%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SEU094+1 : 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 : n013.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 08:58:02 AM UTC 2026
% Result : Theorem 34.36s 34.68s
% Output : Proof 34.45s
% 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_arytm_3,axiom,
! [A] :
( ordinal(A)
=> ! [B] :
( element(B,A)
=> ( ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B) ) ) ),
file('theBenchmark.p',cc1_arytm_3) ).
fof(cc1_finset_1,axiom,
! [A] :
( empty(A)
=> finite(A) ),
file('theBenchmark.p',cc1_finset_1) ).
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_arytm_3,axiom,
! [A] :
( ( ordinal(A)
& empty(A) )
=> ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc2_arytm_3) ).
fof(cc2_finset_1,axiom,
! [A] :
( finite(A)
=> ! [B] :
( element(B,powerset(A))
=> finite(B) ) ),
file('theBenchmark.p',cc2_finset_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(cc4_arytm_3,axiom,
! [A] :
( element(A,positive_rationals)
=> ( ordinal(A)
=> ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ) ),
file('theBenchmark.p',cc4_arytm_3) ).
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_subset_1,axiom,
! [A] : ~ empty(powerset(A)),
file('theBenchmark.p',fc1_subset_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_ordinal1,axiom,
! [A] :
( ordinal(A)
=> ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) ) ),
file('theBenchmark.p',fc4_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc8_arytm_3,axiom,
~ empty(positive_rationals),
file('theBenchmark.p',fc8_arytm_3) ).
fof(l22_finset_1,axiom,
! [A] :
( ( ! [B] :
( in(B,A)
=> finite(B) )
& finite(A) )
=> finite(union(A)) ),
file('theBenchmark.p',l22_finset_1) ).
fof(rc1_arytm_3,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_arytm_3) ).
fof(rc1_finset_1,axiom,
? [A] :
( finite(A)
& ~ empty(A) ),
file('theBenchmark.p',rc1_finset_1) ).
fof(rc1_funcop_1,axiom,
? [A] :
( function_yielding(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc1_funcop_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_ordinal2,axiom,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
file('theBenchmark.p',rc1_ordinal2) ).
fof(rc1_relat_1,axiom,
? [A] :
( relation(A)
& empty(A) ),
file('theBenchmark.p',rc1_relat_1) ).
fof(rc1_subset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc1_subset_1) ).
fof(rc1_xboole_0,axiom,
? [A] : empty(A),
file('theBenchmark.p',rc1_xboole_0) ).
fof(rc2_arytm_3,axiom,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
file('theBenchmark.p',rc2_arytm_3) ).
fof(rc2_finset_1,axiom,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_finset_1) ).
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_ordinal2,axiom,
? [A] :
( ordinal_yielding(A)
& transfinite_sequence(A)
& function(A)
& relation(A) ),
file('theBenchmark.p',rc2_ordinal2) ).
fof(rc2_relat_1,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('theBenchmark.p',rc2_relat_1) ).
fof(rc2_subset_1,axiom,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
file('theBenchmark.p',rc2_subset_1) ).
fof(rc2_xboole_0,axiom,
? [A] : ~ empty(A),
file('theBenchmark.p',rc2_xboole_0) ).
fof(rc3_arytm_3,axiom,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& element(A,positive_rationals) ),
file('theBenchmark.p',rc3_arytm_3) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ empty(A)
=> ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) ) ),
file('theBenchmark.p',rc3_finset_1) ).
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(t100_zfmisc_1,axiom,
! [A] : subset(A,powerset(union(A))),
file('theBenchmark.p',t100_zfmisc_1) ).
fof(t13_finset_1,axiom,
! [A,B] :
( ( finite(B)
& subset(A,B) )
=> finite(A) ),
file('theBenchmark.p',t13_finset_1) ).
fof(t1_subset,axiom,
! [A,B] :
( in(A,B)
=> element(A,B) ),
file('theBenchmark.p',t1_subset) ).
fof(t24_finset_1,axiom,
! [A] :
( finite(A)
<=> finite(powerset(A)) ),
file('theBenchmark.p',t24_finset_1) ).
fof(t25_finset_1,conjecture,
! [A] :
( ( ! [B] :
( in(B,A)
=> finite(B) )
& finite(A) )
<=> finite(union(A)) ),
file('theBenchmark.p',t25_finset_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(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(t92_zfmisc_1,axiom,
! [A,B] :
( in(A,B)
=> subset(A,union(B)) ),
file('theBenchmark.p',t92_zfmisc_1) ).
fof(f_1_1,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ~ in(U_0,U_1)
| ~ in(U_1,U_0) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
! [U_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] :
( ! [B] :
( ( ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B) )
| ~ element(B,A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_arytm_3]) ).
fof(f_2_2,plain,
! [U_3] :
( ! [U_2] :
( ( ordinal(U_2)
& epsilon_connected(U_2)
& epsilon_transitive(U_2) )
| ~ element(U_2,U_3) )
| ~ ordinal(U_3) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_2] :
( ordinal(U_2)
| ~ sP0(U_2) )
& ! [U_2] :
( epsilon_connected(U_2)
| ~ sP0(U_2) )
& ! [U_2] :
( epsilon_transitive(U_2)
| ~ sP0(U_2) )
& ! [U_3,U_2] :
( sP0(U_2)
| ~ element(U_2,U_3)
| ~ ordinal(U_3) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_2_2]) ).
cnf(f_2_4,plain,
( sP0(U_2)
| ~ element(U_2,U_3)
| ~ ordinal(U_3) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( epsilon_transitive(U_2)
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_6,plain,
( epsilon_connected(U_2)
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_7,plain,
( ordinal(U_2)
| ~ sP0(U_2) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [A] :
( finite(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_finset_1]) ).
fof(f_3_2,plain,
! [U_4] :
( finite(U_4)
| ~ empty(U_4) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
! [U_4] :
( finite(U_4)
| ~ empty(U_4) ),
inference(definitional_conversion,[status(esa)],[f_3_2]) ).
cnf(f_3_4,plain,
( finite(U_4)
| ~ empty(U_4) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [A] :
( function(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_funct_1]) ).
fof(f_4_2,plain,
! [U_5] :
( function(U_5)
| ~ empty(U_5) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5] :
( function(U_5)
| ~ empty(U_5) ),
inference(definitional_conversion,[status(esa)],[f_4_2]) ).
cnf(f_4_4,plain,
( function(U_5)
| ~ empty(U_5) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [A] :
( ( epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[cc1_ordinal1]) ).
fof(f_5_2,plain,
! [U_6] :
( ( epsilon_connected(U_6)
& epsilon_transitive(U_6) )
| ~ ordinal(U_6) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_6] :
( epsilon_connected(U_6)
| ~ sP1(U_6) )
& ! [U_6] :
( epsilon_transitive(U_6)
| ~ sP1(U_6) )
& ! [U_6] :
( sP1(U_6)
| ~ ordinal(U_6) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP1(U_6)
| ~ ordinal(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( epsilon_transitive(U_6)
| ~ sP1(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( epsilon_connected(U_6)
| ~ sP1(U_6) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A] :
( relation(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc1_relat_1]) ).
fof(f_6_2,plain,
! [U_7] :
( relation(U_7)
| ~ empty(U_7) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_7] :
( relation(U_7)
| ~ empty(U_7) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( relation(U_7)
| ~ empty(U_7) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [A] :
( ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A)
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc2_arytm_3]) ).
fof(f_7_2,plain,
! [U_8] :
( ( natural(U_8)
& ordinal(U_8)
& epsilon_connected(U_8)
& epsilon_transitive(U_8) )
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_8] :
( natural(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( ordinal(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( epsilon_connected(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( epsilon_transitive(U_8)
| ~ sP2(U_8) )
& ! [U_8] :
( sP2(U_8)
| ~ ordinal(U_8)
| ~ empty(U_8) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_7_2]) ).
cnf(f_7_4,plain,
( sP2(U_8)
| ~ ordinal(U_8)
| ~ empty(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( epsilon_transitive(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( epsilon_connected(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_7,plain,
( ordinal(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_8,plain,
( natural(U_8)
| ~ sP2(U_8) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A] :
( ! [B] :
( finite(B)
| ~ element(B,powerset(A)) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[cc2_finset_1]) ).
fof(f_8_2,plain,
! [U_10] :
( ! [U_9] :
( finite(U_9)
| ~ element(U_9,powerset(U_10)) )
| ~ finite(U_10) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_9,U_10] :
( finite(U_9)
| ~ element(U_9,powerset(U_10))
| ~ finite(U_10) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( finite(U_9)
| ~ element(U_9,powerset(U_10))
| ~ finite(U_10) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_11] :
( ( one_to_one(U_11)
& function(U_11)
& relation(U_11) )
| ~ function(U_11)
| ~ empty(U_11)
| ~ relation(U_11) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_11] :
( one_to_one(U_11)
| ~ sP3(U_11) )
& ! [U_11] :
( function(U_11)
| ~ sP3(U_11) )
& ! [U_11] :
( relation(U_11)
| ~ sP3(U_11) )
& ! [U_11] :
( sP3(U_11)
| ~ function(U_11)
| ~ empty(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)
| ~ function(U_11)
| ~ empty(U_11)
| ~ relation(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( relation(U_11)
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( function(U_11)
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( one_to_one(U_11)
| ~ sP3(U_11) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [A] :
( ordinal(A)
| ~ epsilon_connected(A)
| ~ epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[cc2_ordinal1]) ).
fof(f_10_2,plain,
! [U_12] :
( ordinal(U_12)
| ~ epsilon_connected(U_12)
| ~ epsilon_transitive(U_12) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_12] :
( ordinal(U_12)
| ~ epsilon_connected(U_12)
| ~ epsilon_transitive(U_12) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( ordinal(U_12)
| ~ epsilon_connected(U_12)
| ~ epsilon_transitive(U_12) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] :
( ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[cc3_ordinal1]) ).
fof(f_11_2,plain,
! [U_13] :
( ( ordinal(U_13)
& epsilon_connected(U_13)
& epsilon_transitive(U_13) )
| ~ empty(U_13) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_13] :
( ordinal(U_13)
| ~ sP4(U_13) )
& ! [U_13] :
( epsilon_connected(U_13)
| ~ sP4(U_13) )
& ! [U_13] :
( epsilon_transitive(U_13)
| ~ sP4(U_13) )
& ! [U_13] :
( sP4(U_13)
| ~ empty(U_13) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP4(U_13)
| ~ empty(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_5,plain,
( epsilon_transitive(U_13)
| ~ sP4(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( epsilon_connected(U_13)
| ~ sP4(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_7,plain,
( ordinal(U_13)
| ~ sP4(U_13) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [A] :
( ( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) )
| ~ ordinal(A)
| ~ element(A,positive_rationals) ),
inference(fof_nnf,[status(thm)],[cc4_arytm_3]) ).
fof(f_12_2,plain,
! [U_14] :
( ( natural(U_14)
& ordinal(U_14)
& epsilon_connected(U_14)
& epsilon_transitive(U_14) )
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_14] :
( natural(U_14)
| ~ sP5(U_14) )
& ! [U_14] :
( ordinal(U_14)
| ~ sP5(U_14) )
& ! [U_14] :
( epsilon_connected(U_14)
| ~ sP5(U_14) )
& ! [U_14] :
( epsilon_transitive(U_14)
| ~ sP5(U_14) )
& ! [U_14] :
( sP5(U_14)
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP5(U_14)
| ~ ordinal(U_14)
| ~ element(U_14,positive_rationals) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_5,plain,
( epsilon_transitive(U_14)
| ~ sP5(U_14) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( epsilon_connected(U_14)
| ~ sP5(U_14) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_7,plain,
( ordinal(U_14)
| ~ sP5(U_14) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_8,plain,
( natural(U_14)
| ~ sP5(U_14) ),
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_16] :
? [U_15] : element(U_15,U_16),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_16] : element(sK1(U_16),U_16),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_15,sK1(U_16))],[f_13_2]) ).
fof(f_13_4,plain,
! [U_16] : element(sK1(U_16),U_16),
inference(definitional_conversion,[status(esa)],[f_13_3]) ).
cnf(f_13_5,plain,
element(sK1(U_16),U_16),
inference(clausify,[status(thm)],[f_13_4]) ).
fof(f_14_1,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc12_relat_1]) ).
fof(f_14_2,plain,
( relation_empty_yielding(empty_set)
& relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_14_1]) ).
cnf(f_14_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
cnf(f_14_5,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_1,plain,
! [A] : ~ empty(powerset(A)),
inference(fof_nnf,[status(thm)],[fc1_subset_1]) ).
fof(f_15_2,plain,
! [U_17] : ~ empty(powerset(U_17)),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_17] : ~ empty(powerset(U_17)),
inference(definitional_conversion,[status(esa)],[f_15_2]) ).
cnf(f_15_4,plain,
~ empty(powerset(U_17)),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_16_1,plain,
empty(empty_set),
inference(fof_nnf,[status(thm)],[fc1_xboole_0]) ).
fof(f_16_2,plain,
empty(empty_set),
inference(definitional_conversion,[status(esa)],[f_16_1]) ).
cnf(f_16_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_16_2]) ).
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]) ).
fof(f_17_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_17_1]) ).
cnf(f_17_3,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
relation_empty_yielding(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_6,plain,
one_to_one(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_7,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_8,plain,
epsilon_transitive(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_9,plain,
epsilon_connected(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
cnf(f_17_10,plain,
ordinal(empty_set),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [A] :
( ( ordinal(union(A))
& epsilon_connected(union(A))
& epsilon_transitive(union(A)) )
| ~ ordinal(A) ),
inference(fof_nnf,[status(thm)],[fc4_ordinal1]) ).
fof(f_18_2,plain,
! [U_18] :
( ( ordinal(union(U_18))
& epsilon_connected(union(U_18))
& epsilon_transitive(union(U_18)) )
| ~ ordinal(U_18) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
( ! [U_18] :
( ordinal(union(U_18))
| ~ sP6(U_18) )
& ! [U_18] :
( epsilon_connected(union(U_18))
| ~ sP6(U_18) )
& ! [U_18] :
( epsilon_transitive(union(U_18))
| ~ sP6(U_18) )
& ! [U_18] :
( sP6(U_18)
| ~ ordinal(U_18) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_18_2]) ).
cnf(f_18_4,plain,
( sP6(U_18)
| ~ ordinal(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_5,plain,
( epsilon_transitive(union(U_18))
| ~ sP6(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_6,plain,
( epsilon_connected(union(U_18))
| ~ sP6(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
cnf(f_18_7,plain,
( ordinal(union(U_18))
| ~ sP6(U_18) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_19_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_19_1]) ).
cnf(f_19_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_19_2]) ).
cnf(f_19_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
~ empty(positive_rationals),
inference(fof_nnf,[status(thm)],[fc8_arytm_3]) ).
fof(f_20_2,plain,
~ empty(positive_rationals),
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
~ empty(positive_rationals),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_21_1,plain,
! [A] :
( finite(union(A))
| ? [B] :
( ~ finite(B)
& in(B,A) )
| ~ finite(A) ),
inference(fof_nnf,[status(thm)],[l22_finset_1]) ).
fof(f_21_2,plain,
! [U_20] :
( finite(union(U_20))
| ? [U_19] :
( ~ finite(U_19)
& in(U_19,U_20) )
| ~ finite(U_20) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_20] :
( finite(union(U_20))
| ( ~ finite(sK2(U_20))
& in(sK2(U_20),U_20) )
| ~ finite(U_20) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_19,sK2(U_20))],[f_21_2]) ).
fof(f_21_4,plain,
( ! [U_20] :
( ~ finite(sK2(U_20))
| ~ sP7(U_20) )
& ! [U_20] :
( in(sK2(U_20),U_20)
| ~ sP7(U_20) )
& ! [U_20] :
( finite(union(U_20))
| sP7(U_20)
| ~ finite(U_20) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_21_3]) ).
cnf(f_21_5,plain,
( finite(union(U_20))
| sP7(U_20)
| ~ finite(U_20) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_6,plain,
( in(sK2(U_20),U_20)
| ~ sP7(U_20) ),
inference(clausify,[status(thm)],[f_21_4]) ).
cnf(f_21_7,plain,
( ~ finite(sK2(U_20))
| ~ sP7(U_20) ),
inference(clausify,[status(thm)],[f_21_4]) ).
fof(f_22_1,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_arytm_3]) ).
fof(f_22_2,plain,
? [U_21] :
( natural(U_21)
& ordinal(U_21)
& epsilon_connected(U_21)
& epsilon_transitive(U_21)
& ~ empty(U_21) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
( natural(sK3)
& ordinal(sK3)
& epsilon_connected(sK3)
& epsilon_transitive(sK3)
& ~ empty(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_21,sK3)],[f_22_2]) ).
fof(f_22_4,plain,
( natural(sK3)
& ordinal(sK3)
& epsilon_connected(sK3)
& epsilon_transitive(sK3)
& ~ empty(sK3) ),
inference(definitional_conversion,[status(esa)],[f_22_3]) ).
cnf(f_22_5,plain,
~ empty(sK3),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_6,plain,
epsilon_transitive(sK3),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_7,plain,
epsilon_connected(sK3),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_8,plain,
ordinal(sK3),
inference(clausify,[status(thm)],[f_22_4]) ).
cnf(f_22_9,plain,
natural(sK3),
inference(clausify,[status(thm)],[f_22_4]) ).
fof(f_23_1,plain,
? [A] :
( finite(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_finset_1]) ).
fof(f_23_2,plain,
? [U_22] :
( finite(U_22)
& ~ empty(U_22) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
( finite(sK4)
& ~ empty(sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_22,sK4)],[f_23_2]) ).
fof(f_23_4,plain,
( finite(sK4)
& ~ empty(sK4) ),
inference(definitional_conversion,[status(esa)],[f_23_3]) ).
cnf(f_23_5,plain,
~ empty(sK4),
inference(clausify,[status(thm)],[f_23_4]) ).
cnf(f_23_6,plain,
finite(sK4),
inference(clausify,[status(thm)],[f_23_4]) ).
fof(f_24_1,plain,
? [A] :
( function_yielding(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funcop_1]) ).
fof(f_24_2,plain,
? [U_23] :
( function_yielding(U_23)
& function(U_23)
& relation(U_23) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( function_yielding(sK5)
& function(sK5)
& relation(sK5) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_23,sK5)],[f_24_2]) ).
fof(f_24_4,plain,
( function_yielding(sK5)
& function(sK5)
& relation(sK5) ),
inference(definitional_conversion,[status(esa)],[f_24_3]) ).
cnf(f_24_5,plain,
relation(sK5),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_6,plain,
function(sK5),
inference(clausify,[status(thm)],[f_24_4]) ).
cnf(f_24_7,plain,
function_yielding(sK5),
inference(clausify,[status(thm)],[f_24_4]) ).
fof(f_25_1,plain,
? [A] :
( function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc1_funct_1]) ).
fof(f_25_2,plain,
? [U_24] :
( function(U_24)
& relation(U_24) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_24,sK6)],[f_25_2]) ).
fof(f_25_4,plain,
( function(sK6)
& relation(sK6) ),
inference(definitional_conversion,[status(esa)],[f_25_3]) ).
cnf(f_25_5,plain,
relation(sK6),
inference(clausify,[status(thm)],[f_25_4]) ).
cnf(f_25_6,plain,
function(sK6),
inference(clausify,[status(thm)],[f_25_4]) ).
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_25] :
( ordinal(U_25)
& epsilon_connected(U_25)
& epsilon_transitive(U_25) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_25,sK7)],[f_26_2]) ).
fof(f_26_4,plain,
( ordinal(sK7)
& epsilon_connected(sK7)
& epsilon_transitive(sK7) ),
inference(definitional_conversion,[status(esa)],[f_26_3]) ).
cnf(f_26_5,plain,
epsilon_transitive(sK7),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_6,plain,
epsilon_connected(sK7),
inference(clausify,[status(thm)],[f_26_4]) ).
cnf(f_26_7,plain,
ordinal(sK7),
inference(clausify,[status(thm)],[f_26_4]) ).
fof(f_27_1,plain,
? [A] :
( being_limit_ordinal(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ),
inference(fof_nnf,[status(thm)],[rc1_ordinal2]) ).
fof(f_27_2,plain,
? [U_26] :
( being_limit_ordinal(U_26)
& ordinal(U_26)
& epsilon_connected(U_26)
& epsilon_transitive(U_26) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( being_limit_ordinal(sK8)
& ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_26,sK8)],[f_27_2]) ).
fof(f_27_4,plain,
( being_limit_ordinal(sK8)
& ordinal(sK8)
& epsilon_connected(sK8)
& epsilon_transitive(sK8) ),
inference(definitional_conversion,[status(esa)],[f_27_3]) ).
cnf(f_27_5,plain,
epsilon_transitive(sK8),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_6,plain,
epsilon_connected(sK8),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_7,plain,
ordinal(sK8),
inference(clausify,[status(thm)],[f_27_4]) ).
cnf(f_27_8,plain,
being_limit_ordinal(sK8),
inference(clausify,[status(thm)],[f_27_4]) ).
fof(f_28_1,plain,
? [A] :
( relation(A)
& empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_relat_1]) ).
fof(f_28_2,plain,
? [U_27] :
( relation(U_27)
& empty(U_27) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
( relation(sK9)
& empty(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_27,sK9)],[f_28_2]) ).
fof(f_28_4,plain,
( relation(sK9)
& empty(sK9) ),
inference(definitional_conversion,[status(esa)],[f_28_3]) ).
cnf(f_28_5,plain,
empty(sK9),
inference(clausify,[status(thm)],[f_28_4]) ).
cnf(f_28_6,plain,
relation(sK9),
inference(clausify,[status(thm)],[f_28_4]) ).
fof(f_29_1,plain,
! [A] :
( ? [B] :
( ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc1_subset_1]) ).
fof(f_29_2,plain,
! [U_29] :
( ? [U_28] :
( ~ empty(U_28)
& element(U_28,powerset(U_29)) )
| empty(U_29) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_29] :
( ( ~ empty(sK10(U_29))
& element(sK10(U_29),powerset(U_29)) )
| empty(U_29) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_28,sK10(U_29))],[f_29_2]) ).
fof(f_29_4,plain,
( ! [U_29] :
( ~ empty(sK10(U_29))
| ~ sP8(U_29) )
& ! [U_29] :
( element(sK10(U_29),powerset(U_29))
| ~ sP8(U_29) )
& ! [U_29] :
( sP8(U_29)
| empty(U_29) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_29_3]) ).
cnf(f_29_5,plain,
( sP8(U_29)
| empty(U_29) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_6,plain,
( element(sK10(U_29),powerset(U_29))
| ~ sP8(U_29) ),
inference(clausify,[status(thm)],[f_29_4]) ).
cnf(f_29_7,plain,
( ~ empty(sK10(U_29))
| ~ sP8(U_29) ),
inference(clausify,[status(thm)],[f_29_4]) ).
fof(f_30_1,plain,
? [A] : empty(A),
inference(fof_nnf,[status(thm)],[rc1_xboole_0]) ).
fof(f_30_2,plain,
? [U_30] : empty(U_30),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
empty(sK11),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_30,sK11)],[f_30_2]) ).
fof(f_30_4,plain,
empty(sK11),
inference(definitional_conversion,[status(esa)],[f_30_3]) ).
cnf(f_30_5,plain,
empty(sK11),
inference(clausify,[status(thm)],[f_30_4]) ).
fof(f_31_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A)
& element(A,positive_rationals) ),
inference(fof_nnf,[status(thm)],[rc2_arytm_3]) ).
fof(f_31_2,plain,
? [U_31] :
( ordinal(U_31)
& epsilon_connected(U_31)
& epsilon_transitive(U_31)
& ~ empty(U_31)
& element(U_31,positive_rationals) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12)
& element(sK12,positive_rationals) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_31,sK12)],[f_31_2]) ).
fof(f_31_4,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& ~ empty(sK12)
& element(sK12,positive_rationals) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_5,plain,
element(sK12,positive_rationals),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_6,plain,
~ empty(sK12),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_7,plain,
epsilon_transitive(sK12),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_8,plain,
epsilon_connected(sK12),
inference(clausify,[status(thm)],[f_31_4]) ).
cnf(f_31_9,plain,
ordinal(sK12),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_32_1,plain,
! [A] :
? [B] :
( finite(B)
& natural(B)
& ordinal(B)
& epsilon_connected(B)
& epsilon_transitive(B)
& one_to_one(B)
& function(B)
& relation(B)
& empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_finset_1]) ).
fof(f_32_2,plain,
! [U_33] :
? [U_32] :
( finite(U_32)
& natural(U_32)
& ordinal(U_32)
& epsilon_connected(U_32)
& epsilon_transitive(U_32)
& one_to_one(U_32)
& function(U_32)
& relation(U_32)
& empty(U_32)
& element(U_32,powerset(U_33)) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_33] :
( finite(sK13(U_33))
& natural(sK13(U_33))
& ordinal(sK13(U_33))
& epsilon_connected(sK13(U_33))
& epsilon_transitive(sK13(U_33))
& one_to_one(sK13(U_33))
& function(sK13(U_33))
& relation(sK13(U_33))
& empty(sK13(U_33))
& element(sK13(U_33),powerset(U_33)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_32,sK13(U_33))],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_33] : finite(sK13(U_33))
& ! [U_33] : natural(sK13(U_33))
& ! [U_33] : ordinal(sK13(U_33))
& ! [U_33] : epsilon_connected(sK13(U_33))
& ! [U_33] : epsilon_transitive(sK13(U_33))
& ! [U_33] : one_to_one(sK13(U_33))
& ! [U_33] : function(sK13(U_33))
& ! [U_33] : relation(sK13(U_33))
& ! [U_33] : empty(sK13(U_33))
& ! [U_33] : element(sK13(U_33),powerset(U_33)) ),
inference(definitional_conversion,[status(esa)],[f_32_3]) ).
cnf(f_32_5,plain,
element(sK13(U_33),powerset(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
empty(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
relation(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_8,plain,
function(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_9,plain,
one_to_one(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_10,plain,
epsilon_transitive(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_11,plain,
epsilon_connected(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_12,plain,
ordinal(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_13,plain,
natural(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_14,plain,
finite(sK13(U_33)),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_1,plain,
? [A] :
( function(A)
& empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_funct_1]) ).
fof(f_33_2,plain,
? [U_34] :
( function(U_34)
& empty(U_34)
& relation(U_34) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( function(sK14)
& empty(sK14)
& relation(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_34,sK14)],[f_33_2]) ).
fof(f_33_4,plain,
( function(sK14)
& empty(sK14)
& relation(sK14) ),
inference(definitional_conversion,[status(esa)],[f_33_3]) ).
cnf(f_33_5,plain,
relation(sK14),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_6,plain,
empty(sK14),
inference(clausify,[status(thm)],[f_33_4]) ).
cnf(f_33_7,plain,
function(sK14),
inference(clausify,[status(thm)],[f_33_4]) ).
fof(f_34_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_34_2,plain,
? [U_35] :
( ordinal(U_35)
& epsilon_connected(U_35)
& epsilon_transitive(U_35)
& empty(U_35)
& one_to_one(U_35)
& function(U_35)
& relation(U_35) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15)
& empty(sK15)
& one_to_one(sK15)
& function(sK15)
& relation(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_35,sK15)],[f_34_2]) ).
fof(f_34_4,plain,
( ordinal(sK15)
& epsilon_connected(sK15)
& epsilon_transitive(sK15)
& empty(sK15)
& one_to_one(sK15)
& function(sK15)
& relation(sK15) ),
inference(definitional_conversion,[status(esa)],[f_34_3]) ).
cnf(f_34_5,plain,
relation(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_6,plain,
function(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_7,plain,
one_to_one(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_8,plain,
empty(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_9,plain,
epsilon_transitive(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_10,plain,
epsilon_connected(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
cnf(f_34_11,plain,
ordinal(sK15),
inference(clausify,[status(thm)],[f_34_4]) ).
fof(f_35_1,plain,
? [A] :
( ordinal_yielding(A)
& transfinite_sequence(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc2_ordinal2]) ).
fof(f_35_2,plain,
? [U_36] :
( ordinal_yielding(U_36)
& transfinite_sequence(U_36)
& function(U_36)
& relation(U_36) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ordinal_yielding(sK16)
& transfinite_sequence(sK16)
& function(sK16)
& relation(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_36,sK16)],[f_35_2]) ).
fof(f_35_4,plain,
( ordinal_yielding(sK16)
& transfinite_sequence(sK16)
& function(sK16)
& relation(sK16) ),
inference(definitional_conversion,[status(esa)],[f_35_3]) ).
cnf(f_35_5,plain,
relation(sK16),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_6,plain,
function(sK16),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_7,plain,
transfinite_sequence(sK16),
inference(clausify,[status(thm)],[f_35_4]) ).
cnf(f_35_8,plain,
ordinal_yielding(sK16),
inference(clausify,[status(thm)],[f_35_4]) ).
fof(f_36_1,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc2_relat_1]) ).
fof(f_36_2,plain,
? [U_37] :
( relation(U_37)
& ~ empty(U_37) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
( relation(sK17)
& ~ empty(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_37,sK17)],[f_36_2]) ).
fof(f_36_4,plain,
( relation(sK17)
& ~ empty(sK17) ),
inference(definitional_conversion,[status(esa)],[f_36_3]) ).
cnf(f_36_5,plain,
~ empty(sK17),
inference(clausify,[status(thm)],[f_36_4]) ).
cnf(f_36_6,plain,
relation(sK17),
inference(clausify,[status(thm)],[f_36_4]) ).
fof(f_37_1,plain,
! [A] :
? [B] :
( empty(B)
& element(B,powerset(A)) ),
inference(fof_nnf,[status(thm)],[rc2_subset_1]) ).
fof(f_37_2,plain,
! [U_39] :
? [U_38] :
( empty(U_38)
& element(U_38,powerset(U_39)) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_39] :
( empty(sK18(U_39))
& element(sK18(U_39),powerset(U_39)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_38,sK18(U_39))],[f_37_2]) ).
fof(f_37_4,plain,
( ! [U_39] : empty(sK18(U_39))
& ! [U_39] : element(sK18(U_39),powerset(U_39)) ),
inference(definitional_conversion,[status(esa)],[f_37_3]) ).
cnf(f_37_5,plain,
element(sK18(U_39),powerset(U_39)),
inference(clausify,[status(thm)],[f_37_4]) ).
cnf(f_37_6,plain,
empty(sK18(U_39)),
inference(clausify,[status(thm)],[f_37_4]) ).
fof(f_38_1,plain,
? [A] : ~ empty(A),
inference(fof_nnf,[status(thm)],[rc2_xboole_0]) ).
fof(f_38_2,plain,
? [U_40] : ~ empty(U_40),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
~ empty(sK19),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_40,sK19)],[f_38_2]) ).
fof(f_38_4,plain,
~ empty(sK19),
inference(definitional_conversion,[status(esa)],[f_38_3]) ).
cnf(f_38_5,plain,
~ empty(sK19),
inference(clausify,[status(thm)],[f_38_4]) ).
fof(f_39_1,plain,
? [A] :
( natural(A)
& ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& empty(A)
& element(A,positive_rationals) ),
inference(fof_nnf,[status(thm)],[rc3_arytm_3]) ).
fof(f_39_2,plain,
? [U_41] :
( natural(U_41)
& ordinal(U_41)
& epsilon_connected(U_41)
& epsilon_transitive(U_41)
& empty(U_41)
& element(U_41,positive_rationals) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
( natural(sK20)
& ordinal(sK20)
& epsilon_connected(sK20)
& epsilon_transitive(sK20)
& empty(sK20)
& element(sK20,positive_rationals) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_41,sK20)],[f_39_2]) ).
fof(f_39_4,plain,
( natural(sK20)
& ordinal(sK20)
& epsilon_connected(sK20)
& epsilon_transitive(sK20)
& empty(sK20)
& element(sK20,positive_rationals) ),
inference(definitional_conversion,[status(esa)],[f_39_3]) ).
cnf(f_39_5,plain,
element(sK20,positive_rationals),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_6,plain,
empty(sK20),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_7,plain,
epsilon_transitive(sK20),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_8,plain,
epsilon_connected(sK20),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_9,plain,
ordinal(sK20),
inference(clausify,[status(thm)],[f_39_4]) ).
cnf(f_39_10,plain,
natural(sK20),
inference(clausify,[status(thm)],[f_39_4]) ).
fof(f_40_1,plain,
! [A] :
( ? [B] :
( finite(B)
& ~ empty(B)
& element(B,powerset(A)) )
| empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_finset_1]) ).
fof(f_40_2,plain,
! [U_43] :
( ? [U_42] :
( finite(U_42)
& ~ empty(U_42)
& element(U_42,powerset(U_43)) )
| empty(U_43) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_43] :
( ( finite(sK21(U_43))
& ~ empty(sK21(U_43))
& element(sK21(U_43),powerset(U_43)) )
| empty(U_43) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_42,sK21(U_43))],[f_40_2]) ).
fof(f_40_4,plain,
( ! [U_43] :
( finite(sK21(U_43))
| ~ sP9(U_43) )
& ! [U_43] :
( ~ empty(sK21(U_43))
| ~ sP9(U_43) )
& ! [U_43] :
( element(sK21(U_43),powerset(U_43))
| ~ sP9(U_43) )
& ! [U_43] :
( sP9(U_43)
| empty(U_43) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9])],[f_40_3]) ).
cnf(f_40_5,plain,
( sP9(U_43)
| empty(U_43) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_6,plain,
( element(sK21(U_43),powerset(U_43))
| ~ sP9(U_43) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_7,plain,
( ~ empty(sK21(U_43))
| ~ sP9(U_43) ),
inference(clausify,[status(thm)],[f_40_4]) ).
cnf(f_40_8,plain,
( finite(sK21(U_43))
| ~ sP9(U_43) ),
inference(clausify,[status(thm)],[f_40_4]) ).
fof(f_41_1,plain,
? [A] :
( one_to_one(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_funct_1]) ).
fof(f_41_2,plain,
? [U_44] :
( one_to_one(U_44)
& function(U_44)
& relation(U_44) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
( one_to_one(sK22)
& function(sK22)
& relation(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_44,sK22)],[f_41_2]) ).
fof(f_41_4,plain,
( one_to_one(sK22)
& function(sK22)
& relation(sK22) ),
inference(definitional_conversion,[status(esa)],[f_41_3]) ).
cnf(f_41_5,plain,
relation(sK22),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_6,plain,
function(sK22),
inference(clausify,[status(thm)],[f_41_4]) ).
cnf(f_41_7,plain,
one_to_one(sK22),
inference(clausify,[status(thm)],[f_41_4]) ).
fof(f_42_1,plain,
? [A] :
( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A)
& ~ empty(A) ),
inference(fof_nnf,[status(thm)],[rc3_ordinal1]) ).
fof(f_42_2,plain,
? [U_45] :
( ordinal(U_45)
& epsilon_connected(U_45)
& epsilon_transitive(U_45)
& ~ empty(U_45) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
( ordinal(sK23)
& epsilon_connected(sK23)
& epsilon_transitive(sK23)
& ~ empty(sK23) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_45,sK23)],[f_42_2]) ).
fof(f_42_4,plain,
( ordinal(sK23)
& epsilon_connected(sK23)
& epsilon_transitive(sK23)
& ~ empty(sK23) ),
inference(definitional_conversion,[status(esa)],[f_42_3]) ).
cnf(f_42_5,plain,
~ empty(sK23),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_6,plain,
epsilon_transitive(sK23),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_7,plain,
epsilon_connected(sK23),
inference(clausify,[status(thm)],[f_42_4]) ).
cnf(f_42_8,plain,
ordinal(sK23),
inference(clausify,[status(thm)],[f_42_4]) ).
fof(f_43_1,plain,
? [A] :
( relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc3_relat_1]) ).
fof(f_43_2,plain,
? [U_46] :
( relation_empty_yielding(U_46)
& relation(U_46) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
( relation_empty_yielding(sK24)
& relation(sK24) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_46,sK24)],[f_43_2]) ).
fof(f_43_4,plain,
( relation_empty_yielding(sK24)
& relation(sK24) ),
inference(definitional_conversion,[status(esa)],[f_43_3]) ).
cnf(f_43_5,plain,
relation(sK24),
inference(clausify,[status(thm)],[f_43_4]) ).
cnf(f_43_6,plain,
relation_empty_yielding(sK24),
inference(clausify,[status(thm)],[f_43_4]) ).
fof(f_44_1,plain,
? [A] :
( function(A)
& relation_empty_yielding(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_funct_1]) ).
fof(f_44_2,plain,
? [U_47] :
( function(U_47)
& relation_empty_yielding(U_47)
& relation(U_47) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( function(sK25)
& relation_empty_yielding(sK25)
& relation(sK25) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_47,sK25)],[f_44_2]) ).
fof(f_44_4,plain,
( function(sK25)
& relation_empty_yielding(sK25)
& relation(sK25) ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
relation(sK25),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
relation_empty_yielding(sK25),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_7,plain,
function(sK25),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,plain,
? [A] :
( transfinite_sequence(A)
& function(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc4_ordinal1]) ).
fof(f_45_2,plain,
? [U_48] :
( transfinite_sequence(U_48)
& function(U_48)
& relation(U_48) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
( transfinite_sequence(sK26)
& function(sK26)
& relation(sK26) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_48,sK26)],[f_45_2]) ).
fof(f_45_4,plain,
( transfinite_sequence(sK26)
& function(sK26)
& relation(sK26) ),
inference(definitional_conversion,[status(esa)],[f_45_3]) ).
cnf(f_45_5,plain,
relation(sK26),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_6,plain,
function(sK26),
inference(clausify,[status(thm)],[f_45_4]) ).
cnf(f_45_7,plain,
transfinite_sequence(sK26),
inference(clausify,[status(thm)],[f_45_4]) ).
fof(f_46_1,plain,
? [A] :
( function(A)
& relation_non_empty(A)
& relation(A) ),
inference(fof_nnf,[status(thm)],[rc5_funct_1]) ).
fof(f_46_2,plain,
? [U_49] :
( function(U_49)
& relation_non_empty(U_49)
& relation(U_49) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( function(sK27)
& relation_non_empty(sK27)
& relation(sK27) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_49,sK27)],[f_46_2]) ).
fof(f_46_4,plain,
( function(sK27)
& relation_non_empty(sK27)
& relation(sK27) ),
inference(definitional_conversion,[status(esa)],[f_46_3]) ).
cnf(f_46_5,plain,
relation(sK27),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_6,plain,
relation_non_empty(sK27),
inference(clausify,[status(thm)],[f_46_4]) ).
cnf(f_46_7,plain,
function(sK27),
inference(clausify,[status(thm)],[f_46_4]) ).
fof(f_47_1,plain,
! [A,B] : subset(A,A),
inference(fof_nnf,[status(thm)],[reflexivity_r1_tarski]) ).
fof(f_47_2,plain,
! [U_51,U_50] : subset(U_51,U_51),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_51] : subset(U_51,U_51),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_51] : subset(U_51,U_51),
inference(definitional_conversion,[status(esa)],[f_47_3]) ).
cnf(f_47_5,plain,
subset(U_51,U_51),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_48_1,plain,
! [A] : subset(A,powerset(union(A))),
inference(fof_nnf,[status(thm)],[t100_zfmisc_1]) ).
fof(f_48_2,plain,
! [U_52] : subset(U_52,powerset(union(U_52))),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_52] : subset(U_52,powerset(union(U_52))),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
subset(U_52,powerset(union(U_52))),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [A,B] :
( finite(A)
| ~ finite(B)
| ~ subset(A,B) ),
inference(fof_nnf,[status(thm)],[t13_finset_1]) ).
fof(f_49_2,plain,
! [U_54,U_53] :
( finite(U_54)
| ~ finite(U_53)
| ~ subset(U_54,U_53) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_54] :
( ! [U_53] :
( ~ finite(U_53)
| ~ subset(U_54,U_53) )
| finite(U_54) ),
inference(miniscope,[status(thm)],[f_49_2]) ).
fof(f_49_4,plain,
! [U_53,U_54] :
( ~ finite(U_53)
| ~ subset(U_54,U_53)
| finite(U_54) ),
inference(definitional_conversion,[status(esa)],[f_49_3]) ).
cnf(f_49_5,plain,
( ~ finite(U_53)
| ~ subset(U_54,U_53)
| finite(U_54) ),
inference(clausify,[status(thm)],[f_49_4]) ).
fof(f_50_1,plain,
! [A,B] :
( element(A,B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t1_subset]) ).
fof(f_50_2,plain,
! [U_56,U_55] :
( element(U_56,U_55)
| ~ in(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_56,U_55] :
( element(U_56,U_55)
| ~ in(U_56,U_55) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( element(U_56,U_55)
| ~ in(U_56,U_55) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [A] :
( ( finite(A)
| ~ finite(powerset(A)) )
& ( finite(powerset(A))
| ~ finite(A) ) ),
inference(fof_nnf,[status(thm)],[t24_finset_1]) ).
fof(f_51_2,plain,
! [U_57] :
( ( finite(U_57)
| ~ finite(powerset(U_57)) )
& ( finite(powerset(U_57))
| ~ finite(U_57) ) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_59] :
( finite(U_59)
| ~ finite(powerset(U_59)) )
& ! [U_58] :
( finite(powerset(U_58))
| ~ finite(U_58) ) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
( ! [U_59] :
( finite(U_59)
| ~ finite(powerset(U_59)) )
& ! [U_58] :
( finite(powerset(U_58))
| ~ finite(U_58) ) ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
( finite(powerset(U_58))
| ~ finite(U_58) ),
inference(clausify,[status(thm)],[f_51_4]) ).
cnf(f_51_6,plain,
( finite(U_59)
| ~ finite(powerset(U_59)) ),
inference(clausify,[status(thm)],[f_51_4]) ).
fof(f_52_1,negated_conjecture,
~ ! [A] :
( ( ! [B] :
( in(B,A)
=> finite(B) )
& finite(A) )
<=> finite(union(A)) ),
inference(negate,[status(cth)],[t25_finset_1]) ).
fof(f_52_2,negated_conjecture,
? [A] :
( ( ( ? [B] :
( ~ finite(B)
& in(B,A) )
| ~ finite(A) )
& finite(union(A)) )
| ( ~ finite(union(A))
& ! [B] :
( finite(B)
| ~ in(B,A) )
& finite(A) ) ),
inference(fof_nnf,[status(thm)],[f_52_1]) ).
fof(f_52_3,negated_conjecture,
? [U_62] :
( ( ( ? [U_61] :
( ~ finite(U_61)
& in(U_61,U_62) )
| ~ finite(U_62) )
& finite(union(U_62)) )
| ( ~ finite(union(U_62))
& ! [U_60] :
( finite(U_60)
| ~ in(U_60,U_62) )
& finite(U_62) ) ),
inference(variable_rename,[status(thm)],[f_52_2]) ).
fof(f_52_4,negated_conjecture,
( ? [U_64] :
( ( ? [U_61] :
( ~ finite(U_61)
& in(U_61,U_64) )
| ~ finite(U_64) )
& finite(union(U_64)) )
| ? [U_63] :
( ~ finite(union(U_63))
& ! [U_60] :
( finite(U_60)
| ~ in(U_60,U_63) )
& finite(U_63) ) ),
inference(miniscope,[status(thm)],[f_52_3]) ).
fof(f_52_5,negated_conjecture,
( ? [U_64] :
( ( ? [U_61] :
( ~ finite(U_61)
& in(U_61,U_64) )
| ~ finite(U_64) )
& finite(union(U_64)) )
| ( ~ finite(union(sK28))
& ! [U_60] :
( finite(U_60)
| ~ in(U_60,sK28) )
& finite(sK28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_63,sK28)],[f_52_4]) ).
fof(f_52_6,negated_conjecture,
( ( ( ? [U_61] :
( ~ finite(U_61)
& in(U_61,sK29) )
| ~ finite(sK29) )
& finite(union(sK29)) )
| ( ~ finite(union(sK28))
& ! [U_60] :
( finite(U_60)
| ~ in(U_60,sK28) )
& finite(sK28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_64,sK29)],[f_52_5]) ).
fof(f_52_7,negated_conjecture,
( ( ( ( ~ finite(sK30)
& in(sK30,sK29) )
| ~ finite(sK29) )
& finite(union(sK29)) )
| ( ~ finite(union(sK28))
& ! [U_60] :
( finite(U_60)
| ~ in(U_60,sK28) )
& finite(sK28) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_61,sK30)],[f_52_6]) ).
fof(f_52_8,negated_conjecture,
( ( ~ finite(sK30)
| ~ sP11 )
& ( in(sK30,sK29)
| ~ sP11 )
& ( sP11
| ~ finite(sK29)
| ~ sP12 )
& ( finite(union(sK29))
| ~ sP12 )
& ! [U_60] :
( ~ finite(union(sK28))
| ~ sP10(U_60) )
& ! [U_60] :
( finite(U_60)
| ~ in(U_60,sK28)
| ~ sP10(U_60) )
& ! [U_60] :
( finite(sK28)
| ~ sP10(U_60) )
& ! [U_60] :
( sP12
| sP10(U_60) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10,sP11,sP12])],[f_52_7]) ).
cnf(f_52_9,negated_conjecture,
( sP12
| sP10(U_60) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_10,negated_conjecture,
( finite(sK28)
| ~ sP10(U_60) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_11,negated_conjecture,
( finite(U_60)
| ~ in(U_60,sK28)
| ~ sP10(U_60) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_12,negated_conjecture,
( ~ finite(union(sK28))
| ~ sP10(U_60) ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_13,negated_conjecture,
( finite(union(sK29))
| ~ sP12 ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_14,negated_conjecture,
( sP11
| ~ finite(sK29)
| ~ sP12 ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_15,negated_conjecture,
( in(sK30,sK29)
| ~ sP11 ),
inference(clausify,[status(thm)],[f_52_8]) ).
cnf(f_52_16,negated_conjecture,
( ~ finite(sK30)
| ~ sP11 ),
inference(clausify,[status(thm)],[f_52_8]) ).
fof(f_53_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_53_2,plain,
! [U_66,U_65] :
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_66,U_65] :
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( in(U_66,U_65)
| empty(U_65)
| ~ element(U_66,U_65) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_68,U_67] :
( ( element(U_68,powerset(U_67))
| ~ subset(U_68,U_67) )
& ( subset(U_68,U_67)
| ~ element(U_68,powerset(U_67)) ) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
( ! [U_72,U_70] :
( element(U_72,powerset(U_70))
| ~ subset(U_72,U_70) )
& ! [U_71,U_69] :
( subset(U_71,U_69)
| ~ element(U_71,powerset(U_69)) ) ),
inference(miniscope,[status(thm)],[f_54_2]) ).
fof(f_54_4,plain,
( ! [U_70,U_72] :
( element(U_72,powerset(U_70))
| ~ subset(U_72,U_70) )
& ! [U_69,U_71] :
( subset(U_71,U_69)
| ~ element(U_71,powerset(U_69)) ) ),
inference(definitional_conversion,[status(esa)],[f_54_3]) ).
cnf(f_54_5,plain,
( subset(U_71,U_69)
| ~ element(U_71,powerset(U_69)) ),
inference(clausify,[status(thm)],[f_54_4]) ).
cnf(f_54_6,plain,
( element(U_72,powerset(U_70))
| ~ subset(U_72,U_70) ),
inference(clausify,[status(thm)],[f_54_4]) ).
fof(f_55_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_55_2,plain,
! [U_75,U_74,U_73] :
( element(U_75,U_73)
| ~ element(U_74,powerset(U_73))
| ~ in(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_74,U_75,U_73] :
( element(U_75,U_73)
| ~ element(U_74,powerset(U_73))
| ~ in(U_75,U_74) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( element(U_75,U_73)
| ~ element(U_74,powerset(U_73))
| ~ in(U_75,U_74) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_56_2,plain,
! [U_78,U_77,U_76] :
( ~ empty(U_76)
| ~ element(U_77,powerset(U_76))
| ~ in(U_78,U_77) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_78,U_77] :
( ! [U_76] :
( ~ empty(U_76)
| ~ element(U_77,powerset(U_76)) )
| ~ in(U_78,U_77) ),
inference(miniscope,[status(thm)],[f_56_2]) ).
fof(f_56_4,plain,
! [U_77,U_76,U_78] :
( ~ empty(U_76)
| ~ element(U_77,powerset(U_76))
| ~ in(U_78,U_77) ),
inference(definitional_conversion,[status(esa)],[f_56_3]) ).
cnf(f_56_5,plain,
( ~ empty(U_76)
| ~ element(U_77,powerset(U_76))
| ~ in(U_78,U_77) ),
inference(clausify,[status(thm)],[f_56_4]) ).
fof(f_57_1,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t6_boole]) ).
fof(f_57_2,plain,
! [U_79] :
( U_79 = empty_set
| ~ empty(U_79) ),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_79] :
( U_79 = empty_set
| ~ empty(U_79) ),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
( U_79 = empty_set
| ~ empty(U_79) ),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t7_boole]) ).
fof(f_58_2,plain,
! [U_81,U_80] :
( ~ empty(U_80)
| ~ in(U_81,U_80) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_80,U_81] :
( ~ empty(U_80)
| ~ in(U_81,U_80) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( ~ empty(U_80)
| ~ in(U_81,U_80) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_59_2,plain,
! [U_83,U_82] :
( ~ empty(U_82)
| U_83 = U_82
| ~ empty(U_83) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_83] :
( ! [U_82] :
( ~ empty(U_82)
| U_83 = U_82 )
| ~ empty(U_83) ),
inference(miniscope,[status(thm)],[f_59_2]) ).
fof(f_59_4,plain,
! [U_82,U_83] :
( ~ empty(U_82)
| U_83 = U_82
| ~ empty(U_83) ),
inference(definitional_conversion,[status(esa)],[f_59_3]) ).
cnf(f_59_5,plain,
( ~ empty(U_82)
| U_83 = U_82
| ~ empty(U_83) ),
inference(clausify,[status(thm)],[f_59_4]) ).
fof(f_60_1,plain,
! [A,B] :
( subset(A,union(B))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t92_zfmisc_1]) ).
fof(f_60_2,plain,
! [U_85,U_84] :
( subset(U_85,union(U_84))
| ~ in(U_85,U_84) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_85,U_84] :
( subset(U_85,union(U_84))
| ~ in(U_85,U_84) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( subset(U_85,union(U_84))
| ~ in(U_85,U_84) ),
inference(clausify,[status(thm)],[f_60_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,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( union(Eq_x_0) = union(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,
( sK10(Eq_x_0) = sK10(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( sK13(Eq_x_0) = sK13(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( sK18(Eq_x_0) = sK18(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_11,axiom,
( sK21(Eq_x_0) = sK21(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,axiom,
( ordinal(Eq_y_0)
| ~ ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_14,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_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,
( empty(Eq_y_0)
| ~ empty(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_18,axiom,
( finite(Eq_y_0)
| ~ finite(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_19,axiom,
( function(Eq_y_0)
| ~ function(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_20,axiom,
( relation(Eq_y_0)
| ~ relation(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_21,axiom,
( natural(Eq_y_0)
| ~ natural(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_22,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_23,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_24,axiom,
( function_yielding(Eq_y_0)
| ~ function_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_25,axiom,
( being_limit_ordinal(Eq_y_0)
| ~ being_limit_ordinal(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_26,axiom,
( transfinite_sequence(Eq_y_0)
| ~ transfinite_sequence(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_27,axiom,
( ordinal_yielding(Eq_y_0)
| ~ ordinal_yielding(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_28,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_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,
( sP0(Eq_y_0)
| ~ sP0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_31,axiom,
( sP1(Eq_y_0)
| ~ sP1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_32,axiom,
( sP2(Eq_y_0)
| ~ sP2(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_33,axiom,
( sP3(Eq_y_0)
| ~ sP3(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_34,axiom,
( sP4(Eq_y_0)
| ~ sP4(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_35,axiom,
( sP5(Eq_y_0)
| ~ sP5(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_36,axiom,
( sP6(Eq_y_0)
| ~ sP6(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_37,axiom,
( sP7(Eq_y_0)
| ~ sP7(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_38,axiom,
( sP8(Eq_y_0)
| ~ sP8(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_39,axiom,
( sP9(Eq_y_0)
| ~ sP9(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_40,axiom,
( sP10(Eq_y_0)
| ~ sP10(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 : SEU094+1 : 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
% 0.09/0.35 % Computer : n013.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 23:18:46 UTC 2026
% 0.09/0.35 % CPUTime :
% 34.36/34.68 % SZS status Theorem for theBenchmark
% 34.36/34.68 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------