TSTP Solution File: SET641+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 14:35:00 EDT 2023
% Result : Theorem 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 34
% Syntax : Number of formulae : 68 ( 9 unt; 26 typ; 0 def)
% Number of atoms : 186 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 232 ( 88 ~; 89 |; 18 &)
% ( 7 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 22 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 4 con; 0-3 aty)
% Number of variables : 79 ( 2 sgn; 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_25,type,
subset_type: $i > $i ).
tff(decl_26,type,
relation_type: ( $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: ( $i * $i ) > $o ).
tff(decl_30,type,
power_set: $i > $i ).
tff(decl_31,type,
member_type: $i > $i ).
tff(decl_32,type,
empty: $i > $o ).
tff(decl_33,type,
relation_like: $i > $o ).
tff(decl_34,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk5_1: $i > $i ).
tff(decl_39,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk7_1: $i > $i ).
tff(decl_41,type,
esk8_1: $i > $i ).
tff(decl_42,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk11_1: $i > $i ).
tff(decl_45,type,
esk12_0: $i ).
tff(decl_46,type,
esk13_0: $i ).
tff(decl_47,type,
esk14_0: $i ).
fof(p5,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/sandbox2/benchmark/theBenchmark.p',p5) ).
fof(p18,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p18) ).
fof(prove_relset_1_3,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_3) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(p10,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/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(p12,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/sandbox2/benchmark/theBenchmark.p',p12) ).
fof(p7,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/sandbox2/benchmark/theBenchmark.p',p7) ).
fof(p1,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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(c_0_8,plain,
! [X22,X23,X24] :
( ( ~ subset(X22,X23)
| ~ ilf_type(X24,set_type)
| ~ member(X24,X22)
| member(X24,X23)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ilf_type(esk4_2(X22,X23),set_type)
| subset(X22,X23)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( member(esk4_2(X22,X23),X22)
| subset(X22,X23)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ~ member(esk4_2(X22,X23),X23)
| subset(X22,X23)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,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)],[p5])])])])]) ).
fof(c_0_9,plain,
! [X56] : ilf_type(X56,set_type),
inference(variable_rename,[status(thm)],[p18]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( subset(X1,cross_product(X2,X3))
=> ilf_type(X1,relation_type(X2,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_3]) ).
fof(c_0_11,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
fof(c_0_12,plain,
! [X33,X34,X35] :
( ( ~ member(X33,power_set(X34))
| ~ ilf_type(X35,set_type)
| ~ member(X35,X33)
| member(X35,X34)
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( ilf_type(esk6_2(X33,X34),set_type)
| member(X33,power_set(X34))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( member(esk6_2(X33,X34),X33)
| member(X33,power_set(X34))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( ~ member(esk6_2(X33,X34),X34)
| member(X33,power_set(X34))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,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)],[p10])])])])]) ).
cnf(c_0_13,plain,
( member(X3,X2)
| ~ subset(X1,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_8]) ).
cnf(c_0_14,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& subset(esk12_0,cross_product(esk13_0,esk14_0))
& ~ ilf_type(esk12_0,relation_type(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,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)],[p12]) ).
fof(c_0_17,plain,
! [X42,X43] :
( ( ~ empty(X42)
| ~ ilf_type(X43,set_type)
| ~ member(X43,X42)
| ~ ilf_type(X42,set_type) )
& ( ilf_type(esk8_1(X42),set_type)
| empty(X42)
| ~ ilf_type(X42,set_type) )
& ( member(esk8_1(X42),X42)
| empty(X42)
| ~ ilf_type(X42,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)],[c_0_11])])])])]) ).
cnf(c_0_18,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( member(X1,X2)
| ~ subset(X3,X2)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
subset(esk12_0,cross_product(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X38,X39] :
( ( ~ ilf_type(X38,member_type(X39))
| member(X38,X39)
| empty(X39)
| ~ ilf_type(X39,set_type)
| ~ ilf_type(X38,set_type) )
& ( ~ member(X38,X39)
| ilf_type(X38,member_type(X39))
| empty(X39)
| ~ ilf_type(X39,set_type)
| ~ ilf_type(X38,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_22,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
( member(X1,power_set(X2))
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_14]),c_0_14])]) ).
cnf(c_0_24,negated_conjecture,
( member(X1,cross_product(esk13_0,esk14_0))
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_26,plain,
! [X28,X29] :
( ( ~ ilf_type(X29,subset_type(X28))
| ilf_type(X29,member_type(power_set(X28)))
| ~ ilf_type(X29,set_type)
| ~ ilf_type(X28,set_type) )
& ( ~ ilf_type(X29,member_type(power_set(X28)))
| ilf_type(X29,subset_type(X28))
| ~ ilf_type(X29,set_type)
| ~ ilf_type(X28,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
cnf(c_0_27,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_14]),c_0_14])]) ).
cnf(c_0_29,negated_conjecture,
( member(X1,power_set(cross_product(esk13_0,esk14_0)))
| ~ member(esk6_2(X1,cross_product(esk13_0,esk14_0)),esk12_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
( member(esk6_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_14]),c_0_14])]) ).
fof(c_0_31,plain,
! [X6,X7,X8,X9] :
( ( ~ ilf_type(X8,subset_type(cross_product(X6,X7)))
| ilf_type(X8,relation_type(X6,X7))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( ~ ilf_type(X9,relation_type(X6,X7))
| ilf_type(X9,subset_type(cross_product(X6,X7)))
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_32,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_14]),c_0_14])]),c_0_28]) ).
cnf(c_0_34,negated_conjecture,
member(esk12_0,power_set(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_14]),c_0_14])]) ).
cnf(c_0_37,negated_conjecture,
ilf_type(esk12_0,member_type(power_set(cross_product(esk13_0,esk14_0)))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_14]),c_0_14])]) ).
cnf(c_0_39,negated_conjecture,
ilf_type(esk12_0,subset_type(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
~ ilf_type(esk12_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET641+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Sat Aug 26 11:31:13 EDT 2023
% 0.10/0.28 % CPUTime :
% 0.14/0.47 start to proof: theBenchmark
% 0.14/0.49 % Version : CSE_E---1.5
% 0.14/0.49 % Problem : theBenchmark.p
% 0.14/0.49 % Proof found
% 0.14/0.49 % SZS status Theorem for theBenchmark.p
% 0.14/0.49 % SZS output start Proof
% See solution above
% 0.14/0.50 % Total time : 0.018000 s
% 0.14/0.50 % SZS output end Proof
% 0.14/0.50 % Total time : 0.021000 s
%------------------------------------------------------------------------------