%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM394+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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:14 PM UTC 2026
% Result : Theorem 0.29s 1.62s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named 187)
% Comments :
%------------------------------------------------------------------------------
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(t26_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ordinal_subset(X1,X2)
| in(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_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(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(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(reflexivity_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ordinal_subset(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_ordinal1) ).
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_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_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(cc1_funct_1,axiom,
! [X1] :
( empty(X1)
=> function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
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(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_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_ordinal1,axiom,
? [X1] :
( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_ordinal1) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(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_36,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
fof(i_0_37,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
fof(i_0_38,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ( ordinal_subset(X1,X2)
| in(X2,X1) ) ) ),
inference(assume_negation,[status(cth)],[t26_ordinal1]) ).
fof(i_0_39,plain,
? [X1] : ~ empty(X1),
inference(fof_simplification,[status(thm)],[rc2_xboole_0]) ).
fof(i_0_40,plain,
? [X1] :
( ~ empty(X1)
& relation(X1) ),
inference(fof_simplification,[status(thm)],[rc2_relat_1]) ).
fof(i_0_41,plain,
! [X96,X97,X98] :
( ~ in(X96,X97)
| ~ element(X97,powerset(X98))
| element(X96,X98) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(i_0_42,plain,
! [X99,X100,X101] :
( ~ in(X99,X100)
| ~ element(X100,powerset(X101))
| ~ empty(X101) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
fof(i_0_43,plain,
! [X81,X82] :
( ( ~ ordinal_subset(X81,X82)
| subset(X81,X82)
| ~ ordinal(X81)
| ~ ordinal(X82) )
& ( ~ subset(X81,X82)
| ordinal_subset(X81,X82)
| ~ ordinal(X81)
| ~ ordinal(X82) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
fof(i_0_44,plain,
! [X94,X95] :
( ( ~ element(X94,powerset(X95))
| subset(X94,X95) )
& ( ~ subset(X94,X95)
| element(X94,powerset(X95)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(i_0_45,plain,
! [X88,X89] :
( ~ ordinal(X88)
| ~ ordinal(X89)
| in(X88,X89)
| X88 = X89
| in(X89,X88) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_36])])]) ).
fof(i_0_46,plain,
! [X55,X56] :
( ~ in(X55,X56)
| ~ in(X56,X55) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_37])]) ).
fof(i_0_47,plain,
! [X64,X65,X66] :
( ( ~ epsilon_transitive(X64)
| ~ in(X65,X64)
| subset(X65,X64) )
& ( in(esk1_1(X66),X66)
| epsilon_transitive(X66) )
& ( ~ subset(esk1_1(X66),X66)
| epsilon_transitive(X66) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_ordinal1])])])])])]) ).
fof(i_0_48,plain,
! [X62,X63] :
( ~ ordinal(X62)
| ~ ordinal(X63)
| ordinal_subset(X62,X63)
| ordinal_subset(X63,X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(i_0_49,plain,
! [X92,X93] :
( ~ element(X92,X93)
| empty(X93)
| in(X92,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(i_0_50,plain,
! [X86,X87] :
( ~ in(X86,X87)
| element(X86,X87) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(i_0_51,plain,
! [X103,X104] :
( ~ in(X103,X104)
| ~ empty(X104) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(i_0_52,plain,
! [X83,X84] :
( ~ ordinal(X83)
| ~ ordinal(X84)
| ordinal_subset(X83,X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[reflexivity_r1_ordinal1])]) ).
fof(i_0_53,plain,
! [X60] :
( ( relation(X60)
| ~ relation(X60)
| ~ empty(X60)
| ~ function(X60) )
& ( function(X60)
| ~ relation(X60)
| ~ empty(X60)
| ~ function(X60) )
& ( one_to_one(X60)
| ~ relation(X60)
| ~ empty(X60)
| ~ function(X60) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_funct_1])])]) ).
fof(i_0_54,plain,
! [X68] : element(esk2_1(X68),X68),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(i_0_55,plain,
! [X61] :
( ~ epsilon_transitive(X61)
| ~ epsilon_connected(X61)
| ordinal(X61) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc2_ordinal1])]) ).
fof(i_0_56,negated_conjecture,
( ordinal(esk14_0)
& ordinal(esk15_0)
& ~ ordinal_subset(esk14_0,esk15_0)
& ~ in(esk15_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_38])])]) ).
fof(i_0_57,plain,
! [X105,X106] :
( ~ empty(X105)
| X105 = X106
| ~ empty(X106) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(i_0_58,plain,
! [X85] : subset(X85,X85),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
fof(i_0_59,plain,
! [X59] :
( ~ empty(X59)
| relation(X59) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relat_1])]) ).
fof(i_0_60,plain,
! [X58] :
( ( epsilon_transitive(X58)
| ~ ordinal(X58) )
& ( epsilon_connected(X58)
| ~ ordinal(X58) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(i_0_61,plain,
! [X57] :
( ~ empty(X57)
| function(X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_funct_1])]) ).
fof(i_0_62,plain,
! [X102] :
( ~ empty(X102)
| X102 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(i_0_63,plain,
~ empty(esk9_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_39])]) ).
fof(i_0_64,plain,
( ~ empty(esk8_0)
& relation(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[i_0_40])]) ).
fof(i_0_65,plain,
( relation(esk13_0)
& relation_non_empty(esk13_0)
& function(esk13_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc5_funct_1])]) ).
fof(i_0_66,plain,
( relation(esk12_0)
& relation_empty_yielding(esk12_0)
& function(esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc4_funct_1])]) ).
fof(i_0_67,plain,
( relation(esk11_0)
& relation_empty_yielding(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_relat_1])]) ).
fof(i_0_68,plain,
( relation(esk10_0)
& function(esk10_0)
& one_to_one(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc3_funct_1])]) ).
fof(i_0_69,plain,
( relation(esk7_0)
& empty(esk7_0)
& function(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(i_0_70,plain,
( empty(esk5_0)
& relation(esk5_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_relat_1])]) ).
fof(i_0_71,plain,
( relation(esk3_0)
& function(esk3_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_1])]) ).
fof(i_0_72,plain,
( epsilon_transitive(esk4_0)
& epsilon_connected(esk4_0)
& ordinal(esk4_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_ordinal1])]) ).
fof(i_0_73,plain,
empty(esk6_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
cnf(i_0_74,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[i_0_41]),
[final] ).
cnf(i_0_75,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[i_0_42]),
[final] ).
cnf(i_0_76,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_77,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_43]),
[final] ).
cnf(i_0_78,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_79,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_45]),
[final] ).
cnf(i_0_80,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_46]),
[final] ).
cnf(i_0_81,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_82,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_48]),
[final] ).
cnf(i_0_83,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_44]),
[final] ).
cnf(i_0_84,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_49]),
[final] ).
cnf(i_0_85,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_50]),
[final] ).
cnf(i_0_86,plain,
( epsilon_transitive(X1)
| ~ subset(esk1_1(X1),X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_87,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_51]),
[final] ).
cnf(i_0_88,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[i_0_52]),
[final] ).
cnf(i_0_89,plain,
( one_to_one(X1)
| ~ relation(X1)
| ~ empty(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[i_0_53]),
[final] ).
cnf(i_0_90,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[i_0_47]),
[final] ).
cnf(i_0_91,plain,
element(esk2_1(X1),X1),
inference(split_conjunct,[status(thm)],[i_0_54]),
[final] ).
cnf(i_0_92,plain,
( ordinal(X1)
| ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1) ),
inference(split_conjunct,[status(thm)],[i_0_55]),
[final] ).
cnf(i_0_93,negated_conjecture,
~ ordinal_subset(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_94,negated_conjecture,
~ in(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_95,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[i_0_57]),
[final] ).
cnf(i_0_96,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_58]),
[final] ).
cnf(i_0_97,plain,
( relation(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_59]),
[final] ).
cnf(i_0_98,plain,
( epsilon_connected(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_99,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[i_0_60]),
[final] ).
cnf(i_0_100,plain,
( function(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_61]),
[final] ).
cnf(i_0_101,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[i_0_62]),
[final] ).
cnf(i_0_102,plain,
~ empty(esk9_0),
inference(split_conjunct,[status(thm)],[i_0_63]),
[final] ).
cnf(i_0_103,plain,
~ empty(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_104,plain,
relation_non_empty(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_105,plain,
relation_empty_yielding(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_106,plain,
relation_empty_yielding(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_107,plain,
relation_empty_yielding(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_108,plain,
one_to_one(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_109,plain,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_110,plain,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_111,plain,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[i_0_67]),
[final] ).
cnf(i_0_112,plain,
relation(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_113,plain,
relation(esk8_0),
inference(split_conjunct,[status(thm)],[i_0_64]),
[final] ).
cnf(i_0_114,plain,
relation(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_115,plain,
relation(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_116,plain,
relation(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_117,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_118,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_119,plain,
epsilon_connected(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_120,plain,
epsilon_transitive(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_121,negated_conjecture,
ordinal(esk15_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_122,negated_conjecture,
ordinal(esk14_0),
inference(split_conjunct,[status(thm)],[i_0_56]),
[final] ).
cnf(i_0_123,plain,
ordinal(esk4_0),
inference(split_conjunct,[status(thm)],[i_0_72]),
[final] ).
cnf(i_0_124,plain,
function(esk13_0),
inference(split_conjunct,[status(thm)],[i_0_65]),
[final] ).
cnf(i_0_125,plain,
function(esk12_0),
inference(split_conjunct,[status(thm)],[i_0_66]),
[final] ).
cnf(i_0_126,plain,
function(esk10_0),
inference(split_conjunct,[status(thm)],[i_0_68]),
[final] ).
cnf(i_0_127,plain,
function(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_128,plain,
function(esk3_0),
inference(split_conjunct,[status(thm)],[i_0_71]),
[final] ).
cnf(i_0_129,plain,
empty(esk7_0),
inference(split_conjunct,[status(thm)],[i_0_69]),
[final] ).
cnf(i_0_130,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[i_0_73]),
[final] ).
cnf(i_0_131,plain,
empty(esk5_0),
inference(split_conjunct,[status(thm)],[i_0_70]),
[final] ).
cnf(i_0_132,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc4_relat_1]),
[final] ).
cnf(i_0_133,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]),
[final] ).
cnf(i_0_134,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]),
[final] ).
cnf(i_0_135,axiom,
X1 = X1 ).
cnf(i_0_136,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_137,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_138,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_139,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_140,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_141,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_142,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_143,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_144,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_145,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_146,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_147,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_148,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_149,axiom,
( X1 != X2
| ~ ordinal_subset(X1,X3)
| ordinal_subset(X2,X3) ) ).
cnf(i_0_150,axiom,
( X1 != X2
| ~ ordinal_subset(X3,X1)
| ordinal_subset(X3,X2) ) ).
cnf(i_0_151,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_152,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_153,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_154,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_135_001,axiom,
X1 = X1 ).
cnf(i_0_136_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_137_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_138_004,axiom,
( X1 != X2
| ~ element(X1,X3)
| element(X2,X3) ) ).
cnf(i_0_139_005,axiom,
( X1 != X2
| ~ element(X3,X1)
| element(X3,X2) ) ).
cnf(i_0_140_006,axiom,
( X1 != X2
| ~ function(X1)
| function(X2) ) ).
cnf(i_0_141_007,axiom,
( X1 != X2
| ~ epsilon_connected(X1)
| epsilon_connected(X2) ) ).
cnf(i_0_142_008,axiom,
( X1 != X2
| ~ relation_non_empty(X1)
| relation_non_empty(X2) ) ).
cnf(i_0_143_009,axiom,
( X1 != X2
| ~ relation_empty_yielding(X1)
| relation_empty_yielding(X2) ) ).
cnf(i_0_144_010,axiom,
( X1 != X2
| ~ in(X1,X3)
| in(X2,X3) ) ).
cnf(i_0_145_011,axiom,
( X1 != X2
| ~ in(X3,X1)
| in(X3,X2) ) ).
cnf(i_0_146_012,axiom,
( X1 != X2
| ~ empty(X1)
| empty(X2) ) ).
cnf(i_0_147_013,axiom,
( X1 != X2
| ~ subset(X1,X3)
| subset(X2,X3) ) ).
cnf(i_0_148_014,axiom,
( X1 != X2
| ~ subset(X3,X1)
| subset(X3,X2) ) ).
cnf(i_0_149_015,axiom,
( X1 != X2
| ~ ordinal_subset(X1,X3)
| ordinal_subset(X2,X3) ) ).
cnf(i_0_150_016,axiom,
( X1 != X2
| ~ ordinal_subset(X3,X1)
| ordinal_subset(X3,X2) ) ).
cnf(i_0_151_017,axiom,
( X1 != X2
| ~ ordinal(X1)
| ordinal(X2) ) ).
cnf(i_0_152_018,axiom,
( X1 != X2
| ~ epsilon_transitive(X1)
| epsilon_transitive(X2) ) ).
cnf(i_0_153_019,axiom,
( X1 != X2
| ~ one_to_one(X1)
| one_to_one(X2) ) ).
cnf(i_0_154_020,axiom,
( X1 != X2
| ~ relation(X1)
| relation(X2) ) ).
cnf(i_0_155,plain,
( ~ ordinal(X1)
| ordinal_subset(X1,X1) ),
inference(scs_inference,[],[i_0_121,i_0_88]) ).
cnf(i_0_156,plain,
subset(esk2_1(powerset(X1)),X1),
inference(scs_inference,[],[i_0_91,i_0_78]) ).
cnf(i_0_157,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_158,plain,
( ~ element(X1,powerset(X2))
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_159,plain,
epsilon_connected(esk15_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_78,i_0_98]) ).
cnf(i_0_160,plain,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_161,plain,
epsilon_transitive(esk15_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_78,i_0_98,i_0_99]) ).
cnf(i_0_162,plain,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_99]) ).
cnf(i_0_163,plain,
~ in(X1,esk7_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_129,i_0_78,i_0_98,i_0_99,i_0_87]) ).
cnf(i_0_164,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_165,plain,
epsilon_transitive(esk7_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_129,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90]) ).
cnf(i_0_166,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_167,plain,
relation(esk6_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97]) ).
cnf(i_0_168,plain,
( ~ empty(X1)
| relation(X1) ),
inference(rename_variables,[],[i_0_97]) ).
cnf(i_0_169,plain,
function(esk6_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100]) ).
cnf(i_0_170,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_100]) ).
cnf(i_0_171,plain,
in(esk2_1(esk9_0),esk9_0),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_157,i_0_102,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84]) ).
cnf(i_0_172,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_173,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_174,plain,
~ in(X1,esk2_1(powerset(esk7_0))),
inference(scs_inference,[],[i_0_121,i_0_91,i_0_157,i_0_172,i_0_102,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75]) ).
cnf(i_0_175,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_176,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_177,plain,
esk7_0 != esk9_0,
inference(scs_inference,[],[i_0_121,i_0_91,i_0_157,i_0_172,i_0_102,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146]) ).
cnf(i_0_178,plain,
ordinal_subset(esk15_0,esk15_0),
inference(scs_inference,[],[i_0_121,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77]) ).
cnf(i_0_179,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_180,plain,
( ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X2) ),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_181,plain,
ordinal_subset(esk15_0,esk14_0),
inference(scs_inference,[],[i_0_93,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82]) ).
cnf(i_0_182,plain,
( ordinal_subset(X1,X2)
| ~ ordinal(X2)
| ~ ordinal(X1)
| ordinal_subset(X2,X1) ),
inference(rename_variables,[],[i_0_82]) ).
cnf(i_0_183,plain,
one_to_one(esk7_0),
inference(scs_inference,[],[i_0_93,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89]) ).
cnf(i_0_184,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_185,plain,
~ in(esk9_0,esk2_1(esk9_0)),
inference(scs_inference,[],[i_0_93,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80]) ).
cnf(i_0_186,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_187,plain,
( X1 != esk15_0
| ~ in(X1,esk14_0) ),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144]) ).
cnf(i_0_188,plain,
esk9_0 != esk2_1(powerset(esk7_0)),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145]) ).
cnf(i_0_189,plain,
esk15_0 != esk14_0,
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149]) ).
cnf(i_0_190,plain,
subset(esk15_0,esk14_0),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76]) ).
cnf(i_0_191,plain,
( ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| subset(X1,X2) ),
inference(rename_variables,[],[i_0_76]) ).
cnf(i_0_192,plain,
in(esk14_0,esk15_0),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79]) ).
cnf(i_0_193,plain,
( X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_79]) ).
cnf(i_0_194,plain,
element(esk14_0,esk15_0),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79,i_0_85]) ).
cnf(i_0_195,plain,
( ~ in(X1,X2)
| element(X1,X2) ),
inference(rename_variables,[],[i_0_85]) ).
cnf(i_0_196,plain,
( X1 != esk15_0
| ~ ordinal_subset(esk14_0,X1) ),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79,i_0_85,i_0_150]) ).
cnf(i_0_197,plain,
( ordinal(X1)
| esk15_0 != X1 ),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79,i_0_85,i_0_150,i_0_151]) ).
cnf(i_0_198,plain,
( element(X1,X2)
| ~ in(X1,esk2_1(powerset(X2))) ),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_175,i_0_102,i_0_114,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79,i_0_85,i_0_150,i_0_151,i_0_74]) ).
cnf(i_0_199,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_200,plain,
( ~ element(X1,powerset(X2))
| element(X3,X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_201,plain,
( ~ in(X1,esk4_0)
| subset(X1,esk4_0) ),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_175,i_0_102,i_0_114,i_0_120,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79,i_0_85,i_0_150,i_0_151,i_0_74,i_0_81]) ).
cnf(i_0_202,plain,
( ~ epsilon_transitive(X1)
| ~ in(X2,X1)
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_203,plain,
( ~ epsilon_connected(esk7_0)
| ordinal(esk7_0) ),
inference(scs_inference,[],[i_0_93,i_0_94,i_0_121,i_0_122,i_0_96,i_0_91,i_0_157,i_0_172,i_0_175,i_0_102,i_0_114,i_0_120,i_0_127,i_0_129,i_0_130,i_0_78,i_0_98,i_0_99,i_0_87,i_0_90,i_0_97,i_0_100,i_0_84,i_0_75,i_0_146,i_0_77,i_0_82,i_0_89,i_0_80,i_0_144,i_0_145,i_0_149,i_0_76,i_0_79,i_0_85,i_0_150,i_0_151,i_0_74,i_0_81,i_0_92]) ).
cnf(i_0_204,plain,
( ~ epsilon_transitive(X1)
| ~ epsilon_connected(X1)
| ordinal(X1) ),
inference(rename_variables,[],[i_0_92]) ).
cnf(i_0_205,plain,
~ in(esk15_0,esk14_0),
inference(equality_inference,[],[187]) ).
cnf(i_0_206,plain,
~ ordinal_subset(esk14_0,esk15_0),
inference(equality_inference,[],[196]) ).
cnf(i_0_207,plain,
ordinal(esk15_0),
inference(equality_inference,[],[197]) ).
cnf(i_0_208,plain,
epsilon_connected(esk14_0),
inference(scs_inference,[],[i_0_122,i_0_98]) ).
cnf(i_0_209,plain,
( ~ ordinal(X1)
| epsilon_connected(X1) ),
inference(rename_variables,[],[i_0_98]) ).
cnf(i_0_210,plain,
~ in(X1,esk5_0),
inference(scs_inference,[],[i_0_122,i_0_131,i_0_98,i_0_87]) ).
cnf(i_0_211,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_212,plain,
epsilon_transitive(esk5_0),
inference(scs_inference,[],[i_0_122,i_0_131,i_0_98,i_0_87,i_0_90]) ).
cnf(i_0_213,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_214,plain,
function(esk5_0),
inference(scs_inference,[],[i_0_122,i_0_131,i_0_98,i_0_87,i_0_90,i_0_100]) ).
cnf(i_0_215,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_100]) ).
cnf(i_0_216,plain,
epsilon_transitive(esk14_0),
inference(scs_inference,[],[i_0_122,i_0_131,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99]) ).
cnf(i_0_217,plain,
( ~ ordinal(X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_99]) ).
cnf(i_0_218,plain,
in(esk2_1(esk8_0),esk8_0),
inference(scs_inference,[],[i_0_122,i_0_103,i_0_131,i_0_91,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84]) ).
cnf(i_0_219,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_220,plain,
( ~ element(X1,X2)
| empty(X2)
| in(X1,X2) ),
inference(rename_variables,[],[i_0_84]) ).
cnf(i_0_221,plain,
~ in(X1,esk2_1(powerset(esk5_0))),
inference(scs_inference,[],[i_0_122,i_0_103,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75]) ).
cnf(i_0_222,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_223,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_224,plain,
subset(esk14_0,esk15_0),
inference(scs_inference,[],[i_0_122,i_0_161,i_0_192,i_0_103,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81]) ).
cnf(i_0_225,plain,
( ~ epsilon_transitive(X1)
| ~ in(X2,X1)
| subset(X2,X1) ),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_226,plain,
esk9_0 != esk7_0,
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_103,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145]) ).
cnf(i_0_227,plain,
~ in(X1,esk7_0),
inference(rename_variables,[],[i_0_163]) ).
cnf(i_0_228,plain,
esk5_0 != esk8_0,
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_103,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146]) ).
cnf(i_0_229,plain,
ordinal_subset(esk14_0,esk14_0),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77]) ).
cnf(i_0_230,plain,
subset(X1,X1),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_231,plain,
( ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2)
| ordinal_subset(X1,X2) ),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_232,plain,
one_to_one(esk5_0),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_115,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89]) ).
cnf(i_0_233,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_234,plain,
esk14_0 != esk15_0,
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_115,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196]) ).
cnf(i_0_235,plain,
~ in(esk8_0,esk2_1(esk8_0)),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_115,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80]) ).
cnf(i_0_236,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_80]) ).
cnf(i_0_237,plain,
( function(X1)
| esk13_0 != X1 ),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_115,i_0_124,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80,i_0_140]) ).
cnf(i_0_238,plain,
( epsilon_connected(X1)
| esk15_0 != X1 ),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_159,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_115,i_0_124,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80,i_0_140,i_0_141]) ).
cnf(i_0_239,plain,
( relation_non_empty(X1)
| esk13_0 != X1 ),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_159,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_104,i_0_115,i_0_124,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80,i_0_140,i_0_141,i_0_142]) ).
cnf(i_0_240,plain,
( relation_empty_yielding(X1)
| esk12_0 != X1 ),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_159,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_104,i_0_105,i_0_115,i_0_124,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80,i_0_140,i_0_141,i_0_142,i_0_143]) ).
cnf(i_0_241,plain,
( epsilon_transitive(X1)
| esk15_0 != X1 ),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_159,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_104,i_0_105,i_0_115,i_0_124,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80,i_0_140,i_0_141,i_0_142,i_0_143,i_0_152]) ).
cnf(i_0_242,plain,
( one_to_one(X1)
| esk10_0 != X1 ),
inference(scs_inference,[],[i_0_122,i_0_171,i_0_159,i_0_161,i_0_192,i_0_163,i_0_96,i_0_103,i_0_104,i_0_105,i_0_108,i_0_115,i_0_124,i_0_131,i_0_91,i_0_219,i_0_98,i_0_87,i_0_90,i_0_100,i_0_99,i_0_84,i_0_75,i_0_81,i_0_145,i_0_146,i_0_77,i_0_89,i_0_196,i_0_80,i_0_140,i_0_141,i_0_142,i_0_143,i_0_152,i_0_153]) ).
cnf(i_0_243,plain,
function(esk13_0),
inference(equality_inference,[],[237]) ).
cnf(i_0_244,plain,
epsilon_connected(esk15_0),
inference(equality_inference,[],[238]) ).
cnf(i_0_245,plain,
relation_non_empty(esk13_0),
inference(equality_inference,[],[239]) ).
cnf(i_0_246,plain,
relation_empty_yielding(esk12_0),
inference(equality_inference,[],[240]) ).
cnf(i_0_247,plain,
epsilon_transitive(esk15_0),
inference(equality_inference,[],[241]) ).
cnf(i_0_248,plain,
one_to_one(esk10_0),
inference(equality_inference,[],[242]) ).
cnf(i_0_249,plain,
~ in(X1,empty_set),
inference(scs_inference,[],[i_0_134,i_0_87]) ).
cnf(i_0_250,plain,
( ~ empty(X1)
| ~ in(X2,X1) ),
inference(rename_variables,[],[i_0_87]) ).
cnf(i_0_251,plain,
epsilon_transitive(empty_set),
inference(scs_inference,[],[i_0_134,i_0_87,i_0_90]) ).
cnf(i_0_252,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_253,plain,
function(empty_set),
inference(scs_inference,[],[i_0_134,i_0_87,i_0_90,i_0_100]) ).
cnf(i_0_254,plain,
( ~ empty(X1)
| function(X1) ),
inference(rename_variables,[],[i_0_100]) ).
cnf(i_0_255,plain,
~ in(X1,esk2_1(powerset(empty_set))),
inference(scs_inference,[],[i_0_134,i_0_91,i_0_87,i_0_90,i_0_100,i_0_75]) ).
cnf(i_0_256,plain,
element(esk2_1(X1),X1),
inference(rename_variables,[],[i_0_91]) ).
cnf(i_0_257,plain,
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X3,X1) ),
inference(rename_variables,[],[i_0_75]) ).
cnf(i_0_258,plain,
empty_set != esk9_0,
inference(scs_inference,[],[i_0_134,i_0_91,i_0_102,i_0_87,i_0_90,i_0_100,i_0_75,i_0_146]) ).
cnf(i_0_259,plain,
esk15_0 != esk2_1(powerset(esk7_0)),
inference(scs_inference,[],[i_0_192,i_0_174,i_0_134,i_0_91,i_0_102,i_0_87,i_0_90,i_0_100,i_0_75,i_0_146,i_0_145]) ).
cnf(i_0_260,plain,
~ in(X1,esk2_1(powerset(esk7_0))),
inference(rename_variables,[],[i_0_174]) ).
cnf(i_0_261,plain,
one_to_one(empty_set),
inference(scs_inference,[],[i_0_192,i_0_174,i_0_134,i_0_118,i_0_91,i_0_102,i_0_87,i_0_90,i_0_100,i_0_75,i_0_146,i_0_145,i_0_89]) ).
cnf(i_0_262,plain,
( ~ relation(X1)
| ~ empty(X1)
| ~ function(X1)
| one_to_one(X1) ),
inference(rename_variables,[],[i_0_89]) ).
cnf(i_0_263,plain,
$false,
inference(scs_inference,[],[i_0_93,i_0_122,i_0_121,i_0_192,i_0_174,i_0_224,i_0_134,i_0_118,i_0_91,i_0_102,i_0_87,i_0_90,i_0_100,i_0_75,i_0_146,i_0_145,i_0_89,i_0_77]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM394+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n020.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 00:31:05 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.29/1.62 % Version : CSE_E---1.7
% 0.29/1.62 % Problem : theBenchmark.p
% 0.29/1.62 % SZS status Theorem for theBenchmark.p
% 0.29/1.62 % SZS output start CNFRefutation
% See solution above
% 0.58/1.97 % Total time : 1.272s
%------------------------------------------------------------------------------