%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM409+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 : n003.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 08:52:10 AM UTC 2026
% Result : Theorem 74.36s 74.64s
% Output : Proof 74.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 20
% Syntax : Number of formulae : 168 ( 73 unt; 0 def)
% Number of atoms : 419 ( 21 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 408 ( 157 ~; 148 |; 93 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-1 aty)
% Number of variables : 152 ( 3 sgn 107 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cc3_ordinal1,axiom,
! [A] :
( empty(A)
=> ( ordinal(A)
& epsilon_connected(A)
& epsilon_transitive(A) ) ),
file('theBenchmark.p',cc3_ordinal1) ).
fof(d7_ordinal1,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ( transfinite_sequence(A)
<=> ordinal(relation_dom(A)) ) ),
file('theBenchmark.p',d7_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(existence_m1_subset_1,axiom,
! [A] :
? [B] : element(B,A),
file('theBenchmark.p',existence_m1_subset_1) ).
fof(fc2_ordinal1,axiom,
( ordinal(empty_set)
& epsilon_connected(empty_set)
& epsilon_transitive(empty_set)
& empty(empty_set)
& one_to_one(empty_set)
& function(empty_set)
& relation_empty_yielding(empty_set)
& relation(empty_set) ),
file('theBenchmark.p',fc2_ordinal1) ).
fof(fc4_relat_1,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('theBenchmark.p',fc4_relat_1) ).
fof(fc7_relat_1,axiom,
! [A] :
( empty(A)
=> ( relation(relation_dom(A))
& empty(relation_dom(A)) ) ),
file('theBenchmark.p',fc7_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(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(t2_subset,axiom,
! [A,B] :
( element(A,B)
=> ( in(A,B)
| empty(B) ) ),
file('theBenchmark.p',t2_subset) ).
fof(t2_xboole_1,axiom,
! [A] : subset(empty_set,A),
file('theBenchmark.p',t2_xboole_1) ).
fof(t3_subset,axiom,
! [A,B] :
( element(A,powerset(B))
<=> subset(A,B) ),
file('theBenchmark.p',t3_subset) ).
fof(t45_ordinal1,conjecture,
! [A] : transfinite_sequence_of(empty_set,A),
file('theBenchmark.p',t45_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(t8_boole,axiom,
! [A,B] :
~ ( empty(B)
& A != B
& empty(A) ),
file('theBenchmark.p',t8_boole) ).
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_7,plain,
( ordinal(U_7)
| ~ sP2(U_7) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_11_1,plain,
! [A] :
( ( ( transfinite_sequence(A)
| ~ ordinal(relation_dom(A)) )
& ( ordinal(relation_dom(A))
| ~ transfinite_sequence(A) ) )
| ~ function(A)
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d7_ordinal1]) ).
fof(f_11_2,plain,
! [U_26] :
( ( ( transfinite_sequence(U_26)
| ~ ordinal(relation_dom(U_26)) )
& ( ordinal(relation_dom(U_26))
| ~ transfinite_sequence(U_26) ) )
| ~ function(U_26)
| ~ relation(U_26) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
( ! [U_26] :
( transfinite_sequence(U_26)
| ~ ordinal(relation_dom(U_26))
| ~ sP7(U_26) )
& ! [U_26] :
( ordinal(relation_dom(U_26))
| ~ transfinite_sequence(U_26)
| ~ sP7(U_26) )
& ! [U_26] :
( sP7(U_26)
| ~ function(U_26)
| ~ relation(U_26) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_11_2]) ).
cnf(f_11_4,plain,
( sP7(U_26)
| ~ function(U_26)
| ~ relation(U_26) ),
inference(clausify,[status(thm)],[f_11_3]) ).
cnf(f_11_6,plain,
( transfinite_sequence(U_26)
| ~ ordinal(relation_dom(U_26))
| ~ sP7(U_26) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_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_12_2,plain,
! [U_28,U_27] :
( ( ( transfinite_sequence_of(U_27,U_28)
| ~ subset(relation_rng(U_27),U_28) )
& ( subset(relation_rng(U_27),U_28)
| ~ transfinite_sequence_of(U_27,U_28) ) )
| ~ transfinite_sequence(U_27)
| ~ function(U_27)
| ~ relation(U_27) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
( ! [U_28,U_27] :
( transfinite_sequence_of(U_27,U_28)
| ~ subset(relation_rng(U_27),U_28)
| ~ sP8(U_28,U_27) )
& ! [U_28,U_27] :
( subset(relation_rng(U_27),U_28)
| ~ transfinite_sequence_of(U_27,U_28)
| ~ sP8(U_28,U_27) )
& ! [U_28,U_27] :
( sP8(U_28,U_27)
| ~ transfinite_sequence(U_27)
| ~ function(U_27)
| ~ relation(U_27) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_12_2]) ).
cnf(f_12_4,plain,
( sP8(U_28,U_27)
| ~ transfinite_sequence(U_27)
| ~ function(U_27)
| ~ relation(U_27) ),
inference(clausify,[status(thm)],[f_12_3]) ).
cnf(f_12_6,plain,
( transfinite_sequence_of(U_27,U_28)
| ~ subset(relation_rng(U_27),U_28)
| ~ sP8(U_28,U_27) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_15_1,plain,
! [A] :
? [B] : element(B,A),
inference(fof_nnf,[status(thm)],[existence_m1_subset_1]) ).
fof(f_15_2,plain,
! [U_34] :
? [U_33] : element(U_33,U_34),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
! [U_34] : element(sK6(U_34),U_34),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_33,sK6(U_34))],[f_15_2]) ).
fof(f_15_4,plain,
! [U_34] : element(sK6(U_34),U_34),
inference(definitional_conversion,[status(esa)],[f_15_3]) ).
cnf(f_15_5,plain,
element(sK6(U_34),U_34),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_19_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_19_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_19_1]) ).
cnf(f_19_5,plain,
function(empty_set),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(fof_nnf,[status(thm)],[fc4_relat_1]) ).
fof(f_20_2,plain,
( relation(empty_set)
& empty(empty_set) ),
inference(definitional_conversion,[status(esa)],[f_20_1]) ).
cnf(f_20_3,plain,
empty(empty_set),
inference(clausify,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
relation(empty_set),
inference(clausify,[status(thm)],[f_20_2]) ).
fof(f_24_1,plain,
! [A] :
( ( relation(relation_dom(A))
& empty(relation_dom(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc7_relat_1]) ).
fof(f_24_2,plain,
! [U_40] :
( ( relation(relation_dom(U_40))
& empty(relation_dom(U_40)) )
| ~ empty(U_40) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
( ! [U_40] :
( relation(relation_dom(U_40))
| ~ sP10(U_40) )
& ! [U_40] :
( empty(relation_dom(U_40))
| ~ sP10(U_40) )
& ! [U_40] :
( sP10(U_40)
| ~ empty(U_40) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_24_2]) ).
cnf(f_24_4,plain,
( sP10(U_40)
| ~ empty(U_40) ),
inference(clausify,[status(thm)],[f_24_3]) ).
cnf(f_24_5,plain,
( empty(relation_dom(U_40))
| ~ sP10(U_40) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [A] :
( ( relation(relation_rng(A))
& empty(relation_rng(A)) )
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[fc8_relat_1]) ).
fof(f_25_2,plain,
! [U_41] :
( ( relation(relation_rng(U_41))
& empty(relation_rng(U_41)) )
| ~ empty(U_41) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
( ! [U_41] :
( relation(relation_rng(U_41))
| ~ sP11(U_41) )
& ! [U_41] :
( empty(relation_rng(U_41))
| ~ sP11(U_41) )
& ! [U_41] :
( sP11(U_41)
| ~ empty(U_41) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_25_2]) ).
cnf(f_25_4,plain,
( sP11(U_41)
| ~ empty(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
cnf(f_25_5,plain,
( empty(relation_rng(U_41))
| ~ sP11(U_41) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_31_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_31_2,plain,
? [U_47] :
( ordinal(U_47)
& epsilon_connected(U_47)
& epsilon_transitive(U_47)
& empty(U_47)
& one_to_one(U_47)
& function(U_47)
& relation(U_47) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& empty(sK12)
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_47,sK12)],[f_31_2]) ).
fof(f_31_4,plain,
( ordinal(sK12)
& epsilon_connected(sK12)
& epsilon_transitive(sK12)
& empty(sK12)
& one_to_one(sK12)
& function(sK12)
& relation(sK12) ),
inference(definitional_conversion,[status(esa)],[f_31_3]) ).
cnf(f_31_8,plain,
empty(sK12),
inference(clausify,[status(thm)],[f_31_4]) ).
fof(f_42_1,plain,
! [A,B] :
( in(A,B)
| empty(B)
| ~ element(A,B) ),
inference(fof_nnf,[status(thm)],[t2_subset]) ).
fof(f_42_2,plain,
! [U_61,U_60] :
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_61,U_60] :
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( in(U_61,U_60)
| empty(U_60)
| ~ element(U_61,U_60) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_1,plain,
! [A] : subset(empty_set,A),
inference(fof_nnf,[status(thm)],[t2_xboole_1]) ).
fof(f_43_2,plain,
! [U_62] : subset(empty_set,U_62),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_62] : subset(empty_set,U_62),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
subset(empty_set,U_62),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_64,U_63] :
( ( element(U_64,powerset(U_63))
| ~ subset(U_64,U_63) )
& ( subset(U_64,U_63)
| ~ element(U_64,powerset(U_63)) ) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
( ! [U_68,U_66] :
( element(U_68,powerset(U_66))
| ~ subset(U_68,U_66) )
& ! [U_67,U_65] :
( subset(U_67,U_65)
| ~ element(U_67,powerset(U_65)) ) ),
inference(miniscope,[status(thm)],[f_44_2]) ).
fof(f_44_4,plain,
( ! [U_68,U_66] :
( element(U_68,powerset(U_66))
| ~ subset(U_68,U_66) )
& ! [U_67,U_65] :
( subset(U_67,U_65)
| ~ element(U_67,powerset(U_65)) ) ),
inference(definitional_conversion,[status(esa)],[f_44_3]) ).
cnf(f_44_5,plain,
( subset(U_67,U_65)
| ~ element(U_67,powerset(U_65)) ),
inference(clausify,[status(thm)],[f_44_4]) ).
cnf(f_44_6,plain,
( element(U_68,powerset(U_66))
| ~ subset(U_68,U_66) ),
inference(clausify,[status(thm)],[f_44_4]) ).
fof(f_45_1,negated_conjecture,
~ ! [A] : transfinite_sequence_of(empty_set,A),
inference(negate,[status(cth)],[t45_ordinal1]) ).
fof(f_45_2,negated_conjecture,
? [A] : ~ transfinite_sequence_of(empty_set,A),
inference(fof_nnf,[status(thm)],[f_45_1]) ).
fof(f_45_3,negated_conjecture,
? [U_69] : ~ transfinite_sequence_of(empty_set,U_69),
inference(variable_rename,[status(thm)],[f_45_2]) ).
fof(f_45_4,negated_conjecture,
~ transfinite_sequence_of(empty_set,sK21),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_69,sK21)],[f_45_3]) ).
fof(f_45_5,negated_conjecture,
~ transfinite_sequence_of(empty_set,sK21),
inference(definitional_conversion,[status(esa)],[f_45_4]) ).
cnf(f_45_6,negated_conjecture,
~ transfinite_sequence_of(empty_set,sK21),
inference(clausify,[status(thm)],[f_45_5]) ).
fof(f_46_1,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t4_subset]) ).
fof(f_46_2,plain,
! [U_72,U_71,U_70] :
( element(U_72,U_70)
| ~ element(U_71,powerset(U_70))
| ~ in(U_72,U_71) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_70,U_71,U_72] :
( element(U_72,U_70)
| ~ element(U_71,powerset(U_70))
| ~ in(U_72,U_71) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( element(U_72,U_70)
| ~ element(U_71,powerset(U_70))
| ~ in(U_72,U_71) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(fof_nnf,[status(thm)],[t5_subset]) ).
fof(f_47_2,plain,
! [U_75,U_74,U_73] :
( ~ empty(U_73)
| ~ element(U_74,powerset(U_73))
| ~ in(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_75,U_74] :
( ! [U_73] :
( ~ empty(U_73)
| ~ element(U_74,powerset(U_73)) )
| ~ in(U_75,U_74) ),
inference(miniscope,[status(thm)],[f_47_2]) ).
fof(f_47_4,plain,
! [U_74,U_75,U_73] :
( ~ empty(U_73)
| ~ element(U_74,powerset(U_73))
| ~ in(U_75,U_74) ),
inference(definitional_conversion,[status(esa)],[f_47_3]) ).
cnf(f_47_5,plain,
( ~ empty(U_73)
| ~ element(U_74,powerset(U_73))
| ~ in(U_75,U_74) ),
inference(clausify,[status(thm)],[f_47_4]) ).
fof(f_51_1,plain,
! [A,B] :
( ~ empty(B)
| A = B
| ~ empty(A) ),
inference(fof_nnf,[status(thm)],[t8_boole]) ).
fof(f_51_2,plain,
! [U_81,U_80] :
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_81] :
( ! [U_80] :
( ~ empty(U_80)
| U_81 = U_80 )
| ~ empty(U_81) ),
inference(miniscope,[status(thm)],[f_51_2]) ).
fof(f_51_4,plain,
! [U_80,U_81] :
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(definitional_conversion,[status(esa)],[f_51_3]) ).
cnf(f_51_5,plain,
( ~ empty(U_80)
| U_81 = U_80
| ~ empty(U_81) ),
inference(clausify,[status(thm)],[f_51_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_9,axiom,
( powerset(Eq_x_0) = powerset(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,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(t1,plain,
~ transfinite_sequence_of(empty_set,sK21),
inference(start,[status(thm),parent(0:0)],[f_45_6]) ).
cnf(t2,plain,
( ~ subset(relation_rng(empty_set),sK21)
| ~ sP8(sK21,empty_set)
| transfinite_sequence_of(empty_set,sK21) ),
inference(extension,[status(thm),parent(t1:1)],[f_12_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ function(empty_set)
| ~ transfinite_sequence(empty_set)
| ~ relation(empty_set)
| sP8(sK21,empty_set) ),
inference(extension,[status(thm),parent(t2:2)],[f_12_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
relation(empty_set),
inference(extension,[status(thm),parent(t4:2)],[f_20_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(l3,lemma,
relation(empty_set),
inference(lemma,[status(cth),parent(t4:2),below(t2:2)],[t4:2]) ).
cnf(t8,plain,
( ~ ordinal(relation_dom(empty_set))
| ~ sP7(empty_set)
| transfinite_sequence(empty_set) ),
inference(extension,[status(thm),parent(t4:3)],[f_11_6]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ function(empty_set)
| ~ relation(empty_set)
| sP7(empty_set) ),
inference(extension,[status(thm),parent(t8:2)],[f_11_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
relation(empty_set),
inference(lemma_extension,[status(thm),parent(t10:2)],[l3:1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
function(empty_set),
inference(extension,[status(thm),parent(t10:3)],[f_19_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( ~ sP2(relation_dom(empty_set))
| ordinal(relation_dom(empty_set)) ),
inference(extension,[status(thm),parent(t8:3)],[f_7_7]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:3]) ).
cnf(t18,plain,
( ~ empty(relation_dom(empty_set))
| sP2(relation_dom(empty_set)) ),
inference(extension,[status(thm),parent(t16:2)],[f_7_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( ~ sP10(empty_set)
| empty(relation_dom(empty_set)) ),
inference(extension,[status(thm),parent(t18:2)],[f_24_5]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
( ~ empty(empty_set)
| sP10(empty_set) ),
inference(extension,[status(thm),parent(t20:2)],[f_24_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
empty(empty_set),
inference(extension,[status(thm),parent(t22:2)],[f_20_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
function(empty_set),
inference(extension,[status(thm),parent(t4:4)],[f_19_5]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t4:4]) ).
cnf(t28,plain,
( ~ element(relation_rng(empty_set),powerset(sK21))
| subset(relation_rng(empty_set),sK21) ),
inference(extension,[status(thm),parent(t2:3)],[f_44_5]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:3]) ).
cnf(t30,plain,
( powerset(sK21) != powerset(sK21)
| ~ element(empty_set,powerset(sK21))
| empty_set != relation_rng(empty_set)
| element(relation_rng(empty_set),powerset(sK21)) ),
inference(extension,[status(thm),parent(t28:2)],[equality_27]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( ~ empty(relation_rng(empty_set))
| ~ empty(empty_set)
| empty_set = relation_rng(empty_set) ),
inference(extension,[status(thm),parent(t30:2)],[f_51_5]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
( in(sK6(empty_set),empty_set)
| ~ element(sK6(empty_set),empty_set)
| empty(empty_set) ),
inference(extension,[status(thm),parent(t32:2)],[f_42_4]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( ~ element(empty_set,powerset(empty_set))
| ~ in(sK6(empty_set),empty_set)
| element(sK6(empty_set),empty_set) ),
inference(extension,[status(thm),parent(t34:2)],[f_46_4]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
( empty(empty_set)
| ~ element(sK6(empty_set),empty_set)
| in(sK6(empty_set),empty_set) ),
inference(extension,[status(thm),parent(t36:2)],[f_42_4]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
element(sK6(empty_set),empty_set),
inference(extension,[status(thm),parent(t38:2)],[f_15_5]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t38:2]) ).
cnf(t42,plain,
$false,
inference(reduction,[status(thm),parent(t38:3)],[t38:3,t32:2]) ).
cnf(t43,plain,
( ~ subset(empty_set,empty_set)
| element(empty_set,powerset(empty_set)) ),
inference(extension,[status(thm),parent(t36:3)],[f_44_6]) ).
cnf(t44,plain,
$false,
inference(connection,[status(thm),parent(t43:1)],[t43:1,t36:3]) ).
cnf(t45,plain,
subset(empty_set,empty_set),
inference(extension,[status(thm),parent(t43:2)],[f_43_4]) ).
cnf(t46,plain,
$false,
inference(connection,[status(thm),parent(t45:1)],[t45:1,t43:2]) ).
cnf(t47,plain,
( ~ element(empty_set,powerset(sK12))
| ~ empty(sK12)
| ~ in(sK6(empty_set),empty_set) ),
inference(extension,[status(thm),parent(t34:3)],[f_47_5]) ).
cnf(t48,plain,
$false,
inference(connection,[status(thm),parent(t47:1)],[t47:1,t34:3]) ).
cnf(t49,plain,
empty(sK12),
inference(extension,[status(thm),parent(t47:2)],[f_31_8]) ).
cnf(t50,plain,
$false,
inference(connection,[status(thm),parent(t49:1)],[t49:1,t47:2]) ).
cnf(t51,plain,
( ~ subset(empty_set,sK12)
| element(empty_set,powerset(sK12)) ),
inference(extension,[status(thm),parent(t47:3)],[f_44_6]) ).
cnf(t52,plain,
$false,
inference(connection,[status(thm),parent(t51:1)],[t51:1,t47:3]) ).
cnf(t53,plain,
subset(empty_set,sK12),
inference(extension,[status(thm),parent(t51:2)],[f_43_4]) ).
cnf(t54,plain,
$false,
inference(connection,[status(thm),parent(t53:1)],[t53:1,t51:2]) ).
cnf(l16,lemma,
empty(empty_set),
inference(lemma,[status(cth),parent(t32:2),below(t30:2)],[t32:2]) ).
cnf(t55,plain,
( ~ sP11(empty_set)
| empty(relation_rng(empty_set)) ),
inference(extension,[status(thm),parent(t32:3)],[f_25_5]) ).
cnf(t56,plain,
$false,
inference(connection,[status(thm),parent(t55:1)],[t55:1,t32:3]) ).
cnf(t57,plain,
( ~ empty(empty_set)
| sP11(empty_set) ),
inference(extension,[status(thm),parent(t55:2)],[f_25_4]) ).
cnf(t58,plain,
$false,
inference(connection,[status(thm),parent(t57:1)],[t57:1,t55:2]) ).
cnf(t59,plain,
empty(empty_set),
inference(lemma_extension,[status(thm),parent(t57:2)],[l16:1]) ).
cnf(t60,plain,
$false,
inference(connection,[status(thm),parent(t59:1)],[t59:1,t57:2]) ).
cnf(t61,plain,
( ~ subset(empty_set,sK21)
| element(empty_set,powerset(sK21)) ),
inference(extension,[status(thm),parent(t30:3)],[f_44_6]) ).
cnf(t62,plain,
$false,
inference(connection,[status(thm),parent(t61:1)],[t61:1,t30:3]) ).
cnf(t63,plain,
subset(empty_set,sK21),
inference(extension,[status(thm),parent(t61:2)],[f_43_4]) ).
cnf(t64,plain,
$false,
inference(connection,[status(thm),parent(t63:1)],[t63:1,t61:2]) ).
cnf(t65,plain,
( sK21 != sK21
| powerset(sK21) = powerset(sK21) ),
inference(extension,[status(thm),parent(t30:4)],[equality_9]) ).
cnf(t66,plain,
$false,
inference(connection,[status(thm),parent(t65:1)],[t65:1,t30:4]) ).
cnf(t67,plain,
( sK21 != sK21
| sK21 = sK21 ),
inference(extension,[status(thm),parent(t65:2)],[equality_2]) ).
cnf(t68,plain,
$false,
inference(connection,[status(thm),parent(t67:1)],[t67:1,t65:2]) ).
cnf(t69,plain,
sK21 = sK21,
inference(extension,[status(thm),parent(t67:2)],[equality_1]) ).
cnf(t70,plain,
$false,
inference(connection,[status(thm),parent(t69:1)],[t69:1,t67:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM409+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
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 18:23:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 74.36/74.64 % SZS status Theorem for theBenchmark
% 74.36/74.64 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------