TSTP Solution File: SET594+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 14:34:41 EDT 2023
% Result : Theorem 13.97s 14.10s
% Output : CNFRefutation 13.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 17
% Syntax : Number of formulae : 83 ( 27 unt; 9 typ; 0 def)
% Number of atoms : 167 ( 37 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 143 ( 50 ~; 70 |; 14 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 6 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 182 ( 19 sgn; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
union: ( $i * $i ) > $i ).
tff(decl_25,type,
intersection: ( $i * $i ) > $i ).
tff(decl_26,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk3_0: $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
fof(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
fof(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_th53,conjecture,
! [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
=> subset(X1,union(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th53) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
fof(c_0_8,plain,
! [X4,X5,X6,X7,X8] :
( ( ~ subset(X4,X5)
| ~ member(X6,X4)
| member(X6,X5) )
& ( member(esk1_2(X7,X8),X7)
| subset(X7,X8) )
& ( ~ member(esk1_2(X7,X8),X8)
| subset(X7,X8) ) ),
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_defn])])])])])]) ).
fof(c_0_9,plain,
! [X10,X11,X12] :
( ( ~ member(X12,union(X10,X11))
| member(X12,X10)
| member(X12,X11) )
& ( ~ member(X12,X10)
| member(X12,union(X10,X11)) )
& ( ~ member(X12,X11)
| member(X12,union(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
fof(c_0_10,plain,
! [X13,X14,X15] :
( ( member(X15,X13)
| ~ member(X15,intersection(X13,X14)) )
& ( member(X15,X14)
| ~ member(X15,intersection(X13,X14)) )
& ( ~ member(X15,X13)
| ~ member(X15,X14)
| member(X15,intersection(X13,X14)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_18,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( ~ member(X25,X23)
| member(X25,X24)
| X23 != X24 )
& ( ~ member(X26,X24)
| member(X26,X23)
| X23 != X24 )
& ( ~ member(esk2_2(X27,X28),X27)
| ~ member(esk2_2(X27,X28),X28)
| X27 = X28 )
& ( member(esk2_2(X27,X28),X27)
| member(esk2_2(X27,X28),X28)
| X27 = X28 ) ),
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)],[equal_member_defn])])])])])]) ).
cnf(c_0_19,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_11,c_0_13]) ).
cnf(c_0_20,plain,
( member(esk1_2(X1,X2),X3)
| subset(X1,X2)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
fof(c_0_22,plain,
! [X20,X21] : intersection(X20,X21) = intersection(X21,X20),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_23,plain,
( member(esk1_2(intersection(X1,X2),X3),X2)
| subset(intersection(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_24,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_26,plain,
! [X16,X17] :
( ( subset(X16,X17)
| X16 != X17 )
& ( subset(X17,X16)
| X16 != X17 )
& ( ~ subset(X16,X17)
| ~ subset(X17,X16)
| X16 = X17 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_27,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_28,plain,
( member(esk1_2(X1,X2),union(X3,X1))
| subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_30,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_11,c_0_23]) ).
cnf(c_0_31,plain,
( intersection(X1,X2) = X3
| member(esk2_2(intersection(X1,X2),X3),X3)
| member(esk2_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
subset(X1,intersection(X1,union(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_36,plain,
subset(intersection(X1,X2),X1),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_37,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_38,plain,
( intersection(X1,X2) = X1
| member(esk2_2(intersection(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_40,plain,
( member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2)
| subset(union(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_33,c_0_15]) ).
fof(c_0_41,negated_conjecture,
~ ! [X1,X2,X3] :
( union(intersection(X1,X2),intersection(X1,X3)) = X1
=> subset(X1,union(X2,X3)) ),
inference(assume_negation,[status(cth)],[prove_th53]) ).
cnf(c_0_42,plain,
intersection(X1,union(X2,X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_43,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_32]) ).
cnf(c_0_45,plain,
( member(esk1_2(union(X1,X2),union(X2,X3)),X1)
| subset(union(X1,X2),union(X2,X3)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
fof(c_0_46,negated_conjecture,
( union(intersection(esk3_0,esk4_0),intersection(esk3_0,esk5_0)) = esk3_0
& ~ subset(esk3_0,union(esk4_0,esk5_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])]) ).
cnf(c_0_47,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_16,c_0_12]) ).
cnf(c_0_48,plain,
( member(esk1_2(union(X1,X2),X2),X1)
| subset(union(X1,X2),X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_42]),c_0_42]) ).
cnf(c_0_49,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_13]),c_0_38]) ).
cnf(c_0_50,plain,
( intersection(union(X1,X2),X3) = union(X1,X2)
| member(esk2_2(intersection(union(X1,X2),X3),union(X1,X2)),X1)
| member(esk2_2(intersection(union(X1,X2),X3),union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).
cnf(c_0_51,plain,
subset(union(X1,X2),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_52,negated_conjecture,
union(intersection(esk3_0,esk4_0),intersection(esk3_0,esk5_0)) = esk3_0,
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
subset(union(X1,union(X2,union(X3,X1))),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_39,c_0_12]) ).
cnf(c_0_55,plain,
( intersection(X1,X2) = X2
| ~ member(esk2_2(intersection(X1,X2),X2),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_29]) ).
cnf(c_0_56,plain,
( union(X1,X2) = X2
| member(esk2_2(X2,union(X1,X2)),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_29]),c_0_42]),c_0_29]),c_0_42]) ).
fof(c_0_57,plain,
! [X18,X19] : union(X18,X19) = union(X19,X18),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_58,negated_conjecture,
subset(esk3_0,union(intersection(esk3_0,esk5_0),union(intersection(esk3_0,esk4_0),X1))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_59,plain,
union(X1,union(X2,union(X3,X1))) = union(X2,union(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_53]),c_0_21])]) ).
cnf(c_0_60,plain,
subset(union(X1,union(union(X2,X1),X3)),union(union(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_61,plain,
( union(X1,X2) = X2
| ~ member(esk2_2(X2,union(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_62,plain,
( union(intersection(X1,X2),X3) = X3
| member(esk2_2(X3,union(intersection(X1,X2),X3)),X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_56]) ).
cnf(c_0_63,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_64,plain,
subset(intersection(X1,X2),intersection(X2,intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_65,negated_conjecture,
subset(esk3_0,union(intersection(esk3_0,esk5_0),union(X1,union(X2,intersection(esk3_0,esk4_0))))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_66,plain,
union(X1,union(union(X2,X1),X3)) = union(union(X2,X1),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_60]),c_0_21])]) ).
cnf(c_0_67,plain,
union(X1,intersection(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_68,plain,
intersection(X1,intersection(X2,X1)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_64]),c_0_30])]) ).
cnf(c_0_69,negated_conjecture,
subset(esk3_0,union(union(X1,intersection(esk3_0,esk5_0)),union(X2,intersection(esk3_0,esk4_0)))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
union(X1,intersection(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_71,negated_conjecture,
subset(esk3_0,union(esk5_0,union(X1,intersection(esk3_0,esk4_0)))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_72,negated_conjecture,
~ subset(esk3_0,union(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_73,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_70]),c_0_63]),c_0_72]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SET594+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n029.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 09:32:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.22/0.63 start to proof: theBenchmark
% 13.97/14.10 % Version : CSE_E---1.5
% 13.97/14.10 % Problem : theBenchmark.p
% 13.97/14.10 % Proof found
% 13.97/14.10 % SZS status Theorem for theBenchmark.p
% 13.97/14.10 % SZS output start Proof
% See solution above
% 13.97/14.11 % Total time : 13.463000 s
% 13.97/14.11 % SZS output end Proof
% 13.97/14.11 % Total time : 13.466000 s
%------------------------------------------------------------------------------