%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEU089+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:10:36 PM UTC 2026
% Result : Theorem 0.31s 1.62s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named c_0_77)
% Comments :
%------------------------------------------------------------------------------
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(t20_finset_1,conjecture,
! [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(d3_zfmisc_1,axiom,
! [X1,X2,X3] : cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_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(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_60,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_61,negated_conjecture,
~ ! [X1,X2,X3] :
( ( finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product3(X1,X2,X3)) ),
inference(assume_negation,[status(cth)],[t20_finset_1]) ).
fof(i_0_62,plain,
! [X116,X117,X118] :
( empty(X116)
| empty(X117)
| empty(X118)
| ~ empty(cartesian_product3(X116,X117,X118)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_60])]) ).
fof(i_0_63,plain,
! [X106,X107,X108] : cartesian_product3(X106,X107,X108) = cartesian_product2(cartesian_product2(X106,X107),X108),
inference(variable_rename,[status(thm)],[d3_zfmisc_1]) ).
fof(i_0_64,negated_conjecture,
( finite(esk27_0)
& finite(esk28_0)
& finite(esk29_0)
& ~ finite(cartesian_product3(esk27_0,esk28_0,esk29_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_61])])]) ).
fof(i_0_65,plain,
! [X1,X2] :
( ( ~ empty(X1)
& ~ empty(X2) )
=> ~ empty(cartesian_product2(X1,X2)) ),
inference(fof_simplification,[status(thm)],[fc4_subset_1]) ).
fof(i_0_66,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_67,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2)
& finite(X2) ) ),
inference(fof_simplification,[status(thm)],[rc3_finset_1]) ).
fof(i_0_68,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(i_0_69,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
fof(i_0_70,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_71,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
inference(fof_simplification,[status(thm)],[rc3_ordinal1]) ).
fof(i_0_72,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_73,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_74,plain,
? [X1] :
( ~ empty(X1)
& finite(X1) ),
inference(fof_simplification,[status(thm)],[rc1_finset_1]) ).
fof(i_0_75,plain,
? [X1] :
( ~ empty(X1)
& epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1)
& natural(X1) ),
inference(fof_simplification,[status(thm)],[rc1_arytm_3]) ).
cnf(i_0_76,plain,
( empty(X1)
| empty(X2)
| empty(X3)
| ~ empty(cartesian_product3(X1,X2,X3)) ),
inference(split_conjunct,[status(thm)],[i_0_62]) ).
cnf(i_0_77,plain,
cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
inference(split_conjunct,[status(thm)],[i_0_63]) ).
fof(i_0_78,plain,
! [X96,X97,X98] :
( ~ element(X98,powerset(cartesian_product2(X96,X97)))
| relation(X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(i_0_79,negated_conjecture,
~ finite(cartesian_product3(esk27_0,esk28_0,esk29_0)),
inference(split_conjunct,[status(thm)],[i_0_64]) ).
fof(i_0_80,plain,
! [X160,X161,X162] :
( ~ in(X160,X161)
| ~ element(X161,powerset(X162))
| element(X160,X162) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_81,plain,
! [X163,X164,X165] :
( ~ in(X163,X164)
| ~ element(X164,powerset(X165))
| ~ empty(X165) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_82,plain,
! [X114,X115] :
( empty(X114)
| empty(X115)
| ~ empty(cartesian_product2(X114,X115)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_65])]) ).
fof(i_0_83,plain,
! [X158,X159] :
( ( ~ element(X158,powerset(X159))
| subset(X158,X159) )
& ( ~ subset(X158,X159)
| element(X158,powerset(X159)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_84,plain,
! [X88,X89] :
( ~ in(X88,X89)
| ~ in(X89,X88) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_66])]) ).
fof(i_0_85,plain,
! [X149,X150] :
( ~ finite(X149)
| ~ finite(X150)
| finite(cartesian_product2(X149,X150)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t19_finset_1])]) ).
fof(i_0_86,plain,
! [X111,X112] :
( ~ finite(X111)
| ~ finite(X112)
| finite(cartesian_product2(X111,X112)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])]) ).
fof(i_0_87,plain,
! [X100,X101] :
( ~ finite(X100)
| ~ element(X101,powerset(X100))
| finite(X101) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_finset_1])])]) ).
fof(i_0_88,plain,
! [X156,X157] :
( ~ element(X156,X157)
| empty(X157)
| in(X156,X157) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_89,plain,
! [X151,X152] :
( ~ in(X151,X152)
| element(X151,X152) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_90,plain,
! [X90,X91] :
( ( epsilon_transitive(X91)
| ~ element(X91,X90)
| ~ ordinal(X90) )
& ( epsilon_connected(X91)
| ~ element(X91,X90)
| ~ ordinal(X90) )
& ( ordinal(X91)
| ~ element(X91,X90)
| ~ ordinal(X90) ) ),
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_91,plain,
! [X105] :
( ( epsilon_transitive(X105)
| ~ ordinal(X105)
| ~ element(X105,positive_rationals) )
& ( epsilon_connected(X105)
| ~ ordinal(X105)
| ~ element(X105,positive_rationals) )
& ( ordinal(X105)
| ~ ordinal(X105)
| ~ element(X105,positive_rationals) )
& ( natural(X105)
| ~ ordinal(X105)
| ~ element(X105,positive_rationals) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc4_arytm_3])])]) ).
fof(i_0_92,plain,
! [X140] :
( ( element(esk20_1(X140),powerset(X140))
| empty(X140) )
& ( ~ empty(esk20_1(X140))
| empty(X140) )
& ( finite(esk20_1(X140))
| empty(X140) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_67])])])]) ).
fof(i_0_93,plain,
! [X126] :
( ( element(esk9_1(X126),powerset(X126))
| empty(X126) )
& ( ~ empty(esk9_1(X126))
| empty(X126) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_68])])])]) ).
fof(i_0_94,plain,
! [X167,X168] :
( ~ in(X167,X168)
| ~ empty(X168) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_95,plain,
! [X136] :
( element(esk17_1(X136),powerset(X136))
& empty(esk17_1(X136)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(i_0_96,plain,
! [X130] :
( element(esk12_1(X130),powerset(X130))
& empty(esk12_1(X130))
& relation(esk12_1(X130))
& function(esk12_1(X130))
& one_to_one(esk12_1(X130))
& epsilon_transitive(esk12_1(X130))
& epsilon_connected(esk12_1(X130))
& ordinal(esk12_1(X130))
& natural(esk12_1(X130))
& finite(esk12_1(X130)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_finset_1])]) ).
fof(i_0_97,plain,
! [X102] :
( ( relation(X102)
| ~ relation(X102)
| ~ empty(X102)
| ~ function(X102) )
& ( function(X102)
| ~ relation(X102)
| ~ empty(X102)
| ~ function(X102) )
& ( one_to_one(X102)
| ~ relation(X102)
| ~ empty(X102)
| ~ function(X102) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_98,plain,
! [X109] : element(esk1_1(X109),X109),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_99,plain,
! [X99] :
( ( epsilon_transitive(X99)
| ~ empty(X99)
| ~ ordinal(X99) )
& ( epsilon_connected(X99)
| ~ empty(X99)
| ~ ordinal(X99) )
& ( ordinal(X99)
| ~ empty(X99)
| ~ ordinal(X99) )
& ( natural(X99)
| ~ empty(X99)
| ~ ordinal(X99) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_arytm_3])])]) ).
fof(i_0_100,plain,
! [X103] :
( ~ epsilon_transitive(X103)
| ~ epsilon_connected(X103)
| ordinal(X103) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_101,plain,
! [X113] : ~ empty(powerset(X113)),
inference(variable_rename,[status(thm)],[i_0_69]) ).
fof(i_0_102,plain,
! [X169,X170] :
( ~ empty(X169)
| X169 = X170
| ~ empty(X170) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_103,plain,
! [X148] : subset(X148,X148),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_104,plain,
! [X95] :
( ~ empty(X95)
| relation(X95) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_105,plain,
! [X93] :
( ~ empty(X93)
| function(X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_106,plain,
! [X92] :
( ~ empty(X92)
| finite(X92) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_finset_1])]) ).
fof(i_0_107,plain,
! [X104] :
( ( epsilon_transitive(X104)
| ~ empty(X104) )
& ( epsilon_connected(X104)
| ~ empty(X104) )
& ( ordinal(X104)
| ~ empty(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
fof(i_0_108,plain,
! [X94] :
( ( epsilon_transitive(X94)
| ~ ordinal(X94) )
& ( epsilon_connected(X94)
| ~ ordinal(X94) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_109,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_110,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_70])]) ).
fof(i_0_111,plain,
! [X166] :
( ~ empty(X166)
| X166 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_112,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_71])]) ).
fof(i_0_113,plain,
~ empty(esk18_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_72])]) ).
fof(i_0_114,plain,
( ~ empty(esk16_0)
& relation(esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_73])]) ).
fof(i_0_115,plain,
( ~ empty(esk3_0)
& finite(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_74])]) ).
fof(i_0_116,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_75])]) ).
fof(i_0_117,plain,
~ empty(positive_rationals),
inference(fof_simplification,[status(thm)],[fc8_arytm_3]) ).
fof(i_0_118,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_119,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_120,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_121,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_122,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_123,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_124,plain,
( relation(esk23_0)
& relation_empty_yielding(esk23_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_125,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_126,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_127,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_128,plain,
( empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_129,plain,
( relation(esk5_0)
& function(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_130,plain,
empty(esk10_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(i_0_131,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_132,plain,
( empty(X3)
| empty(X2)
| empty(X1)
| ~ empty(cartesian_product2(cartesian_product2(X1,X2),X3)) ),
inference(rw,[status(thm)],[i_0_76,c_0_77]),
[final] ).
cnf(i_0_133,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[i_0_78]),
[final] ).
cnf(i_0_134,negated_conjecture,
~ finite(cartesian_product2(cartesian_product2(esk27_0,esk28_0),esk29_0)),
inference(rw,[status(thm)],[i_0_79,c_0_77]),
[final] ).
cnf(i_0_135,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_80]),
[final] ).
cnf(i_0_136,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_81]),
[final] ).
cnf(i_0_137,plain,
( empty(X1)
| empty(X2)
| ~ empty(cartesian_product2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[i_0_82]),
[final] ).
cnf(i_0_138,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_139,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_84]),
[final] ).
cnf(i_0_140,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_85]),
[final] ).
cnf(i_0_141,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[i_0_86]),
[final] ).
cnf(i_0_142,plain,
( finite(X2)
| ~ finite(X1)
| ~ element(X2,powerset(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_87]),
[final] ).
cnf(i_0_143,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_83]),
[final] ).
cnf(i_0_144,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_88]),
[final] ).
cnf(i_0_145,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_89]),
[final] ).
cnf(i_0_146,plain,
( epsilon_connected(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_147,plain,
( epsilon_transitive(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_148,plain,
( ordinal(X1)
| ~ element(X1,X2)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_90]),
[final] ).
cnf(i_0_149,plain,
( natural(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_150,plain,
( epsilon_connected(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_151,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1)
| ~ element(X1,positive_rationals) ),
inference(split_conjunct,[status(thm)],[i_0_91]),
[final] ).
cnf(i_0_152,plain,
( element(esk20_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_153,plain,
( element(esk9_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_154,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_94]),
[final] ).
cnf(i_0_155,plain,
element(esk17_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_156,plain,
element(esk12_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_157,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_97]),
[final] ).
cnf(i_0_158,plain,
( empty(X1)
| ~ empty(esk20_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_159,plain,
( empty(X1)
| ~ empty(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[i_0_93]),
[final] ).
cnf(i_0_160,plain,
element(esk1_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_98]),
[final] ).
cnf(i_0_161,plain,
( natural(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_162,plain,
( epsilon_connected(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_163,plain,
( epsilon_transitive(X1)
| ~ empty(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_99]),
[final] ).
cnf(i_0_164,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_100]),
[final] ).
cnf(i_0_165,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[i_0_101]),
[final] ).
cnf(i_0_166,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_102]),
[final] ).
cnf(i_0_167,plain,
( finite(esk20_1(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_92]),
[final] ).
cnf(i_0_168,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_103]),
[final] ).
cnf(i_0_169,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_104]),
[final] ).
cnf(i_0_170,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_105]),
[final] ).
cnf(i_0_171,plain,
( finite(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_106]),
[final] ).
cnf(i_0_172,plain,
( epsilon_connected(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_173,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_174,plain,
( epsilon_transitive(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_175,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_108]),
[final] ).
cnf(i_0_176,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_107]),
[final] ).
cnf(i_0_177,plain,
element(esk19_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_178,plain,
element(esk11_0,positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_179,plain,
one_to_one(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_180,plain,
natural(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_181,plain,
relation(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_182,plain,
function(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_183,plain,
finite(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_184,plain,
empty(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_95]),
[final] ).
cnf(i_0_185,plain,
empty(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_186,plain,
epsilon_connected(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_187,plain,
epsilon_transitive(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_188,plain,
ordinal(esk12_1(X1)),
inference(split_conjunct,[status(thm)],[i_0_96]),
[final] ).
cnf(i_0_189,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_111]),
[final] ).
cnf(i_0_190,plain,
~ empty(esk22_0),
inference(split_conjunct,[status(thm)],[i_0_112]),
[final] ).
cnf(i_0_191,plain,
~ empty(esk18_0),
inference(split_conjunct,[status(thm)],[i_0_113]),
[final] ).
cnf(i_0_192,plain,
~ empty(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_193,plain,
~ empty(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_194,plain,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_195,plain,
~ empty(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_196,plain,
~ empty(positive_rationals),
inference(split_conjunct,[status(thm)],[i_0_117]),
[final] ).
cnf(i_0_197,plain,
relation_non_empty(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_198,plain,
ordinal_yielding(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_199,plain,
transfinite_sequence(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_200,plain,
transfinite_sequence(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_201,plain,
being_limit_ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_202,plain,
function_yielding(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_203,plain,
relation_empty_yielding(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_204,plain,
relation_empty_yielding(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_205,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_206,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_207,plain,
one_to_one(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_208,plain,
one_to_one(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_209,plain,
one_to_one(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_210,plain,
natural(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_211,plain,
natural(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[final] ).
cnf(i_0_212,plain,
relation(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_213,plain,
relation(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_214,plain,
relation(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_215,plain,
relation(esk23_0),
inference(split_conjunct,[status(thm)],[i_0_124]),
[final] ).
cnf(i_0_216,plain,
relation(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_217,plain,
relation(esk16_0),
inference(split_conjunct,[status(thm)],[i_0_114]),
[final] ).
cnf(i_0_218,plain,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_219,plain,
relation(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_220,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_221,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[final] ).
cnf(i_0_222,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_223,plain,
relation(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_224,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_225,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_226,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_227,plain,
function(esk26_0),
inference(split_conjunct,[status(thm)],[i_0_118]),
[final] ).
cnf(i_0_228,plain,
function(esk25_0),
inference(split_conjunct,[status(thm)],[i_0_120]),
[final] ).
cnf(i_0_229,plain,
function(esk24_0),
inference(split_conjunct,[status(thm)],[i_0_123]),
[final] ).
cnf(i_0_230,plain,
function(esk21_0),
inference(split_conjunct,[status(thm)],[i_0_125]),
[final] ).
cnf(i_0_231,plain,
function(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_119]),
[final] ).
cnf(i_0_232,plain,
function(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_233,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_234,plain,
function(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_129]),
[final] ).
cnf(i_0_235,plain,
function(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_122]),
[final] ).
cnf(i_0_236,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]),
[final] ).
cnf(i_0_237,negated_conjecture,
finite(esk29_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_238,negated_conjecture,
finite(esk28_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_239,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_240,plain,
finite(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_115]),
[final] ).
cnf(i_0_241,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_242,plain,
empty(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_243,plain,
empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_127]),
[final] ).
cnf(i_0_244,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_130]),
[final] ).
cnf(i_0_245,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_128]),
[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_112]),
[final] ).
cnf(i_0_251,plain,
epsilon_connected(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_252,plain,
epsilon_connected(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_253,plain,
epsilon_connected(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_254,plain,
epsilon_connected(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_255,plain,
epsilon_connected(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_256,plain,
epsilon_connected(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[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_112]),
[final] ).
cnf(i_0_259,plain,
epsilon_transitive(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_260,plain,
epsilon_transitive(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_261,plain,
epsilon_transitive(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_262,plain,
epsilon_transitive(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_263,plain,
epsilon_transitive(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_264,plain,
epsilon_transitive(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[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_112]),
[final] ).
cnf(i_0_267,plain,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[i_0_109]),
[final] ).
cnf(i_0_268,plain,
ordinal(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_126]),
[final] ).
cnf(i_0_269,plain,
ordinal(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_110]),
[final] ).
cnf(i_0_270,plain,
ordinal(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_121]),
[final] ).
cnf(i_0_271,plain,
ordinal(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_131]),
[final] ).
cnf(i_0_272,plain,
ordinal(esk2_0),
inference(split_conjunct,[status(thm)],[i_0_116]),
[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
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_278,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_279,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_280,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_281,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_282,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_283,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_284,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_285,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_286,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_287,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_288,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_289,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_290,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_291,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_292,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,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
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_296,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_297,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
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_278_005,axiom,
( X1 != X2
| ~ natural(X1)
| natural(X2) ) ).
cnf(i_0_279_006,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_280_007,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_281_008,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_282_009,axiom,
( X1 != X2
| ~ ordinal_yielding(X1)
| ordinal_yielding(X2) ) ).
cnf(i_0_283_010,axiom,
( X1 != X2
| ~ transfinite_sequence(X1)
| transfinite_sequence(X2) ) ).
cnf(i_0_284_011,axiom,
( X1 != X2
| ~ being_limit_ordinal(X1)
| being_limit_ordinal(X2) ) ).
cnf(i_0_285_012,axiom,
( X1 != X2
| ~ function_yielding(X1)
| function_yielding(X2) ) ).
cnf(i_0_286_013,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_287_014,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_288_015,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_289_016,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_290_017,axiom,
( X1 != X2
| ~ finite(X1)
| finite(X2) ) ).
cnf(i_0_291_018,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_292_019,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,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
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_296_023,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_297_024,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_298,plain,
finite(esk19_0),
inference(scs_inference,[],[i_0_241,i_0_171]) ).
cnf(i_0_299,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_300,plain,
relation(esk17_1(cartesian_product2(X1,X2))),
inference(scs_inference,[],[i_0_155,i_0_241,i_0_171,i_0_133]) ).
cnf(i_0_301,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_302,plain,
( ~ element(X1,powerset(cartesian_product2(X2,X3)))
| relation(X1) ),
inference(rename_variables,[],[i_0_133]) ).
cnf(i_0_303,plain,
subset(esk17_1(X1),X1),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_171,i_0_133,i_0_138]) ).
cnf(i_0_304,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_138]) ).
cnf(i_0_305,plain,
~ in(X1,esk19_0),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_171,i_0_133,i_0_138,i_0_154]) ).
cnf(i_0_306,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_154]) ).
cnf(i_0_307,plain,
relation(esk19_0),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169]) ).
cnf(i_0_308,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_309,plain,
function(esk19_0),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170]) ).
cnf(i_0_310,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_311,plain,
epsilon_connected(esk13_0),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_243,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172]) ).
cnf(i_0_312,plain,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_313,plain,
epsilon_transitive(esk13_0),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_243,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174]) ).
cnf(i_0_314,plain,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_315,plain,
ordinal(esk13_0),
inference(scs_inference,[],[i_0_155,i_0_301,i_0_241,i_0_243,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176]) ).
cnf(i_0_316,plain,
( ~ empty(X1)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_317,plain,
esk29_0 != cartesian_product2(cartesian_product2(esk27_0,esk28_0),esk29_0),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_241,i_0_243,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290]) ).
cnf(i_0_318,plain,
~ finite(cartesian_product2(esk27_0,esk28_0)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_241,i_0_243,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141]) ).
cnf(i_0_319,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(rename_variables,[],[i_0_141]) ).
cnf(i_0_320,plain,
finite(esk17_1(esk29_0)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_241,i_0_243,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142]) ).
cnf(i_0_321,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_322,plain,
( ~ element(X1,powerset(X2))
| finite(X1)
| ~ finite(X2) ),
inference(rename_variables,[],[i_0_142]) ).
cnf(i_0_323,plain,
in(esk17_1(X1),powerset(X1)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_241,i_0_243,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144]) ).
cnf(i_0_324,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_325,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_144]) ).
cnf(i_0_326,plain,
esk19_0 != esk22_0,
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_241,i_0_243,i_0_190,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277]) ).
cnf(i_0_327,plain,
powerset(X1) != esk19_0,
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_241,i_0_243,i_0_190,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292]) ).
cnf(i_0_328,plain,
~ in(X1,esk17_1(esk19_0)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_241,i_0_243,i_0_190,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136]) ).
cnf(i_0_329,plain,
element(esk17_1(X1),powerset(X1)),
inference(rename_variables,[],[i_0_155]) ).
cnf(i_0_330,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_136]) ).
cnf(i_0_331,plain,
epsilon_connected(esk1_1(esk22_0)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_241,i_0_243,i_0_190,i_0_266,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146]) ).
cnf(i_0_332,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_333,plain,
( ~ ordinal(X1)
| epsilon_connected(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_146]) ).
cnf(i_0_334,plain,
epsilon_transitive(esk1_1(esk22_0)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_332,i_0_241,i_0_243,i_0_190,i_0_266,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147]) ).
cnf(i_0_335,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_336,plain,
( ~ ordinal(X1)
| epsilon_transitive(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_147]) ).
cnf(i_0_337,plain,
ordinal(esk1_1(esk22_0)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_332,i_0_335,i_0_241,i_0_243,i_0_190,i_0_266,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148]) ).
cnf(i_0_338,plain,
element(esk1_1(X1),X1),
inference(rename_variables,[],[i_0_160]) ).
cnf(i_0_339,plain,
( ~ ordinal(X1)
| ordinal(X2)
| ~ element(X2,X1) ),
inference(rename_variables,[],[i_0_148]) ).
cnf(i_0_340,plain,
natural(esk11_0),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_332,i_0_335,i_0_241,i_0_243,i_0_178,i_0_190,i_0_266,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149]) ).
cnf(i_0_341,plain,
( ~ element(X1,positive_rationals)
| ~ ordinal(X1)
| natural(X1) ),
inference(rename_variables,[],[i_0_149]) ).
cnf(i_0_342,plain,
natural(esk14_0),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161]) ).
cnf(i_0_343,plain,
( ~ empty(X1)
| ~ ordinal(X1)
| natural(X1) ),
inference(rename_variables,[],[i_0_161]) ).
cnf(i_0_344,plain,
one_to_one(esk13_0),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_220,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157]) ).
cnf(i_0_345,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_157]) ).
cnf(i_0_346,plain,
~ in(powerset(X1),esk17_1(X1)),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_220,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139]) ).
cnf(i_0_347,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_139]) ).
cnf(i_0_348,plain,
( element(X1,X2)
| ~ in(X1,esk17_1(X2)) ),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_329,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_220,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139,i_0_135]) ).
cnf(i_0_349,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_135]) ).
cnf(i_0_350,plain,
( natural(X1)
| esk19_0 != X1 ),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_329,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_210,i_0_220,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139,i_0_135,i_0_278]) ).
cnf(i_0_351,plain,
( one_to_one(X1)
| esk21_0 != X1 ),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_329,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_207,i_0_210,i_0_220,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139,i_0_135,i_0_278,i_0_279]) ).
cnf(i_0_352,plain,
( function(X1)
| esk26_0 != X1 ),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_329,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_207,i_0_210,i_0_220,i_0_227,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139,i_0_135,i_0_278,i_0_279,i_0_280]) ).
cnf(i_0_353,plain,
( relation_non_empty(X1)
| esk26_0 != X1 ),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_329,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_197,i_0_207,i_0_210,i_0_220,i_0_227,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139,i_0_135,i_0_278,i_0_279,i_0_280,i_0_281]) ).
cnf(i_0_354,plain,
( ordinal_yielding(X1)
| esk15_0 != X1 ),
inference(scs_inference,[],[i_0_134,i_0_237,i_0_155,i_0_301,i_0_321,i_0_324,i_0_329,i_0_160,i_0_332,i_0_335,i_0_241,i_0_242,i_0_243,i_0_178,i_0_190,i_0_197,i_0_198,i_0_207,i_0_210,i_0_220,i_0_227,i_0_233,i_0_266,i_0_268,i_0_269,i_0_165,i_0_171,i_0_133,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_290,i_0_141,i_0_142,i_0_144,i_0_277,i_0_292,i_0_136,i_0_146,i_0_147,i_0_148,i_0_149,i_0_161,i_0_157,i_0_139,i_0_135,i_0_278,i_0_279,i_0_280,i_0_281,i_0_282]) ).
cnf(i_0_355,plain,
natural(esk19_0),
inference(equality_inference,[],[350]) ).
cnf(i_0_356,plain,
one_to_one(esk21_0),
inference(equality_inference,[],[351]) ).
cnf(i_0_357,plain,
function(esk26_0),
inference(equality_inference,[],[352]) ).
cnf(i_0_358,plain,
relation_non_empty(esk26_0),
inference(equality_inference,[],[353]) ).
cnf(i_0_359,plain,
ordinal_yielding(esk15_0),
inference(equality_inference,[],[354]) ).
cnf(i_0_360,plain,
finite(esk10_0),
inference(scs_inference,[],[i_0_244,i_0_171]) ).
cnf(i_0_361,plain,
( ~ empty(X1)
| finite(X1) ),
inference(rename_variables,[],[i_0_171]) ).
cnf(i_0_362,plain,
subset(esk12_1(X1),X1),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138]) ).
cnf(i_0_363,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_138]) ).
cnf(i_0_364,plain,
~ in(X1,esk10_0),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138,i_0_154]) ).
cnf(i_0_365,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_154]) ).
cnf(i_0_366,plain,
relation(esk10_0),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138,i_0_154,i_0_169]) ).
cnf(i_0_367,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_169]) ).
cnf(i_0_368,plain,
function(esk10_0),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138,i_0_154,i_0_169,i_0_170]) ).
cnf(i_0_369,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_170]) ).
cnf(i_0_370,plain,
epsilon_connected(esk10_0),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172]) ).
cnf(i_0_371,plain,
( ~ empty(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_172]) ).
cnf(i_0_372,plain,
epsilon_transitive(esk10_0),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174]) ).
cnf(i_0_373,plain,
( ~ empty(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_374,plain,
ordinal(esk10_0),
inference(scs_inference,[],[i_0_156,i_0_244,i_0_171,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176]) ).
cnf(i_0_375,plain,
( ~ empty(X1)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_176]) ).
cnf(i_0_376,plain,
$false,
inference(scs_inference,[],[i_0_238,i_0_239,i_0_318,i_0_156,i_0_244,i_0_171,i_0_138,i_0_154,i_0_169,i_0_170,i_0_172,i_0_174,i_0_176,i_0_141]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU089+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
% 0.16/0.33 % Computer : n005.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:43:00 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.31/1.62 % Version : CSE_E---1.7
% 0.31/1.62 % Problem : theBenchmark.p
% 0.31/1.62 % SZS status Theorem for theBenchmark.p
% 0.31/1.62 % SZS output start CNFRefutation
% See solution above
% 0.61/1.94 % Total time : 1.272s
%------------------------------------------------------------------------------