TSTP Solution File: SET678+3 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SET678+3 : TPTP v8.2.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:55:17 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 17
% Syntax : Number of formulae : 99 ( 10 unt; 0 def)
% Number of atoms : 362 ( 27 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 450 ( 187 ~; 185 |; 23 &)
% ( 7 <=>; 48 =>; 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 : 196 ( 7 sgn 83 !; 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/benchmark/theBenchmark.p',p28) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p27) ).
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/benchmark/theBenchmark.p',p32) ).
fof(p38,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p38) ).
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/benchmark/theBenchmark.p',p7) ).
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/benchmark/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/benchmark/theBenchmark.p',p33) ).
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/benchmark/theBenchmark.p',p34) ).
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/benchmark/theBenchmark.p',p22) ).
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/benchmark/theBenchmark.p',p35) ).
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/benchmark/theBenchmark.p',prove_relset_1_45) ).
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/benchmark/theBenchmark.p',p1) ).
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/benchmark/theBenchmark.p',p19) ).
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/benchmark/theBenchmark.p',p2) ).
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/benchmark/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/benchmark/theBenchmark.p',p15) ).
fof(p13,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,binary_relation_type)
<=> ( relation_like(X1)
& ilf_type(X1,set_type) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p13) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ( ilf_type(X1,member_type(X2))
<=> member(X1,X2) ) ) ),
inference(fof_simplification,[status(thm)],[p28]) ).
fof(c_0_18,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p27]) ).
fof(c_0_19,plain,
! [X47,X48,X49] :
( ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,set_type)
| ~ ilf_type(X49,relation_type(X47,X48))
| domain(X47,X48,X49) = domain_of(X49) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])])]) ).
fof(c_0_20,plain,
! [X36] : ilf_type(X36,set_type),
inference(variable_rename,[status(thm)],[p38]) ).
fof(c_0_21,plain,
! [X37,X38] :
( ( ~ ilf_type(X38,identity_relation_of_type(X37))
| ilf_type(X38,relation_type(X37,X37))
| ~ ilf_type(X38,set_type)
| ~ ilf_type(X37,set_type) )
& ( ~ ilf_type(X38,relation_type(X37,X37))
| ilf_type(X38,identity_relation_of_type(X37))
| ~ ilf_type(X38,set_type)
| ~ ilf_type(X37,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])])]) ).
fof(c_0_22,plain,
! [X68,X69,X70] :
( ( ~ member(X68,power_set(X69))
| ~ ilf_type(X70,set_type)
| ~ member(X70,X68)
| member(X70,X69)
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( ilf_type(esk13_2(X68,X69),set_type)
| member(X68,power_set(X69))
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( member(esk13_2(X68,X69),X68)
| member(X68,power_set(X69))
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) )
& ( ~ member(esk13_2(X68,X69),X69)
| member(X68,power_set(X69))
| ~ ilf_type(X69,set_type)
| ~ ilf_type(X68,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])])])])]) ).
fof(c_0_23,plain,
! [X72,X73] :
( ( ~ ilf_type(X72,member_type(X73))
| member(X72,X73)
| empty(X73)
| ~ ilf_type(X73,set_type)
| ~ ilf_type(X72,set_type) )
& ( ~ member(X72,X73)
| ilf_type(X72,member_type(X73))
| empty(X73)
| ~ ilf_type(X73,set_type)
| ~ ilf_type(X72,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])])]) ).
fof(c_0_24,plain,
! [X100] :
( ( ~ empty(power_set(X100))
| ~ ilf_type(X100,set_type) )
& ( ilf_type(power_set(X100),set_type)
| ~ ilf_type(X100,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_25,plain,
! [X88,X89,X90] :
( ~ ilf_type(X88,set_type)
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X90,relation_type(X88,X89))
| ilf_type(domain(X88,X89,X90),subset_type(X88)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p33])])])]) ).
cnf(c_0_26,plain,
( domain(X1,X2,X3) = domain_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_28,plain,
( ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_29,plain,
! [X58,X59,X60] :
( ~ ilf_type(X58,set_type)
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X60,relation_type(X58,X59))
| range(X58,X59,X60) = range_of(X60) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])])]) ).
cnf(c_0_30,plain,
( member(X3,X2)
| ~ member(X1,power_set(X2))
| ~ ilf_type(X3,set_type)
| ~ member(X3,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
( member(X1,X2)
| empty(X2)
| ~ ilf_type(X1,member_type(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_33,plain,
! [X98,X99] :
( ( ~ ilf_type(X99,subset_type(X98))
| ilf_type(X99,member_type(power_set(X98)))
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) )
& ( ~ ilf_type(X99,member_type(power_set(X98)))
| ilf_type(X99,subset_type(X98))
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X98,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])])])]) ).
cnf(c_0_34,plain,
( ilf_type(domain(X1,X2,X3),subset_type(X1))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,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_26,c_0_27]),c_0_27])]) ).
cnf(c_0_36,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_28,c_0_27]),c_0_27])]) ).
cnf(c_0_37,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_38,plain,
! [X91,X92,X93] :
( ~ ilf_type(X91,set_type)
| ~ ilf_type(X92,set_type)
| ~ ilf_type(X93,relation_type(X91,X92))
| ilf_type(range(X91,X92,X93),subset_type(X92)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p35])])])]) ).
cnf(c_0_39,plain,
( range(X1,X2,X3) = range_of(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_40,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_30,c_0_27]),c_0_27]),c_0_27])]) ).
cnf(c_0_41,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_31,c_0_27]),c_0_27])]) ).
cnf(c_0_42,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_27])]) ).
cnf(c_0_43,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,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_34,c_0_27]),c_0_27])]) ).
cnf(c_0_45,plain,
( domain(X1,X1,X2) = domain_of(X2)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_46,plain,
( ilf_type(X1,identity_relation_of_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_27]),c_0_27])]) ).
cnf(c_0_47,plain,
( ilf_type(range(X1,X2,X3),subset_type(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_48,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_39,c_0_27]),c_0_27])]) ).
cnf(c_0_49,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_40,c_0_41]),c_0_42]) ).
cnf(c_0_50,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_43,c_0_27]),c_0_27])]) ).
cnf(c_0_51,plain,
( ilf_type(domain_of(X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]) ).
fof(c_0_52,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]) ).
cnf(c_0_53,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_47,c_0_27]),c_0_27])]) ).
cnf(c_0_54,plain,
( range(X1,X1,X2) = range_of(X2)
| ~ ilf_type(X2,identity_relation_of_type(X1)) ),
inference(spm,[status(thm)],[c_0_48,c_0_36]) ).
fof(c_0_55,plain,
! [X8,X9] :
( ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,binary_relation_type)
| ~ subset(domain_of(X9),X8)
| compose(identity_relation_of(X8),X9) = X9 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p1])])])]) ).
cnf(c_0_56,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,plain,
( ilf_type(domain_of(X1),subset_type(X2))
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_36]) ).
fof(c_0_58,negated_conjecture,
( ilf_type(esk1_0,set_type)
& ilf_type(esk2_0,identity_relation_of_type(esk1_0))
& ( compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0
| compose(identity_relation_of(esk1_0),esk2_0) != esk2_0 ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
fof(c_0_59,plain,
! [X41,X42,X43] :
( ( ~ subset(X41,X42)
| ~ ilf_type(X43,set_type)
| ~ member(X43,X41)
| member(X43,X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ilf_type(esk7_2(X41,X42),set_type)
| subset(X41,X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( member(esk7_2(X41,X42),X41)
| subset(X41,X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) )
& ( ~ member(esk7_2(X41,X42),X42)
| subset(X41,X42)
| ~ ilf_type(X42,set_type)
| ~ ilf_type(X41,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])])])]) ).
cnf(c_0_60,plain,
( ilf_type(range_of(X1),subset_type(X2))
| ~ ilf_type(X1,relation_type(X2,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_46]) ).
cnf(c_0_61,plain,
( compose(identity_relation_of(X1),X2) = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ subset(domain_of(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
fof(c_0_62,plain,
! [X10,X11] :
( ~ ilf_type(X10,set_type)
| ~ ilf_type(X11,binary_relation_type)
| ~ subset(range_of(X11),X10)
| compose(X11,identity_relation_of(X10)) = X11 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_63,plain,
( member(X1,X2)
| ~ member(X1,domain_of(X3))
| ~ ilf_type(X3,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
ilf_type(esk2_0,identity_relation_of_type(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_65,plain,
( member(esk7_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_66,plain,
( ilf_type(range_of(X1),subset_type(X2))
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_60,c_0_36]) ).
fof(c_0_67,plain,
! [X94,X95,X96] :
( ~ ilf_type(X94,set_type)
| ~ ilf_type(X95,set_type)
| ~ ilf_type(X96,subset_type(cross_product(X94,X95)))
| relation_like(X96) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])])]) ).
fof(c_0_68,plain,
! [X84,X85,X86,X87] :
( ( ~ ilf_type(X86,subset_type(cross_product(X84,X85)))
| ilf_type(X86,relation_type(X84,X85))
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) )
& ( ~ ilf_type(X87,relation_type(X84,X85))
| ilf_type(X87,subset_type(cross_product(X84,X85)))
| ~ ilf_type(X85,set_type)
| ~ ilf_type(X84,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p15])])])])]) ).
cnf(c_0_69,negated_conjecture,
( compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0
| compose(identity_relation_of(esk1_0),esk2_0) != esk2_0 ),
inference(split_conjunct,[status(thm)],[c_0_58]) ).
cnf(c_0_70,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_61,c_0_27])]) ).
cnf(c_0_71,plain,
( compose(X2,identity_relation_of(X1)) = X2
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,binary_relation_type)
| ~ subset(range_of(X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_72,plain,
( subset(X1,X2)
| ~ member(esk7_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_73,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,domain_of(esk2_0)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_74,plain,
( member(esk7_2(X1,X2),X1)
| subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_27]),c_0_27])]) ).
cnf(c_0_75,plain,
( member(X1,X2)
| ~ member(X1,range_of(X3))
| ~ ilf_type(X3,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_66]) ).
cnf(c_0_76,plain,
( relation_like(X3)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,subset_type(cross_product(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,plain,
( ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_78,negated_conjecture,
( compose(esk2_0,identity_relation_of(esk1_0)) != esk2_0
| ~ subset(domain_of(esk2_0),esk1_0)
| ~ ilf_type(esk2_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
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_71,c_0_27])]) ).
cnf(c_0_80,plain,
( subset(X1,X2)
| ~ member(esk7_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_27]),c_0_27])]) ).
cnf(c_0_81,negated_conjecture,
( member(esk7_2(domain_of(esk2_0),X1),esk1_0)
| subset(domain_of(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( member(X1,esk1_0)
| ~ member(X1,range_of(esk2_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_64]) ).
fof(c_0_83,plain,
! [X57] :
( ( relation_like(X57)
| ~ ilf_type(X57,binary_relation_type)
| ~ ilf_type(X57,set_type) )
& ( ilf_type(X57,set_type)
| ~ ilf_type(X57,binary_relation_type)
| ~ ilf_type(X57,set_type) )
& ( ~ relation_like(X57)
| ~ ilf_type(X57,set_type)
| ilf_type(X57,binary_relation_type)
| ~ ilf_type(X57,set_type) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
cnf(c_0_84,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_76,c_0_27]),c_0_27])]) ).
cnf(c_0_85,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_77,c_0_27]),c_0_27])]) ).
cnf(c_0_86,negated_conjecture,
( ~ subset(domain_of(esk2_0),esk1_0)
| ~ subset(range_of(esk2_0),esk1_0)
| ~ ilf_type(esk2_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
subset(domain_of(esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( member(esk7_2(range_of(esk2_0),X1),esk1_0)
| subset(range_of(esk2_0),X1) ),
inference(spm,[status(thm)],[c_0_82,c_0_74]) ).
cnf(c_0_89,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_90,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,negated_conjecture,
( ~ subset(range_of(esk2_0),esk1_0)
| ~ ilf_type(esk2_0,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_87])]) ).
cnf(c_0_92,negated_conjecture,
subset(range_of(esk2_0),esk1_0),
inference(spm,[status(thm)],[c_0_80,c_0_88]) ).
cnf(c_0_93,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_89]) ).
cnf(c_0_94,plain,
( relation_like(X1)
| ~ ilf_type(X1,identity_relation_of_type(X2)) ),
inference(spm,[status(thm)],[c_0_90,c_0_36]) ).
cnf(c_0_95,negated_conjecture,
~ ilf_type(esk2_0,binary_relation_type),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_92])]) ).
cnf(c_0_96,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93,c_0_27])]) ).
cnf(c_0_97,negated_conjecture,
relation_like(esk2_0),
inference(spm,[status(thm)],[c_0_94,c_0_64]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET678+3 : TPTP v8.2.0. Released v2.2.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 13:14:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.54 # Version: 3.1.0
% 0.20/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54 # Starting sh5l with 300s (1) cores
% 0.20/0.54 # sh5l with pid 17855 completed with status 0
% 0.20/0.54 # Result found by sh5l
% 0.20/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54 # Starting sh5l with 300s (1) cores
% 0.20/0.54 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/0.54 # Search class: FGHSF-FFMS31-SFFFFFNN
% 0.20/0.54 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 148s (1) cores
% 0.20/0.54 # G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with pid 17867 completed with status 0
% 0.20/0.54 # Result found by G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y
% 0.20/0.54 # Preprocessing class: FSLSSMSSSSSNFFN.
% 0.20/0.54 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.54 # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.20/0.54 # Starting new_bool_3 with 300s (1) cores
% 0.20/0.54 # Starting new_bool_1 with 300s (1) cores
% 0.20/0.54 # Starting sh5l with 300s (1) cores
% 0.20/0.54 # SinE strategy is gf500_gu_R04_F100_L20000
% 0.20/0.54 # Search class: FGHSF-FFMS31-SFFFFFNN
% 0.20/0.54 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.54 # Starting G-E--_207_C01_F1_SE_CS_SP_PI_S5PRR_S0Y with 148s (1) cores
% 0.20/0.54 # Preprocessing time : 0.002 s
% 0.20/0.54
% 0.20/0.54 # Proof found!
% 0.20/0.54 # SZS status Theorem
% 0.20/0.54 # SZS output start CNFRefutation
% See solution above
% 0.20/0.54 # Parsed axioms : 39
% 0.20/0.54 # Removed by relevancy pruning/SinE : 0
% 0.20/0.54 # Initial clauses : 71
% 0.20/0.54 # Removed in clause preprocessing : 5
% 0.20/0.54 # Initial clauses in saturation : 66
% 0.20/0.54 # Processed clauses : 404
% 0.20/0.54 # ...of these trivial : 14
% 0.20/0.54 # ...subsumed : 95
% 0.20/0.54 # ...remaining for further processing : 295
% 0.20/0.54 # Other redundant clauses eliminated : 2
% 0.20/0.54 # Clauses deleted for lack of memory : 0
% 0.20/0.54 # Backward-subsumed : 21
% 0.20/0.54 # Backward-rewritten : 5
% 0.20/0.54 # Generated clauses : 881
% 0.20/0.54 # ...of the previous two non-redundant : 847
% 0.20/0.54 # ...aggressively subsumed : 0
% 0.20/0.54 # Contextual simplify-reflections : 5
% 0.20/0.54 # Paramodulations : 879
% 0.20/0.54 # Factorizations : 0
% 0.20/0.54 # NegExts : 0
% 0.20/0.54 # Equation resolutions : 2
% 0.20/0.54 # Disequality decompositions : 0
% 0.20/0.54 # Total rewrite steps : 183
% 0.20/0.54 # ...of those cached : 136
% 0.20/0.54 # Propositional unsat checks : 0
% 0.20/0.54 # Propositional check models : 0
% 0.20/0.54 # Propositional check unsatisfiable : 0
% 0.20/0.54 # Propositional clauses : 0
% 0.20/0.54 # Propositional clauses after purity: 0
% 0.20/0.54 # Propositional unsat core size : 0
% 0.20/0.54 # Propositional preprocessing time : 0.000
% 0.20/0.54 # Propositional encoding time : 0.000
% 0.20/0.54 # Propositional solver time : 0.000
% 0.20/0.54 # Success case prop preproc time : 0.000
% 0.20/0.54 # Success case prop encoding time : 0.000
% 0.20/0.54 # Success case prop solver time : 0.000
% 0.20/0.54 # Current number of processed clauses : 268
% 0.20/0.54 # Positive orientable unit clauses : 41
% 0.20/0.54 # Positive unorientable unit clauses: 0
% 0.20/0.54 # Negative unit clauses : 3
% 0.20/0.54 # Non-unit-clauses : 224
% 0.20/0.54 # Current number of unprocessed clauses: 506
% 0.20/0.54 # ...number of literals in the above : 1777
% 0.20/0.54 # Current number of archived formulas : 0
% 0.20/0.54 # Current number of archived clauses : 26
% 0.20/0.54 # Clause-clause subsumption calls (NU) : 6986
% 0.20/0.54 # Rec. Clause-clause subsumption calls : 3532
% 0.20/0.54 # Non-unit clause-clause subsumptions : 102
% 0.20/0.54 # Unit Clause-clause subsumption calls : 568
% 0.20/0.54 # Rewrite failures with RHS unbound : 0
% 0.20/0.54 # BW rewrite match attempts : 15
% 0.20/0.54 # BW rewrite match successes : 3
% 0.20/0.54 # Condensation attempts : 0
% 0.20/0.54 # Condensation successes : 0
% 0.20/0.54 # Termbank termtop insertions : 20304
% 0.20/0.54 # Search garbage collected termcells : 1636
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.045 s
% 0.20/0.54 # System time : 0.004 s
% 0.20/0.54 # Total time : 0.049 s
% 0.20/0.54 # Maximum resident set size: 2016 pages
% 0.20/0.54
% 0.20/0.54 # -------------------------------------------------
% 0.20/0.54 # User time : 0.048 s
% 0.20/0.54 # System time : 0.005 s
% 0.20/0.54 # Total time : 0.053 s
% 0.20/0.54 # Maximum resident set size: 1748 pages
% 0.20/0.54 % E---3.1 exiting
% 0.20/0.54 % E exiting
%------------------------------------------------------------------------------