TSTP Solution File: SEU235+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n026.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 : Thu Aug 31 16:23:39 EDT 2023
% Result : Theorem 19.34s 19.40s
% Output : CNFRefutation 19.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 54
% Syntax : Number of formulae : 198 ( 17 unt; 32 typ; 0 def)
% Number of atoms : 472 ( 29 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 510 ( 204 ~; 232 |; 46 &)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 17 >; 5 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 15 con; 0-2 aty)
% Number of variables : 201 ( 5 sgn; 88 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
ordinal: $i > $o ).
tff(decl_26,type,
epsilon_transitive: $i > $o ).
tff(decl_27,type,
epsilon_connected: $i > $o ).
tff(decl_28,type,
relation: $i > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
esk1_1: $i > $i ).
tff(decl_37,type,
esk2_1: $i > $i ).
tff(decl_38,type,
esk3_0: $i ).
tff(decl_39,type,
esk4_0: $i ).
tff(decl_40,type,
esk5_0: $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_0: $i ).
tff(decl_43,type,
esk8_0: $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_0: $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
tff(decl_50,type,
esk15_0: $i ).
tff(decl_51,type,
esk16_0: $i ).
tff(decl_52,type,
esk17_1: $i > $i ).
tff(decl_53,type,
esk18_2: ( $i * $i ) > $i ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t32_ordinal1,conjecture,
! [X1,X2] :
( ordinal(X2)
=> ~ ( subset(X1,X2)
& X1 != empty_set
& ! [X3] :
( ordinal(X3)
=> ~ ( in(X3,X1)
& ! [X4] :
( ordinal(X4)
=> ( in(X4,X1)
=> ordinal_subset(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t32_ordinal1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(t7_tarski,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& ! [X3] :
~ ( in(X3,X2)
& ! [X4] :
~ ( in(X4,X2)
& in(X4,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_tarski) ).
fof(t4_subset,axiom,
! [X1,X2,X3] :
( ( in(X1,X2)
& element(X2,powerset(X3)) )
=> element(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(t24_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_ordinal1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(cc3_ordinal1,axiom,
! [X1] :
( empty(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1)
& ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc3_ordinal1) ).
fof(t23_ordinal1,axiom,
! [X1,X2] :
( ordinal(X2)
=> ( in(X1,X2)
=> ordinal(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(antisymmetry_r2_hidden,axiom,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(fc2_ordinal1,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(c_0_22,plain,
! [X44,X45] :
( ~ element(X44,X45)
| empty(X45)
| in(X44,X45) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_23,plain,
! [X19] : element(esk2_1(X19),X19),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
fof(c_0_24,plain,
! [X55,X56,X57] :
( ~ in(X55,X56)
| ~ element(X56,powerset(X57))
| ~ empty(X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_25,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
element(esk2_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_27,plain,
! [X50,X51] :
( ( ~ element(X50,powerset(X51))
| subset(X50,X51) )
& ( ~ subset(X50,X51)
| element(X50,powerset(X51)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_28,plain,
! [X37] : subset(X37,X37),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_29,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
( empty(X1)
| in(esk2_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,negated_conjecture,
~ ! [X1,X2] :
( ordinal(X2)
=> ~ ( subset(X1,X2)
& X1 != empty_set
& ! [X3] :
( ordinal(X3)
=> ~ ( in(X3,X1)
& ! [X4] :
( ordinal(X4)
=> ( in(X4,X1)
=> ordinal_subset(X3,X4) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[t32_ordinal1]) ).
fof(c_0_34,plain,
! [X58] :
( ~ empty(X58)
| X58 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
cnf(c_0_35,plain,
( empty(X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
fof(c_0_36,plain,
! [X61,X62,X64] :
( ( in(esk18_2(X61,X62),X62)
| ~ in(X61,X62) )
& ( ~ in(X64,X62)
| ~ in(X64,esk18_2(X61,X62))
| ~ in(X61,X62) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_tarski])])])])]) ).
cnf(c_0_37,plain,
element(X1,powerset(X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
fof(c_0_38,plain,
! [X52,X53,X54] :
( ~ in(X52,X53)
| ~ element(X53,powerset(X54))
| element(X52,X54) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t4_subset])]) ).
fof(c_0_39,negated_conjecture,
! [X48] :
( ordinal(esk16_0)
& subset(esk15_0,esk16_0)
& esk15_0 != empty_set
& ( ordinal(esk17_1(X48))
| ~ in(X48,esk15_0)
| ~ ordinal(X48) )
& ( in(esk17_1(X48),esk15_0)
| ~ in(X48,esk15_0)
| ~ ordinal(X48) )
& ( ~ ordinal_subset(X48,esk17_1(X48))
| ~ in(X48,esk15_0)
| ~ ordinal(X48) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])])]) ).
cnf(c_0_40,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( empty(esk2_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
fof(c_0_42,plain,
! [X38,X39] :
( ~ in(X38,X39)
| element(X38,X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_43,plain,
( in(esk18_2(X1,X2),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,plain,
( empty(powerset(X1))
| in(X1,powerset(X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_37]) ).
cnf(c_0_45,plain,
( element(X1,X3)
| ~ in(X1,X2)
| ~ element(X2,powerset(X3)) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_46,negated_conjecture,
subset(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_47,plain,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ in(X1,X2)
& X1 != X2
& ~ in(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[t24_ordinal1]) ).
cnf(c_0_48,plain,
( esk2_1(powerset(X1)) = empty_set
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_49,plain,
! [X59,X60] :
( ~ in(X59,X60)
| ~ empty(X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
cnf(c_0_50,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,plain,
( empty(powerset(X1))
| in(esk18_2(X1,powerset(X1)),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,plain,
( element(esk2_1(X1),X2)
| empty(X1)
| ~ element(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_53,negated_conjecture,
element(esk15_0,powerset(esk16_0)),
inference(spm,[status(thm)],[c_0_31,c_0_46]) ).
fof(c_0_54,plain,
! [X42,X43] :
( ~ ordinal(X42)
| ~ ordinal(X43)
| in(X42,X43)
| X42 = X43
| in(X43,X42) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
fof(c_0_55,plain,
! [X12] :
( ( epsilon_transitive(X12)
| ~ empty(X12) )
& ( epsilon_connected(X12)
| ~ empty(X12) )
& ( ordinal(X12)
| ~ empty(X12) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc3_ordinal1])])]) ).
cnf(c_0_56,plain,
( ~ in(X1,X2)
| ~ in(X1,esk18_2(X3,X2))
| ~ in(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_57,plain,
( empty(powerset(X1))
| in(empty_set,powerset(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_58,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_59,plain,
( element(esk18_2(X1,powerset(X1)),powerset(X1))
| empty(powerset(X1)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_60,plain,
! [X40,X41] :
( ~ ordinal(X41)
| ~ in(X40,X41)
| ordinal(X40) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_ordinal1])]) ).
cnf(c_0_61,negated_conjecture,
( element(esk2_1(esk15_0),esk16_0)
| empty(esk15_0) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_62,negated_conjecture,
( empty(esk15_0)
| ~ empty(esk16_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_53]) ).
fof(c_0_63,plain,
! [X1,X2] :
( in(X1,X2)
=> ~ in(X2,X1) ),
inference(fof_simplification,[status(thm)],[antisymmetry_r2_hidden]) ).
cnf(c_0_64,plain,
( in(X1,X2)
| X1 = X2
| in(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_65,plain,
( ordinal(X1)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
( ~ empty(X1)
| ~ in(X2,esk18_2(empty_set,powerset(X1)))
| ~ in(X2,powerset(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_67,plain,
( empty(esk18_2(X1,powerset(X1)))
| empty(powerset(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_59]) ).
fof(c_0_68,plain,
! [X15,X16,X17] :
( ( ~ epsilon_transitive(X15)
| ~ in(X16,X15)
| subset(X16,X15) )
& ( in(esk1_1(X17),X17)
| epsilon_transitive(X17) )
& ( ~ subset(esk1_1(X17),X17)
| epsilon_transitive(X17) ) ),
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])])])])])]) ).
cnf(c_0_69,negated_conjecture,
( in(esk17_1(X1),esk15_0)
| ~ in(X1,esk15_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_70,plain,
( ordinal(X2)
| ~ ordinal(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_71,negated_conjecture,
( empty(esk15_0)
| in(esk2_1(esk15_0),esk16_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_61]),c_0_62]) ).
cnf(c_0_72,negated_conjecture,
ordinal(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_73,negated_conjecture,
( ordinal(esk17_1(X1))
| ~ in(X1,esk15_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_74,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
fof(c_0_75,plain,
! [X65,X66] :
( ~ empty(X65)
| X65 = X66
| ~ empty(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_76,plain,
! [X5,X6] :
( ~ in(X5,X6)
| ~ in(X6,X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])]) ).
cnf(c_0_77,plain,
( X1 = X2
| in(X2,X1)
| ~ element(X2,powerset(X3))
| ~ ordinal(X2)
| ~ ordinal(X1)
| ~ empty(X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_64]) ).
cnf(c_0_78,plain,
( ordinal(esk2_1(powerset(X1)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_65,c_0_41]) ).
cnf(c_0_79,plain,
( empty(powerset(X1))
| ~ empty(X1)
| ~ in(esk2_1(powerset(X1)),esk18_2(empty_set,powerset(X1))) ),
inference(spm,[status(thm)],[c_0_66,c_0_30]) ).
cnf(c_0_80,plain,
( esk18_2(X1,powerset(X1)) = empty_set
| empty(powerset(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_81,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_82,plain,
( element(empty_set,powerset(X1))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_26,c_0_48]) ).
cnf(c_0_83,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]) ).
cnf(c_0_84,plain,
( in(esk1_1(X1),X1)
| epsilon_transitive(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_85,negated_conjecture,
( empty(esk15_0)
| in(esk17_1(esk2_1(esk15_0)),esk15_0)
| ~ ordinal(esk2_1(esk15_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_30]) ).
cnf(c_0_86,negated_conjecture,
( ordinal(esk2_1(esk15_0))
| empty(esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72])]) ).
cnf(c_0_87,negated_conjecture,
( ordinal(esk17_1(esk2_1(esk15_0)))
| empty(esk15_0)
| ~ ordinal(esk2_1(esk15_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_30]) ).
fof(c_0_88,plain,
! [X33,X34] :
( ( ~ ordinal_subset(X33,X34)
| subset(X33,X34)
| ~ ordinal(X33)
| ~ ordinal(X34) )
& ( ~ subset(X33,X34)
| ordinal_subset(X33,X34)
| ~ ordinal(X33)
| ~ ordinal(X34) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
fof(c_0_89,plain,
! [X13,X14] :
( ~ ordinal(X13)
| ~ ordinal(X14)
| ordinal_subset(X13,X14)
| ordinal_subset(X14,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
cnf(c_0_90,plain,
subset(esk2_1(powerset(X1)),X1),
inference(spm,[status(thm)],[c_0_74,c_0_26]) ).
cnf(c_0_91,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_92,plain,
( ~ in(X1,X2)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_93,plain,
( X1 = esk2_1(powerset(X2))
| in(esk2_1(powerset(X2)),X1)
| ~ ordinal(X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_26]),c_0_78]) ).
cnf(c_0_94,plain,
( empty(powerset(empty_set))
| ~ in(esk2_1(powerset(empty_set)),empty_set) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_95,plain,
( X1 = empty_set
| in(empty_set,X1)
| ~ ordinal(X1)
| ~ empty(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_82]),c_0_83])]) ).
cnf(c_0_96,negated_conjecture,
( ~ ordinal_subset(X1,esk17_1(X1))
| ~ in(X1,esk15_0)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_97,plain,
( epsilon_transitive(X1)
| in(esk18_2(esk1_1(X1),X1),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_84]) ).
cnf(c_0_98,negated_conjecture,
( empty(esk15_0)
| in(esk17_1(esk2_1(esk15_0)),esk15_0) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_99,negated_conjecture,
( ordinal(esk17_1(esk2_1(esk15_0)))
| empty(esk15_0) ),
inference(spm,[status(thm)],[c_0_87,c_0_86]) ).
cnf(c_0_100,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_101,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_102,plain,
( subset(X1,X2)
| ~ empty(esk2_1(powerset(X2)))
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_103,plain,
( X1 = esk2_1(powerset(X2))
| ~ ordinal(X1)
| ~ empty(X2)
| ~ in(X1,esk2_1(powerset(X2))) ),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_104,plain,
( esk2_1(powerset(empty_set)) = empty_set
| empty(powerset(empty_set)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_93]),c_0_83]),c_0_81])]) ).
cnf(c_0_105,plain,
( X1 = empty_set
| ~ ordinal(X1)
| ~ empty(X2)
| ~ in(X1,empty_set) ),
inference(spm,[status(thm)],[c_0_92,c_0_95]) ).
cnf(c_0_106,negated_conjecture,
( empty(esk15_0)
| ~ ordinal_subset(esk2_1(esk15_0),esk17_1(esk2_1(esk15_0)))
| ~ ordinal(esk2_1(esk15_0)) ),
inference(spm,[status(thm)],[c_0_96,c_0_30]) ).
cnf(c_0_107,plain,
( element(esk18_2(esk1_1(X1),X1),X2)
| epsilon_transitive(X1)
| ~ element(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_97]) ).
cnf(c_0_108,plain,
( epsilon_transitive(X1)
| ~ element(X1,powerset(X2))
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_84]) ).
cnf(c_0_109,negated_conjecture,
( empty(esk15_0)
| ~ ordinal_subset(esk17_1(esk2_1(esk15_0)),esk17_1(esk17_1(esk2_1(esk15_0)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_98]),c_0_99]) ).
cnf(c_0_110,plain,
( subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_111,negated_conjecture,
( ordinal(esk17_1(esk17_1(esk2_1(esk15_0))))
| empty(esk15_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_98]),c_0_99]) ).
cnf(c_0_112,plain,
( ordinal_subset(X1,X2)
| ~ subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_88]) ).
cnf(c_0_113,plain,
( subset(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_102,c_0_41]) ).
cnf(c_0_114,plain,
( X1 = empty_set
| ~ ordinal(X1)
| ~ in(X1,empty_set) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_81])]),c_0_105]) ).
cnf(c_0_115,negated_conjecture,
( empty(esk15_0)
| ~ ordinal_subset(esk2_1(esk15_0),esk17_1(esk2_1(esk15_0))) ),
inference(spm,[status(thm)],[c_0_106,c_0_86]) ).
cnf(c_0_116,negated_conjecture,
( element(esk18_2(esk1_1(esk15_0),esk15_0),esk16_0)
| epsilon_transitive(esk15_0) ),
inference(spm,[status(thm)],[c_0_107,c_0_53]) ).
cnf(c_0_117,negated_conjecture,
( epsilon_transitive(esk15_0)
| ~ empty(esk16_0) ),
inference(spm,[status(thm)],[c_0_108,c_0_53]) ).
cnf(c_0_118,negated_conjecture,
( subset(esk17_1(esk17_1(esk2_1(esk15_0))),esk17_1(esk2_1(esk15_0)))
| empty(esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_99]),c_0_111]) ).
cnf(c_0_119,plain,
( ordinal_subset(X1,X2)
| ~ empty(X1)
| ~ empty(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_65]),c_0_65]) ).
cnf(c_0_120,plain,
( X1 = empty_set
| in(empty_set,X1)
| ~ ordinal(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_64]),c_0_83])]) ).
cnf(c_0_121,negated_conjecture,
( subset(esk17_1(esk2_1(esk15_0)),esk2_1(esk15_0))
| empty(esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_110]),c_0_86]),c_0_99]) ).
fof(c_0_122,plain,
! [X8] :
( ( epsilon_transitive(X8)
| ~ ordinal(X8) )
& ( epsilon_connected(X8)
| ~ ordinal(X8) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
cnf(c_0_123,negated_conjecture,
( epsilon_transitive(esk15_0)
| in(esk18_2(esk1_1(esk15_0),esk15_0),esk16_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_116]),c_0_117]) ).
cnf(c_0_124,negated_conjecture,
( element(esk17_1(esk17_1(esk2_1(esk15_0))),powerset(esk17_1(esk2_1(esk15_0))))
| empty(esk15_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_118]) ).
cnf(c_0_125,negated_conjecture,
( empty(esk15_0)
| ~ empty(esk17_1(esk17_1(esk2_1(esk15_0))))
| ~ empty(esk17_1(esk2_1(esk15_0))) ),
inference(spm,[status(thm)],[c_0_109,c_0_119]) ).
cnf(c_0_126,plain,
( X1 = empty_set
| element(empty_set,X2)
| ~ element(X1,powerset(X2))
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_120]) ).
cnf(c_0_127,negated_conjecture,
( element(esk17_1(esk2_1(esk15_0)),powerset(esk2_1(esk15_0)))
| empty(esk15_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_121]) ).
cnf(c_0_128,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_129,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_130,negated_conjecture,
( epsilon_transitive(esk15_0)
| in(esk17_1(esk18_2(esk1_1(esk15_0),esk15_0)),esk15_0)
| ~ ordinal(esk18_2(esk1_1(esk15_0),esk15_0)) ),
inference(spm,[status(thm)],[c_0_69,c_0_97]) ).
cnf(c_0_131,negated_conjecture,
( epsilon_transitive(esk15_0)
| ordinal(esk18_2(esk1_1(esk15_0),esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_123]),c_0_72])]) ).
cnf(c_0_132,negated_conjecture,
( empty(esk15_0)
| ~ empty(esk17_1(esk2_1(esk15_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_124]),c_0_125]) ).
cnf(c_0_133,negated_conjecture,
( esk17_1(esk2_1(esk15_0)) = empty_set
| element(empty_set,esk2_1(esk15_0))
| empty(esk15_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_99]) ).
cnf(c_0_134,negated_conjecture,
( empty(esk15_0)
| ~ empty(esk17_1(esk2_1(esk15_0)))
| ~ empty(esk2_1(esk15_0)) ),
inference(spm,[status(thm)],[c_0_115,c_0_119]) ).
cnf(c_0_135,negated_conjecture,
( epsilon_transitive(esk15_0)
| ~ ordinal_subset(esk18_2(esk1_1(esk15_0),esk15_0),esk17_1(esk18_2(esk1_1(esk15_0),esk15_0)))
| ~ ordinal(esk18_2(esk1_1(esk15_0),esk15_0)) ),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_136,plain,
( X1 = X2
| subset(X1,X2)
| in(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_64]),c_0_129]) ).
cnf(c_0_137,negated_conjecture,
( epsilon_transitive(esk15_0)
| ordinal(esk17_1(esk18_2(esk1_1(esk15_0),esk15_0)))
| ~ ordinal(esk18_2(esk1_1(esk15_0),esk15_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_97]) ).
cnf(c_0_138,plain,
( epsilon_transitive(X1)
| ~ in(X2,esk18_2(esk1_1(X1),X1))
| ~ in(X2,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_84]) ).
cnf(c_0_139,negated_conjecture,
( epsilon_transitive(esk15_0)
| in(esk17_1(esk18_2(esk1_1(esk15_0),esk15_0)),esk15_0) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_140,negated_conjecture,
( element(empty_set,esk2_1(esk15_0))
| empty(esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_81])]) ).
cnf(c_0_141,negated_conjecture,
( empty(esk15_0)
| ~ empty(esk2_1(esk15_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_127]),c_0_134]) ).
cnf(c_0_142,negated_conjecture,
( epsilon_transitive(esk15_0)
| ~ ordinal_subset(esk18_2(esk1_1(esk15_0),esk15_0),esk17_1(esk18_2(esk1_1(esk15_0),esk15_0))) ),
inference(spm,[status(thm)],[c_0_135,c_0_131]) ).
cnf(c_0_143,plain,
( X1 = X2
| ordinal_subset(X1,X2)
| in(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_136]) ).
cnf(c_0_144,negated_conjecture,
( epsilon_transitive(esk15_0)
| ordinal(esk17_1(esk18_2(esk1_1(esk15_0),esk15_0))) ),
inference(spm,[status(thm)],[c_0_137,c_0_131]) ).
cnf(c_0_145,negated_conjecture,
( epsilon_transitive(esk15_0)
| ~ in(esk17_1(esk18_2(esk1_1(esk15_0),esk15_0)),esk18_2(esk1_1(esk15_0),esk15_0)) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_146,negated_conjecture,
( empty(esk15_0)
| in(empty_set,esk2_1(esk15_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_140]),c_0_141]) ).
cnf(c_0_147,plain,
( subset(esk2_1(X1),X1)
| empty(X1)
| ~ epsilon_transitive(X1) ),
inference(spm,[status(thm)],[c_0_128,c_0_30]) ).
cnf(c_0_148,negated_conjecture,
( esk17_1(esk18_2(esk1_1(esk15_0),esk15_0)) = esk18_2(esk1_1(esk15_0),esk15_0)
| epsilon_transitive(esk15_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_131]),c_0_144]),c_0_145]) ).
cnf(c_0_149,negated_conjecture,
( element(empty_set,X1)
| empty(esk15_0)
| ~ element(esk2_1(esk15_0),powerset(X1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_146]) ).
cnf(c_0_150,plain,
( element(esk2_1(X1),powerset(X1))
| empty(X1)
| ~ epsilon_transitive(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_147]) ).
cnf(c_0_151,negated_conjecture,
( epsilon_transitive(esk15_0)
| ~ ordinal_subset(esk18_2(esk1_1(esk15_0),esk15_0),esk18_2(esk1_1(esk15_0),esk15_0)) ),
inference(spm,[status(thm)],[c_0_142,c_0_148]) ).
cnf(c_0_152,plain,
( ordinal_subset(X1,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_112,c_0_32]) ).
cnf(c_0_153,negated_conjecture,
( element(empty_set,esk15_0)
| empty(esk15_0)
| ~ epsilon_transitive(esk15_0) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_154,negated_conjecture,
epsilon_transitive(esk15_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_131]) ).
cnf(c_0_155,plain,
( subset(X1,X2)
| subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_110]) ).
cnf(c_0_156,negated_conjecture,
( element(empty_set,esk15_0)
| empty(esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_153,c_0_154])]) ).
cnf(c_0_157,plain,
( element(X1,powerset(X2))
| subset(X2,X1)
| ~ ordinal(X2)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_155]) ).
cnf(c_0_158,negated_conjecture,
( empty(esk15_0)
| in(empty_set,esk15_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_156]) ).
cnf(c_0_159,plain,
( subset(X1,X2)
| ~ ordinal(X2)
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_157]),c_0_65]),c_0_113]) ).
cnf(c_0_160,negated_conjecture,
( empty(esk15_0)
| ~ ordinal_subset(empty_set,esk17_1(empty_set)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_158]),c_0_83])]) ).
cnf(c_0_161,plain,
( ordinal_subset(X1,X2)
| ~ ordinal(X2)
| ~ empty(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_159]),c_0_65]) ).
cnf(c_0_162,negated_conjecture,
( empty(esk15_0)
| ~ ordinal(esk17_1(empty_set)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_81])]) ).
cnf(c_0_163,negated_conjecture,
empty(esk15_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_158]),c_0_83])]),c_0_162]) ).
cnf(c_0_164,negated_conjecture,
esk15_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_165,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_163]),c_0_164]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU235+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 14:17:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 19.34/19.40 % Version : CSE_E---1.5
% 19.34/19.40 % Problem : theBenchmark.p
% 19.34/19.40 % Proof found
% 19.34/19.40 % SZS status Theorem for theBenchmark.p
% 19.34/19.40 % SZS output start Proof
% See solution above
% 19.34/19.41 % Total time : 18.823000 s
% 19.34/19.41 % SZS output end Proof
% 19.34/19.41 % Total time : 18.828000 s
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