TSTP Solution File: SET656+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET656+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 : n004.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 14:35:04 EDT 2023
% Result : Theorem 1.15s 1.23s
% Output : CNFRefutation 1.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 80 ( 8 unt; 33 typ; 0 def)
% Number of atoms : 194 ( 8 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 243 ( 96 ~; 95 |; 18 &)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 49 ( 27 >; 22 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 6 con; 0-4 aty)
% Number of variables : 92 ( 2 sgn; 45 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
intersection: ( $i * $i ) > $i ).
tff(decl_26,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_27,type,
member: ( $i * $i ) > $o ).
tff(decl_28,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
subset_type: $i > $i ).
tff(decl_30,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_31,type,
binary_relation_type: $i ).
tff(decl_32,type,
relation_like: $i > $o ).
tff(decl_33,type,
power_set: $i > $i ).
tff(decl_34,type,
member_type: $i > $i ).
tff(decl_35,type,
empty: $i > $o ).
tff(decl_36,type,
intersection4: ( $i * $i * $i * $i ) > $i ).
tff(decl_37,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk6_0: $i ).
tff(decl_43,type,
esk7_1: $i > $i ).
tff(decl_44,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk10_1: $i > $i ).
tff(decl_47,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk14_1: $i > $i ).
tff(decl_51,type,
esk15_1: $i > $i ).
tff(decl_52,type,
esk16_0: $i ).
tff(decl_53,type,
esk17_0: $i ).
tff(decl_54,type,
esk18_0: $i ).
fof(p21,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(p20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p20) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p19) ).
fof(p30,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p30) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).
fof(prove_relset_1_18,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> intersection(X3,cross_product(X1,X2)) = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_18) ).
fof(p17,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p17) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
=> intersection(X1,X2) = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(c_0_9,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p21]) ).
fof(c_0_10,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p20]) ).
fof(c_0_11,plain,
! [X53,X54,X55] :
( ( ~ member(X53,power_set(X54))
| ~ ilf_type(X55,set_type)
| ~ member(X55,X53)
| member(X55,X54)
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) )
& ( ilf_type(esk9_2(X53,X54),set_type)
| member(X53,power_set(X54))
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) )
& ( member(esk9_2(X53,X54),X53)
| member(X53,power_set(X54))
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) )
& ( ~ member(esk9_2(X53,X54),X54)
| member(X53,power_set(X54))
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])])]) ).
fof(c_0_12,plain,
! [X88] : ilf_type(X88,set_type),
inference(variable_rename,[status(thm)],[p30]) ).
fof(c_0_13,plain,
! [X58,X59] :
( ( ~ ilf_type(X58,member_type(X59))
| member(X58,X59)
| empty(X59)
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) )
& ( ~ member(X58,X59)
| ilf_type(X58,member_type(X59))
| empty(X59)
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X57] :
( ( ~ empty(power_set(X57))
| ~ ilf_type(X57,set_type) )
& ( ilf_type(power_set(X57),set_type)
| ~ ilf_type(X57,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
cnf(c_0_15,plain,
( member(X3,X2)
| ~ member(X1,power_set(X2))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X41,X42] :
( ( ~ ilf_type(X42,subset_type(X41))
| ilf_type(X42,member_type(power_set(X41)))
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ~ ilf_type(X42,member_type(power_set(X41)))
| ilf_type(X42,subset_type(X41))
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
cnf(c_0_20,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16])]) ).
cnf(c_0_21,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_16]),c_0_16])]) ).
cnf(c_0_22,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_16])]) ).
cnf(c_0_23,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,plain,
! [X22,X23,X24,X25] :
( ( ~ ilf_type(X24,subset_type(cross_product(X22,X23)))
| ilf_type(X24,relation_type(X22,X23))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ~ ilf_type(X25,relation_type(X22,X23))
| ilf_type(X25,subset_type(cross_product(X22,X23)))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
cnf(c_0_25,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,member_type(power_set(X2))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_26,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_16]),c_0_16])]) ).
cnf(c_0_27,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> intersection(X3,cross_product(X1,X2)) = X3 ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_18]) ).
fof(c_0_29,plain,
! [X48,X49,X50] :
( ( ~ subset(X48,X49)
| ~ ilf_type(X50,set_type)
| ~ member(X50,X48)
| member(X50,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( ilf_type(esk8_2(X48,X49),set_type)
| subset(X48,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( member(esk8_2(X48,X49),X48)
| subset(X48,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( ~ member(esk8_2(X48,X49),X49)
| subset(X48,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])])]) ).
cnf(c_0_30,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_16]),c_0_16])]) ).
fof(c_0_32,negated_conjecture,
( ilf_type(esk16_0,set_type)
& ilf_type(esk17_0,set_type)
& ilf_type(esk18_0,relation_type(esk16_0,esk17_0))
& intersection(esk18_0,cross_product(esk16_0,esk17_0)) != esk18_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_33,plain,
! [X6,X7] :
( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| ~ subset(X6,X7)
| intersection(X6,X7) = X6 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ member(esk8_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,negated_conjecture,
ilf_type(esk18_0,relation_type(esk16_0,esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_37,plain,
( intersection(X1,X2) = X1
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_38,plain,
( subset(X1,X2)
| ~ member(esk8_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_16]),c_0_16])]) ).
cnf(c_0_39,negated_conjecture,
( member(X1,cross_product(esk16_0,esk17_0))
| ~ member(X1,esk18_0) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
( member(esk8_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_41,negated_conjecture,
intersection(esk18_0,cross_product(esk16_0,esk17_0)) != esk18_0,
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( intersection(X1,X2) = X1
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_16]),c_0_16])]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,cross_product(esk16_0,esk17_0))
| ~ member(esk8_2(X1,cross_product(esk16_0,esk17_0)),esk18_0) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
( member(esk8_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_16]),c_0_16])]) ).
cnf(c_0_45,negated_conjecture,
~ subset(esk18_0,cross_product(esk16_0,esk17_0)),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET656+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n004.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 : Sat Aug 26 13:43:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 1.15/1.23 % Version : CSE_E---1.5
% 1.15/1.23 % Problem : theBenchmark.p
% 1.15/1.23 % Proof found
% 1.15/1.23 % SZS status Theorem for theBenchmark.p
% 1.15/1.23 % SZS output start Proof
% See solution above
% 1.15/1.24 % Total time : 0.655000 s
% 1.15/1.24 % SZS output end Proof
% 1.15/1.24 % Total time : 0.658000 s
%------------------------------------------------------------------------------