TSTP Solution File: SET678+3 by ET---2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : SET678+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 00:53:05 EDT 2022
% Result : Theorem 0.28s 1.46s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 90 ( 15 unt; 0 def)
% Number of atoms : 328 ( 26 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 401 ( 163 ~; 166 |; 21 &)
% ( 6 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-3 aty)
% Number of variables : 174 ( 8 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(p28,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p28) ).
fof(p38,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p38) ).
fof(p22,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,subset_type(X1))
<=> ilf_type(X2,member_type(power_set(X1))) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p22) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p27) ).
fof(p35,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/sandbox2/solver/bin/../tmp/theBenchmark.p',p35) ).
fof(p34,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/sandbox2/solver/bin/../tmp/theBenchmark.p',p34) ).
fof(p7,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ilf_type(X2,identity_relation_of_type(X1))
<=> ilf_type(X2,relation_type(X1,X1)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p7) ).
fof(prove_relset_1_45,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( compose(X2,identity_relation_of(X1)) = X2
& compose(identity_relation_of(X1),X2) = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',prove_relset_1_45) ).
fof(p26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X1,power_set(X2))
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p26) ).
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(domain(X1,X2,X3),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p33) ).
fof(p32,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> domain(X1,X2,X3) = domain_of(X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p32) ).
fof(p25,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> relation_like(X3) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p25) ).
fof(p15,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p15) ).
fof(p19,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( subset(X1,X2)
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ( member(X3,X1)
=> member(X3,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p19) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p13) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(range_of(X2),X1)
=> compose(X2,identity_relation_of(X1)) = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p2) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( subset(domain_of(X2),X1)
=> compose(identity_relation_of(X1),X2) = X2 ) ) ),
file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',p1) ).
fof(c_0_17,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)],[p28])])])])])])]) ).
fof(c_0_18,plain,
! [X2] : ilf_type(X2,set_type),
inference(variable_rename,[status(thm)],[p38]) ).
fof(c_0_19,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)],[p22])])])])])]) ).
fof(c_0_20,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)],[p27])])])]) ).
fof(c_0_21,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)],[p35])])])])]) ).
fof(c_0_22,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)],[p34])])])])]) ).
fof(c_0_23,plain,
! [X3,X4] :
( ( ~ ilf_type(X4,identity_relation_of_type(X3))
| ilf_type(X4,relation_type(X3,X3))
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X3,set_type) )
& ( ~ ilf_type(X4,relation_type(X3,X3))
| ilf_type(X4,identity_relation_of_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)],[p7])])])])])]) ).
fof(c_0_24,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,identity_relation_of_type(X1))
=> ( compose(X2,identity_relation_of(X1)) = X2
& compose(identity_relation_of(X1),X2) = X2 ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_45]) ).
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(esk12_2(X4,X5),set_type)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk12_2(X4,X5),X4)
| member(X4,power_set(X5))
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk12_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)],[p26])])])])])])]) ).
cnf(c_0_26,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_17]) ).
cnf(c_0_27,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
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_19]) ).
cnf(c_0_29,plain,
( ~ ilf_type(X1,set_type)
| ~ empty(power_set(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,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_21]) ).
cnf(c_0_31,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_22]) ).
cnf(c_0_32,plain,
( ilf_type(X2,relation_type(X1,X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_33,negated_conjecture,
( ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,identity_relation_of_type(esk15_0))
& ( compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0
| compose(identity_relation_of(esk15_0),esk16_0) != esk16_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_24])])])])]) ).
fof(c_0_34,plain,
! [X4,X5,X6] :
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,relation_type(X4,X5))
| ilf_type(domain(X4,X5,X6),subset_type(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)],[p33])])])])]) ).
fof(c_0_35,plain,
! [X4,X5,X6] :
( ~ ilf_type(X4,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X6,relation_type(X4,X5))
| domain(X4,X5,X6) = domain_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])])])])]) ).
cnf(c_0_36,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_37,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_26,c_0_27]),c_0_27])]) ).
cnf(c_0_38,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_27]),c_0_27])]) ).
cnf(c_0_39,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_27])]) ).
cnf(c_0_40,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_30,c_0_27]),c_0_27])]) ).
cnf(c_0_41,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_31,c_0_27]),c_0_27])]) ).
cnf(c_0_42,plain,
( ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_27]),c_0_27])]) ).
cnf(c_0_43,negated_conjecture,
ilf_type(esk16_0,identity_relation_of_type(esk15_0)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_44,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)],[p25])])])])]) ).
fof(c_0_45,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)],[p15])])])])])]) ).
cnf(c_0_46,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_47,plain,
( domain(X1,X2,X3) = domain_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_35]) ).
cnf(c_0_48,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_36,c_0_27]),c_0_27]),c_0_27])]) ).
cnf(c_0_49,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_50,plain,
( ilf_type(range_of(X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X3,X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_51,negated_conjecture,
ilf_type(esk16_0,relation_type(esk15_0,esk15_0)),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
fof(c_0_52,plain,
! [X4,X5,X6] :
( ( ~ subset(X4,X5)
| ~ ilf_type(X6,set_type)
| ~ member(X6,X4)
| member(X6,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ilf_type(esk7_2(X4,X5),set_type)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( member(esk7_2(X4,X5),X4)
| subset(X4,X5)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X4,set_type) )
& ( ~ member(esk7_2(X4,X5),X5)
| subset(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_53,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)],[p13])])]) ).
cnf(c_0_54,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_44]) ).
cnf(c_0_55,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_45]) ).
cnf(c_0_56,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_27]),c_0_27])]) ).
cnf(c_0_57,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_27]),c_0_27])]) ).
cnf(c_0_58,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_59,negated_conjecture,
ilf_type(range_of(esk16_0),subset_type(esk15_0)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_60,plain,
( subset(X1,X2)
| member(esk7_2(X1,X2),X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_61,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_53]) ).
cnf(c_0_62,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_54,c_0_27]),c_0_27])]) ).
cnf(c_0_63,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_55,c_0_27]),c_0_27])]) ).
cnf(c_0_64,plain,
( ilf_type(domain_of(X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
fof(c_0_65,plain,
! [X3,X4] :
( ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ subset(range_of(X4),X3)
| compose(X4,identity_relation_of(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_66,plain,
( subset(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(esk7_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_67,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,range_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,plain,
( member(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_27]),c_0_27])]) ).
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_61]) ).
cnf(c_0_70,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_71,negated_conjecture,
ilf_type(domain_of(esk16_0),subset_type(esk15_0)),
inference(spm,[status(thm)],[c_0_64,c_0_51]) ).
cnf(c_0_72,plain,
( compose(X1,identity_relation_of(X2)) = X1
| ~ subset(range_of(X1),X2)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_73,plain,
( subset(X1,X2)
| ~ member(esk7_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_27]),c_0_27])]) ).
cnf(c_0_74,negated_conjecture,
( member(esk7_2(range_of(esk16_0),X1),esk15_0)
| subset(range_of(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_27])]) ).
cnf(c_0_76,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_70,c_0_51]) ).
fof(c_0_77,plain,
! [X3,X4] :
( ~ ilf_type(X3,set_type)
| ~ ilf_type(X4,binary_relation_type)
| ~ subset(domain_of(X4),X3)
| compose(identity_relation_of(X3),X4) = 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)],[p1])])])])]) ).
cnf(c_0_78,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,domain_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_58,c_0_71]) ).
cnf(c_0_79,plain,
( compose(X1,identity_relation_of(X2)) = X1
| ~ subset(range_of(X1),X2)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_27])]) ).
cnf(c_0_80,negated_conjecture,
subset(range_of(esk16_0),esk15_0),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,negated_conjecture,
ilf_type(esk16_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_82,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ subset(domain_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_83,negated_conjecture,
( member(esk7_2(domain_of(esk16_0),X1),esk15_0)
| subset(domain_of(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_78,c_0_68]) ).
cnf(c_0_84,negated_conjecture,
( compose(identity_relation_of(esk15_0),esk16_0) != esk16_0
| compose(esk16_0,identity_relation_of(esk15_0)) != esk16_0 ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_85,negated_conjecture,
compose(esk16_0,identity_relation_of(esk15_0)) = esk16_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_86,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ subset(domain_of(X2),X1)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_82,c_0_27])]) ).
cnf(c_0_87,negated_conjecture,
subset(domain_of(esk16_0),esk15_0),
inference(spm,[status(thm)],[c_0_73,c_0_83]) ).
cnf(c_0_88,negated_conjecture,
compose(identity_relation_of(esk15_0),esk16_0) != esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_89,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_81])]),c_0_88]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET678+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.15 % Command : run_ET %s %d
% 0.16/0.37 % Computer : n027.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Mon Jul 11 05:00:03 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.28/1.46 # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.28/1.46 # Preprocessing time : 0.020 s
% 0.28/1.46
% 0.28/1.46 # Proof found!
% 0.28/1.46 # SZS status Theorem
% 0.28/1.46 # SZS output start CNFRefutation
% See solution above
% 0.28/1.46 # Proof object total steps : 90
% 0.28/1.46 # Proof object clause steps : 55
% 0.28/1.46 # Proof object formula steps : 35
% 0.28/1.46 # Proof object conjectures : 19
% 0.28/1.46 # Proof object clause conjectures : 16
% 0.28/1.46 # Proof object formula conjectures : 3
% 0.28/1.46 # Proof object initial clauses used : 19
% 0.28/1.46 # Proof object initial formulas used : 17
% 0.28/1.46 # Proof object generating inferences : 18
% 0.28/1.46 # Proof object simplifying inferences : 54
% 0.28/1.46 # Training examples: 0 positive, 0 negative
% 0.28/1.46 # Parsed axioms : 39
% 0.28/1.46 # Removed by relevancy pruning/SinE : 0
% 0.28/1.46 # Initial clauses : 71
% 0.28/1.46 # Removed in clause preprocessing : 5
% 0.28/1.46 # Initial clauses in saturation : 66
% 0.28/1.46 # Processed clauses : 1291
% 0.28/1.46 # ...of these trivial : 14
% 0.28/1.46 # ...subsumed : 568
% 0.28/1.46 # ...remaining for further processing : 709
% 0.28/1.46 # Other redundant clauses eliminated : 1
% 0.28/1.46 # Clauses deleted for lack of memory : 0
% 0.28/1.46 # Backward-subsumed : 40
% 0.28/1.46 # Backward-rewritten : 2
% 0.28/1.46 # Generated clauses : 7121
% 0.28/1.46 # ...of the previous two non-trivial : 6925
% 0.28/1.46 # Contextual simplify-reflections : 785
% 0.28/1.46 # Paramodulations : 7117
% 0.28/1.46 # Factorizations : 0
% 0.28/1.46 # Equation resolutions : 4
% 0.28/1.46 # Current number of processed clauses : 666
% 0.28/1.46 # Positive orientable unit clauses : 59
% 0.28/1.46 # Positive unorientable unit clauses: 0
% 0.28/1.46 # Negative unit clauses : 3
% 0.28/1.46 # Non-unit-clauses : 604
% 0.28/1.46 # Current number of unprocessed clauses: 5152
% 0.28/1.46 # ...number of literals in the above : 29204
% 0.28/1.46 # Current number of archived formulas : 0
% 0.28/1.46 # Current number of archived clauses : 42
% 0.28/1.46 # Clause-clause subsumption calls (NU) : 144307
% 0.28/1.46 # Rec. Clause-clause subsumption calls : 51919
% 0.28/1.46 # Non-unit clause-clause subsumptions : 1216
% 0.28/1.46 # Unit Clause-clause subsumption calls : 2118
% 0.28/1.46 # Rewrite failures with RHS unbound : 0
% 0.28/1.46 # BW rewrite match attempts : 16
% 0.28/1.46 # BW rewrite match successes : 2
% 0.28/1.46 # Condensation attempts : 0
% 0.28/1.46 # Condensation successes : 0
% 0.28/1.46 # Termbank termtop insertions : 185402
% 0.28/1.46
% 0.28/1.46 # -------------------------------------------------
% 0.28/1.46 # User time : 0.210 s
% 0.28/1.46 # System time : 0.014 s
% 0.28/1.46 # Total time : 0.223 s
% 0.28/1.46 # Maximum resident set size: 12328 pages
% 0.31/23.45 eprover: CPU time limit exceeded, terminating
% 0.31/23.45 eprover: CPU time limit exceeded, terminating
% 0.31/23.45 eprover: CPU time limit exceeded, terminating
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.47 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.47 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.48 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.48 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.48 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.48 eprover: No such file or directory
% 0.31/23.48 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.48 eprover: No such file or directory
% 0.31/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.49 eprover: No such file or directory
% 0.31/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.49 eprover: No such file or directory
% 0.31/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.49 eprover: No such file or directory
% 0.31/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.49 eprover: No such file or directory
% 0.31/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.49 eprover: No such file or directory
% 0.31/23.49 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.49 eprover: No such file or directory
% 0.31/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.50 eprover: No such file or directory
% 0.31/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.50 eprover: No such file or directory
% 0.31/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.50 eprover: No such file or directory
% 0.31/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.50 eprover: No such file or directory
% 0.31/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.50 eprover: No such file or directory
% 0.31/23.50 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.50 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.51 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.51 eprover: No such file or directory
% 0.31/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.52 eprover: No such file or directory
% 0.31/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.31/23.52 eprover: No such file or directory
% 0.31/23.52 eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.31/23.52 eprover: No such file or directory
%------------------------------------------------------------------------------