%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU295+3 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 05:11:23 PM UTC 2026
% Result : Theorem 0.26s 1.60s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 114
% Syntax : Number of formulae : 327 ( 130 unt; 0 def)
% Number of atoms : 765 ( 77 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 704 ( 266 ~; 221 |; 186 &)
% ( 1 <=>; 30 =>; 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 : 350 ( 19 sgn 117 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t15_finset_1,conjecture,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t15_finset_1) ).
fof(rc3_finset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_finset_1) ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rc2_arytm_3) ).
fof(rc3_ordinal1,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(rc1_finset_1,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_finset_1) ).
fof(rc1_arytm_3,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(fc1_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_relat_1) ).
fof(cc2_finset_1,axiom,
! [X1] :
( finite(X1)
=> ! [X2] :
( element(X2,powerset(X1))
=> finite(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finset_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(t17_xboole_1,axiom,
! [X1,X2] : subset(set_intersection2(X1,X2),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_xboole_1) ).
fof(fc11_finset_1,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc11_finset_1) ).
fof(fc10_finset_1,axiom,
! [X1,X2] :
( finite(X2)
=> finite(set_intersection2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc10_finset_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t13_finset_1,axiom,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(cc1_arytm_3,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( element(X2,X1)
=> ( epsilon_transitive(X2)
& epsilon_connected(X2)
& ordinal(X2) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cc4_arytm_3) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(commutativity_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X2) = set_intersection2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',cc2_funct_1) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cc2_arytm_3) ).
fof(cc2_ordinal1,axiom,
! [X1] :
( ( epsilon_transitive(X1)
& epsilon_connected(X1) )
=> ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_ordinal1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(idempotence_k3_xboole_0,axiom,
! [X1,X2] : set_intersection2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t2_boole,axiom,
! [X1] : set_intersection2(X1,empty_set) = empty_set,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_boole) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(cc1_finset_1,axiom,
! [X1] :
( empty(X1)
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finset_1) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
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/sandbox/benchmark/theBenchmark.p',rc3_arytm_3) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(fc8_arytm_3,axiom,
~ empty(positive_rationals),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc8_arytm_3) ).
fof(rc5_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_non_empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_funct_1) ).
fof(rc2_ordinal2,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1)
& ordinal_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_ordinal2) ).
fof(rc4_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& transfinite_sequence(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rc1_ordinal2) ).
fof(rc1_funcop_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& function_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(rc1_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_ordinal1) ).
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/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc4_relat_1,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(i_0_62,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_63,negated_conjecture,
~ ! [X1,X2] :
( finite(X1)
=> finite(set_intersection2(X1,X2)) ),
inference(assume_negation,[status(cth)],[t15_finset_1]) ).
fof(i_0_64,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_65,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_66,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_67,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_68,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_69,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_70,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_71,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
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,
! [X157,X158,X159] :
( ~ in(X157,X158)
| ~ element(X158,powerset(X159))
| element(X157,X159) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_74,plain,
! [X160,X161,X162] :
( ~ in(X160,X161)
| ~ element(X161,powerset(X162))
| ~ empty(X162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_75,plain,
! [X155,X156] :
( ( ~ element(X155,powerset(X156))
| subset(X155,X156) )
& ( ~ subset(X155,X156)
| element(X155,powerset(X156)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_76,plain,
! [X87,X88] :
( ~ in(X87,X88)
| ~ in(X88,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_62])]) ).
fof(i_0_77,plain,
! [X110,X111] :
( ~ relation(X110)
| ~ relation(X111)
| relation(set_intersection2(X110,X111)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_relat_1])]) ).
fof(i_0_78,plain,
! [X96,X97] :
( ~ finite(X96)
| ~ element(X97,powerset(X96))
| finite(X97) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_79,plain,
! [X153,X154] :
( ~ element(X153,X154)
| empty(X154)
| in(X153,X154) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_80,plain,
! [X148,X149] : subset(set_intersection2(X148,X149),X148),
inference(variable_rename,[status(thm)],[t17_xboole_1]) ).
fof(i_0_81,negated_conjecture,
( finite(esk27_0)
& ~ finite(set_intersection2(esk27_0,esk28_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_63])])]) ).
fof(i_0_82,plain,
! [X108,X109] :
( ~ finite(X108)
| finite(set_intersection2(X108,X109)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc11_finset_1])]) ).
fof(i_0_83,plain,
! [X106,X107] :
( ~ finite(X107)
| finite(set_intersection2(X106,X107)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc10_finset_1])]) ).
fof(i_0_84,plain,
! [X150,X151] :
( ~ in(X150,X151)
| element(X150,X151) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_85,plain,
! [X144,X145] :
( ~ subset(X144,X145)
| ~ finite(X145)
| finite(X144) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])]) ).
fof(i_0_86,plain,
! [X89,X90] :
( ( epsilon_transitive(X90)
| ~ element(X90,X89)
| ~ ordinal(X89) )
& ( epsilon_connected(X90)
| ~ element(X90,X89)
| ~ ordinal(X89) )
& ( ordinal(X90)
| ~ element(X90,X89)
| ~ ordinal(X89) ) ),
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_87,plain,
! [X101] :
( ( epsilon_transitive(X101)
| ~ ordinal(X101)
| ~ element(X101,positive_rationals) )
& ( epsilon_connected(X101)
| ~ ordinal(X101)
| ~ element(X101,positive_rationals) )
& ( ordinal(X101)
| ~ ordinal(X101)
| ~ element(X101,positive_rationals) )
& ( natural(X101)
| ~ ordinal(X101)
| ~ element(X101,positive_rationals) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_arytm_3])])]) ).
fof(i_0_88,plain,
! [X135] :
( ( element(esk20_1(X135),powerset(X135))
| empty(X135) )
& ( ~ empty(esk20_1(X135))
| empty(X135) )
& ( finite(esk20_1(X135))
| empty(X135) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_64])])])]) ).
fof(i_0_89,plain,
! [X121] :
( ( element(esk9_1(X121),powerset(X121))
| empty(X121) )
& ( ~ empty(esk9_1(X121))
| empty(X121) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_65])])])]) ).
fof(i_0_90,plain,
! [X164,X165] :
( ~ in(X164,X165)
| ~ empty(X165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_91,plain,
! [X102,X103] : set_intersection2(X102,X103) = set_intersection2(X103,X102),
inference(variable_rename,[status(thm)],[commutativity_k3_xboole_0]) ).
fof(i_0_92,plain,
! [X131] :
( element(esk17_1(X131),powerset(X131))
& empty(esk17_1(X131)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_93,plain,
! [X125] :
( element(esk12_1(X125),powerset(X125))
& empty(esk12_1(X125))
& relation(esk12_1(X125))
& function(esk12_1(X125))
& one_to_one(esk12_1(X125))
& epsilon_transitive(esk12_1(X125))
& epsilon_connected(esk12_1(X125))
& ordinal(esk12_1(X125))
& natural(esk12_1(X125))
& finite(esk12_1(X125)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_94,plain,
! [X98] :
( ( relation(X98)
| ~ relation(X98)
| ~ empty(X98)
| ~ function(X98) )
& ( function(X98)
| ~ relation(X98)
| ~ empty(X98)
| ~ function(X98) )
& ( one_to_one(X98)
| ~ relation(X98)
| ~ empty(X98)
| ~ function(X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_95,plain,
! [X104] : element(esk1_1(X104),X104),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_96,plain,
! [X95] :
( ( epsilon_transitive(X95)
| ~ empty(X95)
| ~ ordinal(X95) )
& ( epsilon_connected(X95)
| ~ empty(X95)
| ~ ordinal(X95) )
& ( ordinal(X95)
| ~ empty(X95)
| ~ ordinal(X95) )
& ( natural(X95)
| ~ empty(X95)
| ~ ordinal(X95) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_arytm_3])])]) ).
fof(i_0_97,plain,
! [X99] :
( ~ epsilon_transitive(X99)
| ~ epsilon_connected(X99)
| ordinal(X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_98,plain,
! [X112] : ~ empty(powerset(X112)),
inference(variable_rename,[status(thm)],[i_0_66]) ).
fof(i_0_99,plain,
! [X166,X167] :
( ~ empty(X166)
| X166 = X167
| ~ empty(X167) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_100,plain,
! [X113] : set_intersection2(X113,X113) = X113,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k3_xboole_0])]) ).
fof(i_0_101,plain,
! [X143] : subset(X143,X143),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_102,plain,
! [X152] : set_intersection2(X152,empty_set) = empty_set,
inference(variable_rename,[status(thm)],[t2_boole]) ).
fof(i_0_103,plain,
! [X94] :
( ~ empty(X94)
| relation(X94) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_104,plain,
! [X92] :
( ~ empty(X92)
| function(X92) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_105,plain,
! [X91] :
( ~ empty(X91)
| finite(X91) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_106,plain,
! [X100] :
( ( epsilon_transitive(X100)
| ~ empty(X100) )
& ( epsilon_connected(X100)
| ~ empty(X100) )
& ( ordinal(X100)
| ~ empty(X100) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_107,plain,
! [X93] :
( ( epsilon_transitive(X93)
| ~ ordinal(X93) )
& ( epsilon_connected(X93)
| ~ ordinal(X93) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_108,plain,
( element(esk19_0,positive_rationals)
& empty(esk19_0)
& epsilon_transitive(esk19_0)
& epsilon_connected(esk19_0)
& ordinal(esk19_0)
& natural(esk19_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_arytm_3])]) ).
fof(i_0_109,plain,
( element(esk11_0,positive_rationals)
& ~ empty(esk11_0)
& epsilon_transitive(esk11_0)
& epsilon_connected(esk11_0)
& ordinal(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_67])]) ).
fof(i_0_110,plain,
! [X163] :
( ~ empty(X163)
| X163 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_111,plain,
( ~ empty(esk22_0)
& epsilon_transitive(esk22_0)
& epsilon_connected(esk22_0)
& ordinal(esk22_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_68])]) ).
fof(i_0_112,plain,
~ empty(esk18_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_69])]) ).
fof(i_0_113,plain,
( ~ empty(esk16_0)
& relation(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_70])]) ).
fof(i_0_114,plain,
( ~ empty(esk3_0)
& finite(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_71])]) ).
fof(i_0_115,plain,
( ~ empty(esk2_0)
& epsilon_transitive(esk2_0)
& epsilon_connected(esk2_0)
& ordinal(esk2_0)
& natural(esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_72])]) ).
fof(i_0_116,plain,
~ empty(positive_rationals),
inference(fof_simplification,[status(thm)],[fc8_arytm_3]) ).
fof(i_0_117,plain,
( relation(esk26_0)
& relation_non_empty(esk26_0)
& function(esk26_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_118,plain,
( relation(esk15_0)
& function(esk15_0)
& transfinite_sequence(esk15_0)
& ordinal_yielding(esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal2])]) ).
fof(i_0_119,plain,
( relation(esk25_0)
& function(esk25_0)
& transfinite_sequence(esk25_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_ordinal1])]) ).
fof(i_0_120,plain,
( epsilon_transitive(esk7_0)
& epsilon_connected(esk7_0)
& ordinal(esk7_0)
& being_limit_ordinal(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal2])]) ).
fof(i_0_121,plain,
( relation(esk4_0)
& function(esk4_0)
& function_yielding(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funcop_1])]) ).
fof(i_0_122,plain,
( relation(esk24_0)
& relation_empty_yielding(esk24_0)
& function(esk24_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_123,plain,
( relation(esk23_0)
& relation_empty_yielding(esk23_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_124,plain,
( relation(esk21_0)
& function(esk21_0)
& one_to_one(esk21_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_125,plain,
( relation(esk14_0)
& function(esk14_0)
& one_to_one(esk14_0)
& empty(esk14_0)
& epsilon_transitive(esk14_0)
& epsilon_connected(esk14_0)
& ordinal(esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_ordinal1])]) ).
fof(i_0_126,plain,
( relation(esk13_0)
& empty(esk13_0)
& function(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_127,plain,
( empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_128,plain,
( relation(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_129,plain,
empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(i_0_130,plain,
( epsilon_transitive(esk6_0)
& epsilon_connected(esk6_0)
& ordinal(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
cnf(i_0_131,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_132,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_74]),
[final] ).
cnf(i_0_133,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_134,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_76]),
[final] ).
cnf(i_0_135,plain,
( relation(set_intersection2(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[i_0_77]),
[final] ).
cnf(i_0_136,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_137,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_75]),
[final] ).
cnf(i_0_138,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_79]),
[final] ).
cnf(i_0_139,plain,
subset(set_intersection2(X1,X2),X1),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_140,negated_conjecture,
~ finite(set_intersection2(esk27_0,esk28_0)),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_141,plain,
( finite(set_intersection2(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_142,plain,
( finite(set_intersection2(X2,X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_143,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_144,plain,
( finite(X1)
| ~ subset(X1,X2)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_145,plain,
( epsilon_connected(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_146,plain,
( epsilon_transitive(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_147,plain,
( ordinal(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_148,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_149,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_150,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_151,plain,
( element(esk20_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_152,plain,
( element(esk9_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_153,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_154,plain,
set_intersection2(X1,X2) = set_intersection2(X2,X1),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_155,plain,
element(esk17_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_156,plain,
element(esk12_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_157,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_158,plain,
( empty(X1)
| ~ empty(esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_159,plain,
( empty(X1)
| ~ empty(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_160,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_161,plain,
( natural(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_162,plain,
( epsilon_connected(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_163,plain,
( epsilon_transitive(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_164,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_165,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_166,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_167,plain,
( finite(esk20_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_168,plain,
set_intersection2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_169,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_170,plain,
set_intersection2(X1,empty_set) = empty_set,
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_171,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_172,plain,
( function(X1)
| ~ empty(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,
( epsilon_connected(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_transitive(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,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_179,plain,
element(esk19_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_180,plain,
element(esk11_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_181,plain,
one_to_one(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_182,plain,
natural(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_183,plain,
relation(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_184,plain,
function(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_185,plain,
finite(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_186,plain,
empty(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_187,plain,
empty(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_188,plain,
epsilon_connected(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_189,plain,
epsilon_transitive(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_190,plain,
ordinal(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_191,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_192,plain,
~ empty(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_193,plain,
~ empty(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_194,plain,
~ empty(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_195,plain,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_196,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_197,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_198,plain,
~ empty(positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_199,plain,
relation_non_empty(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_200,plain,
ordinal_yielding(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_201,plain,
transfinite_sequence(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_202,plain,
transfinite_sequence(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_203,plain,
being_limit_ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_204,plain,
function_yielding(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_205,plain,
relation_empty_yielding(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_206,plain,
relation_empty_yielding(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_207,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_208,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_209,plain,
one_to_one(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_210,plain,
one_to_one(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_211,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_212,plain,
natural(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_213,plain,
natural(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_214,plain,
relation(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_215,plain,
relation(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_216,plain,
relation(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_217,plain,
relation(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_218,plain,
relation(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_219,plain,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_220,plain,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_221,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_222,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_223,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_224,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_225,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_226,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_227,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_228,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_229,plain,
function(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_230,plain,
function(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_231,plain,
function(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_232,plain,
function(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_233,plain,
function(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_234,plain,
function(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_235,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_236,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_237,plain,
function(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_238,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_239,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_240,plain,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_241,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_242,plain,
empty(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_243,plain,
empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_244,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_245,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_246,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_247,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_248,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_249,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_250,plain,
epsilon_connected(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_251,plain,
epsilon_connected(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_252,plain,
epsilon_connected(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_253,plain,
epsilon_connected(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_254,plain,
epsilon_connected(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_255,plain,
epsilon_connected(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_256,plain,
epsilon_connected(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_257,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_258,plain,
epsilon_transitive(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_259,plain,
epsilon_transitive(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_260,plain,
epsilon_transitive(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_261,plain,
epsilon_transitive(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_262,plain,
epsilon_transitive(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_263,plain,
epsilon_transitive(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_264,plain,
epsilon_transitive(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_265,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_266,plain,
ordinal(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_267,plain,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_268,plain,
ordinal(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_269,plain,
ordinal(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_270,plain,
ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_271,plain,
ordinal(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_272,plain,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_273,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_274,axiom,
X1 = X1 ).
cnf(i_0_275,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_276,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_277,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_278,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_279,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_280,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_281,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_282,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_283,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_284,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_285,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_286,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_287,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_288,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_289,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_290,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_291,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_292,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_293,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_294,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_295,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_297,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_298,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_299,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_274_001,axiom,
X1 = X1 ).
cnf(i_0_275_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_276_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_277_004,axiom,
( X1 != X2
| set_intersection2(X1,X3) = set_intersection2(X2,X3) ) ).
cnf(i_0_278_005,axiom,
( X1 != X2
| set_intersection2(X3,X1) = set_intersection2(X3,X2) ) ).
cnf(i_0_279_006,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_280_007,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_281_008,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_282_009,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_283_010,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_284_011,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_285_012,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_286_013,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_287_014,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_288_015,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_289_016,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_290_017,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_291_018,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_292_019,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_293_020,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_294_021,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_295_022,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_296_023,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_297_024,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_298_025,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_299_026,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_300,plain,
$false,
inference(scs_inference,[],[i_0_140,i_0_239,i_0_141]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU295+3 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:54:41 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 0.26/1.60 % Version : CSE_E---1.7
% 0.26/1.60 % Problem : theBenchmark.p
% 0.26/1.60 % SZS status Theorem for theBenchmark.p
% 0.26/1.60 % SZS output start CNFRefutation
% See solution above
% 0.26/1.62 % Total time : 1.271s
%------------------------------------------------------------------------------