TSTP Solution File: SET670+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET670+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n006.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 00:53:01 EDT 2022
% Result : Theorem 2.03s 267.19s
% Output : CNFRefutation 2.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 17
% Syntax : Number of formulae : 126 ( 21 unt; 0 def)
% Number of atoms : 558 ( 9 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 751 ( 319 ~; 331 |; 36 &)
% ( 8 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-4 aty)
% Number of variables : 340 ( 37 sgn 102 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p7,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)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p7) ).
fof(p28,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p28) ).
fof(prove_relset_1_33,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,X3))
=> ilf_type(restrict4(X1,X3,X4,X2),relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',prove_relset_1_33) ).
fof(p4,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',p4) ).
fof(p18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( relation_like(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
=> ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p18) ).
fof(p20,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',p20) ).
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,binary_relation_type)
=> ( member(ordered_pair(X2,X3),restrict(X4,X1))
<=> ( member(X2,X1)
& member(ordered_pair(X2,X3),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p3) ).
fof(p19,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',p19) ).
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',p5) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p27) ).
fof(p26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> restrict4(X1,X2,X3,X4) = restrict(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p26) ).
fof(p11,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',p11) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> relation_like(cross_product(X1,X2)) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(ordered_pair(X3,X4),X1)
=> member(ordered_pair(X3,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p',p1) ).
fof(p22,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',p22) ).
fof(p21,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',p21) ).
fof(p13,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',p13) ).
fof(c_0_17,plain,
! [X6,X7,X8,X9,X10] :
( ( member(X8,X6)
| ~ member(ordered_pair(X8,X9),X10)
| ~ ilf_type(X10,relation_type(X6,X7))
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( member(X9,X7)
| ~ member(ordered_pair(X8,X9),X10)
| ~ ilf_type(X10,relation_type(X6,X7))
| ~ 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(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])])]) ).
fof(c_0_18,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p28]) ).
fof(c_0_19,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,X3))
=> ilf_type(restrict4(X1,X3,X4,X2),relation_type(X2,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_33]) ).
fof(c_0_20,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)],[p4])])])])])]) ).
fof(c_0_21,plain,
! [X5,X6,X10,X11] :
( ( ilf_type(esk6_2(X5,X6),set_type)
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk7_2(X5,X6),set_type)
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( X6 = ordered_pair(esk6_2(X5,X6),esk7_2(X5,X6))
| ~ member(X6,X5)
| ~ ilf_type(X6,set_type)
| ~ relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ilf_type(esk8_1(X5),set_type)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( member(esk8_1(X5),X5)
| relation_like(X5)
| ~ ilf_type(X5,set_type) )
& ( ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,set_type)
| esk8_1(X5) != ordered_pair(X10,X11)
| relation_like(X5)
| ~ 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)],[p18])])])])])])]) ).
cnf(c_0_22,plain,
( member(X4,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,relation_type(X1,X2))
| ~ member(ordered_pair(X3,X4),X5) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,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(esk12_0,esk14_0))
& ~ ilf_type(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),relation_type(esk13_0,esk14_0)) ),
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_19])])])])]) ).
cnf(c_0_25,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_20]) ).
cnf(c_0_26,plain,
( X2 = ordered_pair(esk6_2(X1,X2),esk7_2(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ relation_like(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_27,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)],[p20])])])])])])]) ).
fof(c_0_28,plain,
! [X5,X6,X7,X8] :
( ( member(X6,X5)
| ~ member(ordered_pair(X6,X7),restrict(X8,X5))
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( member(ordered_pair(X6,X7),X8)
| ~ member(ordered_pair(X6,X7),restrict(X8,X5))
| ~ ilf_type(X8,binary_relation_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X5,set_type) )
& ( ~ member(X6,X5)
| ~ member(ordered_pair(X6,X7),X8)
| member(ordered_pair(X6,X7),restrict(X8,X5))
| ~ ilf_type(X8,binary_relation_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)],[p3])])])])])]) ).
cnf(c_0_29,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_31,negated_conjecture,
ilf_type(esk15_0,relation_type(esk12_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,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_25,c_0_23]),c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_33,plain,
( ordered_pair(esk6_2(X1,X2),esk7_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_23]),c_0_23])]) ).
cnf(c_0_34,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_27]) ).
cnf(c_0_35,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_27]) ).
cnf(c_0_36,plain,
( member(ordered_pair(X2,X3),X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_37,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)],[p19])])])])]) ).
fof(c_0_38,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_39,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X8,set_type)
| ilf_type(restrict4(X5,X6,X7,X8),relation_type(X5,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)],[p27])])])])]) ).
fof(c_0_40,plain,
! [X5,X6,X7,X8] :
( ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,relation_type(X5,X6))
| ~ ilf_type(X8,set_type)
| restrict4(X5,X6,X7,X8) = restrict(X7,X8) ),
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)],[p26])])])])]) ).
cnf(c_0_41,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_23]),c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_42,negated_conjecture,
( member(X1,esk14_0)
| ~ member(ordered_pair(X2,X1),esk15_0) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_43,plain,
( member(esk6_2(X1,X2),X3)
| ~ relation_like(X1)
| ~ member(X2,cross_product(X3,X4))
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_44,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_34,c_0_23]),c_0_23])]) ).
cnf(c_0_45,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_35,c_0_23]),c_0_23])]) ).
cnf(c_0_46,plain,
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X3,X4))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_47,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_37]) ).
cnf(c_0_48,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_38]) ).
cnf(c_0_49,plain,
( ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_50,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
fof(c_0_51,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)],[p11])])]) ).
cnf(c_0_52,plain,
( member(X1,cross_product(X2,X3))
| ~ relation_like(X4)
| ~ member(esk7_2(X4,X1),X3)
| ~ member(esk6_2(X4,X1),X2)
| ~ member(X1,X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_53,negated_conjecture,
( member(esk7_2(X1,X2),esk14_0)
| ~ relation_like(X1)
| ~ member(X2,esk15_0)
| ~ member(X2,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_33]) ).
cnf(c_0_54,plain,
( member(esk6_2(X1,ordered_pair(X2,X3)),X4)
| ~ relation_like(X1)
| ~ member(ordered_pair(X2,X3),X1)
| ~ member(X3,X5)
| ~ member(X2,X4) ),
inference(spm,[status(thm)],[c_0_43,c_0_41]) ).
cnf(c_0_55,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
fof(c_0_56,plain,
! [X3,X4] :
( ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| relation_like(cross_product(X3,X4)) ),
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_57,plain,
( member(X1,X2)
| ~ relation_like(X3)
| ~ member(X1,restrict(X2,X4))
| ~ member(X1,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_46,c_0_33]) ).
cnf(c_0_58,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_47,c_0_23]),c_0_23])]) ).
cnf(c_0_59,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_48,c_0_23]),c_0_23])]) ).
cnf(c_0_60,plain,
( ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_61,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_62,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_51]) ).
cnf(c_0_63,negated_conjecture,
( member(X1,cross_product(X2,esk14_0))
| ~ relation_like(X3)
| ~ member(esk6_2(X3,X1),X2)
| ~ member(X1,esk15_0)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_64,plain,
( member(esk6_2(X1,ordered_pair(X2,X3)),X4)
| ~ relation_like(X1)
| ~ member(ordered_pair(X2,X3),X1)
| ~ member(X2,X4) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,plain,
( relation_like(cross_product(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_66,plain,
( member(esk9_2(restrict(X1,X2),X3),X1)
| member(restrict(X1,X2),power_set(X3))
| ~ relation_like(X4)
| ~ member(esk9_2(restrict(X1,X2),X3),X4)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_57,c_0_45]) ).
cnf(c_0_67,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
( ilf_type(restrict(X1,X2),relation_type(X3,X4))
| ~ ilf_type(X1,relation_type(X3,X4)) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_62]) ).
cnf(c_0_70,negated_conjecture,
( member(ordered_pair(X1,X2),cross_product(X3,esk14_0))
| ~ relation_like(X4)
| ~ member(ordered_pair(X1,X2),esk15_0)
| ~ member(ordered_pair(X1,X2),X4)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
relation_like(cross_product(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_23]),c_0_23])]) ).
cnf(c_0_72,plain,
( member(esk9_2(restrict(X1,X2),X3),X1)
| member(restrict(X1,X2),power_set(X3))
| ~ relation_like(restrict(X1,X2))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_66,c_0_45]) ).
cnf(c_0_73,plain,
( relation_like(restrict(X1,X2))
| ~ ilf_type(X1,relation_type(X3,X4)) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_23])]) ).
cnf(c_0_75,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_67,c_0_31]) ).
cnf(c_0_76,plain,
( relation_like(restrict4(X1,X2,X3,X4))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[c_0_67,c_0_60]) ).
cnf(c_0_77,negated_conjecture,
( member(ordered_pair(X1,X2),cross_product(X3,esk14_0))
| ~ member(ordered_pair(X1,X2),esk15_0)
| ~ member(X1,X3)
| ~ member(X2,X4)
| ~ member(X1,X5) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_41]),c_0_71])]) ).
cnf(c_0_78,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_27]) ).
cnf(c_0_79,plain,
( member(restrict(X1,X2),power_set(X1))
| ~ relation_like(restrict(X1,X2))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_44,c_0_72]) ).
cnf(c_0_80,negated_conjecture,
relation_like(restrict(esk15_0,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_31]) ).
cnf(c_0_81,negated_conjecture,
ilf_type(esk15_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_82,plain,
( ilf_type(restrict4(X1,X2,X3,X4),binary_relation_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[c_0_74,c_0_76]) ).
fof(c_0_83,plain,
! [X5,X6,X7,X8] :
( ( ~ subset(X5,X6)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X8,set_type)
| ~ member(ordered_pair(X7,X8),X5)
| member(ordered_pair(X7,X8),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ilf_type(esk1_2(X5,X6),set_type)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ilf_type(esk2_2(X5,X6),set_type)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( member(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X5)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_type) )
& ( ~ member(ordered_pair(esk1_2(X5,X6),esk2_2(X5,X6)),X6)
| subset(X5,X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,binary_relation_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_84,negated_conjecture,
( member(ordered_pair(X1,X2),cross_product(X3,esk14_0))
| ~ member(ordered_pair(X1,X2),esk15_0)
| ~ member(X1,X3)
| ~ member(X1,X4) ),
inference(spm,[status(thm)],[c_0_77,c_0_55]) ).
cnf(c_0_85,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_78,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_86,negated_conjecture,
member(restrict(esk15_0,X1),power_set(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_81])]) ).
cnf(c_0_87,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,relation_type(X3,X4)) ),
inference(spm,[status(thm)],[c_0_82,c_0_61]) ).
cnf(c_0_88,plain,
( subset(X1,X2)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_89,negated_conjecture,
( member(ordered_pair(X1,X2),cross_product(X3,esk14_0))
| ~ member(ordered_pair(X1,X2),esk15_0)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_84,c_0_55]) ).
cnf(c_0_90,plain,
ilf_type(cross_product(X1,X2),binary_relation_type),
inference(spm,[status(thm)],[c_0_74,c_0_71]) ).
cnf(c_0_91,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,restrict(esk15_0,X2)) ),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_92,plain,
( subset(X1,X2)
| member(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_93,negated_conjecture,
ilf_type(restrict(esk15_0,X1),binary_relation_type),
inference(spm,[status(thm)],[c_0_87,c_0_31]) ).
cnf(c_0_94,plain,
( member(X2,X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ member(ordered_pair(X2,X3),restrict(X4,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_95,plain,
( member(ordered_pair(X3,X4),X2)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ member(ordered_pair(X3,X4),X1)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_96,negated_conjecture,
( subset(X1,cross_product(X2,esk14_0))
| ~ member(ordered_pair(esk1_2(X1,cross_product(X2,esk14_0)),esk2_2(X1,cross_product(X2,esk14_0))),esk15_0)
| ~ member(esk1_2(X1,cross_product(X2,esk14_0)),X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_97,negated_conjecture,
( member(ordered_pair(esk1_2(restrict(esk15_0,X1),X2),esk2_2(restrict(esk15_0,X1),X2)),esk15_0)
| subset(restrict(esk15_0,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93])]) ).
cnf(c_0_98,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),restrict(X4,X2))
| ~ ilf_type(X4,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_23]),c_0_23]),c_0_23])]) ).
cnf(c_0_99,plain,
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),X4)
| ~ subset(X4,X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_23]),c_0_23])]) ).
cnf(c_0_100,negated_conjecture,
( subset(restrict(esk15_0,X1),cross_product(X2,esk14_0))
| ~ member(esk1_2(restrict(esk15_0,X1),cross_product(X2,esk14_0)),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_93]),c_0_90])]) ).
cnf(c_0_101,plain,
( member(esk1_2(restrict(X1,X2),X3),X2)
| subset(restrict(X1,X2),X3)
| ~ ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X3,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_98,c_0_92]) ).
cnf(c_0_102,plain,
( member(X1,X2)
| ~ relation_like(X3)
| ~ member(X1,X4)
| ~ member(X1,X3)
| ~ subset(X4,X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X4,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_99,c_0_33]) ).
cnf(c_0_103,negated_conjecture,
subset(restrict(esk15_0,X1),cross_product(X1,esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_93]),c_0_81]),c_0_90])]) ).
cnf(c_0_104,negated_conjecture,
( member(X1,cross_product(X2,esk14_0))
| ~ relation_like(X3)
| ~ member(X1,restrict(esk15_0,X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_90]),c_0_93])]) ).
fof(c_0_105,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)],[p22])])])])])])]) ).
cnf(c_0_106,negated_conjecture,
( member(esk9_2(restrict(esk15_0,X1),X2),cross_product(X1,esk14_0))
| member(restrict(esk15_0,X1),power_set(X2))
| ~ relation_like(X3)
| ~ member(esk9_2(restrict(esk15_0,X1),X2),X3) ),
inference(spm,[status(thm)],[c_0_104,c_0_45]) ).
cnf(c_0_107,negated_conjecture,
( member(esk9_2(restrict(esk15_0,X1),X2),esk15_0)
| member(restrict(esk15_0,X1),power_set(X2)) ),
inference(spm,[status(thm)],[c_0_91,c_0_45]) ).
fof(c_0_108,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)],[p21])])])]) ).
fof(c_0_109,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)],[p13])])])])])]) ).
cnf(c_0_110,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_105]) ).
cnf(c_0_111,negated_conjecture,
( member(esk9_2(restrict(esk15_0,X1),X2),cross_product(X1,esk14_0))
| member(restrict(esk15_0,X1),power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_75])]) ).
cnf(c_0_112,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_113,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_109]) ).
cnf(c_0_114,plain,
( empty(X1)
| ilf_type(X2,member_type(X1))
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_23]),c_0_23])]) ).
cnf(c_0_115,negated_conjecture,
member(restrict(esk15_0,X1),power_set(cross_product(X1,esk14_0))),
inference(spm,[status(thm)],[c_0_44,c_0_111]) ).
cnf(c_0_116,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_112,c_0_23])]) ).
cnf(c_0_117,plain,
( ilf_type(X3,relation_type(X1,X2))
| ~ 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_38]) ).
cnf(c_0_118,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_113,c_0_23]),c_0_23])]) ).
cnf(c_0_119,negated_conjecture,
ilf_type(restrict(esk15_0,X1),member_type(power_set(cross_product(X1,esk14_0)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_120,negated_conjecture,
~ ilf_type(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_121,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_117,c_0_23]),c_0_23])]) ).
cnf(c_0_122,negated_conjecture,
ilf_type(restrict(esk15_0,X1),subset_type(cross_product(X1,esk14_0))),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_123,negated_conjecture,
~ ilf_type(restrict(esk15_0,esk13_0),relation_type(esk13_0,esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_61]),c_0_31])]) ).
cnf(c_0_124,negated_conjecture,
ilf_type(restrict(esk15_0,X1),relation_type(X1,esk14_0)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_125,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_123,c_0_124])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET670+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : run_ET %s %d
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 05:53:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/23.40 eprover: CPU time limit exceeded, terminating
% 0.37/23.40 eprover: CPU time limit exceeded, terminating
% 0.37/23.41 eprover: CPU time limit exceeded, terminating
% 0.37/23.41 eprover: CPU time limit exceeded, terminating
% 0.53/46.42 eprover: CPU time limit exceeded, terminating
% 0.53/46.43 eprover: CPU time limit exceeded, terminating
% 0.53/46.44 eprover: CPU time limit exceeded, terminating
% 0.53/46.46 eprover: CPU time limit exceeded, terminating
% 0.69/69.45 eprover: CPU time limit exceeded, terminating
% 0.69/69.46 eprover: CPU time limit exceeded, terminating
% 0.69/69.47 eprover: CPU time limit exceeded, terminating
% 0.69/69.49 eprover: CPU time limit exceeded, terminating
% 0.85/92.47 eprover: CPU time limit exceeded, terminating
% 0.85/92.48 eprover: CPU time limit exceeded, terminating
% 0.85/92.49 eprover: CPU time limit exceeded, terminating
% 0.85/92.50 eprover: CPU time limit exceeded, terminating
% 1.00/115.51 eprover: CPU time limit exceeded, terminating
% 1.00/115.52 eprover: CPU time limit exceeded, terminating
% 1.00/115.52 eprover: CPU time limit exceeded, terminating
% 1.09/128.42 eprover: CPU time limit exceeded, terminating
% 1.16/138.54 eprover: CPU time limit exceeded, terminating
% 1.16/138.55 eprover: CPU time limit exceeded, terminating
% 1.24/151.46 eprover: CPU time limit exceeded, terminating
% 1.27/157.22 eprover: CPU time limit exceeded, terminating
% 1.30/161.56 eprover: CPU time limit exceeded, terminating
% 1.30/161.57 eprover: CPU time limit exceeded, terminating
% 1.39/174.49 eprover: CPU time limit exceeded, terminating
% 1.43/180.25 eprover: CPU time limit exceeded, terminating
% 1.46/184.59 eprover: CPU time limit exceeded, terminating
% 1.55/197.56 eprover: CPU time limit exceeded, terminating
% 1.57/199.92 eprover: CPU time limit exceeded, terminating
% 1.59/203.28 eprover: CPU time limit exceeded, terminating
% 1.62/207.61 eprover: CPU time limit exceeded, terminating
% 1.73/221.91 eprover: CPU time limit exceeded, terminating
% 1.73/222.94 eprover: CPU time limit exceeded, terminating
% 1.75/226.32 eprover: CPU time limit exceeded, terminating
% 1.88/245.98 eprover: CPU time limit exceeded, terminating
% 1.91/249.35 eprover: CPU time limit exceeded, terminating
% 2.03/267.19 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # Preprocessing time : 0.019 s
% 2.03/267.19 # Running protocol protocol_eprover_f6eb5f7f05126ea361481ae651a4823314e3d740 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,20000,1.0)
% 2.03/267.19 # Preprocessing time : 0.018 s
% 2.03/267.19 # Running protocol protocol_eprover_a172c605141d0894bf6fdc293a5220c6c2a32117 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # Preprocessing time : 0.011 s
% 2.03/267.19 # Running protocol protocol_eprover_f8b0f932169414d689b89e2a8b18d4600533b975 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # Preprocessing time : 0.020 s
% 2.03/267.19 # Running protocol protocol_eprover_fc511518e5f98a6b2c7baef820b71b6d1abb3e55 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,02,80,1.0)
% 2.03/267.19 # Preprocessing time : 0.011 s
% 2.03/267.19 # Running protocol protocol_eprover_95b56b3f38545d2cfee43b45856d192a814b65d5 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # Preprocessing time : 0.020 s
% 2.03/267.19 # Running protocol protocol_eprover_6017f334107ca4679a9978dd19d7c76a8bd36e48 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # SinE strategy is GSinE(CountFormulas,,1.4,,02,20000,1.0)
% 2.03/267.19 # Preprocessing time : 0.011 s
% 2.03/267.19 # Running protocol protocol_eprover_29f46a864b4eba32a7d0333eeab34cc2a3bfeeb2 for 23 seconds:
% 2.03/267.19 # SinE strategy is GSinE(CountFormulas,hypos,1.1,,04,500,1.0)
% 2.03/267.19 # Preprocessing time : 0.010 s
% 2.03/267.19
% 2.03/267.19 # Failure: Out of unprocessed clauses!
% 2.03/267.19 # OLD status GaveUp
% 2.03/267.19 # Parsed axioms : 29
% 2.03/267.19 # Removed by relevancy pruning/SinE : 17
% 2.03/267.19 # Initial clauses : 19
% 2.03/267.19 # Removed in clause preprocessing : 2
% 2.03/267.19 # Initial clauses in saturation : 17
% 2.03/267.19 # Processed clauses : 15897
% 2.03/267.19 # ...of these trivial : 7287
% 2.03/267.19 # ...subsumed : 0
% 2.03/267.19 # ...remaining for further processing : 8610
% 2.03/267.19 # Other redundant clauses eliminated : 0
% 2.03/267.19 # Clauses deleted for lack of memory : 144
% 2.03/267.19 # Backward-subsumed : 0
% 2.03/267.19 # Backward-rewritten : 7622
% 2.03/267.19 # Generated clauses : 16307
% 2.03/267.19 # ...of the previous two non-trivial : 23926
% 2.03/267.19 # Contextual simplify-reflections : 0
% 2.03/267.19 # Paramodulations : 16307
% 2.03/267.19 # Factorizations : 0
% 2.03/267.19 # Equation resolutions : 0
% 2.03/267.19 # Current number of processed clauses : 988
% 2.03/267.19 # Positive orientable unit clauses : 979
% 2.03/267.19 # Positive unorientable unit clauses: 0
% 2.03/267.19 # Negative unit clauses : 1
% 2.03/267.19 # Non-unit-clauses : 8
% 2.03/267.19 # Current number of unprocessed clauses: 0
% 2.03/267.19 # ...number of literals in the above : 0
% 2.03/267.19 # Current number of archived formulas : 0
% 2.03/267.19 # Current number of archived clauses : 7622
% 2.03/267.19 # Clause-clause subsumption calls (NU) : 5
% 2.03/267.19 # Rec. Clause-clause subsumption calls : 3
% 2.03/267.19 # Non-unit clause-clause subsumptions : 0
% 2.03/267.19 # Unit Clause-clause subsumption calls : 2
% 2.03/267.19 # Rewrite failures with RHS unbound : 0
% 2.03/267.19 # BW rewrite match attempts : 333075
% 2.03/267.19 # BW rewrite match successes : 325
% 2.03/267.19 # Condensation attempts : 0
% 2.03/267.19 # Condensation successes : 0
% 2.03/267.19 # Termbank termtop insertions : 6114753
% 2.03/267.19
% 2.03/267.19 # -------------------------------------------------
% 2.03/267.19 # User time : 15.196 s
% 2.03/267.19 # System time : 0.121 s
% 2.03/267.19 # Total time : 15.317 s
% 2.03/267.19 # Maximum resident set size: 169492 pages
% 2.03/267.19 # Running protocol protocol_eprover_6c6e328223588bd61ac14315e52cd57432d78a40 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # SinE strategy is GSinE(CountFormulas,hypos,1.2,,04,20000,1.0)
% 2.03/267.19 # Preprocessing time : 0.011 s
% 2.03/267.19 # Running protocol protocol_eprover_d060f57557112503de4e70311f17201fbe20b6a3 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # Preprocessing time : 0.011 s
% 2.03/267.19 # Running protocol protocol_eprover_7e73d521eed2eff17dc17155adefb3ab5d9c1092 for 23 seconds:
% 2.03/267.19
% 2.03/267.19 # Failure: Resource limit exceeded (time)
% 2.03/267.19 # OLD status Res
% 2.03/267.19 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,03,80,1.0)
% 2.03/267.19 # Preprocessing time : 0.020 s
% 2.03/267.19 # Running protocol protocol_eprover_d352e266807dcdd44825904f97f73b76738a5cd0 for 23 seconds:
% 2.03/267.19 # Preprocessing time : 0.021 s
% 2.03/267.19
% 2.03/267.19 # Proof found!
% 2.03/267.19 # SZS status Theorem
% 2.03/267.19 # SZS output start CNFRefutation
% See solution above
% 2.03/267.19 # Proof object total steps : 126
% 2.03/267.19 # Proof object clause steps : 91
% 2.03/267.19 # Proof object formula steps : 35
% 2.03/267.19 # Proof object conjectures : 32
% 2.03/267.19 # Proof object clause conjectures : 29
% 2.03/267.19 # Proof object formula conjectures : 3
% 2.03/267.19 # Proof object initial clauses used : 25
% 2.03/267.19 # Proof object initial formulas used : 17
% 2.03/267.19 # Proof object generating inferences : 44
% 2.03/267.19 # Proof object simplifying inferences : 95
% 2.03/267.19 # Training examples: 0 positive, 0 negative
% 2.03/267.19 # Parsed axioms : 29
% 2.03/267.19 # Removed by relevancy pruning/SinE : 0
% 2.03/267.19 # Initial clauses : 58
% 2.03/267.19 # Removed in clause preprocessing : 3
% 2.03/267.19 # Initial clauses in saturation : 55
% 2.03/267.19 # Processed clauses : 48515
% 2.03/267.19 # ...of these trivial : 235
% 2.03/267.19 # ...subsumed : 28485
% 2.03/267.19 # ...remaining for further processing : 19795
% 2.03/267.19 # Other redundant clauses eliminated : 0
% 2.03/267.19 # Clauses deleted for lack of memory : 936925
% 2.03/267.19 # Backward-subsumed : 393
% 2.03/267.19 # Backward-rewritten : 249
% 2.03/267.19 # Generated clauses : 1430941
% 2.03/267.19 # ...of the previous two non-trivial : 1390306
% 2.03/267.19 # Contextual simplify-reflections : 0
% 2.03/267.19 # Paramodulations : 1429265
% 2.03/267.19 # Factorizations : 0
% 2.03/267.19 # Equation resolutions : 13
% 2.03/267.19 # Current number of processed clauses : 19149
% 2.03/267.19 # Positive orientable unit clauses : 1213
% 2.03/267.19 # Positive unorientable unit clauses: 0
% 2.03/267.19 # Negative unit clauses : 65
% 2.03/267.19 # Non-unit-clauses : 17871
% 2.03/267.19 # Current number of unprocessed clauses: 134158
% 2.03/267.19 # ...number of literals in the above : 678660
% 2.03/267.19 # Current number of archived formulas : 0
% 2.03/267.19 # Current number of archived clauses : 646
% 2.03/267.19 # Clause-clause subsumption calls (NU) : 34623176
% 2.03/267.19 # Rec. Clause-clause subsumption calls : 11721712
% 2.03/267.19 # Non-unit clause-clause subsumptions : 26430
% 2.03/267.19 # Unit Clause-clause subsumption calls : 1496598
% 2.03/267.19 # Rewrite failures with RHS unbound : 0
% 2.03/267.19 # BW rewrite match attempts : 47394
% 2.03/267.19 # BW rewrite match successes : 97
% 2.03/267.19 # Condensation attempts : 0
% 2.03/267.19 # Condensation successes : 0
% 2.03/267.19 # Termbank termtop insertions : 33224026
% 2.03/267.19
% 2.03/267.19 # -------------------------------------------------
% 2.03/267.19 # User time : 20.011 s
% 2.03/267.19 # System time : 0.149 s
% 2.03/267.19 # Total time : 20.160 s
% 2.03/267.19 # Maximum resident set size: 160476 pages
%------------------------------------------------------------------------------