TSTP Solution File: SET645+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET645+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 : n021.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 14:35:01 EDT 2023
% Result : Theorem 0.20s 0.58s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 35
% Syntax : Number of formulae : 72 ( 13 unt; 27 typ; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 243 ( 94 ~; 89 |; 23 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 6 con; 0-2 aty)
% Number of variables : 87 ( 6 sgn; 47 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
subset_type: $i > $i ).
tff(decl_30,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_31,type,
power_set: $i > $i ).
tff(decl_32,type,
member_type: $i > $i ).
tff(decl_33,type,
empty: $i > $o ).
tff(decl_34,type,
relation_like: $i > $o ).
tff(decl_35,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk2_1: $i > $i ).
tff(decl_37,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk5_1: $i > $i ).
tff(decl_40,type,
esk6_1: $i > $i ).
tff(decl_41,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk9_1: $i > $i ).
tff(decl_44,type,
esk10_0: $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_0: $i ).
fof(p4,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',p4) ).
fof(p21,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p21) ).
fof(prove_relset_1_7,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_7) ).
fof(p15,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',p15) ).
fof(p10,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',p10) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p14) ).
fof(p13,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',p13) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(c_0_8,plain,
! [X17,X18,X19,X20] :
( ( ~ ilf_type(X19,subset_type(cross_product(X17,X18)))
| ilf_type(X19,relation_type(X17,X18))
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) )
& ( ~ ilf_type(X20,relation_type(X17,X18))
| ilf_type(X20,subset_type(cross_product(X17,X18)))
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).
fof(c_0_9,plain,
! [X62] : ilf_type(X62,set_type),
inference(variable_rename,[status(thm)],[p21]) ).
fof(c_0_10,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_7]) ).
fof(c_0_11,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)],[p15]) ).
fof(c_0_12,plain,
! [X31,X32] :
( ( ~ ilf_type(X32,subset_type(X31))
| ilf_type(X32,member_type(power_set(X31)))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) )
& ( ~ ilf_type(X32,member_type(power_set(X31)))
| ilf_type(X32,subset_type(X31))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])])]) ).
cnf(c_0_13,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_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(esk10_0,set_type)
& ilf_type(esk11_0,set_type)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk10_0,esk11_0))
& member(ordered_pair(esk12_0,esk13_0),esk14_0)
& ( ~ member(esk12_0,esk10_0)
| ~ member(esk13_0,esk11_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)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p14]) ).
fof(c_0_17,plain,
! [X39,X40,X41] :
( ( ~ member(X39,power_set(X40))
| ~ ilf_type(X41,set_type)
| ~ member(X41,X39)
| member(X41,X40)
| ~ ilf_type(X40,set_type)
| ~ ilf_type(X39,set_type) )
& ( ilf_type(esk4_2(X39,X40),set_type)
| member(X39,power_set(X40))
| ~ ilf_type(X40,set_type)
| ~ ilf_type(X39,set_type) )
& ( member(esk4_2(X39,X40),X39)
| member(X39,power_set(X40))
| ~ ilf_type(X40,set_type)
| ~ ilf_type(X39,set_type) )
& ( ~ member(esk4_2(X39,X40),X40)
| member(X39,power_set(X40))
| ~ ilf_type(X40,set_type)
| ~ ilf_type(X39,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)],[p13])])])])]) ).
fof(c_0_18,plain,
! [X44,X45] :
( ( ~ ilf_type(X44,member_type(X45))
| member(X44,X45)
| empty(X45)
| ~ ilf_type(X45,set_type)
| ~ ilf_type(X44,set_type) )
& ( ~ member(X44,X45)
| ilf_type(X44,member_type(X45))
| empty(X45)
| ~ ilf_type(X45,set_type)
| ~ ilf_type(X44,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])]) ).
cnf(c_0_19,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_12]) ).
cnf(c_0_20,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_13,c_0_14]),c_0_14])]) ).
cnf(c_0_21,negated_conjecture,
ilf_type(esk14_0,relation_type(esk10_0,esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_22,plain,
! [X43] :
( ( ~ empty(power_set(X43))
| ~ ilf_type(X43,set_type) )
& ( ilf_type(power_set(X43),set_type)
| ~ ilf_type(X43,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,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_18]) ).
cnf(c_0_25,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_19,c_0_14]),c_0_14])]) ).
cnf(c_0_26,negated_conjecture,
ilf_type(esk14_0,subset_type(cross_product(esk10_0,esk11_0))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_28,plain,
! [X6,X7,X8,X9] :
( ( member(X6,X8)
| ~ member(ordered_pair(X6,X7),cross_product(X8,X9))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( member(X7,X9)
| ~ member(ordered_pair(X6,X7),cross_product(X8,X9))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( ~ member(X6,X8)
| ~ member(X7,X9)
| member(ordered_pair(X6,X7),cross_product(X8,X9))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ 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_29,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_23,c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_30,negated_conjecture,
member(ordered_pair(esk12_0,esk13_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_31,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_24,c_0_14]),c_0_14])]) ).
cnf(c_0_32,negated_conjecture,
ilf_type(esk14_0,member_type(power_set(cross_product(esk10_0,esk11_0)))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_14])]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
( member(ordered_pair(esk12_0,esk13_0),X1)
| ~ member(esk14_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
member(esk14_0,power_set(cross_product(esk10_0,esk11_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_37,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),cross_product(X2,X4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_14]),c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_38,negated_conjecture,
member(ordered_pair(esk12_0,esk13_0),cross_product(esk10_0,esk11_0)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_40,negated_conjecture,
( ~ member(esk12_0,esk10_0)
| ~ member(esk13_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_41,negated_conjecture,
member(esk12_0,esk10_0),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),cross_product(X4,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_14]),c_0_14]),c_0_14]),c_0_14])]) ).
cnf(c_0_43,negated_conjecture,
~ member(esk13_0,esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_38]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET645+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.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 08:50:56 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.58 % Version : CSE_E---1.5
% 0.20/0.58 % Problem : theBenchmark.p
% 0.20/0.58 % Proof found
% 0.20/0.58 % SZS status Theorem for theBenchmark.p
% 0.20/0.58 % SZS output start Proof
% See solution above
% 0.20/0.58 % Total time : 0.011000 s
% 0.20/0.58 % SZS output end Proof
% 0.20/0.58 % Total time : 0.015000 s
%------------------------------------------------------------------------------