%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU083+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 : n018.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 05:10:36 PM UTC 2026
% Result : Theorem 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 114
% Syntax : Number of formulae : 330 ( 128 unt; 0 def)
% Number of atoms : 779 ( 77 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 727 ( 278 ~; 225 |; 190 &)
% ( 1 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 25 con; 0-2 aty)
% Number of variables : 354 ( 17 sgn 121 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fc2_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(fc3_xboole_0,axiom,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t14_finset_1,conjecture,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t14_finset_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(rc2_arytm_3,axiom,
? [X1] :
( element(X1,positive_rationals)
& ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
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(rc1_arytm_3,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(rc1_finset_1,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_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(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(l3_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_finset_1) ).
fof(fc9_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
fof(fc2_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_union2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_relat_1) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
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(cc1_arytm_3,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_arytm_3) ).
fof(cc4_arytm_3,axiom,
! [X1] :
( element(X1,positive_rationals)
=> ( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc4_arytm_3) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(rc2_finset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2)
& relation(X2)
& function(X2)
& one_to_one(X2)
& epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2)
& natural(X2)
& finite(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
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(cc2_arytm_3,axiom,
! [X1] :
( ( empty(X1)
& ordinal(X1) )
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_arytm_3) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t1_boole,axiom,
! [X1] : set_union2(X1,empty_set) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
fof(cc1_finset_1,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
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_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(rc3_arytm_3,axiom,
? [X1] :
( element(X1,positive_rationals)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(fc8_arytm_3,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(rc1_funcop_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& function_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(rc2_ordinal2,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1)
& ordinal_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(rc4_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_ordinal1) ).
fof(rc1_ordinal2,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& being_limit_ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal2) ).
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(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(rc1_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_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(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_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(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
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_62,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc2_xboole_0]) ).
fof(i_0_63,plain,
! [X1,X2] :
( ~ empty(X1)
=> ~ empty(set_union2(X2,X1)) ),
inference(fof_simplification,[status(thm)],[fc3_xboole_0]) ).
fof(i_0_64,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_65,negated_conjecture,
~ ! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
inference(assume_negation,[status(cth)],[t14_finset_1]) ).
fof(i_0_66,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_67,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_68,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_69,plain,
? [X1] :
( element(X1,positive_rationals)
& ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc2_arytm_3]) ).
fof(i_0_70,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_71,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_72,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[rc1_arytm_3]) ).
fof(i_0_73,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_74,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_75,plain,
! [X93,X94,X95] :
( ~ in(X93,X94)
| ~ element(X94,powerset(X95))
| element(X93,X95) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_76,plain,
! [X96,X97,X98] :
( ~ in(X96,X97)
| ~ element(X97,powerset(X98))
| ~ empty(X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_77,plain,
! [X117,X118] :
( empty(X117)
| ~ empty(set_union2(X117,X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_62])]) ).
fof(i_0_78,plain,
! [X119,X120] :
( empty(X119)
| ~ empty(set_union2(X120,X119)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_63])]) ).
fof(i_0_79,plain,
! [X123,X124] :
( ( ~ element(X123,powerset(X124))
| subset(X123,X124) )
& ( ~ subset(X123,X124)
| element(X123,powerset(X124)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_80,plain,
! [X88,X89] :
( ~ in(X88,X89)
| ~ in(X89,X88) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_64])]) ).
fof(i_0_81,plain,
! [X166,X167] :
( ~ finite(X166)
| ~ finite(X167)
| finite(set_union2(X166,X167)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l3_finset_1])]) ).
fof(i_0_82,plain,
! [X133,X134] :
( ~ finite(X133)
| ~ finite(X134)
| finite(set_union2(X133,X134)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_finset_1])]) ).
fof(i_0_83,plain,
! [X106,X107] :
( ~ relation(X106)
| ~ relation(X107)
| relation(set_union2(X106,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc2_relat_1])]) ).
fof(i_0_84,plain,
! [X102,X103] :
( ~ finite(X102)
| ~ element(X103,powerset(X102))
| finite(X103) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_85,plain,
! [X121,X122] :
( ~ element(X121,X122)
| empty(X122)
| in(X121,X122) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_86,negated_conjecture,
( finite(esk27_0)
& finite(esk28_0)
& ~ finite(set_union2(esk27_0,esk28_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_65])])]) ).
fof(i_0_87,plain,
! [X91,X92] :
( ~ in(X91,X92)
| element(X91,X92) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_88,plain,
! [X109,X110] :
( ( epsilon_transitive(X110)
| ~ element(X110,X109)
| ~ ordinal(X109) )
& ( epsilon_connected(X110)
| ~ element(X110,X109)
| ~ ordinal(X109) )
& ( ordinal(X110)
| ~ element(X110,X109)
| ~ ordinal(X109) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_arytm_3])])])]) ).
fof(i_0_89,plain,
! [X112] :
( ( epsilon_transitive(X112)
| ~ ordinal(X112)
| ~ element(X112,positive_rationals) )
& ( epsilon_connected(X112)
| ~ ordinal(X112)
| ~ element(X112,positive_rationals) )
& ( ordinal(X112)
| ~ ordinal(X112)
| ~ element(X112,positive_rationals) )
& ( natural(X112)
| ~ ordinal(X112)
| ~ element(X112,positive_rationals) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_arytm_3])])]) ).
fof(i_0_90,plain,
! [X157] :
( ( element(esk22_1(X157),powerset(X157))
| empty(X157) )
& ( ~ empty(esk22_1(X157))
| empty(X157) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_66])])])]) ).
fof(i_0_91,plain,
! [X138] :
( ( element(esk4_1(X138),powerset(X138))
| empty(X138) )
& ( ~ empty(esk4_1(X138))
| empty(X138) )
& ( finite(esk4_1(X138))
| empty(X138) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_67])])])]) ).
fof(i_0_92,plain,
! [X126,X127] :
( ~ in(X126,X127)
| ~ empty(X127) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_93,plain,
! [X130,X131] : set_union2(X130,X131) = set_union2(X131,X130),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(i_0_94,plain,
! [X159] :
( element(esk23_1(X159),powerset(X159))
& empty(esk23_1(X159)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_95,plain,
! [X136] :
( element(esk3_1(X136),powerset(X136))
& empty(esk3_1(X136))
& relation(esk3_1(X136))
& function(esk3_1(X136))
& one_to_one(esk3_1(X136))
& epsilon_transitive(esk3_1(X136))
& epsilon_connected(esk3_1(X136))
& ordinal(esk3_1(X136))
& natural(esk3_1(X136))
& finite(esk3_1(X136)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_96,plain,
! [X105] :
( ( relation(X105)
| ~ relation(X105)
| ~ empty(X105)
| ~ function(X105) )
& ( function(X105)
| ~ relation(X105)
| ~ empty(X105)
| ~ function(X105) )
& ( one_to_one(X105)
| ~ relation(X105)
| ~ empty(X105)
| ~ function(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_97,plain,
! [X99] : element(esk1_1(X99),X99),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_98,plain,
! [X111] :
( ( epsilon_transitive(X111)
| ~ empty(X111)
| ~ ordinal(X111) )
& ( epsilon_connected(X111)
| ~ empty(X111)
| ~ ordinal(X111) )
& ( ordinal(X111)
| ~ empty(X111)
| ~ ordinal(X111) )
& ( natural(X111)
| ~ empty(X111)
| ~ ordinal(X111) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_arytm_3])])]) ).
fof(i_0_99,plain,
! [X114] :
( ~ epsilon_transitive(X114)
| ~ epsilon_connected(X114)
| ordinal(X114) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_100,plain,
! [X116] : ~ empty(powerset(X116)),
inference(variable_rename,[status(thm)],[i_0_68]) ).
fof(i_0_101,plain,
! [X128,X129] :
( ~ empty(X128)
| X128 = X129
| ~ empty(X129) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_102,plain,
! [X132] : set_union2(X132,X132) = X132,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
fof(i_0_103,plain,
! [X87] : subset(X87,X87),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_104,plain,
! [X90] : set_union2(X90,empty_set) = X90,
inference(variable_rename,[status(thm)],[t1_boole]) ).
fof(i_0_105,plain,
! [X101] :
( ~ empty(X101)
| finite(X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_106,plain,
! [X115] :
( ( epsilon_transitive(X115)
| ~ empty(X115) )
& ( epsilon_connected(X115)
| ~ empty(X115) )
& ( ordinal(X115)
| ~ empty(X115) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_107,plain,
! [X113] :
( ( epsilon_transitive(X113)
| ~ ordinal(X113) )
& ( epsilon_connected(X113)
| ~ ordinal(X113) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_108,plain,
! [X104] :
( ~ empty(X104)
| function(X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_109,plain,
! [X108] :
( ~ empty(X108)
| relation(X108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_110,plain,
( element(esk17_0,positive_rationals)
& empty(esk17_0)
& epsilon_transitive(esk17_0)
& epsilon_connected(esk17_0)
& ordinal(esk17_0)
& natural(esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_arytm_3])]) ).
fof(i_0_111,plain,
( element(esk16_0,positive_rationals)
& ~ empty(esk16_0)
& epsilon_transitive(esk16_0)
& epsilon_connected(esk16_0)
& ordinal(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_69])]) ).
fof(i_0_112,plain,
! [X125] :
( ~ empty(X125)
| X125 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_113,plain,
~ empty(esk25_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_70])]) ).
fof(i_0_114,plain,
( ~ empty(esk20_0)
& epsilon_transitive(esk20_0)
& epsilon_connected(esk20_0)
& ordinal(esk20_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_71])]) ).
fof(i_0_115,plain,
( ~ empty(esk15_0)
& epsilon_transitive(esk15_0)
& epsilon_connected(esk15_0)
& ordinal(esk15_0)
& natural(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_72])]) ).
fof(i_0_116,plain,
( ~ empty(esk13_0)
& relation(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_73])]) ).
fof(i_0_117,plain,
( ~ empty(esk2_0)
& finite(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_74])]) ).
fof(i_0_118,plain,
~ empty(positive_rationals),
inference(fof_simplification,[status(thm)],[fc8_arytm_3]) ).
fof(i_0_119,plain,
( relation(esk26_0)
& function(esk26_0)
& function_yielding(esk26_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funcop_1])]) ).
fof(i_0_120,plain,
( relation(esk11_0)
& function(esk11_0)
& transfinite_sequence(esk11_0)
& ordinal_yielding(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal2])]) ).
fof(i_0_121,plain,
( relation(esk21_0)
& function(esk21_0)
& transfinite_sequence(esk21_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_ordinal1])]) ).
fof(i_0_122,plain,
( epsilon_transitive(esk10_0)
& epsilon_connected(esk10_0)
& ordinal(esk10_0)
& being_limit_ordinal(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal2])]) ).
fof(i_0_123,plain,
( relation(esk9_0)
& relation_non_empty(esk9_0)
& function(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_124,plain,
( relation(esk19_0)
& function(esk19_0)
& one_to_one(esk19_0)
& empty(esk19_0)
& epsilon_transitive(esk19_0)
& epsilon_connected(esk19_0)
& ordinal(esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal1])]) ).
fof(i_0_125,plain,
( epsilon_transitive(esk18_0)
& epsilon_connected(esk18_0)
& ordinal(esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
fof(i_0_126,plain,
( relation(esk7_0)
& function(esk7_0)
& one_to_one(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_127,plain,
( relation(esk8_0)
& relation_empty_yielding(esk8_0)
& function(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_128,plain,
( relation(esk6_0)
& empty(esk6_0)
& function(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_129,plain,
( relation(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_130,plain,
( relation(esk14_0)
& relation_empty_yielding(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_131,plain,
( empty(esk12_0)
& relation(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_132,plain,
empty(esk24_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_133,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_134,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_135,plain,
( empty(X1)
| ~ empty(set_union2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_136,plain,
( empty(X1)
| ~ empty(set_union2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_137,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_138,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_139,plain,
( finite(set_union2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_140,plain,
( finite(set_union2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_141,plain,
( relation(set_union2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_142,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_143,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_144,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_145,negated_conjecture,
~ finite(set_union2(esk27_0,esk28_0)),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_146,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_147,plain,
( ordinal(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_148,plain,
( epsilon_connected(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_149,plain,
( epsilon_transitive(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_150,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_151,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_152,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_153,plain,
( element(esk22_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_154,plain,
( element(esk4_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_155,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_156,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_157,plain,
element(esk23_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_158,plain,
element(esk3_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_159,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_160,plain,
( empty(X1)
| ~ empty(esk22_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_161,plain,
( empty(X1)
| ~ empty(esk4_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_162,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_163,plain,
( natural(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_164,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_165,plain,
( epsilon_connected(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_166,plain,
( epsilon_transitive(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_167,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_168,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_169,plain,
( finite(esk4_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_170,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_171,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_172,plain,
set_union2(X1,empty_set) = X1,
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_173,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_174,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_175,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_176,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_177,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_178,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_179,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_180,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_181,plain,
element(esk17_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_182,plain,
element(esk16_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_183,plain,
natural(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_184,plain,
finite(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_185,plain,
ordinal(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_186,plain,
epsilon_connected(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_187,plain,
epsilon_transitive(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_188,plain,
one_to_one(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_189,plain,
function(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_190,plain,
relation(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_191,plain,
empty(esk23_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_192,plain,
empty(esk3_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_193,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_194,plain,
~ empty(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_195,plain,
~ empty(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_196,plain,
~ empty(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_197,plain,
~ empty(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_198,plain,
~ empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_199,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_200,plain,
~ empty(positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_201,plain,
function_yielding(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_202,plain,
ordinal_yielding(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_203,plain,
transfinite_sequence(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_204,plain,
transfinite_sequence(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_205,plain,
being_limit_ordinal(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_206,plain,
relation_non_empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_207,plain,
natural(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_208,plain,
natural(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_209,negated_conjecture,
finite(esk28_0),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_210,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_211,plain,
finite(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_212,plain,
ordinal(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_213,plain,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_214,plain,
ordinal(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_215,plain,
ordinal(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_216,plain,
ordinal(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_217,plain,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_218,plain,
ordinal(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_219,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_220,plain,
epsilon_connected(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_221,plain,
epsilon_connected(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_222,plain,
epsilon_connected(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_223,plain,
epsilon_connected(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_224,plain,
epsilon_connected(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_225,plain,
epsilon_connected(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_226,plain,
epsilon_connected(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_227,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_228,plain,
epsilon_transitive(esk20_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_229,plain,
epsilon_transitive(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_230,plain,
epsilon_transitive(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_231,plain,
epsilon_transitive(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_232,plain,
epsilon_transitive(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_233,plain,
epsilon_transitive(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_234,plain,
epsilon_transitive(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_235,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_236,plain,
one_to_one(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_237,plain,
one_to_one(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_238,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_239,plain,
function(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_240,plain,
function(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_241,plain,
function(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_242,plain,
function(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_243,plain,
function(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_244,plain,
function(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_245,plain,
function(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_246,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_247,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_248,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_249,plain,
relation_empty_yielding(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_250,plain,
relation_empty_yielding(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_251,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_252,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_253,plain,
relation(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_254,plain,
relation(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_255,plain,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_256,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_257,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_258,plain,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_259,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_260,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_261,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_262,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_263,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_264,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_265,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_266,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_267,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_268,plain,
empty(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_269,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_270,plain,
empty(esk17_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_271,plain,
empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_272,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_273,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_274,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_275,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_276,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_277,axiom,
X1 = X1 ).
cnf(i_0_278,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_279,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_280,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_281,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_282,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_283,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_284,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_285,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_286,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_287,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_288,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_289,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_290,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_291,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_292,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_293,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_294,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_295,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_297,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_298,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_299,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_300,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_301,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_302,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_277_001,axiom,
X1 = X1 ).
cnf(i_0_278_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_279_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_280_004,axiom,
( X1 != X2
| set_union2(X1,X3) = set_union2(X2,X3) ) ).
cnf(i_0_281_005,axiom,
( X1 != X2
| set_union2(X3,X1) = set_union2(X3,X2) ) ).
cnf(i_0_282_006,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_283_007,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_284_008,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_285_009,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_286_010,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_287_011,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_288_012,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_289_013,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_290_014,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_291_015,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_292_016,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_293_017,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_294_018,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_295_019,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_296_020,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_297_021,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_298_022,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_299_023,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_300_024,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_301_025,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_302_026,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_303,plain,
$false,
inference(scs_inference,[],[i_0_145,i_0_210,i_0_209,i_0_140]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU083+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
% 0.15/0.32 % Computer : n018.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:43:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Theorem for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.63 % Total time : 1.271s
%------------------------------------------------------------------------------