TSTP Solution File: SET812+4 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n029.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 14:35:39 EDT 2023
% Result : Theorem 12.99s 13.16s
% Output : CNFRefutation 12.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 127
% Syntax : Number of formulae : 212 ( 20 unt; 115 typ; 0 def)
% Number of atoms : 250 ( 6 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 262 ( 109 ~; 108 |; 29 &)
% ( 11 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 31 >; 29 *; 0 +; 0 <<)
% Number of predicates : 90 ( 88 usr; 81 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 4 con; 0-3 aty)
% Number of variables : 218 ( 30 sgn; 68 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
on: $i ).
tff(decl_35,type,
set: $i > $o ).
tff(decl_36,type,
member_predicate: $i ).
tff(decl_37,type,
strict_well_order: ( $i * $i ) > $o ).
tff(decl_38,type,
strict_order: ( $i * $i ) > $o ).
tff(decl_39,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
initial_segment: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
suc: $i > $i ).
tff(decl_43,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk4_1: $i > $i ).
tff(decl_47,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk14_0: $i ).
tff(decl_57,type,
epred1_0: $o ).
tff(decl_58,type,
epred2_0: $o ).
tff(decl_59,type,
epred3_0: $o ).
tff(decl_60,type,
epred4_0: $o ).
tff(decl_61,type,
epred5_0: $o ).
tff(decl_62,type,
epred6_0: $o ).
tff(decl_63,type,
epred7_0: $o ).
tff(decl_64,type,
epred8_0: $o ).
tff(decl_65,type,
epred9_0: $o ).
tff(decl_66,type,
epred10_0: $o ).
tff(decl_67,type,
epred11_0: $o ).
tff(decl_68,type,
epred12_0: $o ).
tff(decl_69,type,
epred13_0: $o ).
tff(decl_70,type,
epred14_0: $o ).
tff(decl_71,type,
epred15_0: $o ).
tff(decl_72,type,
epred16_0: $o ).
tff(decl_73,type,
epred17_0: $o ).
tff(decl_74,type,
epred18_0: $o ).
tff(decl_75,type,
epred19_0: $o ).
tff(decl_76,type,
epred20_0: $o ).
tff(decl_77,type,
epred21_0: $o ).
tff(decl_78,type,
epred22_0: $o ).
tff(decl_79,type,
epred23_0: $o ).
tff(decl_80,type,
epred24_0: $o ).
tff(decl_81,type,
epred25_0: $o ).
tff(decl_82,type,
epred26_0: $o ).
tff(decl_83,type,
epred27_0: $o ).
tff(decl_84,type,
epred28_0: $o ).
tff(decl_85,type,
epred29_0: $o ).
tff(decl_86,type,
epred30_0: $o ).
tff(decl_87,type,
epred31_0: $o ).
tff(decl_88,type,
epred32_0: $o ).
tff(decl_89,type,
epred33_0: $o ).
tff(decl_90,type,
epred34_0: $o ).
tff(decl_91,type,
epred35_0: $o ).
tff(decl_92,type,
epred36_0: $o ).
tff(decl_93,type,
epred37_0: $o ).
tff(decl_94,type,
epred38_0: $o ).
tff(decl_95,type,
epred39_0: $o ).
tff(decl_96,type,
epred40_0: $o ).
tff(decl_97,type,
epred41_0: $o ).
tff(decl_98,type,
epred42_0: $o ).
tff(decl_99,type,
epred43_0: $o ).
tff(decl_100,type,
epred44_0: $o ).
tff(decl_101,type,
epred45_0: $o ).
tff(decl_102,type,
epred46_0: $o ).
tff(decl_103,type,
epred47_0: $o ).
tff(decl_104,type,
epred48_0: $o ).
tff(decl_105,type,
epred49_0: $o ).
tff(decl_106,type,
epred50_0: $o ).
tff(decl_107,type,
epred51_0: $o ).
tff(decl_108,type,
epred52_0: $o ).
tff(decl_109,type,
epred53_0: $o ).
tff(decl_110,type,
epred54_0: $o ).
tff(decl_111,type,
epred55_0: $o ).
tff(decl_112,type,
epred56_0: $o ).
tff(decl_113,type,
epred57_0: $o ).
tff(decl_114,type,
epred58_0: $o ).
tff(decl_115,type,
epred59_0: $o ).
tff(decl_116,type,
epred60_0: $o ).
tff(decl_117,type,
epred61_0: $o ).
tff(decl_118,type,
epred62_0: $o ).
tff(decl_119,type,
epred63_0: $o ).
tff(decl_120,type,
epred64_0: $o ).
tff(decl_121,type,
epred65_0: $o ).
tff(decl_122,type,
epred66_0: $o ).
tff(decl_123,type,
epred67_0: $o ).
tff(decl_124,type,
epred68_0: $o ).
tff(decl_125,type,
epred69_0: $o ).
tff(decl_126,type,
epred70_0: $o ).
tff(decl_127,type,
epred71_0: $o ).
tff(decl_128,type,
epred72_0: $o ).
tff(decl_129,type,
epred73_0: $o ).
tff(decl_130,type,
epred74_0: $o ).
tff(decl_131,type,
epred75_0: $o ).
tff(decl_132,type,
epred76_0: $o ).
tff(decl_133,type,
epred77_0: $o ).
tff(decl_134,type,
epred78_0: $o ).
tff(decl_135,type,
epred79_0: $o ).
tff(decl_136,type,
epred80_0: $o ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',difference) ).
fof(empty_set,axiom,
! [X3] : ~ member(X3,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',empty_set) ).
fof(initial_segment,axiom,
! [X3,X6,X1,X5] :
( member(X5,initial_segment(X3,X6,X1))
<=> ( member(X5,X1)
& apply(X6,X5,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',initial_segment) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(product,axiom,
! [X3,X1] :
( member(X3,product(X1))
<=> ! [X5] :
( member(X5,X1)
=> member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',product) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(thV10,conjecture,
! [X1] :
( member(X1,on)
=> equal_set(X1,intersection(X1,power_set(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV10) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(ordinal_number,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(singleton,axiom,
! [X3,X1] :
( member(X3,singleton(X1))
<=> X3 = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',singleton) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(equal_set,axiom,
! [X1,X2] :
( equal_set(X1,X2)
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',equal_set) ).
fof(c_0_12,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
fof(c_0_13,plain,
! [X3] : ~ member(X3,empty_set),
inference(fof_simplification,[status(thm)],[empty_set]) ).
fof(c_0_14,plain,
! [X86,X87,X88,X89] :
( ( member(X89,X88)
| ~ member(X89,initial_segment(X86,X87,X88)) )
& ( apply(X87,X89,X86)
| ~ member(X89,initial_segment(X86,X87,X88)) )
& ( ~ member(X89,X88)
| ~ apply(X87,X89,X86)
| member(X89,initial_segment(X86,X87,X88)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[initial_segment])])]) ).
fof(c_0_15,plain,
! [X34,X35,X37,X38,X39] :
( ( member(esk2_2(X34,X35),X35)
| ~ member(X34,sum(X35)) )
& ( member(X34,esk2_2(X34,X35))
| ~ member(X34,sum(X35)) )
& ( ~ member(X39,X38)
| ~ member(X37,X39)
| member(X37,sum(X38)) ) ),
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)],[sum])])])])])]) ).
fof(c_0_16,plain,
! [X40,X41,X42,X43,X44] :
( ( ~ member(X40,product(X41))
| ~ member(X42,X41)
| member(X40,X42) )
& ( member(esk3_2(X43,X44),X44)
| member(X43,product(X44)) )
& ( ~ member(X43,esk3_2(X43,X44))
| member(X43,product(X44)) ) ),
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)],[product])])])])])]) ).
fof(c_0_17,plain,
! [X26,X27,X28] :
( ( member(X26,X28)
| ~ member(X26,difference(X28,X27)) )
& ( ~ member(X26,X27)
| ~ member(X26,difference(X28,X27)) )
& ( ~ member(X26,X28)
| member(X26,X27)
| member(X26,difference(X28,X27)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
fof(c_0_18,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ subset(X9,X10)
| ~ member(X11,X9)
| member(X11,X10) )
& ( member(esk1_2(X12,X13),X12)
| subset(X12,X13) )
& ( ~ member(esk1_2(X12,X13),X13)
| subset(X12,X13) ) ),
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)],[subset])])])])])]) ).
fof(c_0_19,plain,
! [X25] : ~ member(X25,empty_set),
inference(variable_rename,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( member(X1,X2)
| ~ member(X1,initial_segment(X3,X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> equal_set(X1,intersection(X1,power_set(X1))) ),
inference(assume_negation,[status(cth)],[thV10]) ).
cnf(c_0_23,plain,
( member(esk3_2(X1,X2),X2)
| member(X1,product(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_27,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_28,plain,
( member(esk2_2(X1,initial_segment(X2,X3,X4)),X4)
| ~ member(X1,sum(initial_segment(X2,X3,X4))) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
( member(X3,sum(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_30,negated_conjecture,
( member(esk14_0,on)
& ~ equal_set(esk14_0,intersection(esk14_0,power_set(esk14_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
cnf(c_0_31,plain,
( member(esk3_2(X1,initial_segment(X2,X3,X4)),X4)
| member(X1,product(initial_segment(X2,X3,X4))) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_32,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk1_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_33,plain,
( member(esk1_2(difference(X1,X2),X3),X1)
| subset(difference(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
fof(c_0_34,plain,
! [X17,X18] :
( ( ~ member(X17,power_set(X18))
| subset(X17,X18) )
& ( ~ subset(X17,X18)
| member(X17,power_set(X18)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
cnf(c_0_35,plain,
~ member(X1,sum(initial_segment(X2,X3,empty_set))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( member(esk2_2(X1,X2),sum(X3))
| ~ member(X1,sum(X2))
| ~ member(X2,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( member(X1,X3)
| ~ member(X1,product(X2))
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_39,plain,
member(X1,product(initial_segment(X2,X3,empty_set))),
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_40,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,plain,
subset(difference(X1,X1),X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_42,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_43,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_44,plain,
! [X46,X47,X48] :
( ( set(X46)
| ~ member(X46,on) )
& ( strict_well_order(member_predicate,X46)
| ~ member(X46,on) )
& ( ~ member(X47,X46)
| subset(X47,X46)
| ~ member(X46,on) )
& ( member(esk4_1(X48),X48)
| ~ set(X48)
| ~ strict_well_order(member_predicate,X48)
| member(X48,on) )
& ( ~ subset(esk4_1(X48),X48)
| ~ set(X48)
| ~ strict_well_order(member_predicate,X48)
| member(X48,on) ) ),
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)],[ordinal_number])])])])])]) ).
cnf(c_0_45,plain,
( ~ member(X1,initial_segment(X2,X3,empty_set))
| ~ member(X4,sum(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( member(esk14_0,sum(X1))
| ~ member(on,X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_37]) ).
cnf(c_0_47,plain,
( member(X1,X2)
| ~ member(X2,initial_segment(X3,X4,empty_set)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,plain,
( member(X1,X2)
| ~ member(X1,difference(X3,X3)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( subset(X1,power_set(X2))
| ~ subset(esk1_2(X1,power_set(X2)),X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_50,plain,
( subset(X1,X2)
| ~ member(X1,X2)
| ~ member(X2,on) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_51,negated_conjecture,
~ member(X1,initial_segment(X2,X3,empty_set)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_52,plain,
( member(esk2_2(X1,difference(X2,X2)),X3)
| ~ member(X1,sum(difference(X2,X2))) ),
inference(spm,[status(thm)],[c_0_48,c_0_21]) ).
cnf(c_0_53,plain,
( member(X1,product(difference(X2,X3)))
| ~ member(esk3_2(X1,difference(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_54,plain,
( member(esk3_2(X1,difference(X2,X3)),X2)
| member(X1,product(difference(X2,X3))) ),
inference(spm,[status(thm)],[c_0_26,c_0_23]) ).
cnf(c_0_55,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_56,plain,
( subset(X1,power_set(X2))
| ~ member(esk1_2(X1,power_set(X2)),X2)
| ~ member(X2,on) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
~ member(X1,sum(difference(X2,X2))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_58,plain,
member(X1,product(difference(X2,X2))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
( member(X1,difference(power_set(X2),X3))
| member(X1,X3)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_43]) ).
cnf(c_0_60,plain,
( subset(X1,power_set(X1))
| ~ member(X1,on) ),
inference(spm,[status(thm)],[c_0_56,c_0_25]) ).
cnf(c_0_61,negated_conjecture,
( ~ member(X1,difference(X2,X2))
| ~ member(X3,sum(X1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_62,plain,
( member(X1,X2)
| ~ member(X2,difference(X3,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_58]) ).
cnf(c_0_63,plain,
( member(X1,difference(power_set(power_set(X1)),X2))
| member(X1,X2)
| ~ member(X1,on) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,negated_conjecture,
~ member(X1,difference(X2,X2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_46]),c_0_62]) ).
cnf(c_0_65,negated_conjecture,
( member(esk14_0,difference(power_set(power_set(esk14_0)),X1))
| member(esk14_0,X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_37]) ).
fof(c_0_66,plain,
! [X29,X30] :
( ( ~ member(X29,singleton(X30))
| X29 = X30 )
& ( X29 != X30
| member(X29,singleton(X30)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[singleton])]) ).
cnf(c_0_67,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_68,negated_conjecture,
member(esk14_0,power_set(power_set(esk14_0))),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_70,negated_conjecture,
subset(esk14_0,power_set(esk14_0)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_72,plain,
( esk2_2(X1,singleton(X2)) = X2
| ~ member(X1,sum(singleton(X2))) ),
inference(spm,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_73,negated_conjecture,
( member(X1,power_set(esk14_0))
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_70]) ).
cnf(c_0_74,plain,
( member(X1,X2)
| ~ member(X1,sum(singleton(X2))) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
fof(c_0_75,plain,
! [X19,X20,X21] :
( ( member(X19,X20)
| ~ member(X19,intersection(X20,X21)) )
& ( member(X19,X21)
| ~ member(X19,intersection(X20,X21)) )
& ( ~ member(X19,X20)
| ~ member(X19,X21)
| member(X19,intersection(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_76,negated_conjecture,
( subset(X1,power_set(esk14_0))
| ~ member(esk1_2(X1,power_set(esk14_0)),esk14_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_73]) ).
cnf(c_0_77,plain,
( member(esk1_2(sum(singleton(X1)),X2),X1)
| subset(sum(singleton(X1)),X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_25]) ).
cnf(c_0_78,plain,
( member(X1,singleton(X2))
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
fof(c_0_79,plain,
! [X15,X16] :
( ( subset(X15,X16)
| ~ equal_set(X15,X16) )
& ( subset(X16,X15)
| ~ equal_set(X15,X16) )
& ( ~ subset(X15,X16)
| ~ subset(X16,X15)
| equal_set(X15,X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_set])])]) ).
cnf(c_0_80,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_81,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_82,negated_conjecture,
subset(sum(singleton(esk14_0)),power_set(esk14_0)),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_83,plain,
( member(esk1_2(X1,X2),sum(X3))
| subset(X1,X2)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_84,plain,
member(X1,singleton(X1)),
inference(er,[status(thm)],[c_0_78]) ).
cnf(c_0_85,negated_conjecture,
~ equal_set(esk14_0,intersection(esk14_0,power_set(esk14_0))),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_86,plain,
( equal_set(X1,X2)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_87,plain,
( member(esk1_2(intersection(X1,X2),X3),X1)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_80,c_0_25]) ).
cnf(c_0_88,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
( member(X1,power_set(esk14_0))
| ~ member(X1,sum(singleton(esk14_0))) ),
inference(spm,[status(thm)],[c_0_40,c_0_82]) ).
cnf(c_0_90,plain,
( member(esk1_2(X1,X2),sum(singleton(X1)))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_91,negated_conjecture,
( ~ subset(intersection(esk14_0,power_set(esk14_0)),esk14_0)
| ~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0))) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_87]) ).
cnf(c_0_93,plain,
( subset(X1,intersection(X1,X2))
| ~ member(esk1_2(X1,intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_25]) ).
cnf(c_0_94,negated_conjecture,
( member(esk1_2(esk14_0,X1),power_set(esk14_0))
| subset(esk14_0,X1) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_95,negated_conjecture,
~ subset(esk14_0,intersection(esk14_0,power_set(esk14_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_96,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET812+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:34:10 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 12.99/13.16 % Version : CSE_E---1.5
% 12.99/13.16 % Problem : theBenchmark.p
% 12.99/13.16 % Proof found
% 12.99/13.16 % SZS status Theorem for theBenchmark.p
% 12.99/13.16 % SZS output start Proof
% See solution above
% 12.99/13.18 % Total time : 12.568000 s
% 12.99/13.18 % SZS output end Proof
% 12.99/13.18 % Total time : 12.572000 s
%------------------------------------------------------------------------------