%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU090+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 : n019.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 0.26s 1.61s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_81)
% Comments :
%------------------------------------------------------------------------------
fof(fc6_subset_1,axiom,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& ~ empty(X3)
& ~ empty(X4) )
=> ~ empty(cartesian_product4(X1,X2,X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_subset_1) ).
fof(t21_finset_1,conjecture,
! [X1,X2,X3,X4] :
( ( finite(X1)
& finite(X2)
& finite(X3)
& finite(X4) )
=> finite(cartesian_product4(X1,X2,X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_finset_1) ).
fof(d4_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product4(X1,X2,X3,X4) = cartesian_product2(cartesian_product3(X1,X2,X3),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_zfmisc_1) ).
fof(fc5_subset_1,axiom,
! [X1,X2,X3] :
( ( ~ empty(X1)
& ~ empty(X2)
& ~ empty(X3) )
=> ~ empty(cartesian_product3(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_subset_1) ).
fof(fc4_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_subset_1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
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(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(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(rc3_ordinal1,axiom,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_ordinal1) ).
fof(rc2_xboole_0,axiom,
? [X1] : ~ empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(rc2_relat_1,axiom,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(rc1_finset_1,axiom,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',rc1_arytm_3) ).
fof(t20_finset_1,axiom,
! [X1,X2,X3] :
( ( finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product3(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
fof(fc15_finset_1,axiom,
! [X1,X2,X3] :
( ( finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product3(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc15_finset_1) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_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(t19_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_finset_1) ).
fof(fc14_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_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(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(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(cc1_relat_1,axiom,
! [X1] :
( empty(X1)
=> relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
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(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(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_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(rc1_funcop_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& function_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funcop_1) ).
fof(rc4_funct_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc4_funct_1) ).
fof(rc3_relat_1,axiom,
? [X1] :
( relation(X1)
& relation_empty_yielding(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(rc3_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(rc2_ordinal1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_ordinal1) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_relat_1,axiom,
? [X1] :
( empty(X1)
& relation(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(rc1_funct_1,axiom,
? [X1] :
( relation(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(rc1_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/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/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_63,plain,
! [X1,X2,X3,X4] :
( ( ~ empty(X1)
& ~ empty(X2)
& ~ empty(X3)
& ~ empty(X4) )
=> ~ empty(cartesian_product4(X1,X2,X3,X4)) ),
inference(fof_simplification,[status(thm)],[fc6_subset_1]) ).
fof(i_0_64,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( finite(X1)
& finite(X2)
& finite(X3)
& finite(X4) )
=> finite(cartesian_product4(X1,X2,X3,X4)) ),
inference(assume_negation,[status(cth)],[t21_finset_1]) ).
fof(i_0_65,plain,
! [X136,X137,X138,X139] :
( empty(X136)
| empty(X137)
| empty(X138)
| empty(X139)
| ~ empty(cartesian_product4(X136,X137,X138,X139)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_63])]) ).
fof(i_0_66,plain,
! [X119,X120,X121,X122] : cartesian_product4(X119,X120,X121,X122) = cartesian_product2(cartesian_product3(X119,X120,X121),X122),
inference(variable_rename,[status(thm)],[d4_zfmisc_1]) ).
fof(i_0_67,negated_conjecture,
( finite(esk27_0)
& finite(esk28_0)
& finite(esk29_0)
& finite(esk30_0)
& ~ finite(cartesian_product4(esk27_0,esk28_0,esk29_0,esk30_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_64])])]) ).
fof(i_0_68,plain,
! [X1,X2,X3] :
( ( ~ empty(X1)
& ~ empty(X2)
& ~ empty(X3) )
=> ~ empty(cartesian_product3(X1,X2,X3)) ),
inference(fof_simplification,[status(thm)],[fc5_subset_1]) ).
fof(i_0_69,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc4_subset_1]) ).
fof(i_0_70,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_71,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_72,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_73,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_74,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_75,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_76,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_77,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_78,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_79,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[rc1_arytm_3]) ).
cnf(i_0_80,plain,
( empty(X1)
| empty(X2)
| empty(X3)
| empty(X4)
| ~ empty(cartesian_product4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[i_0_65]) ).
cnf(i_0_81,plain,
cartesian_product4(X1,X2,X3,X4) = cartesian_product2(cartesian_product3(X1,X2,X3),X4),
inference(split_conjunct,[status(thm)],[i_0_66]) ).
cnf(i_0_82,negated_conjecture,
~ finite(cartesian_product4(esk27_0,esk28_0,esk29_0,esk30_0)),
inference(split_conjunct,[status(thm)],[i_0_67]) ).
fof(i_0_83,plain,
! [X133,X134,X135] :
( empty(X133)
| empty(X134)
| empty(X135)
| ~ empty(cartesian_product3(X133,X134,X135)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_68])]) ).
fof(i_0_84,plain,
! [X174,X175,X176] :
( ~ finite(X174)
| ~ finite(X175)
| ~ finite(X176)
| finite(cartesian_product3(X174,X175,X176)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t20_finset_1])]) ).
fof(i_0_85,plain,
! [X127,X128,X129] :
( ~ finite(X127)
| ~ finite(X128)
| ~ finite(X129)
| finite(cartesian_product3(X127,X128,X129)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc15_finset_1])]) ).
fof(i_0_86,plain,
! [X109,X110,X111] :
( ~ element(X111,powerset(cartesian_product2(X109,X110)))
| relation(X111) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(i_0_87,plain,
! [X185,X186,X187] :
( ~ in(X185,X186)
| ~ element(X186,powerset(X187))
| element(X185,X187) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_88,plain,
! [X188,X189,X190] :
( ~ in(X188,X189)
| ~ element(X189,powerset(X190))
| ~ empty(X190) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_89,plain,
! [X131,X132] :
( empty(X131)
| empty(X132)
| ~ empty(cartesian_product2(X131,X132)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_69])]) ).
fof(i_0_90,plain,
! [X183,X184] :
( ( ~ element(X183,powerset(X184))
| subset(X183,X184) )
& ( ~ subset(X183,X184)
| element(X183,powerset(X184)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_91,plain,
! [X101,X102] :
( ~ in(X101,X102)
| ~ in(X102,X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_70])]) ).
fof(i_0_92,plain,
! [X170,X171] :
( ~ finite(X170)
| ~ finite(X171)
| finite(cartesian_product2(X170,X171)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_finset_1])]) ).
fof(i_0_93,plain,
! [X125,X126] :
( ~ finite(X125)
| ~ finite(X126)
| finite(cartesian_product2(X125,X126)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])]) ).
fof(i_0_94,plain,
! [X113,X114] :
( ~ finite(X113)
| ~ element(X114,powerset(X113))
| finite(X114) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_95,plain,
! [X181,X182] :
( ~ element(X181,X182)
| empty(X182)
| in(X181,X182) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_96,plain,
! [X172,X173] :
( ~ in(X172,X173)
| element(X172,X173) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_97,plain,
! [X103,X104] :
( ( epsilon_transitive(X104)
| ~ element(X104,X103)
| ~ ordinal(X103) )
& ( epsilon_connected(X104)
| ~ element(X104,X103)
| ~ ordinal(X103) )
& ( ordinal(X104)
| ~ element(X104,X103)
| ~ ordinal(X103) ) ),
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_98,plain,
! [X118] :
( ( epsilon_transitive(X118)
| ~ ordinal(X118)
| ~ element(X118,positive_rationals) )
& ( epsilon_connected(X118)
| ~ ordinal(X118)
| ~ element(X118,positive_rationals) )
& ( ordinal(X118)
| ~ ordinal(X118)
| ~ element(X118,positive_rationals) )
& ( natural(X118)
| ~ ordinal(X118)
| ~ element(X118,positive_rationals) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_arytm_3])])]) ).
fof(i_0_99,plain,
! [X161] :
( ( element(esk20_1(X161),powerset(X161))
| empty(X161) )
& ( ~ empty(esk20_1(X161))
| empty(X161) )
& ( finite(esk20_1(X161))
| empty(X161) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_71])])])]) ).
fof(i_0_100,plain,
! [X147] :
( ( element(esk9_1(X147),powerset(X147))
| empty(X147) )
& ( ~ empty(esk9_1(X147))
| empty(X147) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_72])])])]) ).
fof(i_0_101,plain,
! [X192,X193] :
( ~ in(X192,X193)
| ~ empty(X193) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_102,plain,
! [X157] :
( element(esk17_1(X157),powerset(X157))
& empty(esk17_1(X157)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_103,plain,
! [X151] :
( element(esk12_1(X151),powerset(X151))
& empty(esk12_1(X151))
& relation(esk12_1(X151))
& function(esk12_1(X151))
& one_to_one(esk12_1(X151))
& epsilon_transitive(esk12_1(X151))
& epsilon_connected(esk12_1(X151))
& ordinal(esk12_1(X151))
& natural(esk12_1(X151))
& finite(esk12_1(X151)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_104,plain,
! [X115] :
( ( relation(X115)
| ~ relation(X115)
| ~ empty(X115)
| ~ function(X115) )
& ( function(X115)
| ~ relation(X115)
| ~ empty(X115)
| ~ function(X115) )
& ( one_to_one(X115)
| ~ relation(X115)
| ~ empty(X115)
| ~ function(X115) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_105,plain,
! [X123] : element(esk1_1(X123),X123),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_106,plain,
! [X112] :
( ( epsilon_transitive(X112)
| ~ empty(X112)
| ~ ordinal(X112) )
& ( epsilon_connected(X112)
| ~ empty(X112)
| ~ ordinal(X112) )
& ( ordinal(X112)
| ~ empty(X112)
| ~ ordinal(X112) )
& ( natural(X112)
| ~ empty(X112)
| ~ ordinal(X112) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_arytm_3])])]) ).
fof(i_0_107,plain,
! [X116] :
( ~ epsilon_transitive(X116)
| ~ epsilon_connected(X116)
| ordinal(X116) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_108,plain,
! [X130] : ~ empty(powerset(X130)),
inference(variable_rename,[status(thm)],[i_0_73]) ).
fof(i_0_109,plain,
! [X194,X195] :
( ~ empty(X194)
| X194 = X195
| ~ empty(X195) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_110,plain,
! [X169] : subset(X169,X169),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_111,plain,
! [X108] :
( ~ empty(X108)
| relation(X108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_112,plain,
! [X106] :
( ~ empty(X106)
| function(X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_113,plain,
! [X105] :
( ~ empty(X105)
| finite(X105) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_114,plain,
! [X117] :
( ( epsilon_transitive(X117)
| ~ empty(X117) )
& ( epsilon_connected(X117)
| ~ empty(X117) )
& ( ordinal(X117)
| ~ empty(X117) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_115,plain,
! [X107] :
( ( epsilon_transitive(X107)
| ~ ordinal(X107) )
& ( epsilon_connected(X107)
| ~ ordinal(X107) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_116,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_117,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_74])]) ).
fof(i_0_118,plain,
! [X191] :
( ~ empty(X191)
| X191 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_119,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_75])]) ).
fof(i_0_120,plain,
~ empty(esk18_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_76])]) ).
fof(i_0_121,plain,
( ~ empty(esk16_0)
& relation(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_77])]) ).
fof(i_0_122,plain,
( ~ empty(esk3_0)
& finite(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_78])]) ).
fof(i_0_123,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_79])]) ).
fof(i_0_124,plain,
~ empty(positive_rationals),
inference(fof_simplification,[status(thm)],[fc8_arytm_3]) ).
fof(i_0_125,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_126,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_127,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_128,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_129,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_130,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_131,plain,
( relation(esk23_0)
& relation_empty_yielding(esk23_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_132,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_133,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_134,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_135,plain,
( empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_136,plain,
( relation(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_137,plain,
empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(i_0_138,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_139,plain,
( empty(X4)
| empty(X3)
| empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(cartesian_product3(X1,X2,X3),X4)) ),
inference(rw,[status(thm)],[i_0_80,c_0_81]),
[final] ).
cnf(i_0_140,negated_conjecture,
~ finite(cartesian_product2(cartesian_product3(esk27_0,esk28_0,esk29_0),esk30_0)),
inference(rw,[status(thm)],[i_0_82,c_0_81]),
[final] ).
cnf(i_0_141,plain,
( empty(X1)
| empty(X2)
| empty(X3)
| ~ empty(cartesian_product3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_142,plain,
( finite(cartesian_product3(X1,X2,X3))
| ~ finite(X1)
| ~ finite(X2)
| ~ finite(X3) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_143,plain,
( finite(cartesian_product3(X1,X2,X3))
| ~ finite(X1)
| ~ finite(X2)
| ~ finite(X3) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_144,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_145,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_146,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_147,plain,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_148,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_149,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_150,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_151,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_152,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_153,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_154,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_155,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_156,plain,
( epsilon_connected(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_157,plain,
( epsilon_transitive(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_158,plain,
( ordinal(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_159,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_160,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_161,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_162,plain,
( element(esk20_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_163,plain,
( element(esk9_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_164,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_165,plain,
element(esk17_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_166,plain,
element(esk12_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_167,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_168,plain,
( empty(X1)
| ~ empty(esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_169,plain,
( empty(X1)
| ~ empty(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_170,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_171,plain,
( natural(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_172,plain,
( epsilon_connected(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_173,plain,
( epsilon_transitive(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_174,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_175,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_176,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_177,plain,
( finite(esk20_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_178,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_179,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_180,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_181,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_182,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_183,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_184,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_185,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_186,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_187,plain,
element(esk19_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_188,plain,
element(esk11_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_189,plain,
one_to_one(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_190,plain,
natural(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_191,plain,
relation(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_192,plain,
function(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_193,plain,
finite(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_194,plain,
empty(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_195,plain,
empty(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_196,plain,
epsilon_connected(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_197,plain,
epsilon_transitive(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_198,plain,
ordinal(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_199,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_200,plain,
~ empty(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_201,plain,
~ empty(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_202,plain,
~ empty(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_203,plain,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_204,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_205,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_206,plain,
~ empty(positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_207,plain,
relation_non_empty(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_208,plain,
ordinal_yielding(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_209,plain,
transfinite_sequence(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_210,plain,
transfinite_sequence(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_211,plain,
being_limit_ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_212,plain,
function_yielding(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_213,plain,
relation_empty_yielding(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_214,plain,
relation_empty_yielding(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_215,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_216,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_217,plain,
one_to_one(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_218,plain,
one_to_one(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_219,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_220,plain,
natural(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_221,plain,
natural(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_222,plain,
relation(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_223,plain,
relation(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_224,plain,
relation(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_225,plain,
relation(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_226,plain,
relation(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_227,plain,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_228,plain,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_229,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_230,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_231,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_232,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_233,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_234,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_235,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_236,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_237,plain,
function(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_238,plain,
function(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_239,plain,
function(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_240,plain,
function(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_132]),
[final] ).
cnf(i_0_241,plain,
function(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_242,plain,
function(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_243,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_244,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_136]),
[final] ).
cnf(i_0_245,plain,
function(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_246,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_247,negated_conjecture,
finite(esk30_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_248,negated_conjecture,
finite(esk29_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_249,negated_conjecture,
finite(esk28_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_250,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_251,plain,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_252,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_253,plain,
empty(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_254,plain,
empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_134]),
[final] ).
cnf(i_0_255,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_137]),
[final] ).
cnf(i_0_256,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_135]),
[final] ).
cnf(i_0_257,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_258,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_259,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_260,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_261,plain,
epsilon_connected(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_262,plain,
epsilon_connected(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_263,plain,
epsilon_connected(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_264,plain,
epsilon_connected(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_265,plain,
epsilon_connected(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_266,plain,
epsilon_connected(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_267,plain,
epsilon_connected(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_268,plain,
epsilon_connected(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_269,plain,
epsilon_transitive(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_270,plain,
epsilon_transitive(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_271,plain,
epsilon_transitive(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_272,plain,
epsilon_transitive(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_273,plain,
epsilon_transitive(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_274,plain,
epsilon_transitive(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_275,plain,
epsilon_transitive(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_276,plain,
epsilon_transitive(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_277,plain,
ordinal(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_278,plain,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_279,plain,
ordinal(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_133]),
[final] ).
cnf(i_0_280,plain,
ordinal(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_281,plain,
ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_282,plain,
ordinal(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_138]),
[final] ).
cnf(i_0_283,plain,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_284,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_285,axiom,
X1 = X1 ).
cnf(i_0_286,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_287,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_288,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_289,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_290,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_291,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_292,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_293,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_294,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_295,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_297,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(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
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_301,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_302,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_303,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_304,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_305,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_306,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_307,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_308,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_285_001,axiom,
X1 = X1 ).
cnf(i_0_286_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_287_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_288_004,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_289_005,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_290_006,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_291_007,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_292_008,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_293_009,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_294_010,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_295_011,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_296_012,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_297_013,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_298_014,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_299_015,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_300_016,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_301_017,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_302_018,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_303_019,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_304_020,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_305_021,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_306_022,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_307_023,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_308_024,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_309,plain,
finite(esk19_0),
inference(scs_inference,[],[i_0_252,i_0_181]) ).
cnf(i_0_310,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_181]) ).
cnf(i_0_311,plain,
relation(esk17_1(cartesian_product2(X1,X2))),
inference(scs_inference,[],[i_0_165,i_0_252,i_0_181,i_0_144]) ).
cnf(i_0_312,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_313,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_314,plain,
subset(esk17_1(X1),X1),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_181,i_0_144,i_0_148]) ).
cnf(i_0_315,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_316,plain,
~ in(X1,esk19_0),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_181,i_0_144,i_0_148,i_0_164]) ).
cnf(i_0_317,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_164]) ).
cnf(i_0_318,plain,
relation(esk19_0),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179]) ).
cnf(i_0_319,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_179]) ).
cnf(i_0_320,plain,
function(esk19_0),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180]) ).
cnf(i_0_321,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_180]) ).
cnf(i_0_322,plain,
epsilon_connected(esk13_0),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_254,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182]) ).
cnf(i_0_323,plain,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_182]) ).
cnf(i_0_324,plain,
epsilon_transitive(esk13_0),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_254,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184]) ).
cnf(i_0_325,plain,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_184]) ).
cnf(i_0_326,plain,
ordinal(esk13_0),
inference(scs_inference,[],[i_0_165,i_0_312,i_0_252,i_0_254,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186]) ).
cnf(i_0_327,plain,
( ~ empty(X1)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_186]) ).
cnf(i_0_328,plain,
esk30_0 != cartesian_product2(cartesian_product3(esk27_0,esk28_0,esk29_0),esk30_0),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_252,i_0_254,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298]) ).
cnf(i_0_329,plain,
~ finite(cartesian_product3(esk27_0,esk28_0,esk29_0)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_252,i_0_254,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151]) ).
cnf(i_0_330,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(rename_variables,[],[i_0_151]) ).
cnf(i_0_331,plain,
finite(esk17_1(esk30_0)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_252,i_0_254,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152]) ).
cnf(i_0_332,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_333,plain,
( ~ element(X1,powerset(X2))
| finite(X1)
| ~ finite(X2) ),
inference(rename_variables,[],[i_0_152]) ).
cnf(i_0_334,plain,
in(esk17_1(X1),powerset(X1)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_252,i_0_254,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154]) ).
cnf(i_0_335,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_336,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_154]) ).
cnf(i_0_337,plain,
esk19_0 != esk22_0,
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_252,i_0_254,i_0_200,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288]) ).
cnf(i_0_338,plain,
powerset(X1) != esk19_0,
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_252,i_0_254,i_0_200,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303]) ).
cnf(i_0_339,plain,
~ in(X1,esk17_1(esk19_0)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_335,i_0_252,i_0_254,i_0_200,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146]) ).
cnf(i_0_340,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_165]) ).
cnf(i_0_341,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_342,plain,
epsilon_connected(esk1_1(esk22_0)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_335,i_0_170,i_0_252,i_0_254,i_0_200,i_0_277,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146,i_0_156]) ).
cnf(i_0_343,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_344,plain,
( ~ ordinal(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_156]) ).
cnf(i_0_345,plain,
epsilon_transitive(esk1_1(esk22_0)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_335,i_0_170,i_0_343,i_0_252,i_0_254,i_0_200,i_0_277,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146,i_0_156,i_0_157]) ).
cnf(i_0_346,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_347,plain,
( ~ ordinal(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_157]) ).
cnf(i_0_348,plain,
ordinal(esk1_1(esk22_0)),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_335,i_0_170,i_0_343,i_0_346,i_0_252,i_0_254,i_0_200,i_0_277,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146,i_0_156,i_0_157,i_0_158]) ).
cnf(i_0_349,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_350,plain,
( ~ ordinal(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_158]) ).
cnf(i_0_351,plain,
natural(esk11_0),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_335,i_0_170,i_0_343,i_0_346,i_0_252,i_0_254,i_0_188,i_0_200,i_0_277,i_0_280,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146,i_0_156,i_0_157,i_0_158,i_0_159]) ).
cnf(i_0_352,plain,
( ~ element(X1,positive_rationals)
| ~ ordinal(X1)
| natural(X1) ),
inference(rename_variables,[],[i_0_159]) ).
cnf(i_0_353,plain,
natural(esk14_0),
inference(scs_inference,[],[i_0_140,i_0_247,i_0_165,i_0_312,i_0_332,i_0_335,i_0_170,i_0_343,i_0_346,i_0_252,i_0_253,i_0_254,i_0_188,i_0_200,i_0_277,i_0_279,i_0_280,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146,i_0_156,i_0_157,i_0_158,i_0_159,i_0_171]) ).
cnf(i_0_354,plain,
( ~ empty(X1)
| ~ ordinal(X1)
| natural(X1) ),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_355,plain,
$false,
inference(scs_inference,[],[i_0_140,i_0_247,i_0_248,i_0_249,i_0_250,i_0_165,i_0_312,i_0_332,i_0_335,i_0_170,i_0_343,i_0_346,i_0_252,i_0_253,i_0_254,i_0_188,i_0_200,i_0_277,i_0_279,i_0_280,i_0_175,i_0_181,i_0_144,i_0_148,i_0_164,i_0_179,i_0_180,i_0_182,i_0_184,i_0_186,i_0_298,i_0_151,i_0_152,i_0_154,i_0_288,i_0_303,i_0_146,i_0_156,i_0_157,i_0_158,i_0_159,i_0_171,i_0_143]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU090+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
% 0.14/0.32 % Computer : n019.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 02:42:59 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.26/1.61 % Version : CSE_E---1.7
% 0.26/1.61 % Problem : theBenchmark.p
% 0.26/1.61 % SZS status Theorem for theBenchmark.p
% 0.26/1.61 % SZS output start CNFRefutation
% See solution above
% 0.47/1.81 % Total time : 1.272s
%------------------------------------------------------------------------------