TSTP Solution File: SET678+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Thu Aug 31 14:35:11 EDT 2023
% Result : Theorem 0.16s 0.60s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 54
% Syntax : Number of formulae : 136 ( 10 unt; 37 typ; 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 types : 2 ( 0 usr)
% Number of type conns : 57 ( 32 >; 25 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-5 aty)
% Number of variables : 196 ( 7 sgn; 83 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
set_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
binary_relation_type: $i ).
tff(decl_25,type,
domain_of: $i > $i ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
identity_relation_of: $i > $i ).
tff(decl_28,type,
compose: ( $i * $i ) > $i ).
tff(decl_29,type,
range_of: $i > $i ).
tff(decl_30,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
member: ( $i * $i ) > $o ).
tff(decl_32,type,
identity_relation_of_type: $i > $i ).
tff(decl_33,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_34,type,
relation_like: $i > $o ).
tff(decl_35,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_36,type,
subset_type: $i > $i ).
tff(decl_37,type,
power_set: $i > $i ).
tff(decl_38,type,
member_type: $i > $i ).
tff(decl_39,type,
empty: $i > $o ).
tff(decl_40,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
compose5: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
esk2_1: $i > $i ).
tff(decl_45,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk5_0: $i ).
tff(decl_48,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk8_1: $i > $i ).
tff(decl_51,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk11_1: $i > $i ).
tff(decl_54,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk13_1: $i > $i ).
tff(decl_56,type,
esk14_1: $i > $i ).
tff(decl_57,type,
esk15_0: $i ).
tff(decl_58,type,
esk16_0: $i ).
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,
! [X82,X83,X84] :
( ~ ilf_type(X82,set_type)
| ~ ilf_type(X83,set_type)
| ~ ilf_type(X84,relation_type(X82,X83))
| domain(X82,X83,X84) = domain_of(X84) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])]) ).
fof(c_0_20,plain,
! [X104] : ilf_type(X104,set_type),
inference(variable_rename,[status(thm)],[p38]) ).
fof(c_0_21,plain,
! [X22,X23] :
( ( ~ ilf_type(X23,identity_relation_of_type(X22))
| ilf_type(X23,relation_type(X22,X22))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ~ ilf_type(X23,relation_type(X22,X22))
| ilf_type(X23,identity_relation_of_type(X22))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p7])])])]) ).
fof(c_0_22,plain,
! [X69,X70,X71] :
( ( ~ member(X69,power_set(X70))
| ~ ilf_type(X71,set_type)
| ~ member(X71,X69)
| member(X71,X70)
| ~ ilf_type(X70,set_type)
| ~ ilf_type(X69,set_type) )
& ( ilf_type(esk12_2(X69,X70),set_type)
| member(X69,power_set(X70))
| ~ ilf_type(X70,set_type)
| ~ ilf_type(X69,set_type) )
& ( member(esk12_2(X69,X70),X69)
| member(X69,power_set(X70))
| ~ ilf_type(X70,set_type)
| ~ ilf_type(X69,set_type) )
& ( ~ member(esk12_2(X69,X70),X70)
| member(X69,power_set(X70))
| ~ ilf_type(X70,set_type)
| ~ ilf_type(X69,set_type) ) ),
inference(distribute,[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,
! [X74,X75] :
( ( ~ ilf_type(X74,member_type(X75))
| member(X74,X75)
| empty(X75)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type) )
& ( ~ member(X74,X75)
| ilf_type(X74,member_type(X75))
| empty(X75)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X74,set_type) ) ),
inference(distribute,[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,
! [X73] :
( ( ~ empty(power_set(X73))
| ~ ilf_type(X73,set_type) )
& ( ilf_type(power_set(X73),set_type)
| ~ ilf_type(X73,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
fof(c_0_25,plain,
! [X85,X86,X87] :
( ~ ilf_type(X85,set_type)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X87,relation_type(X85,X86))
| ilf_type(domain(X85,X86,X87),subset_type(X85)) ),
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,
! [X88,X89,X90] :
( ~ ilf_type(X88,set_type)
| ~ ilf_type(X89,set_type)
| ~ ilf_type(X90,relation_type(X88,X89))
| range(X88,X89,X90) = range_of(X90) ),
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,
! [X55,X56] :
( ( ~ ilf_type(X56,subset_type(X55))
| ilf_type(X56,member_type(power_set(X55)))
| ~ ilf_type(X56,set_type)
| ~ ilf_type(X55,set_type) )
& ( ~ ilf_type(X56,member_type(power_set(X55)))
| ilf_type(X56,subset_type(X55))
| ~ ilf_type(X56,set_type)
| ~ ilf_type(X55,set_type) ) ),
inference(distribute,[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(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,
! [X6,X7] :
( ~ ilf_type(X6,set_type)
| ~ ilf_type(X7,binary_relation_type)
| ~ subset(domain_of(X7),X6)
| compose(identity_relation_of(X6),X7) = X7 ),
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(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(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
fof(c_0_59,plain,
! [X48,X49,X50] :
( ( ~ subset(X48,X49)
| ~ ilf_type(X50,set_type)
| ~ member(X50,X48)
| member(X50,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( ilf_type(esk7_2(X48,X49),set_type)
| subset(X48,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( member(esk7_2(X48,X49),X48)
| subset(X48,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( ~ member(esk7_2(X48,X49),X49)
| subset(X48,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) ) ),
inference(distribute,[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,
! [X8,X9] :
( ~ ilf_type(X8,set_type)
| ~ ilf_type(X9,binary_relation_type)
| ~ subset(range_of(X9),X8)
| compose(X9,identity_relation_of(X8)) = X9 ),
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(esk16_0,identity_relation_of_type(esk15_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,
! [X66,X67,X68] :
( ~ ilf_type(X66,set_type)
| ~ ilf_type(X67,set_type)
| ~ ilf_type(X68,subset_type(cross_product(X66,X67)))
| relation_like(X68) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])]) ).
fof(c_0_68,plain,
! [X38,X39,X40,X41] :
( ( ~ ilf_type(X40,subset_type(cross_product(X38,X39)))
| ilf_type(X40,relation_type(X38,X39))
| ~ ilf_type(X39,set_type)
| ~ ilf_type(X38,set_type) )
& ( ~ ilf_type(X41,relation_type(X38,X39))
| ilf_type(X41,subset_type(cross_product(X38,X39)))
| ~ ilf_type(X39,set_type)
| ~ ilf_type(X38,set_type) ) ),
inference(distribute,[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(esk16_0,identity_relation_of(esk15_0)) != esk16_0
| compose(identity_relation_of(esk15_0),esk16_0) != esk16_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,esk15_0)
| ~ member(X1,domain_of(esk16_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(esk16_0,identity_relation_of(esk15_0)) != esk16_0
| ~ subset(domain_of(esk16_0),esk15_0)
| ~ ilf_type(esk16_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(esk16_0),X1),esk15_0)
| subset(domain_of(esk16_0),X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,range_of(esk16_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_64]) ).
fof(c_0_83,plain,
! [X36] :
( ( relation_like(X36)
| ~ ilf_type(X36,binary_relation_type)
| ~ ilf_type(X36,set_type) )
& ( ilf_type(X36,set_type)
| ~ ilf_type(X36,binary_relation_type)
| ~ ilf_type(X36,set_type) )
& ( ~ relation_like(X36)
| ~ ilf_type(X36,set_type)
| ilf_type(X36,binary_relation_type)
| ~ ilf_type(X36,set_type) ) ),
inference(distribute,[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(esk16_0),esk15_0)
| ~ subset(range_of(esk16_0),esk15_0)
| ~ ilf_type(esk16_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,negated_conjecture,
subset(domain_of(esk16_0),esk15_0),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_88,negated_conjecture,
( member(esk7_2(range_of(esk16_0),X1),esk15_0)
| subset(range_of(esk16_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(esk16_0),esk15_0)
| ~ ilf_type(esk16_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(esk16_0),esk15_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(esk16_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(esk16_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
% 0.09/0.11 % Problem : SET678+3 : TPTP v8.1.2. Released v2.2.0.
% 0.09/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32 % Computer : n002.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Sat Aug 26 15:41:03 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.55 start to proof: theBenchmark
% 0.16/0.60 % Version : CSE_E---1.5
% 0.16/0.60 % Problem : theBenchmark.p
% 0.16/0.60 % Proof found
% 0.16/0.60 % SZS status Theorem for theBenchmark.p
% 0.16/0.60 % SZS output start Proof
% See solution above
% 0.16/0.60 % Total time : 0.040000 s
% 0.16/0.60 % SZS output end Proof
% 0.16/0.60 % Total time : 0.043000 s
%------------------------------------------------------------------------------