%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM410+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:15 PM UTC 2026
% Result : Theorem 0.30s 1.64s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 89
% Syntax : Number of formulae : 264 ( 95 unt; 0 def)
% Number of atoms : 617 ( 59 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 607 ( 254 ~; 216 |; 108 &)
% ( 3 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 16 con; 0-1 aty)
% Number of variables : 283 ( 10 sgn 83 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(fc6_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_relat_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(t46_ordinal1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_ordinal1) ).
fof(rc3_ordinal1,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(d8_ordinal1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(d7_ordinal1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(fc6_funct_1,axiom,
! [X1] :
( ( relation(X1)
& relation_non_empty(X1)
& function(X1) )
=> with_non_empty_elements(relation_rng(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_funct_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(dt_m1_ordinal1,axiom,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ( relation(X2)
& function(X2)
& transfinite_sequence(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(cc2_funct_1,axiom,
! [X1] :
( ( relation(X1)
& empty(X1)
& function(X1) )
=> ( relation(X1)
& function(X1)
& one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(existence_m1_ordinal1,axiom,
! [X1] :
? [X2] : transfinite_sequence_of(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_ordinal1) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(fc8_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_rng(X1))
& relation(relation_rng(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_relat_1) ).
fof(fc7_relat_1,axiom,
! [X1] :
( empty(X1)
=> ( empty(relation_dom(X1))
& relation(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc5_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc4_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc2_ordinal1,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_45,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_46,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_rng(X1)) ),
inference(fof_simplification,[status(thm)],[fc6_relat_1]) ).
fof(i_0_47,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
fof(i_0_48,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ordinal(relation_dom(X1))
=> transfinite_sequence_of(X1,relation_rng(X1)) ) ),
inference(assume_negation,[status(cth)],[t46_ordinal1]) ).
fof(i_0_49,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_50,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_51,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_52,plain,
! [X104,X105,X106] :
( ~ in(X104,X105)
| ~ element(X105,powerset(X106))
| element(X104,X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_53,plain,
! [X69,X70] :
( ( ~ transfinite_sequence_of(X70,X69)
| subset(relation_rng(X70),X69)
| ~ relation(X70)
| ~ function(X70)
| ~ transfinite_sequence(X70) )
& ( ~ subset(relation_rng(X70),X69)
| transfinite_sequence_of(X70,X69)
| ~ relation(X70)
| ~ function(X70)
| ~ transfinite_sequence(X70) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
fof(i_0_54,plain,
! [X107,X108,X109] :
( ~ in(X107,X108)
| ~ element(X108,powerset(X109))
| ~ empty(X109) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_55,plain,
! [X101,X102] :
( ( ~ element(X101,powerset(X102))
| subset(X101,X102) )
& ( ~ subset(X101,X102)
| element(X101,powerset(X102)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_56,plain,
! [X60,X61] :
( ~ in(X60,X61)
| ~ in(X61,X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_45])]) ).
fof(i_0_57,plain,
! [X99,X100] :
( ~ element(X99,X100)
| empty(X100)
| in(X99,X100) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_58,plain,
! [X97,X98] :
( ~ in(X97,X98)
| element(X97,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_59,plain,
! [X68] :
( ( ~ transfinite_sequence(X68)
| ordinal(relation_dom(X68))
| ~ relation(X68)
| ~ function(X68) )
& ( ~ ordinal(relation_dom(X68))
| transfinite_sequence(X68)
| ~ relation(X68)
| ~ function(X68) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])]) ).
fof(i_0_60,plain,
! [X78] :
( ~ relation(X78)
| ~ relation_non_empty(X78)
| ~ function(X78)
| with_non_empty_elements(relation_rng(X78)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc6_funct_1])]) ).
fof(i_0_61,plain,
! [X111,X112] :
( ~ in(X111,X112)
| ~ empty(X112) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_62,plain,
! [X79] :
( empty(X79)
| ~ relation(X79)
| ~ empty(relation_rng(X79)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_46])]) ).
fof(i_0_63,plain,
! [X77] :
( empty(X77)
| ~ relation(X77)
| ~ empty(relation_dom(X77)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_47])]) ).
fof(i_0_64,plain,
! [X71,X72] :
( ( relation(X72)
| ~ transfinite_sequence_of(X72,X71) )
& ( function(X72)
| ~ transfinite_sequence_of(X72,X71) )
& ( transfinite_sequence(X72)
| ~ transfinite_sequence_of(X72,X71) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_ordinal1])])]) ).
fof(i_0_65,plain,
! [X65] :
( ( relation(X65)
| ~ relation(X65)
| ~ empty(X65)
| ~ function(X65) )
& ( function(X65)
| ~ relation(X65)
| ~ empty(X65)
| ~ function(X65) )
& ( one_to_one(X65)
| ~ relation(X65)
| ~ empty(X65)
| ~ function(X65) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_66,negated_conjecture,
( relation(esk17_0)
& function(esk17_0)
& ordinal(relation_dom(esk17_0))
& ~ transfinite_sequence_of(esk17_0,relation_rng(esk17_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_48])])]) ).
fof(i_0_67,plain,
! [X75] : element(esk2_1(X75),X75),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_68,plain,
! [X73] : transfinite_sequence_of(esk1_1(X73),X73),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_ordinal1])]) ).
fof(i_0_69,plain,
! [X66] :
( ~ epsilon_transitive(X66)
| ~ epsilon_connected(X66)
| ordinal(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_70,plain,
! [X81] :
( ( empty(relation_rng(X81))
| ~ empty(X81) )
& ( relation(relation_rng(X81))
| ~ empty(X81) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc8_relat_1])])]) ).
fof(i_0_71,plain,
! [X80] :
( ( empty(relation_dom(X80))
| ~ empty(X80) )
& ( relation(relation_dom(X80))
| ~ empty(X80) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc7_relat_1])])]) ).
fof(i_0_72,plain,
! [X113,X114] :
( ~ empty(X113)
| X113 = X114
| ~ empty(X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_73,plain,
! [X96] : subset(X96,X96),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_74,plain,
! [X64] :
( ~ empty(X64)
| relation(X64) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_75,plain,
! [X63] :
( ( epsilon_transitive(X63)
| ~ ordinal(X63) )
& ( epsilon_connected(X63)
| ~ ordinal(X63) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_76,plain,
! [X67] :
( ( epsilon_transitive(X67)
| ~ empty(X67) )
& ( epsilon_connected(X67)
| ~ empty(X67) )
& ( ordinal(X67)
| ~ empty(X67) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_77,plain,
! [X62] :
( ~ empty(X62)
| function(X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_78,plain,
! [X110] :
( ~ empty(X110)
| X110 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_79,plain,
( ~ empty(esk12_0)
& epsilon_transitive(esk12_0)
& epsilon_connected(esk12_0)
& ordinal(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_49])]) ).
fof(i_0_80,plain,
~ empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_50])]) ).
fof(i_0_81,plain,
( ~ empty(esk9_0)
& relation(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_51])]) ).
fof(i_0_82,plain,
( relation(esk16_0)
& relation_non_empty(esk16_0)
& function(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_83,plain,
( relation(esk14_0)
& relation_empty_yielding(esk14_0)
& function(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_84,plain,
( relation(esk13_0)
& relation_empty_yielding(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_85,plain,
( relation(esk15_0)
& function(esk15_0)
& transfinite_sequence(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_ordinal1])]) ).
fof(i_0_86,plain,
( relation(esk11_0)
& function(esk11_0)
& one_to_one(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_87,plain,
( relation(esk8_0)
& function(esk8_0)
& one_to_one(esk8_0)
& empty(esk8_0)
& epsilon_transitive(esk8_0)
& epsilon_connected(esk8_0)
& ordinal(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal1])]) ).
fof(i_0_88,plain,
( relation(esk7_0)
& empty(esk7_0)
& function(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_89,plain,
( empty(esk5_0)
& relation(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_90,plain,
( relation(esk3_0)
& function(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_91,plain,
( epsilon_transitive(esk4_0)
& epsilon_connected(esk4_0)
& ordinal(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
fof(i_0_92,plain,
empty(esk6_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_93,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_94,plain,
( transfinite_sequence_of(X1,X2)
| ~ subset(relation_rng(X1),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_95,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_96,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_97,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_98,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_99,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_100,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_101,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_102,plain,
( transfinite_sequence(X1)
| ~ ordinal(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_103,plain,
( with_non_empty_elements(relation_rng(X1))
| ~ relation(X1)
| ~ relation_non_empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_104,plain,
( ordinal(relation_dom(X1))
| ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_105,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_106,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_rng(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_107,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_108,plain,
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_109,plain,
( relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_110,plain,
( function(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_111,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_112,negated_conjecture,
~ transfinite_sequence_of(esk17_0,relation_rng(esk17_0)),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_113,plain,
element(esk2_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_114,plain,
transfinite_sequence_of(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_115,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_116,plain,
( relation(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_117,plain,
( relation(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_118,plain,
( empty(relation_rng(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_119,plain,
( empty(relation_dom(X1))
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_120,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_121,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_122,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_123,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_124,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_125,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_126,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_127,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_128,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_129,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_130,negated_conjecture,
ordinal(relation_dom(esk17_0)),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_131,plain,
~ empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_132,plain,
~ empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_133,plain,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_134,plain,
relation_non_empty(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_135,plain,
relation_empty_yielding(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_136,plain,
relation_empty_yielding(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_137,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_138,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_139,plain,
transfinite_sequence(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_140,plain,
one_to_one(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_141,plain,
one_to_one(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_142,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_143,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_144,plain,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_145,plain,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_146,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_147,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_148,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_149,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_150,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_151,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_152,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_153,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_154,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_155,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_156,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_157,plain,
epsilon_connected(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_158,plain,
epsilon_connected(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_159,plain,
epsilon_connected(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_160,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_161,plain,
epsilon_transitive(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_162,plain,
epsilon_transitive(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_163,plain,
epsilon_transitive(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_164,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_165,plain,
ordinal(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_166,plain,
ordinal(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_167,plain,
ordinal(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_168,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_169,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_170,plain,
function(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_171,plain,
function(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_172,plain,
function(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_173,plain,
function(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_174,plain,
function(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_175,plain,
function(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_176,plain,
function(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_177,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_178,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_179,plain,
empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_180,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_181,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_182,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_183,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_184,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_185,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_186,axiom,
X1 = X1 ).
cnf(i_0_187,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_188,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_189,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_190,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_191,axiom,
( X1 != X2
| ~ with_non_empty_elements(X1)
| with_non_empty_elements(X2) ) ).
cnf(i_0_192,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_193,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_194,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_195,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_196,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_197,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_198,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_199,axiom,
( X1 != X2
| ~ transfinite_sequence_of(X1,X3)
| transfinite_sequence_of(X2,X3) ) ).
cnf(i_0_200,axiom,
( X1 != X2
| ~ transfinite_sequence_of(X3,X1)
| transfinite_sequence_of(X3,X2) ) ).
cnf(i_0_201,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_202,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_203,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_204,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_205,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_206,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_207,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_186_001,axiom,
X1 = X1 ).
cnf(i_0_187_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_188_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_189_004,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_190_005,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_191_006,axiom,
( X1 != X2
| ~ with_non_empty_elements(X1)
| with_non_empty_elements(X2) ) ).
cnf(i_0_192_007,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_193_008,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_194_009,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_195_010,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_196_011,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_197_012,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_198_013,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_199_014,axiom,
( X1 != X2
| ~ transfinite_sequence_of(X1,X3)
| transfinite_sequence_of(X2,X3) ) ).
cnf(i_0_200_015,axiom,
( X1 != X2
| ~ transfinite_sequence_of(X3,X1)
| transfinite_sequence_of(X3,X2) ) ).
cnf(i_0_201_016,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_202_017,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_203_018,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_204_019,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_205_020,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_206_021,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_207_022,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_208,plain,
epsilon_connected(relation_dom(esk17_0)),
inference(scs_inference,[],[i_0_130,i_0_123]) ).
cnf(i_0_209,plain,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_123]) ).
cnf(i_0_210,plain,
epsilon_transitive(relation_dom(esk17_0)),
inference(scs_inference,[],[i_0_130,i_0_123,i_0_125]) ).
cnf(i_0_211,plain,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_125]) ).
cnf(i_0_212,plain,
subset(esk2_1(powerset(X1)),X1),
inference(scs_inference,[],[i_0_130,i_0_113,i_0_123,i_0_125,i_0_97]) ).
cnf(i_0_213,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_214,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_215,plain,
~ in(X1,esk8_0),
inference(scs_inference,[],[i_0_130,i_0_178,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105]) ).
cnf(i_0_216,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_105]) ).
cnf(i_0_217,plain,
relation(esk6_0),
inference(scs_inference,[],[i_0_130,i_0_178,i_0_180,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122]) ).
cnf(i_0_218,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_122]) ).
cnf(i_0_219,plain,
epsilon_connected(esk7_0),
inference(scs_inference,[],[i_0_130,i_0_178,i_0_179,i_0_180,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124]) ).
cnf(i_0_220,plain,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_124]) ).
cnf(i_0_221,plain,
epsilon_transitive(esk7_0),
inference(scs_inference,[],[i_0_130,i_0_178,i_0_179,i_0_180,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126]) ).
cnf(i_0_222,plain,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_126]) ).
cnf(i_0_223,plain,
ordinal(esk7_0),
inference(scs_inference,[],[i_0_130,i_0_178,i_0_179,i_0_180,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127]) ).
cnf(i_0_224,plain,
( ~ empty(X1)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_127]) ).
cnf(i_0_225,plain,
function(esk6_0),
inference(scs_inference,[],[i_0_130,i_0_178,i_0_179,i_0_180,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128]) ).
cnf(i_0_226,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_128]) ).
cnf(i_0_227,plain,
esk1_1(relation_rng(esk17_0)) != esk17_0,
inference(scs_inference,[],[i_0_112,i_0_130,i_0_114,i_0_178,i_0_179,i_0_180,i_0_113,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199]) ).
cnf(i_0_228,plain,
transfinite_sequence_of(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_229,plain,
~ in(X1,esk2_1(powerset(esk8_0))),
inference(scs_inference,[],[i_0_112,i_0_130,i_0_114,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96]) ).
cnf(i_0_230,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_231,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_232,plain,
in(esk2_1(esk12_0),esk12_0),
inference(scs_inference,[],[i_0_112,i_0_130,i_0_114,i_0_131,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_230,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96,i_0_100]) ).
cnf(i_0_233,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_234,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_100]) ).
cnf(i_0_235,plain,
esk8_0 != esk12_0,
inference(scs_inference,[],[i_0_112,i_0_130,i_0_114,i_0_131,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_230,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96,i_0_100,i_0_206]) ).
cnf(i_0_236,plain,
esk12_0 != esk8_0,
inference(scs_inference,[],[i_0_112,i_0_130,i_0_114,i_0_131,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_230,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96,i_0_100,i_0_206,i_0_198]) ).
cnf(i_0_237,plain,
transfinite_sequence(esk17_0),
inference(scs_inference,[],[i_0_112,i_0_143,i_0_169,i_0_130,i_0_114,i_0_131,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_230,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96,i_0_100,i_0_206,i_0_198,i_0_102]) ).
cnf(i_0_238,plain,
( ~ ordinal(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| transfinite_sequence(X1) ),
inference(rename_variables,[],[i_0_102]) ).
cnf(i_0_239,plain,
one_to_one(esk7_0),
inference(scs_inference,[],[i_0_112,i_0_143,i_0_169,i_0_130,i_0_114,i_0_131,i_0_151,i_0_175,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_230,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96,i_0_100,i_0_206,i_0_198,i_0_102,i_0_111]) ).
cnf(i_0_240,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_111]) ).
cnf(i_0_241,plain,
$false,
inference(scs_inference,[],[i_0_112,i_0_143,i_0_169,i_0_130,i_0_121,i_0_114,i_0_131,i_0_151,i_0_175,i_0_178,i_0_179,i_0_180,i_0_113,i_0_213,i_0_230,i_0_123,i_0_125,i_0_97,i_0_105,i_0_122,i_0_124,i_0_126,i_0_127,i_0_128,i_0_199,i_0_96,i_0_100,i_0_206,i_0_198,i_0_102,i_0_111,i_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM410+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.18/0.35 % Computer : n005.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 00:31:30 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.21/0.36 % start to proof: theBenchmark
% 0.30/1.64 % Version : CSE_E---1.7
% 0.30/1.64 % Problem : theBenchmark.p
% 0.30/1.64 % SZS status Theorem for theBenchmark.p
% 0.30/1.64 % SZS output start CNFRefutation
% See solution above
% 0.38/1.78 % Total time : 1.271s
%------------------------------------------------------------------------------