TSTP Solution File: SET650+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n003.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 14:35:03 EDT 2023
% Result : Theorem 0.18s 0.61s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 103 ( 8 unt; 32 typ; 0 def)
% Number of atoms : 297 ( 0 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 385 ( 159 ~; 165 |; 24 &)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 26 >; 15 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 6 con; 0-2 aty)
% Number of variables : 136 ( 9 sgn; 56 !; 2 ?; 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,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
range_of: $i > $i ).
tff(decl_29,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_30,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_31,type,
subset_type: $i > $i ).
tff(decl_32,type,
subset: ( $i * $i ) > $o ).
tff(decl_33,type,
relation_like: $i > $o ).
tff(decl_34,type,
power_set: $i > $i ).
tff(decl_35,type,
member_type: $i > $i ).
tff(decl_36,type,
empty: $i > $o ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_1: $i > $i ).
tff(decl_45,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk10_1: $i > $i ).
tff(decl_47,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk13_1: $i > $i ).
tff(decl_50,type,
esk14_1: $i > $i ).
tff(decl_51,type,
esk15_0: $i ).
tff(decl_52,type,
esk16_0: $i ).
tff(decl_53,type,
esk17_0: $i ).
fof(p3,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ! [X5] :
( ilf_type(X5,relation_type(X1,X2))
=> ( member(ordered_pair(X3,X4),X5)
=> ( member(X3,X1)
& member(X4,X2) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p26,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(prove_relset_1_12,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_12) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p18,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/benchmark/theBenchmark.p',p18) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p10,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/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p8,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/benchmark/theBenchmark.p',p8) ).
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/sandbox/benchmark/theBenchmark.p',p13) ).
fof(p23,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/benchmark/theBenchmark.p',p23) ).
fof(c_0_10,plain,
! [X14,X15,X16,X17,X18] :
( ( member(X16,X14)
| ~ member(ordered_pair(X16,X17),X18)
| ~ ilf_type(X18,relation_type(X14,X15))
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) )
& ( member(X17,X15)
| ~ member(ordered_pair(X16,X17),X18)
| ~ ilf_type(X18,relation_type(X14,X15))
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p3])])])]) ).
fof(c_0_11,plain,
! [X74] : ilf_type(X74,set_type),
inference(variable_rename,[status(thm)],[p26]) ).
fof(c_0_12,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( subset(domain_of(X3),X1)
& subset(range_of(X3),X2) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_12]) ).
fof(c_0_13,plain,
! [X10,X11,X13] :
( ( ilf_type(esk2_2(X10,X11),set_type)
| ~ member(X10,range_of(X11))
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,set_type) )
& ( member(ordered_pair(esk2_2(X10,X11),X10),X11)
| ~ member(X10,range_of(X11))
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,set_type) )
& ( ~ ilf_type(X13,set_type)
| ~ member(ordered_pair(X13,X10),X11)
| member(X10,range_of(X11))
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,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)],[p2])])])])]) ).
fof(c_0_14,plain,
! [X51,X52,X53] :
( ( ~ member(X51,power_set(X52))
| ~ ilf_type(X53,set_type)
| ~ member(X53,X51)
| member(X53,X52)
| ~ ilf_type(X52,set_type)
| ~ ilf_type(X51,set_type) )
& ( ilf_type(esk9_2(X51,X52),set_type)
| member(X51,power_set(X52))
| ~ ilf_type(X52,set_type)
| ~ ilf_type(X51,set_type) )
& ( member(esk9_2(X51,X52),X51)
| member(X51,power_set(X52))
| ~ ilf_type(X52,set_type)
| ~ ilf_type(X51,set_type) )
& ( ~ member(esk9_2(X51,X52),X52)
| member(X51,power_set(X52))
| ~ ilf_type(X52,set_type)
| ~ ilf_type(X51,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)],[p18])])])])]) ).
fof(c_0_15,plain,
! [X6,X7,X9] :
( ( ilf_type(esk1_2(X6,X7),set_type)
| ~ member(X6,domain_of(X7))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type) )
& ( member(ordered_pair(X6,esk1_2(X6,X7)),X7)
| ~ member(X6,domain_of(X7))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,set_type) )
& ( ~ ilf_type(X9,set_type)
| ~ member(ordered_pair(X6,X9),X7)
| member(X6,domain_of(X7))
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,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)],[p1])])])])]) ).
cnf(c_0_16,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X5,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,negated_conjecture,
( ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,set_type)
& ilf_type(esk17_0,relation_type(esk15_0,esk16_0))
& ( ~ subset(domain_of(esk17_0),esk15_0)
| ~ subset(range_of(esk17_0),esk16_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_12])])]) ).
cnf(c_0_19,plain,
( member(ordered_pair(esk2_2(X1,X2),X1),X2)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( member(esk9_2(X1,X2),X1)
| member(X1,power_set(X2))
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X4,relation_type(X2,X5))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X5,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,plain,
( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),X4)
| ~ ilf_type(X4,relation_type(X5,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_24,negated_conjecture,
ilf_type(esk17_0,relation_type(esk15_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_25,plain,
( member(ordered_pair(esk2_2(X1,X2),X1),X2)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17])]) ).
cnf(c_0_26,plain,
( member(esk9_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17])]) ).
fof(c_0_27,plain,
! [X36,X37,X38] :
( ( ~ subset(X36,X37)
| ~ ilf_type(X38,set_type)
| ~ member(X38,X36)
| member(X38,X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ilf_type(esk6_2(X36,X37),set_type)
| subset(X36,X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( member(esk6_2(X36,X37),X36)
| subset(X36,X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,set_type) )
& ( ~ member(esk6_2(X36,X37),X37)
| subset(X36,X37)
| ~ ilf_type(X37,set_type)
| ~ ilf_type(X36,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)],[p10])])])])]) ).
cnf(c_0_28,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ ilf_type(X4,relation_type(X2,X5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_17]),c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_29,plain,
( member(ordered_pair(X1,esk1_2(X1,X2)),X2)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_17])]) ).
cnf(c_0_30,plain,
( member(X1,power_set(X2))
| ~ member(esk9_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
( member(X1,esk16_0)
| ~ member(ordered_pair(X2,X1),esk17_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_32,plain,
( member(ordered_pair(esk2_2(esk9_2(range_of(X1),X2),X1),esk9_2(range_of(X1),X2)),X1)
| member(range_of(X1),power_set(X2))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_33,plain,
( member(esk6_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_34,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( member(X1,esk15_0)
| ~ member(ordered_pair(X1,X2),esk17_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_36,plain,
( member(ordered_pair(esk9_2(domain_of(X1),X2),esk1_2(esk9_2(domain_of(X1),X2),X1)),X1)
| member(domain_of(X1),power_set(X2))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_37,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_14]) ).
cnf(c_0_38,plain,
( member(X1,power_set(X2))
| ~ member(esk9_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_17]),c_0_17])]) ).
cnf(c_0_39,negated_conjecture,
( member(esk9_2(range_of(esk17_0),X1),esk16_0)
| member(range_of(esk17_0),power_set(X1))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_40,negated_conjecture,
( ~ subset(domain_of(esk17_0),esk15_0)
| ~ subset(range_of(esk17_0),esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,plain,
( subset(X1,X2)
| member(esk6_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_17]),c_0_17])]) ).
cnf(c_0_42,plain,
( subset(X1,X2)
| ~ member(esk6_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_17]),c_0_17])]) ).
fof(c_0_43,plain,
! [X29,X30,X31,X32] :
( ( ~ ilf_type(X31,subset_type(cross_product(X29,X30)))
| ilf_type(X31,relation_type(X29,X30))
| ~ ilf_type(X30,set_type)
| ~ ilf_type(X29,set_type) )
& ( ~ ilf_type(X32,relation_type(X29,X30))
| ilf_type(X32,subset_type(cross_product(X29,X30)))
| ~ ilf_type(X30,set_type)
| ~ ilf_type(X29,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p8])])])]) ).
cnf(c_0_44,negated_conjecture,
( member(esk9_2(domain_of(esk17_0),X1),esk15_0)
| member(domain_of(esk17_0),power_set(X1))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_45,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_37,c_0_17]),c_0_17]),c_0_17])]) ).
cnf(c_0_46,negated_conjecture,
( member(range_of(esk17_0),power_set(esk16_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,negated_conjecture,
( member(esk6_2(range_of(esk17_0),esk16_0),range_of(esk17_0))
| ~ subset(domain_of(esk17_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_48,negated_conjecture,
( ~ subset(domain_of(esk17_0),esk15_0)
| ~ member(esk6_2(range_of(esk17_0),esk16_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_40,c_0_42]) ).
fof(c_0_49,plain,
! [X44] :
( ( relation_like(X44)
| ~ ilf_type(X44,binary_relation_type)
| ~ ilf_type(X44,set_type) )
& ( ilf_type(X44,set_type)
| ~ ilf_type(X44,binary_relation_type)
| ~ ilf_type(X44,set_type) )
& ( ~ relation_like(X44)
| ~ ilf_type(X44,set_type)
| ilf_type(X44,binary_relation_type)
| ~ ilf_type(X44,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])]) ).
fof(c_0_50,plain,
! [X67,X68,X69] :
( ~ ilf_type(X67,set_type)
| ~ ilf_type(X68,set_type)
| ~ ilf_type(X69,subset_type(cross_product(X67,X68)))
| relation_like(X69) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).
cnf(c_0_51,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_43]) ).
cnf(c_0_52,negated_conjecture,
( member(domain_of(esk17_0),power_set(esk15_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_38,c_0_44]) ).
cnf(c_0_53,negated_conjecture,
( member(X1,esk16_0)
| ~ member(X1,range_of(esk17_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,negated_conjecture,
( member(esk6_2(domain_of(esk17_0),esk15_0),domain_of(esk17_0))
| member(esk6_2(range_of(esk17_0),esk16_0),range_of(esk17_0)) ),
inference(spm,[status(thm)],[c_0_47,c_0_41]) ).
cnf(c_0_55,negated_conjecture,
( member(esk6_2(domain_of(esk17_0),esk15_0),domain_of(esk17_0))
| ~ member(esk6_2(range_of(esk17_0),esk16_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_41]) ).
cnf(c_0_56,negated_conjecture,
( member(esk6_2(range_of(esk17_0),esk16_0),range_of(esk17_0))
| ~ member(esk6_2(domain_of(esk17_0),esk15_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_42]) ).
cnf(c_0_57,negated_conjecture,
( ~ member(esk6_2(range_of(esk17_0),esk16_0),esk16_0)
| ~ member(esk6_2(domain_of(esk17_0),esk15_0),esk15_0) ),
inference(spm,[status(thm)],[c_0_48,c_0_42]) ).
cnf(c_0_58,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_49]) ).
cnf(c_0_59,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_50]) ).
cnf(c_0_60,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_51,c_0_17]),c_0_17])]) ).
cnf(c_0_61,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,domain_of(esk17_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_45,c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( member(esk6_2(domain_of(esk17_0),esk15_0),domain_of(esk17_0))
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( ~ member(esk6_2(domain_of(esk17_0),esk15_0),esk15_0)
| ~ ilf_type(esk17_0,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_56]),c_0_57]) ).
cnf(c_0_64,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_58]) ).
cnf(c_0_65,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_59,c_0_17]),c_0_17])]) ).
cnf(c_0_66,negated_conjecture,
ilf_type(esk17_0,subset_type(cross_product(esk15_0,esk16_0))),
inference(spm,[status(thm)],[c_0_60,c_0_24]) ).
cnf(c_0_67,negated_conjecture,
~ ilf_type(esk17_0,binary_relation_type),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_63]) ).
cnf(c_0_68,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_17])]) ).
cnf(c_0_69,negated_conjecture,
relation_like(esk17_0),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET650+3 : TPTP v8.1.2. Released v2.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sat Aug 26 16:19:39 EDT 2023
% 0.13/0.32 % CPUTime :
% 0.18/0.54 start to proof: theBenchmark
% 0.18/0.61 % Version : CSE_E---1.5
% 0.18/0.61 % Problem : theBenchmark.p
% 0.18/0.61 % Proof found
% 0.18/0.61 % SZS status Theorem for theBenchmark.p
% 0.18/0.61 % SZS output start Proof
% See solution above
% 0.18/0.61 % Total time : 0.055000 s
% 0.18/0.61 % SZS output end Proof
% 0.18/0.61 % Total time : 0.059000 s
%------------------------------------------------------------------------------