TSTP Solution File: SET753+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET753+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 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 14:35:26 EDT 2023
% Result : Theorem 1.37s 1.56s
% Output : CNFRefutation 1.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 79
% Syntax : Number of formulae : 103 ( 9 unt; 75 typ; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 73 ( 27 ~; 25 |; 15 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 249 ( 69 >; 180 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-6 aty)
% Number of functors : 60 ( 60 usr; 6 con; 0-8 aty)
% Number of variables : 62 ( 2 sgn; 34 !; 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,
maps: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
compose_predicate: ( $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_37,type,
compose_function: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_38,type,
equal_maps: ( $i * $i * $i * $i ) > $o ).
tff(decl_39,type,
identity: ( $i * $i ) > $o ).
tff(decl_40,type,
injective: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
surjective: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
one_to_one: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
inverse_predicate: ( $i * $i * $i * $i ) > $o ).
tff(decl_44,type,
inverse_function: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
image2: ( $i * $i ) > $i ).
tff(decl_46,type,
image3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
inverse_image2: ( $i * $i ) > $i ).
tff(decl_48,type,
inverse_image3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
increasing: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_50,type,
decreasing: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_51,type,
isomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_52,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_56,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_58,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_60,type,
esk9_8: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
esk10_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_62,type,
esk11_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_63,type,
esk12_6: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
esk13_7: ( $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(decl_65,type,
esk14_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_66,type,
esk15_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_67,type,
esk16_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_68,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_69,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
esk19_3: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
esk20_3: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
esk21_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_73,type,
esk22_3: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
esk23_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_75,type,
esk24_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_76,type,
esk25_3: ( $i * $i * $i ) > $i ).
tff(decl_77,type,
esk26_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_78,type,
esk27_3: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
esk28_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_80,type,
esk29_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_81,type,
esk30_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_82,type,
esk31_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_83,type,
esk32_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_84,type,
esk33_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_85,type,
esk34_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_86,type,
esk35_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_87,type,
esk36_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_88,type,
esk37_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_89,type,
esk38_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_90,type,
esk39_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_91,type,
esk40_5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_92,type,
esk41_0: $i ).
tff(decl_93,type,
esk42_0: $i ).
tff(decl_94,type,
esk43_0: $i ).
tff(decl_95,type,
esk44_0: $i ).
tff(decl_96,type,
esk45_0: $i ).
fof(thIIa03,conjecture,
! [X6,X1,X2,X3,X5] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& subset(X5,X1) )
=> subset(image2(X6,intersection(X3,X5)),intersection(image2(X6,X3),image2(X6,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIIa03) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(image2,axiom,
! [X6,X1,X5] :
( member(X5,image2(X6,X1))
<=> ? [X3] :
( member(X3,X1)
& apply(X6,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+1.ax',image2) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X1,X2,X3,X5] :
( ( maps(X6,X1,X2)
& subset(X3,X1)
& subset(X5,X1) )
=> subset(image2(X6,intersection(X3,X5)),intersection(image2(X6,X3),image2(X6,X5))) ),
inference(assume_negation,[status(cth)],[thIIa03]) ).
fof(c_0_5,negated_conjecture,
( maps(esk41_0,esk42_0,esk43_0)
& subset(esk44_0,esk42_0)
& subset(esk45_0,esk42_0)
& ~ subset(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_6,plain,
! [X17,X18,X19,X20,X21] :
( ( ~ subset(X17,X18)
| ~ member(X19,X17)
| member(X19,X18) )
& ( member(esk1_2(X20,X21),X20)
| subset(X20,X21) )
& ( ~ member(esk1_2(X20,X21),X21)
| subset(X20,X21) ) ),
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_7,plain,
! [X161,X162,X163,X165,X166,X167,X168] :
( ( member(esk25_3(X161,X162,X163),X162)
| ~ member(X163,image2(X161,X162)) )
& ( apply(X161,esk25_3(X161,X162,X163),X163)
| ~ member(X163,image2(X161,X162)) )
& ( ~ member(X168,X166)
| ~ apply(X165,X168,X167)
| member(X167,image2(X165,X166)) ) ),
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)],[image2])])])])])]) ).
cnf(c_0_8,negated_conjecture,
~ subset(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( apply(X1,esk25_3(X1,X2,X3),X3)
| ~ member(X3,image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
member(esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),image2(esk41_0,intersection(esk44_0,esk45_0))),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
fof(c_0_12,plain,
! [X27,X28,X29] :
( ( member(X27,X28)
| ~ member(X27,intersection(X28,X29)) )
& ( member(X27,X29)
| ~ member(X27,intersection(X28,X29)) )
& ( ~ member(X27,X28)
| ~ member(X27,X29)
| member(X27,intersection(X28,X29)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_13,plain,
( member(esk25_3(X1,X2,X3),X2)
| ~ member(X3,image2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( member(X4,image2(X3,X2))
| ~ member(X1,X2)
| ~ apply(X3,X1,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
apply(esk41_0,esk25_3(esk41_0,intersection(esk44_0,esk45_0),esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)))),esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)))),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
member(esk25_3(esk41_0,intersection(esk44_0,esk45_0),esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)))),intersection(esk44_0,esk45_0)),
inference(spm,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_18,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( member(esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),image2(esk41_0,X1))
| ~ member(esk25_3(esk41_0,intersection(esk44_0,esk45_0),esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)))),X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,negated_conjecture,
member(esk25_3(esk41_0,intersection(esk44_0,esk45_0),esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)))),esk45_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,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_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
member(esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),image2(esk41_0,esk45_0)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
member(esk25_3(esk41_0,intersection(esk44_0,esk45_0),esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0)))),esk44_0),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_26,negated_conjecture,
~ member(esk1_2(image2(esk41_0,intersection(esk44_0,esk45_0)),intersection(image2(esk41_0,esk44_0),image2(esk41_0,esk45_0))),image2(esk41_0,esk44_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_8]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET753+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 16:17:03 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 1.37/1.56 % Version : CSE_E---1.5
% 1.37/1.56 % Problem : theBenchmark.p
% 1.37/1.56 % Proof found
% 1.37/1.56 % SZS status Theorem for theBenchmark.p
% 1.37/1.56 % SZS output start Proof
% See solution above
% 1.37/1.57 % Total time : 0.969000 s
% 1.37/1.57 % SZS output end Proof
% 1.37/1.57 % Total time : 0.973000 s
%------------------------------------------------------------------------------