TSTP Solution File: SET660+3 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET660+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n028.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 00:52:57 EDT 2022
% Result : Theorem 0.27s 1.45s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 96 ( 12 unt; 0 def)
% Number of atoms : 414 ( 54 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 531 ( 213 ~; 227 |; 32 &)
% ( 10 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-3 aty)
% Number of variables : 196 ( 11 sgn 87 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p22,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',p22) ).
fof(p34,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p34) ).
fof(p24,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',p24) ).
fof(p23,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',p23) ).
fof(p17,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',p17) ).
fof(p33,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ilf_type(range(X1,X2,X3),subset_type(X2)) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p33) ).
fof(p14,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> unordered_pair(X1,X2) = unordered_pair(X2,X1) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p14) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = 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(p5,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,set_type)
=> ( X5 = ordered_pair(X3,X4)
<=> X5 = unordered_pair(unordered_pair(X3,X4),singleton(X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p5) ).
fof(prove_relset_1_23,conjecture,
! [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)
=> ( member(X4,X2)
=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X5,X4),X3) ) ) )
<=> range(X1,X2,X3) = X2 ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_relset_1_23) ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),X3)
=> ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p3) ).
fof(p32,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> range(X1,X2,X3) = range_of(X3) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p32) ).
fof(p27,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',p27) ).
fof(p7,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',p7) ).
fof(p15,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',p15) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,range_of(X1))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X2),X1) ) ) ) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',p1) ).
fof(c_0_16,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(esk8_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk8_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk8_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)],[p22])])])])])])]) ).
fof(c_0_17,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p34]) ).
fof(c_0_18,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)],[p24])])])])])])]) ).
fof(c_0_19,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)],[p23])])])]) ).
cnf(c_0_20,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_16]) ).
cnf(c_0_21,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,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_18]) ).
cnf(c_0_23,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_24,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)],[p17])])])])])]) ).
cnf(c_0_25,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_20,c_0_21]),c_0_21]),c_0_21])]) ).
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_22,c_0_21]),c_0_21])]) ).
cnf(c_0_27,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_21])]) ).
cnf(c_0_28,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_24]) ).
fof(c_0_29,plain,
! [X4,X5,X6] :
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(range(X4,X5,X6),subset_type(X5)) ),
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)],[p33])])])])]) ).
fof(c_0_30,plain,
! [X3,X4] :
( ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| unordered_pair(X3,X4) = unordered_pair(X4,X3) ),
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])])])])]) ).
cnf(c_0_31,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,member_type(power_set(X2))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]) ).
cnf(c_0_32,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_28,c_0_21]),c_0_21])]) ).
cnf(c_0_33,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_34,plain,
! [X4,X5,X6] :
( ( ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(X6,X5)
| member(X6,X4)
| ~ ilf_type(X6,set_type)
| X4 != X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk6_2(X4,X5),set_type)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk6_2(X4,X5),X4)
| ~ member(esk6_2(X4,X5),X5)
| X4 = X5
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk6_2(X4,X5),X4)
| member(esk6_2(X4,X5),X5)
| X4 = 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])])])])])])]) ).
fof(c_0_35,plain,
! [X6,X7,X8,X9,X10] :
( ( X10 != ordered_pair(X8,X9)
| X10 = unordered_pair(unordered_pair(X8,X9),singleton(X8))
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| ~ ilf_type(X7,set_type)
| ~ ilf_type(X6,set_type) )
& ( X10 != unordered_pair(unordered_pair(X8,X9),singleton(X8))
| X10 = ordered_pair(X8,X9)
| ~ ilf_type(X10,set_type)
| ~ 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)],[p5])])])])])]) ).
cnf(c_0_36,plain,
( unordered_pair(X1,X2) = unordered_pair(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_37,negated_conjecture,
~ ! [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)
=> ( member(X4,X2)
=> ? [X5] :
( ilf_type(X5,set_type)
& member(ordered_pair(X5,X4),X3) ) ) )
<=> range(X1,X2,X3) = X2 ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_23]) ).
cnf(c_0_38,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,plain,
( ilf_type(range(X1,X2,X3),subset_type(X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_21]),c_0_21])]) ).
cnf(c_0_40,plain,
( X1 = X2
| member(esk6_2(X1,X2),X2)
| member(esk6_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_41,plain,
! [X4,X5,X6] :
( ( member(X4,domain_of(X6))
| ~ member(ordered_pair(X4,X5),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(X5,range_of(X6))
| ~ member(ordered_pair(X4,X5),X6)
| ~ ilf_type(X6,binary_relation_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,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_42,plain,
( X5 = unordered_pair(unordered_pair(X3,X4),singleton(X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| X5 != ordered_pair(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_21]),c_0_21])]) ).
fof(c_0_44,negated_conjecture,
! [X10,X11] :
( ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,relation_type(esk14_0,esk15_0))
& ( ilf_type(esk17_0,set_type)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 )
& ( member(esk17_0,esk15_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 )
& ( ~ ilf_type(X10,set_type)
| ~ member(ordered_pair(X10,esk17_0),esk16_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 )
& ( ilf_type(esk18_1(X11),set_type)
| ~ member(X11,esk15_0)
| ~ ilf_type(X11,set_type)
| range(esk14_0,esk15_0,esk16_0) = esk15_0 )
& ( member(ordered_pair(esk18_1(X11),X11),esk16_0)
| ~ member(X11,esk15_0)
| ~ ilf_type(X11,set_type)
| range(esk14_0,esk15_0,esk16_0) = esk15_0 ) ),
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)],[c_0_37])])])])])])]) ).
cnf(c_0_45,plain,
( member(X1,X2)
| ~ member(X1,range(X3,X2,X4))
| ~ ilf_type(X4,relation_type(X3,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
( X1 = X2
| member(esk6_2(X1,X2),X1)
| member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_21]),c_0_21])]) ).
cnf(c_0_47,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,binary_relation_type)
| ~ member(ordered_pair(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,plain,
( X1 = unordered_pair(singleton(X2),unordered_pair(X2,X3))
| X1 != ordered_pair(X2,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_21]),c_0_21]),c_0_21]),c_0_21]),c_0_21])]) ).
cnf(c_0_49,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(ordered_pair(esk18_1(X1),X1),esk16_0)
| ~ ilf_type(X1,set_type)
| ~ member(X1,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_50,plain,
( X1 = range(X2,X3,X4)
| member(esk6_2(X1,range(X2,X3,X4)),X1)
| member(esk6_2(X1,range(X2,X3,X4)),X3)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,negated_conjecture,
ilf_type(esk16_0,relation_type(esk14_0,esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_21]),c_0_21])]) ).
cnf(c_0_53,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,X2)),
inference(er,[status(thm)],[c_0_48]) ).
cnf(c_0_54,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(ordered_pair(esk18_1(X1),X1),esk16_0)
| ~ member(X1,esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_21])]) ).
cnf(c_0_55,negated_conjecture,
( X1 = range(esk14_0,esk15_0,esk16_0)
| member(esk6_2(X1,range(esk14_0,esk15_0,esk16_0)),esk15_0)
| member(esk6_2(X1,range(esk14_0,esk15_0,esk16_0)),X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
( member(X1,range_of(X2))
| ~ member(unordered_pair(singleton(X3),unordered_pair(X3,X1)),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(unordered_pair(singleton(esk18_1(X1)),unordered_pair(X1,esk18_1(X1))),esk16_0)
| ~ member(X1,esk15_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_53]),c_0_43]) ).
cnf(c_0_58,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(esk6_2(esk15_0,range(esk14_0,esk15_0,esk16_0)),esk15_0) ),
inference(ef,[status(thm)],[c_0_55]) ).
fof(c_0_59,plain,
! [X4,X5,X6] :
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,relation_type(X4,X5))
| range(X4,X5,X6) = range_of(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)],[p32])])])])]) ).
fof(c_0_60,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)],[p27])])])])]) ).
fof(c_0_61,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)],[p7])])])])])]) ).
cnf(c_0_62,plain,
( member(X1,range_of(X2))
| ~ member(unordered_pair(singleton(X3),unordered_pair(X1,X3)),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_56,c_0_43]) ).
cnf(c_0_63,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(unordered_pair(singleton(esk18_1(esk6_2(esk15_0,range(esk14_0,esk15_0,esk16_0)))),unordered_pair(esk6_2(esk15_0,range(esk14_0,esk15_0,esk16_0)),esk18_1(esk6_2(esk15_0,range(esk14_0,esk15_0,esk16_0))))),esk16_0) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
fof(c_0_65,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)],[p15])])]) ).
cnf(c_0_66,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_60]) ).
cnf(c_0_67,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_61]) ).
cnf(c_0_68,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) != esk15_0
| ~ member(ordered_pair(X1,esk17_0),esk16_0)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
fof(c_0_69,plain,
! [X4,X5,X7] :
( ( ilf_type(esk1_2(X4,X5),set_type)
| ~ member(X5,range_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) )
& ( member(ordered_pair(esk1_2(X4,X5),X5),X4)
| ~ member(X5,range_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,binary_relation_type) )
& ( ~ ilf_type(X7,set_type)
| ~ member(ordered_pair(X7,X5),X4)
| member(X5,range_of(X4))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,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_70,plain,
( X1 = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk6_2(X1,X2),X2)
| ~ member(esk6_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_71,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) = esk15_0
| member(esk6_2(esk15_0,range(esk14_0,esk15_0,esk16_0)),range_of(esk16_0))
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_21]),c_0_21])]) ).
cnf(c_0_73,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_65]) ).
cnf(c_0_74,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_66,c_0_21]),c_0_21])]) ).
cnf(c_0_75,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_67,c_0_21]),c_0_21])]) ).
cnf(c_0_76,negated_conjecture,
( range(esk14_0,esk15_0,esk16_0) != esk15_0
| ~ member(ordered_pair(X1,esk17_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_21])]) ).
cnf(c_0_77,plain,
( member(ordered_pair(esk1_2(X1,X2),X2),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,range_of(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_78,plain,
( X1 = X2
| ~ member(esk6_2(X1,X2),X2)
| ~ member(esk6_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_21]),c_0_21])]) ).
cnf(c_0_79,negated_conjecture,
( range_of(esk16_0) = esk15_0
| member(esk6_2(esk15_0,range_of(esk16_0)),range_of(esk16_0))
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_51])]) ).
cnf(c_0_80,negated_conjecture,
( range_of(esk16_0) = esk15_0
| member(esk6_2(esk15_0,range_of(esk16_0)),esk15_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_72]),c_0_51])]) ).
cnf(c_0_81,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_73]) ).
cnf(c_0_82,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_83,negated_conjecture,
( range_of(esk16_0) != esk15_0
| ~ member(ordered_pair(X1,esk17_0),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_72]),c_0_51])]) ).
cnf(c_0_84,plain,
( member(ordered_pair(esk1_2(X1,X2),X2),X1)
| ~ member(X2,range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_21])]) ).
cnf(c_0_85,negated_conjecture,
( range_of(esk16_0) = esk15_0
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_86,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_21])]) ).
cnf(c_0_87,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_82,c_0_51]) ).
cnf(c_0_88,negated_conjecture,
( member(esk17_0,esk15_0)
| range(esk14_0,esk15_0,esk16_0) != esk15_0 ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_89,negated_conjecture,
( range_of(esk16_0) != esk15_0
| ~ member(esk17_0,range_of(esk16_0))
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_90,negated_conjecture,
range_of(esk16_0) = esk15_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_87])]) ).
cnf(c_0_91,negated_conjecture,
( member(esk17_0,esk15_0)
| range_of(esk16_0) != esk15_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_72]),c_0_51])]) ).
cnf(c_0_92,negated_conjecture,
( ~ member(esk17_0,esk15_0)
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_89,c_0_90]),c_0_90])]) ).
cnf(c_0_93,negated_conjecture,
member(esk17_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_90])]) ).
cnf(c_0_94,negated_conjecture,
~ ilf_type(esk16_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93])]) ).
cnf(c_0_95,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_86]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET660+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.14 % Command : run_ET %s %d
% 0.16/0.36 % Computer : n028.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 600
% 0.16/0.36 % DateTime : Sun Jul 10 05:49:42 EDT 2022
% 0.16/0.36 % CPUTime :
% 0.27/1.45 # Running protocol protocol_eprover_29fa5c60d0ee03ec4f64b055553dc135fbe4ee3a for 23 seconds:
% 0.27/1.45 # Preprocessing time : 0.020 s
% 0.27/1.45
% 0.27/1.45 # Proof found!
% 0.27/1.45 # SZS status Theorem
% 0.27/1.45 # SZS output start CNFRefutation
% See solution above
% 0.27/1.45 # Proof object total steps : 96
% 0.27/1.45 # Proof object clause steps : 63
% 0.27/1.45 # Proof object formula steps : 33
% 0.27/1.45 # Proof object conjectures : 26
% 0.27/1.45 # Proof object clause conjectures : 23
% 0.27/1.45 # Proof object formula conjectures : 3
% 0.27/1.45 # Proof object initial clauses used : 20
% 0.27/1.45 # Proof object initial formulas used : 16
% 0.27/1.45 # Proof object generating inferences : 20
% 0.27/1.45 # Proof object simplifying inferences : 76
% 0.27/1.45 # Training examples: 0 positive, 0 negative
% 0.27/1.45 # Parsed axioms : 35
% 0.27/1.45 # Removed by relevancy pruning/SinE : 0
% 0.27/1.45 # Initial clauses : 73
% 0.27/1.45 # Removed in clause preprocessing : 3
% 0.27/1.45 # Initial clauses in saturation : 70
% 0.27/1.45 # Processed clauses : 988
% 0.27/1.45 # ...of these trivial : 25
% 0.27/1.45 # ...subsumed : 297
% 0.27/1.45 # ...remaining for further processing : 666
% 0.27/1.45 # Other redundant clauses eliminated : 3
% 0.27/1.45 # Clauses deleted for lack of memory : 0
% 0.27/1.45 # Backward-subsumed : 83
% 0.27/1.45 # Backward-rewritten : 180
% 0.27/1.45 # Generated clauses : 9709
% 0.27/1.45 # ...of the previous two non-trivial : 9619
% 0.27/1.45 # Contextual simplify-reflections : 195
% 0.27/1.45 # Paramodulations : 9640
% 0.27/1.45 # Factorizations : 62
% 0.27/1.45 # Equation resolutions : 5
% 0.27/1.45 # Current number of processed clauses : 399
% 0.27/1.45 # Positive orientable unit clauses : 50
% 0.27/1.45 # Positive unorientable unit clauses: 1
% 0.27/1.45 # Negative unit clauses : 4
% 0.27/1.45 # Non-unit-clauses : 344
% 0.27/1.45 # Current number of unprocessed clauses: 7311
% 0.27/1.45 # ...number of literals in the above : 34229
% 0.27/1.45 # Current number of archived formulas : 0
% 0.27/1.45 # Current number of archived clauses : 265
% 0.27/1.45 # Clause-clause subsumption calls (NU) : 58070
% 0.27/1.45 # Rec. Clause-clause subsumption calls : 25898
% 0.27/1.45 # Non-unit clause-clause subsumptions : 492
% 0.27/1.45 # Unit Clause-clause subsumption calls : 1244
% 0.27/1.45 # Rewrite failures with RHS unbound : 0
% 0.27/1.45 # BW rewrite match attempts : 29
% 0.27/1.45 # BW rewrite match successes : 15
% 0.27/1.45 # Condensation attempts : 0
% 0.27/1.45 # Condensation successes : 0
% 0.27/1.45 # Termbank termtop insertions : 269774
% 0.27/1.45
% 0.27/1.45 # -------------------------------------------------
% 0.27/1.45 # User time : 0.219 s
% 0.27/1.45 # System time : 0.006 s
% 0.27/1.45 # Total time : 0.225 s
% 0.27/1.45 # Maximum resident set size: 14944 pages
% 0.27/23.44 eprover: CPU time limit exceeded, terminating
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.45 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.45 eprover: No such file or directory
% 0.27/23.46 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.46 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.47 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.47 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.48 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.48 eprover: No such file or directory
% 0.27/23.49 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.49 eprover: No such file or directory
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.50 eprover: CPU time limit exceeded, terminating
% 0.27/23.50 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.50 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.51 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.51 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.52 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.52 eprover: No such file or directory
% 0.27/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.53 eprover: No such file or directory
% 0.27/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.53 eprover: No such file or directory
% 0.27/23.53 eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 0.27/23.53 eprover: No such file or directory
%------------------------------------------------------------------------------