TSTP Solution File: SET640+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET640+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 : n008.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 0.19s 0.70s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 84 ( 9 unt; 27 typ; 0 def)
% Number of atoms : 233 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 290 ( 114 ~; 115 |; 21 &)
% ( 5 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 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 : 22 ( 22 usr; 5 con; 0-3 aty)
% Number of variables : 114 ( 2 sgn; 51 !; 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,
cross_product: ( $i * $i ) > $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
subset_type: $i > $i ).
tff(decl_29,type,
relation_type: ( $i * $i ) > $i ).
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_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $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 ).
tff(decl_48,type,
esk15_0: $i ).
fof(p13,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',p13) ).
fof(p12,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',p12) ).
fof(p11,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',p11) ).
fof(p19,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).
fof(p8,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',p8) ).
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(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(prove_relset_1_2,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> subset(X1,cross_product(X2,X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_2) ).
fof(p6,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',p6) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> subset(X1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p10) ).
fof(c_0_10,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)],[p13]) ).
fof(c_0_11,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p12]) ).
fof(c_0_12,plain,
! [X36,X37,X38] :
( ( ~ member(X36,power_set(X37))
| ~ ilf_type(X38,set_type)
| ~ member(X38,X36)
| member(X38,X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ilf_type(esk6_2(X36,X37),set_type)
| member(X36,power_set(X37))
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( member(esk6_2(X36,X37),X36)
| member(X36,power_set(X37))
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ~ member(esk6_2(X36,X37),X37)
| member(X36,power_set(X37))
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,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)],[p11])])])])]) ).
fof(c_0_13,plain,
! [X59] : ilf_type(X59,set_type),
inference(variable_rename,[status(thm)],[p19]) ).
fof(c_0_14,plain,
! [X41,X42] :
( ( ~ ilf_type(X41,member_type(X42))
| member(X41,X42)
| empty(X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ~ member(X41,X42)
| ilf_type(X41,member_type(X42))
| empty(X42)
| ~ 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)],[c_0_10])])])]) ).
fof(c_0_15,plain,
! [X40] :
( ( ~ empty(power_set(X40))
| ~ ilf_type(X40,set_type) )
& ( ilf_type(power_set(X40),set_type)
| ~ ilf_type(X40,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_16,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_12]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,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_14]) ).
cnf(c_0_19,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_20,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)],[p8])])])]) ).
cnf(c_0_21,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_16,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_22,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_18,c_0_17]),c_0_17])]) ).
cnf(c_0_23,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17])]) ).
cnf(c_0_24,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_20]) ).
fof(c_0_25,plain,
! [X18,X19,X20,X21] :
( ( ~ ilf_type(X20,subset_type(cross_product(X18,X19)))
| ilf_type(X20,relation_type(X18,X19))
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( ~ ilf_type(X21,relation_type(X18,X19))
| ilf_type(X21,subset_type(cross_product(X18,X19)))
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,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_26,plain,
! [X6,X7,X8] :
( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ subset(X6,X7)
| ~ subset(X7,X8)
| subset(X6,X8) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])]) ).
fof(c_0_27,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X2,X3))
=> ( subset(X1,X4)
=> subset(X1,cross_product(X2,X3)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_2]) ).
cnf(c_0_28,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_21,c_0_22]),c_0_23]) ).
cnf(c_0_29,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_24,c_0_17]),c_0_17])]) ).
cnf(c_0_30,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_25]) ).
fof(c_0_31,plain,
! [X25,X26,X27] :
( ( ~ subset(X25,X26)
| ~ ilf_type(X27,set_type)
| ~ member(X27,X25)
| member(X27,X26)
| ~ ilf_type(X26,set_type)
| ~ ilf_type(X25,set_type) )
& ( ilf_type(esk4_2(X25,X26),set_type)
| subset(X25,X26)
| ~ ilf_type(X26,set_type)
| ~ ilf_type(X25,set_type) )
& ( member(esk4_2(X25,X26),X25)
| subset(X25,X26)
| ~ ilf_type(X26,set_type)
| ~ ilf_type(X25,set_type) )
& ( ~ member(esk4_2(X25,X26),X26)
| subset(X25,X26)
| ~ ilf_type(X26,set_type)
| ~ ilf_type(X25,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)],[p6])])])])]) ).
cnf(c_0_32,plain,
( subset(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk13_0,esk14_0))
& subset(esk12_0,esk15_0)
& ~ subset(esk12_0,cross_product(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,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_30,c_0_17]),c_0_17])]) ).
cnf(c_0_36,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_31]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ subset(X3,X2)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_38,negated_conjecture,
subset(esk12_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_40,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
ilf_type(esk15_0,relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ subset(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_43,negated_conjecture,
( subset(X1,esk15_0)
| ~ subset(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,plain,
( member(esk4_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_45,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_17]),c_0_17])]) ).
cnf(c_0_46,negated_conjecture,
( member(X1,cross_product(esk13_0,esk14_0))
| ~ member(X1,esk15_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,X2)
| ~ subset(X2,esk12_0) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
( member(esk4_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_17]),c_0_17])]) ).
fof(c_0_49,plain,
! [X35] :
( ~ ilf_type(X35,set_type)
| subset(X35,X35) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])]) ).
cnf(c_0_50,negated_conjecture,
( subset(X1,cross_product(esk13_0,esk14_0))
| ~ member(esk4_2(X1,cross_product(esk13_0,esk14_0)),esk15_0) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( member(esk4_2(X1,X2),esk15_0)
| subset(X1,X2)
| ~ subset(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
( subset(X1,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_53,negated_conjecture,
~ subset(esk12_0,cross_product(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_54,negated_conjecture,
( subset(X1,cross_product(esk13_0,esk14_0))
| ~ subset(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
subset(X1,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_17])]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET640+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
% 0.13/0.34 % Computer : n008.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 09:56:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.70 % Version : CSE_E---1.5
% 0.19/0.70 % Problem : theBenchmark.p
% 0.19/0.70 % Proof found
% 0.19/0.70 % SZS status Theorem for theBenchmark.p
% 0.19/0.70 % SZS output start Proof
% See solution above
% 0.19/0.71 % Total time : 0.128000 s
% 0.19/0.71 % SZS output end Proof
% 0.19/0.71 % Total time : 0.131000 s
%------------------------------------------------------------------------------