%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM395+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 : n024.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 04:57:14 PM UTC 2026
% Result : Theorem 0.13s 1.51s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 61
% Syntax : Number of formulae : 140 ( 48 unt; 0 def)
% Number of atoms : 306 ( 44 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 289 ( 123 ~; 107 |; 48 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 12 con; 0-1 aty)
% Number of variables : 145 ( 1 sgn 38 !; 14 ?)
% 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(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(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(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
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(d4_ordinal1,axiom,
! [X1] :
( ordinal(X1)
<=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).
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(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
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(t27_ordinal1,conjecture,
ordinal(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_ordinal1) ).
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(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_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(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(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_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(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
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(l18_ordinal1,axiom,
( epsilon_transitive(empty_set)
& epsilon_connected(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l18_ordinal1) ).
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_29,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_30,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_31,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_32,plain,
! [X37,X38] :
( ~ in(X37,X38)
| ~ in(X38,X37) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_29])]) ).
fof(i_0_33,plain,
! [X35,X36] :
( ~ element(X35,X36)
| empty(X36)
| in(X35,X36) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_34,plain,
! [X39,X40] :
( ~ in(X39,X40)
| element(X39,X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_35,plain,
! [X44,X45] :
( ~ in(X44,X45)
| ~ empty(X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_36,plain,
! [X42] :
( ( relation(X42)
| ~ relation(X42)
| ~ empty(X42)
| ~ function(X42) )
& ( function(X42)
| ~ relation(X42)
| ~ empty(X42)
| ~ function(X42) )
& ( one_to_one(X42)
| ~ relation(X42)
| ~ empty(X42)
| ~ function(X42) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_37,plain,
! [X33] : element(esk1_1(X33),X33),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_38,plain,
! [X62] :
( ( epsilon_transitive(X62)
| ~ ordinal(X62) )
& ( epsilon_connected(X62)
| ~ ordinal(X62) )
& ( ~ epsilon_transitive(X62)
| ~ epsilon_connected(X62)
| ordinal(X62) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_ordinal1])])]) ).
fof(i_0_39,plain,
! [X49] :
( ~ epsilon_transitive(X49)
| ~ epsilon_connected(X49)
| ordinal(X49) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_40,plain,
! [X46,X47] :
( ~ empty(X46)
| X46 = X47
| ~ empty(X47) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_41,plain,
! [X48] :
( ( epsilon_transitive(X48)
| ~ ordinal(X48) )
& ( epsilon_connected(X48)
| ~ ordinal(X48) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_42,plain,
! [X43] :
( ~ empty(X43)
| relation(X43) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_43,plain,
! [X41] :
( ~ empty(X41)
| function(X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_44,plain,
! [X61] :
( ~ empty(X61)
| X61 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_45,negated_conjecture,
~ ordinal(empty_set),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t27_ordinal1])]) ).
fof(i_0_46,plain,
~ empty(esk12_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_30])]) ).
fof(i_0_47,plain,
( ~ empty(esk9_0)
& relation(esk9_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_31])]) ).
fof(i_0_48,plain,
( relation(esk7_0)
& relation_non_empty(esk7_0)
& function(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_49,plain,
( relation(esk10_0)
& relation_empty_yielding(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_50,plain,
( relation(esk6_0)
& relation_empty_yielding(esk6_0)
& function(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_51,plain,
( epsilon_transitive(esk2_0)
& epsilon_connected(esk2_0)
& ordinal(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
fof(i_0_52,plain,
( relation(esk5_0)
& function(esk5_0)
& one_to_one(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_53,plain,
( empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_54,plain,
( relation(esk4_0)
& empty(esk4_0)
& function(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_55,plain,
( relation(esk3_0)
& function(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_56,plain,
empty(esk11_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_57,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_32]),
[final] ).
cnf(i_0_58,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_33]),
[final] ).
cnf(i_0_59,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_34]),
[final] ).
cnf(i_0_60,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_35]),
[final] ).
cnf(i_0_61,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_36]),
[final] ).
cnf(i_0_62,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_37]),
[final] ).
cnf(i_0_63,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_64,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_39]),
[final] ).
cnf(i_0_65,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_40]),
[final] ).
cnf(i_0_66,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_67,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_68,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_38]),
[final] ).
cnf(i_0_69,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_70,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_71,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_72,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_73,negated_conjecture,
~ ordinal(empty_set),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_74,plain,
~ empty(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_75,plain,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_76,plain,
relation_non_empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_77,plain,
relation_empty_yielding(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_78,plain,
relation_empty_yielding(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_79,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_80,plain,
epsilon_connected(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_81,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[l18_ordinal1]),
[final] ).
cnf(i_0_82,plain,
epsilon_transitive(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_83,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[l18_ordinal1]),
[final] ).
cnf(i_0_84,plain,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_85,plain,
one_to_one(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_86,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_87,plain,
relation(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_88,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_89,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_90,plain,
relation(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_91,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_92,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_93,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_94,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_95,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_96,plain,
function(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_97,plain,
function(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_98,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_99,plain,
function(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_100,plain,
function(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_101,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_102,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_103,plain,
empty(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_104,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_105,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_106,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_107,axiom,
X1 = X1 ).
cnf(i_0_108,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_109,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_110,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_111,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_112,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_113,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_114,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_115,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_116,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_117,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_118,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_119,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_120,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_121,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_122,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_107_001,axiom,
X1 = X1 ).
cnf(i_0_108_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_109_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_110_004,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_111_005,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_112_006,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_113_007,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_114_008,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_115_009,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_116_010,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_117_011,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_118_012,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_119_013,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_120_014,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_121_015,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_122_016,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_123,plain,
$false,
inference(scs_inference,[],[i_0_73,i_0_83,i_0_81,i_0_64]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM395+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.06 % 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
% 0.07/0.24 % Computer : n024.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 19:30:56 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 0.13/1.51 % Version : CSE_E---1.7
% 0.13/1.51 % Problem : theBenchmark.p
% 0.13/1.51 % SZS status Theorem for theBenchmark.p
% 0.13/1.51 % SZS output start CNFRefutation
% See solution above
% 0.13/1.52 % Total time : 1.261s
%------------------------------------------------------------------------------