%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET644+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n027.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 : 600s
% DateTime : Tue Jul 19 00:52:50 EDT 2022
% Result : Theorem 0.22s 1.42s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 87 ( 17 unt; 0 def)
% Number of atoms : 349 ( 11 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 451 ( 189 ~; 185 |; 35 &)
% ( 6 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-2 aty)
% Number of variables : 171 ( 17 sgn 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p21) ).
fof(p27,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p27) ).
fof(p14,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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p14) ).
fof(p20,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p20) ).
fof(p5,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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p5) ).
fof(prove_relset_1_6,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(X1,X2))
=> ( member(X3,X4)
=> ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,set_type)
& X3 = ordered_pair(X5,X6)
& member(X5,X1)
& member(X6,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_6) ).
fof(p25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p25) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p19) ).
fof(p2,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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,X2)
=> ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X1 = ordered_pair(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p1) ).
fof(p12,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p12) ).
fof(p24,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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p24) ).
fof(c_0_12,plain,
! [X3,X4] :
( ( ~ ilf_type(X3,member_type(X4))
| member(X3,X4)
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ member(X3,X4)
| ilf_type(X3,member_type(X4))
| empty(X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p21])])])])])])]) ).
fof(c_0_13,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p27]) ).
fof(c_0_14,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,subset_type(X3))
| ilf_type(X4,member_type(power_set(X3)))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,member_type(power_set(X3)))
| ilf_type(X4,subset_type(X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p14])])])])])]) ).
fof(c_0_15,plain,
! [X2] :
( ( ~ empty(power_set(X2))
| ~ ilf_type(X2,set_type) )
& ( ilf_type(power_set(X2),set_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p20])])])]) ).
fof(c_0_16,plain,
! [X5,X6,X7,X8] :
( ( ~ ilf_type(X7,subset_type(cross_product(X5,X6)))
| ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X8,relation_type(X5,X6))
| ilf_type(X8,subset_type(cross_product(X5,X6)))
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p5])])])])])]) ).
fof(c_0_17,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(X1,X2))
=> ( member(X3,X4)
=> ? [X5] :
( ilf_type(X5,set_type)
& ? [X6] :
( ilf_type(X6,set_type)
& X3 = ordered_pair(X5,X6)
& member(X5,X1)
& member(X6,X2) ) ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_6]) ).
cnf(c_0_18,plain,
( empty(X2)
| member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,member_type(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ilf_type(X2,member_type(power_set(X1)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,subset_type(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
( ilf_type(X3,subset_type(cross_product(X1,X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,negated_conjecture,
! [X11,X12] :
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,set_type)
& ilf_type(esk3_0,set_type)
& ilf_type(esk4_0,relation_type(esk1_0,esk2_0))
& member(esk3_0,esk4_0)
& ( ~ ilf_type(X11,set_type)
| ~ ilf_type(X12,set_type)
| esk3_0 != ordered_pair(X11,X12)
| ~ member(X11,esk1_0)
| ~ member(X12,esk2_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])])]) ).
fof(c_0_24,plain,
! [X3,X4] :
( ( ~ empty(X3)
| ~ ilf_type(X4,set_type)
| ~ member(X4,X3)
| ~ ilf_type(X3,set_type) )
& ( ilf_type(esk13_1(X3),set_type)
| empty(X3)
| ~ ilf_type(X3,set_type) )
& ( member(esk13_1(X3),X3)
| empty(X3)
| ~ ilf_type(X3,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[p25])])])])])])])]) ).
fof(c_0_25,plain,
! [X4,X5,X6] :
( ( ~ member(X4,power_set(X5))
| ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk9_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk9_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk9_2(X4,X5),X5)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])])])])]) ).
cnf(c_0_26,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_19]),c_0_19])]) ).
cnf(c_0_27,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_20,c_0_19]),c_0_19])]) ).
cnf(c_0_28,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_19])]) ).
cnf(c_0_29,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_22,c_0_19]),c_0_19])]) ).
cnf(c_0_30,negated_conjecture,
ilf_type(esk4_0,relation_type(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( ~ ilf_type(X1,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,plain,
( member(X3,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X3,set_type)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_34,negated_conjecture,
ilf_type(esk4_0,subset_type(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
( empty(X2)
| ilf_type(X1,member_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_36,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_19]),c_0_19])]) ).
cnf(c_0_37,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_32,c_0_19]),c_0_19]),c_0_19])]) ).
cnf(c_0_38,negated_conjecture,
member(esk4_0,power_set(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,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_35,c_0_19]),c_0_19])]),c_0_36]) ).
cnf(c_0_40,negated_conjecture,
( member(X1,cross_product(esk1_0,esk2_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
fof(c_0_41,plain,
! [X5,X6,X7,X8] :
( ( member(X5,X7)
| ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(X6,X8)
| ~ member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(X5,X7)
| ~ member(X6,X8)
| member(ordered_pair(X5,X6),cross_product(X7,X8))
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])])]) ).
cnf(c_0_42,negated_conjecture,
( ilf_type(X1,member_type(cross_product(esk1_0,esk2_0)))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,negated_conjecture,
member(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_44,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk9_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_45,plain,
( member(X1,power_set(X2))
| member(esk9_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_46,plain,
! [X5,X6] :
( ( ilf_type(esk14_2(X5,X6),set_type)
| ~ member(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk15_2(X5,X6),set_type)
| ~ member(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type) )
& ( X5 = ordered_pair(esk14_2(X5,X6),esk15_2(X5,X6))
| ~ member(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])])])])]) ).
cnf(c_0_47,plain,
( member(X2,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,negated_conjecture,
ilf_type(esk3_0,member_type(cross_product(esk1_0,esk2_0))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,plain,
( member(X1,power_set(X2))
| ~ member(esk9_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_19]),c_0_19])]) ).
cnf(c_0_50,plain,
( member(esk9_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_19]),c_0_19])]) ).
cnf(c_0_51,negated_conjecture,
( ~ member(X1,esk2_0)
| ~ member(X2,esk1_0)
| esk3_0 != ordered_pair(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_52,plain,
( X1 = ordered_pair(esk14_2(X1,X2),esk15_2(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,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_47,c_0_19]),c_0_19]),c_0_19]),c_0_19])]) ).
cnf(c_0_54,plain,
( member(X1,X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_55,negated_conjecture,
( ~ empty(cross_product(esk1_0,esk2_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_56,negated_conjecture,
( empty(cross_product(esk1_0,esk2_0))
| member(esk3_0,cross_product(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_26,c_0_48]) ).
cnf(c_0_57,plain,
( empty(X1)
| member(esk13_1(X1),X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_58,plain,
! [X2] :
( ( relation_like(X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ilf_type(X2,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) )
& ( ~ relation_like(X2)
| ~ ilf_type(X2,set_type)
| ilf_type(X2,binary_relation_type)
| ~ ilf_type(X2,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p12])])]) ).
fof(c_0_59,plain,
! [X4,X5,X6] :
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,subset_type(cross_product(X4,X5)))
| relation_like(X6) ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p24])])])])]) ).
cnf(c_0_60,plain,
( ilf_type(X2,subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_61,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,negated_conjecture,
( ordered_pair(X1,X2) != esk3_0
| ~ member(X1,esk1_0)
| ~ member(X2,esk2_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_19]),c_0_19])]) ).
cnf(c_0_63,plain,
( ordered_pair(esk14_2(X1,X2),esk15_2(X1,X2)) = X1
| ~ member(X1,X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_19])]) ).
cnf(c_0_64,negated_conjecture,
( member(X1,esk2_0)
| ~ member(ordered_pair(X2,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_53,c_0_40]) ).
cnf(c_0_65,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_54,c_0_19]),c_0_19]),c_0_19]),c_0_19])]) ).
cnf(c_0_66,negated_conjecture,
( member(esk3_0,cross_product(esk1_0,esk2_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
( empty(X1)
| member(esk13_1(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_19])]) ).
cnf(c_0_68,negated_conjecture,
~ empty(esk4_0),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_69,plain,
( ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1) ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,plain,
( relation_like(X1)
| ~ 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_59]) ).
cnf(c_0_71,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_60,c_0_19]),c_0_19])]) ).
cnf(c_0_72,plain,
ilf_type(X1,member_type(power_set(X1))),
inference(spm,[status(thm)],[c_0_39,c_0_61]) ).
cnf(c_0_73,negated_conjecture,
( X1 != esk3_0
| ~ member(esk14_2(X1,X2),esk1_0)
| ~ member(esk15_2(X1,X2),esk2_0)
| ~ member(X1,X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_74,negated_conjecture,
( member(esk15_2(X1,X2),esk2_0)
| ~ member(X1,esk4_0)
| ~ member(X1,X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_64,c_0_63]) ).
cnf(c_0_75,plain,
( member(esk14_2(X1,X2),X3)
| ~ member(X1,cross_product(X3,X4))
| ~ member(X1,X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_65,c_0_63]) ).
cnf(c_0_76,negated_conjecture,
member(esk3_0,cross_product(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]) ).
cnf(c_0_77,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_69]) ).
cnf(c_0_78,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_70,c_0_19]),c_0_19])]) ).
cnf(c_0_79,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
( X1 != esk3_0
| ~ member(esk14_2(X1,X2),esk1_0)
| ~ member(X1,esk4_0)
| ~ member(X1,X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
( member(esk14_2(esk3_0,X1),esk1_0)
| ~ member(esk3_0,X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_19])]) ).
cnf(c_0_83,plain,
relation_like(cross_product(X1,X2)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,negated_conjecture,
( ~ member(esk3_0,X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_43])]) ).
cnf(c_0_85,plain,
ilf_type(cross_product(X1,X2),binary_relation_type),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_40]),c_0_85]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET644+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : run_ET %s %d
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sun Jul 10 21:11:48 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.22/1.42 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.42 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.42 # Preprocessing time : 0.015 s
% 0.22/1.42
% 0.22/1.42 # Proof found!
% 0.22/1.42 # SZS status Theorem
% 0.22/1.42 # SZS output start CNFRefutation
% See solution above
% 0.22/1.42 # Proof object total steps : 87
% 0.22/1.42 # Proof object clause steps : 62
% 0.22/1.42 # Proof object formula steps : 25
% 0.22/1.42 # Proof object conjectures : 24
% 0.22/1.42 # Proof object clause conjectures : 21
% 0.22/1.42 # Proof object formula conjectures : 3
% 0.22/1.42 # Proof object initial clauses used : 20
% 0.22/1.42 # Proof object initial formulas used : 12
% 0.22/1.42 # Proof object generating inferences : 24
% 0.22/1.42 # Proof object simplifying inferences : 61
% 0.22/1.42 # Training examples: 0 positive, 0 negative
% 0.22/1.42 # Parsed axioms : 28
% 0.22/1.42 # Removed by relevancy pruning/SinE : 7
% 0.22/1.42 # Initial clauses : 50
% 0.22/1.42 # Removed in clause preprocessing : 3
% 0.22/1.42 # Initial clauses in saturation : 47
% 0.22/1.42 # Processed clauses : 134
% 0.22/1.42 # ...of these trivial : 13
% 0.22/1.42 # ...subsumed : 16
% 0.22/1.42 # ...remaining for further processing : 105
% 0.22/1.42 # Other redundant clauses eliminated : 0
% 0.22/1.42 # Clauses deleted for lack of memory : 0
% 0.22/1.42 # Backward-subsumed : 3
% 0.22/1.42 # Backward-rewritten : 3
% 0.22/1.42 # Generated clauses : 247
% 0.22/1.42 # ...of the previous two non-trivial : 218
% 0.22/1.42 # Contextual simplify-reflections : 3
% 0.22/1.42 # Paramodulations : 245
% 0.22/1.42 # Factorizations : 2
% 0.22/1.42 # Equation resolutions : 0
% 0.22/1.42 # Current number of processed clauses : 99
% 0.22/1.42 # Positive orientable unit clauses : 39
% 0.22/1.42 # Positive unorientable unit clauses: 0
% 0.22/1.42 # Negative unit clauses : 3
% 0.22/1.42 # Non-unit-clauses : 57
% 0.22/1.42 # Current number of unprocessed clauses: 124
% 0.22/1.42 # ...number of literals in the above : 429
% 0.22/1.42 # Current number of archived formulas : 0
% 0.22/1.42 # Current number of archived clauses : 6
% 0.22/1.42 # Clause-clause subsumption calls (NU) : 770
% 0.22/1.42 # Rec. Clause-clause subsumption calls : 474
% 0.22/1.42 # Non-unit clause-clause subsumptions : 14
% 0.22/1.42 # Unit Clause-clause subsumption calls : 69
% 0.22/1.42 # Rewrite failures with RHS unbound : 0
% 0.22/1.42 # BW rewrite match attempts : 9
% 0.22/1.42 # BW rewrite match successes : 2
% 0.22/1.42 # Condensation attempts : 0
% 0.22/1.42 # Condensation successes : 0
% 0.22/1.42 # Termbank termtop insertions : 7438
% 0.22/1.42
% 0.22/1.42 # -------------------------------------------------
% 0.22/1.42 # User time : 0.018 s
% 0.22/1.42 # System time : 0.005 s
% 0.22/1.42 # Total time : 0.023 s
% 0.22/1.42 # Maximum resident set size: 3356 pages
% 0.22/23.41 eprover: CPU time limit exceeded, terminating
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.43 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.43 eprover: No such file or directory
% 0.22/23.44 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.44 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.45 eprover: No such file or directory
% 0.22/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.46 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.47 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.48 eprover: No such file or directory
% 0.22/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.22/23.49 eprover: No such file or directory
%------------------------------------------------------------------------------