_41_2,plain,
! [U_57] :
( U_57 = empty_set
| ~ empty(U_57) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_57] :
( U_57 = empty_set
| ~ empty(U_57) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( U_57 = empty_set
| ~ empty(U_57) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_42_2,plain,
! [U_59,U_58] :
( ~ empty(U_58)
| ~ in(U_59,U_58) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_59,U_58] :
( ~ empty(U_58)
| ~ in(U_59,U_58) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( ~ empty(U_58)
| ~ in(U_59,U_58) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_43_2,plain,
! [U_61,U_60] :
( ~ empty(U_60)
| U_61 = U_60
| ~ empty(U_61) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_61] :
( ! [U_60] :
( ~ empty(U_60)
| U_61 = U_60 )
| ~ empty(U_61) ),
inference(miniscope,[status(thm)],[f_43_2]) ).
fof(f_43_4,plain,
! [U_60,U_61] :
( ~ empty(U_60)
| U_61 = U_60
| ~ empty(U_61) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
( ~ empty(U_60)
| U_61 = U_60
| ~ empty(U_61) ),
inference(clausify,[status(thm)],[f_43_4]) ).
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,
( relation_rng(Eq_x_0) = relation_rng(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( sK1(Eq_x_0) = sK1(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( sK2(Eq_x_0) = sK2(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_8,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_9,axiom,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_10,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_11,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_12,axiom,
( epsilon_transitive(Eq_y_0)
| ~ epsilon_transitive(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_13,axiom,
( epsilon_connected(Eq_y_0)
| ~ epsilon_connected(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_15,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_16,axiom,
( transfinite_sequence(Eq_y_0)
| ~ transfinite_sequence(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_17,axiom,
( transfinite_sequence_of(Eq_y_0,Eq_y_1)
| ~ transfinite_sequence_of(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,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_19,axiom,
( element(Eq_y_0,Eq_y_1)
| ~ element(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( relation_empty_yielding(Eq_y_0)
| ~ relation_empty_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,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_22,axiom,
( with_non_empty_elements(Eq_y_0)
| ~ with_non_empty_elements(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_23,axiom,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_24,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( sP3(Eq_y_0,Eq_y_1)
| ~ sP3(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM411+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 19 18:22:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 30.65/31.00 % SZS status Theorem for theBenchmark
% 30.65/31.00 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------