TSTP Solution File: SET652+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET652+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 : Tue May 21 02:55:10 EDT 2024
% Result : Theorem 17.11s 2.64s
% Output : CNFRefutation 17.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 78 ( 17 unt; 0 def)
% Number of atoms : 315 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 388 ( 151 ~; 154 |; 26 &)
% ( 8 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 152 ( 5 sgn 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(p26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p26) ).
fof(prove_relset_1_14,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(X3,X1))
=> ( subset(range_of(X4),X2)
=> ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_14) ).
fof(p3,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)
=> ( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cross_product(X1,X3),cross_product(X2,X4)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(p23,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p23) ).
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(p9,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',p9) ).
fof(p18,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',p18) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> subset(X1,cross_product(domain_of(X1),range_of(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
fof(p24,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',p24) ).
fof(p20,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',p20) ).
fof(p15,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',p15) ).
fof(c_0_14,plain,
! [X10,X11,X12,X13] :
( ( ~ ilf_type(X12,subset_type(cross_product(X10,X11)))
| ilf_type(X12,relation_type(X10,X11))
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,set_type) )
& ( ~ ilf_type(X13,relation_type(X10,X11))
| ilf_type(X13,subset_type(cross_product(X10,X11)))
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])])]) ).
fof(c_0_15,plain,
! [X9] : ilf_type(X9,set_type),
inference(variable_rename,[status(thm)],[p26]) ).
fof(c_0_16,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(X3,X1))
=> ( subset(range_of(X4),X2)
=> ilf_type(X4,relation_type(X3,X2)) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_14]) ).
fof(c_0_17,plain,
! [X23,X24,X25,X26] :
( ~ ilf_type(X23,set_type)
| ~ ilf_type(X24,set_type)
| ~ ilf_type(X25,set_type)
| ~ ilf_type(X26,set_type)
| ~ subset(X23,X24)
| ~ subset(X25,X26)
| subset(cross_product(X23,X25),cross_product(X24,X26)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_18,plain,
! [X17,X18,X19] :
( ( subset(domain_of(X19),X17)
| ~ ilf_type(X19,relation_type(X17,X18))
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) )
& ( subset(range_of(X19),X18)
| ~ ilf_type(X19,relation_type(X17,X18))
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])])]) ).
fof(c_0_19,plain,
! [X47] :
( ( relation_like(X47)
| ~ ilf_type(X47,binary_relation_type)
| ~ ilf_type(X47,set_type) )
& ( ilf_type(X47,set_type)
| ~ ilf_type(X47,binary_relation_type)
| ~ ilf_type(X47,set_type) )
& ( ~ relation_like(X47)
| ~ ilf_type(X47,set_type)
| ilf_type(X47,binary_relation_type)
| ~ ilf_type(X47,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
fof(c_0_20,plain,
! [X37,X38,X39] :
( ~ ilf_type(X37,set_type)
| ~ ilf_type(X38,set_type)
| ~ ilf_type(X39,subset_type(cross_product(X37,X38)))
| relation_like(X39) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])])]) ).
cnf(c_0_21,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_14]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_23,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,set_type)
& ilf_type(esk4_0,relation_type(esk3_0,esk1_0))
& subset(range_of(esk4_0),esk2_0)
& ~ ilf_type(esk4_0,relation_type(esk3_0,esk2_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_24,plain,
( subset(cross_product(X1,X3),cross_product(X2,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ subset(X1,X2)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,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_21,c_0_22]),c_0_22])]) ).
cnf(c_0_29,negated_conjecture,
ilf_type(esk4_0,relation_type(esk3_0,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_30,plain,
! [X20,X21,X22] :
( ~ ilf_type(X20,set_type)
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X22,set_type)
| ~ subset(X20,X21)
| ~ subset(X21,X22)
| subset(X20,X22) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_31,plain,
( subset(cross_product(X1,X2),cross_product(X3,X4))
| ~ subset(X2,X4)
| ~ subset(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_32,negated_conjecture,
subset(range_of(esk4_0),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_33,plain,
( subset(domain_of(X1),X2)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_22])]) ).
cnf(c_0_34,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( relation_like(X1)
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_22]),c_0_22])]) ).
cnf(c_0_36,negated_conjecture,
ilf_type(esk4_0,subset_type(cross_product(esk3_0,esk1_0))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
fof(c_0_37,plain,
! [X27,X28,X29] :
( ( ~ subset(X27,X28)
| ~ ilf_type(X29,set_type)
| ~ member(X29,X27)
| member(X29,X28)
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) )
& ( ilf_type(esk6_2(X27,X28),set_type)
| subset(X27,X28)
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) )
& ( member(esk6_2(X27,X28),X27)
| subset(X27,X28)
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) )
& ( ~ member(esk6_2(X27,X28),X28)
| subset(X27,X28)
| ~ ilf_type(X28,set_type)
| ~ ilf_type(X27,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p9])])])])])]) ).
fof(c_0_38,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(esk11_2(X53,X54),set_type)
| member(X53,power_set(X54))
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) )
& ( member(esk11_2(X53,X54),X53)
| member(X53,power_set(X54))
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) )
& ( ~ member(esk11_2(X53,X54),X54)
| member(X53,power_set(X54))
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])])])])]) ).
cnf(c_0_39,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_30]) ).
cnf(c_0_40,negated_conjecture,
( subset(cross_product(X1,range_of(esk4_0)),cross_product(X2,esk2_0))
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_41,negated_conjecture,
subset(domain_of(esk4_0),esk3_0),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
fof(c_0_42,plain,
! [X42] :
( ~ ilf_type(X42,binary_relation_type)
| subset(X42,cross_product(domain_of(X42),range_of(X42))) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])]) ).
cnf(c_0_43,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_22])]) ).
cnf(c_0_44,negated_conjecture,
relation_like(esk4_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_45,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p24]) ).
cnf(c_0_46,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_37]) ).
cnf(c_0_47,plain,
( member(esk11_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_38]) ).
cnf(c_0_48,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_39,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_49,negated_conjecture,
subset(cross_product(domain_of(esk4_0),range_of(esk4_0)),cross_product(esk3_0,esk2_0)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_50,plain,
( subset(X1,cross_product(domain_of(X1),range_of(X1)))
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_51,negated_conjecture,
ilf_type(esk4_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
fof(c_0_52,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)],[p20]) ).
fof(c_0_53,plain,
! [X44,X45] :
( ( ~ empty(X44)
| ~ ilf_type(X45,set_type)
| ~ member(X45,X44)
| ~ ilf_type(X44,set_type) )
& ( ilf_type(esk8_1(X44),set_type)
| empty(X44)
| ~ ilf_type(X44,set_type) )
& ( member(esk8_1(X44),X44)
| empty(X44)
| ~ ilf_type(X44,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])])]) ).
cnf(c_0_54,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_46,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_55,plain,
( member(esk11_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_22]),c_0_22])]) ).
cnf(c_0_56,negated_conjecture,
( subset(X1,cross_product(esk3_0,esk2_0))
| ~ subset(X1,cross_product(domain_of(esk4_0),range_of(esk4_0))) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_57,negated_conjecture,
subset(esk4_0,cross_product(domain_of(esk4_0),range_of(esk4_0))),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_58,plain,
! [X49,X50] :
( ( ~ ilf_type(X49,member_type(X50))
| member(X49,X50)
| empty(X50)
| ~ ilf_type(X50,set_type)
| ~ ilf_type(X49,set_type) )
& ( ~ member(X49,X50)
| ilf_type(X49,member_type(X50))
| empty(X50)
| ~ ilf_type(X50,set_type)
| ~ ilf_type(X49,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])])]) ).
cnf(c_0_59,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_60,plain,
( member(X1,power_set(X2))
| ~ member(esk11_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_61,plain,
( member(esk11_2(X1,X2),X3)
| member(X1,power_set(X2))
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_62,negated_conjecture,
subset(esk4_0,cross_product(esk3_0,esk2_0)),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_63,plain,
! [X33,X34] :
( ( ~ ilf_type(X34,subset_type(X33))
| ilf_type(X34,member_type(power_set(X33)))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( ~ ilf_type(X34,member_type(power_set(X33)))
| ilf_type(X34,subset_type(X33))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])])]) ).
cnf(c_0_64,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_58]) ).
cnf(c_0_65,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_22]),c_0_22])]) ).
cnf(c_0_66,plain,
( member(X1,power_set(X2))
| ~ member(esk11_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_22]),c_0_22])]) ).
cnf(c_0_67,negated_conjecture,
( member(esk11_2(esk4_0,X1),cross_product(esk3_0,esk2_0))
| member(esk4_0,power_set(X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,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_63]) ).
cnf(c_0_69,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_64,c_0_22]),c_0_22])]),c_0_65]) ).
cnf(c_0_70,negated_conjecture,
member(esk4_0,power_set(cross_product(esk3_0,esk2_0))),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,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_14]) ).
cnf(c_0_72,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_68,c_0_22]),c_0_22])]) ).
cnf(c_0_73,negated_conjecture,
ilf_type(esk4_0,member_type(power_set(cross_product(esk3_0,esk2_0)))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_74,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_71,c_0_22]),c_0_22])]) ).
cnf(c_0_75,negated_conjecture,
ilf_type(esk4_0,subset_type(cross_product(esk3_0,esk2_0))),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_76,negated_conjecture,
~ ilf_type(esk4_0,relation_type(esk3_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET652+3 : TPTP v8.2.0. Released v2.2.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 20 12:23:22 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.11/2.64 # Version: 3.1.0
% 17.11/2.64 # Preprocessing class: FSMSSMSSSSSNFFN.
% 17.11/2.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.11/2.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.11/2.64 # Starting new_bool_3 with 300s (1) cores
% 17.11/2.64 # Starting new_bool_1 with 300s (1) cores
% 17.11/2.64 # Starting sh5l with 300s (1) cores
% 17.11/2.64 # new_bool_3 with pid 21196 completed with status 0
% 17.11/2.64 # Result found by new_bool_3
% 17.11/2.64 # Preprocessing class: FSMSSMSSSSSNFFN.
% 17.11/2.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.11/2.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.11/2.64 # Starting new_bool_3 with 300s (1) cores
% 17.11/2.64 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 17.11/2.64 # Search class: FGHSF-FFMM21-SFFFFFNN
% 17.11/2.64 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 17.11/2.64 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 17.11/2.64 # G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with pid 21199 completed with status 0
% 17.11/2.64 # Result found by G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v
% 17.11/2.64 # Preprocessing class: FSMSSMSSSSSNFFN.
% 17.11/2.64 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 17.11/2.64 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 17.11/2.64 # Starting new_bool_3 with 300s (1) cores
% 17.11/2.64 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 17.11/2.64 # Search class: FGHSF-FFMM21-SFFFFFNN
% 17.11/2.64 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 17.11/2.64 # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2v with 163s (1) cores
% 17.11/2.64 # Preprocessing time : 0.002 s
% 17.11/2.64 # Presaturation interreduction done
% 17.11/2.64
% 17.11/2.64 # Proof found!
% 17.11/2.64 # SZS status Theorem
% 17.11/2.64 # SZS output start CNFRefutation
% See solution above
% 17.11/2.64 # Parsed axioms : 27
% 17.11/2.64 # Removed by relevancy pruning/SinE : 2
% 17.11/2.64 # Initial clauses : 50
% 17.11/2.64 # Removed in clause preprocessing : 1
% 17.11/2.64 # Initial clauses in saturation : 49
% 17.11/2.64 # Processed clauses : 12927
% 17.11/2.64 # ...of these trivial : 121
% 17.11/2.64 # ...subsumed : 9272
% 17.11/2.64 # ...remaining for further processing : 3534
% 17.11/2.64 # Other redundant clauses eliminated : 0
% 17.11/2.64 # Clauses deleted for lack of memory : 0
% 17.11/2.64 # Backward-subsumed : 163
% 17.11/2.64 # Backward-rewritten : 4
% 17.11/2.64 # Generated clauses : 209904
% 17.11/2.64 # ...of the previous two non-redundant : 208126
% 17.11/2.64 # ...aggressively subsumed : 0
% 17.11/2.64 # Contextual simplify-reflections : 4
% 17.11/2.64 # Paramodulations : 209904
% 17.11/2.64 # Factorizations : 0
% 17.11/2.64 # NegExts : 0
% 17.11/2.64 # Equation resolutions : 0
% 17.11/2.64 # Disequality decompositions : 0
% 17.11/2.64 # Total rewrite steps : 2074
% 17.11/2.64 # ...of those cached : 1173
% 17.11/2.64 # Propositional unsat checks : 0
% 17.11/2.64 # Propositional check models : 0
% 17.11/2.64 # Propositional check unsatisfiable : 0
% 17.11/2.64 # Propositional clauses : 0
% 17.11/2.64 # Propositional clauses after purity: 0
% 17.11/2.64 # Propositional unsat core size : 0
% 17.11/2.64 # Propositional preprocessing time : 0.000
% 17.11/2.64 # Propositional encoding time : 0.000
% 17.11/2.64 # Propositional solver time : 0.000
% 17.11/2.64 # Success case prop preproc time : 0.000
% 17.11/2.64 # Success case prop encoding time : 0.000
% 17.11/2.64 # Success case prop solver time : 0.000
% 17.11/2.64 # Current number of processed clauses : 3331
% 17.11/2.64 # Positive orientable unit clauses : 937
% 17.11/2.64 # Positive unorientable unit clauses: 0
% 17.11/2.64 # Negative unit clauses : 9
% 17.11/2.64 # Non-unit-clauses : 2385
% 17.11/2.64 # Current number of unprocessed clauses: 195253
% 17.11/2.64 # ...number of literals in the above : 309495
% 17.11/2.64 # Current number of archived formulas : 0
% 17.11/2.64 # Current number of archived clauses : 203
% 17.11/2.64 # Clause-clause subsumption calls (NU) : 493098
% 17.11/2.64 # Rec. Clause-clause subsumption calls : 450379
% 17.11/2.64 # Non-unit clause-clause subsumptions : 8925
% 17.11/2.64 # Unit Clause-clause subsumption calls : 47154
% 17.11/2.64 # Rewrite failures with RHS unbound : 0
% 17.11/2.64 # BW rewrite match attempts : 6621
% 17.11/2.64 # BW rewrite match successes : 4
% 17.11/2.64 # Condensation attempts : 0
% 17.11/2.64 # Condensation successes : 0
% 17.11/2.64 # Termbank termtop insertions : 3559820
% 17.11/2.64 # Search garbage collected termcells : 1031
% 17.11/2.64
% 17.11/2.64 # -------------------------------------------------
% 17.11/2.64 # User time : 2.001 s
% 17.11/2.64 # System time : 0.092 s
% 17.11/2.64 # Total time : 2.093 s
% 17.11/2.64 # Maximum resident set size: 1848 pages
% 17.11/2.64
% 17.11/2.64 # -------------------------------------------------
% 17.11/2.64 # User time : 2.002 s
% 17.11/2.64 # System time : 0.094 s
% 17.11/2.64 # Total time : 2.096 s
% 17.11/2.64 # Maximum resident set size: 1748 pages
% 17.11/2.64 % E---3.1 exiting
% 17.11/2.64 % E exiting
%------------------------------------------------------------------------------