TSTP Solution File: SET682+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET682+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 : n025.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 14:35:12 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 44
% Syntax : Number of formulae : 112 ( 12 unt; 30 typ; 0 def)
% Number of atoms : 313 ( 8 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 390 ( 159 ~; 146 |; 32 &)
% ( 7 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 23 >; 14 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-3 aty)
% Number of variables : 161 ( 9 sgn; 74 !; 3 ?; 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,
range_of: $i > $i ).
tff(decl_28,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_29,type,
subset_type: $i > $i ).
tff(decl_30,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_31,type,
empty: $i > $o ).
tff(decl_32,type,
member_type: $i > $i ).
tff(decl_33,type,
relation_like: $i > $o ).
tff(decl_34,type,
power_set: $i > $i ).
tff(decl_35,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_36,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_1: $i > $i ).
tff(decl_42,type,
esk5_0: $i ).
tff(decl_43,type,
esk6_1: $i > $i ).
tff(decl_44,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk10_1: $i > $i ).
tff(decl_48,type,
esk11_0: $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_0: $i ).
tff(decl_51,type,
esk14_0: $i ).
fof(p4,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',p4) ).
fof(p15,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',p15) ).
fof(p24,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p24) ).
fof(p12,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',p12) ).
fof(p14,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',p14) ).
fof(p6,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p6) ).
fof(p18,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',p18) ).
fof(p2,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',p2) ).
fof(p23,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',p23) ).
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(X3,range_of(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(prove_relset_1_49,conjecture,
! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_49) ).
fof(p20,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',p20) ).
fof(p10,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',p10) ).
fof(p22,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',p22) ).
fof(c_0_14,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)],[p4]) ).
fof(c_0_15,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p15]) ).
fof(c_0_16,plain,
! [X16,X17] :
( ( ~ ilf_type(X16,member_type(X17))
| member(X16,X17)
| empty(X17)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) )
& ( ~ member(X16,X17)
| ilf_type(X16,member_type(X17))
| empty(X17)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_17,plain,
! [X63] : ilf_type(X63,set_type),
inference(variable_rename,[status(thm)],[p24]) ).
fof(c_0_18,plain,
! [X29,X30] :
( ( ~ ilf_type(X30,subset_type(X29))
| ilf_type(X30,member_type(power_set(X29)))
| ~ ilf_type(X30,set_type)
| ~ ilf_type(X29,set_type) )
& ( ~ ilf_type(X30,member_type(power_set(X29)))
| ilf_type(X30,subset_type(X29))
| ~ 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)],[p12])])])]) ).
fof(c_0_19,plain,
! [X37] :
( ( ~ empty(power_set(X37))
| ~ ilf_type(X37,set_type) )
& ( ilf_type(power_set(X37),set_type)
| ~ ilf_type(X37,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_20,plain,
! [X33,X34,X35] :
( ( ~ member(X33,power_set(X34))
| ~ ilf_type(X35,set_type)
| ~ member(X35,X33)
| member(X35,X34)
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( ilf_type(esk7_2(X33,X34),set_type)
| member(X33,power_set(X34))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( member(esk7_2(X33,X34),X33)
| member(X33,power_set(X34))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,set_type) )
& ( ~ member(esk7_2(X33,X34),X34)
| member(X33,power_set(X34))
| ~ ilf_type(X34,set_type)
| ~ ilf_type(X33,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)],[p14])])])])]) ).
cnf(c_0_21,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_16]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,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_18]) ).
cnf(c_0_24,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p6]) ).
fof(c_0_26,plain,
! [X46,X47,X48] :
( ~ ilf_type(X46,set_type)
| ~ ilf_type(X47,set_type)
| ~ ilf_type(X48,subset_type(cross_product(X46,X47)))
| relation_like(X48) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p18])])]) ).
fof(c_0_27,plain,
! [X9,X10,X11,X12] :
( ( ~ ilf_type(X11,subset_type(cross_product(X9,X10)))
| ilf_type(X11,relation_type(X9,X10))
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X9,set_type) )
& ( ~ ilf_type(X12,relation_type(X9,X10))
| ilf_type(X12,subset_type(cross_product(X9,X10)))
| ~ ilf_type(X10,set_type)
| ~ ilf_type(X9,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
cnf(c_0_28,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_20]) ).
cnf(c_0_29,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_21,c_0_22]),c_0_22])]) ).
cnf(c_0_30,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_23,c_0_22]),c_0_22])]) ).
cnf(c_0_31,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22])]) ).
fof(c_0_32,plain,
! [X60,X61,X62] :
( ~ ilf_type(X60,set_type)
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X62,relation_type(X60,X61))
| ilf_type(range(X60,X61,X62),subset_type(X61)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p23])])]) ).
fof(c_0_33,plain,
! [X20,X21] :
( ( ~ empty(X20)
| ~ ilf_type(X21,set_type)
| ~ member(X21,X20)
| ~ ilf_type(X20,set_type) )
& ( ilf_type(esk4_1(X20),set_type)
| empty(X20)
| ~ ilf_type(X20,set_type) )
& ( member(esk4_1(X20),X20)
| empty(X20)
| ~ ilf_type(X20,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)],[c_0_25])])])])]) ).
fof(c_0_34,plain,
! [X6,X7] :
( ( 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(esk1_2(X6,X7),range_of(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])])])])]) ).
fof(c_0_35,negated_conjecture,
~ ! [X1] :
( ( ~ empty(X1)
& ilf_type(X1,set_type) )
=> ! [X2] :
( ( ~ empty(X2)
& ilf_type(X2,set_type) )
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,member_type(X1))
=> ( member(X4,domain(X1,X2,X3))
=> ? [X5] :
( ilf_type(X5,member_type(X2))
& member(X5,range(X1,X2,X3)) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_49])]) ).
fof(c_0_36,plain,
! [X51,X52,X53] :
( ~ ilf_type(X51,set_type)
| ~ ilf_type(X52,set_type)
| ~ ilf_type(X53,relation_type(X51,X52))
| domain(X51,X52,X53) = domain_of(X53) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p20])])]) ).
fof(c_0_37,plain,
! [X27] :
( ( relation_like(X27)
| ~ ilf_type(X27,binary_relation_type)
| ~ ilf_type(X27,set_type) )
& ( ilf_type(X27,set_type)
| ~ ilf_type(X27,binary_relation_type)
| ~ ilf_type(X27,set_type) )
& ( ~ relation_like(X27)
| ~ ilf_type(X27,set_type)
| ilf_type(X27,binary_relation_type)
| ~ ilf_type(X27,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])]) ).
cnf(c_0_38,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_26]) ).
cnf(c_0_39,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_27]) ).
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_28,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_41,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_42,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_32]) ).
fof(c_0_43,plain,
! [X57,X58,X59] :
( ~ ilf_type(X57,set_type)
| ~ ilf_type(X58,set_type)
| ~ ilf_type(X59,relation_type(X57,X58))
| range(X57,X58,X59) = range_of(X59) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])]) ).
cnf(c_0_44,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
( member(esk1_2(X1,X2),range_of(X2))
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_46,negated_conjecture,
! [X68] :
( ~ empty(esk11_0)
& ilf_type(esk11_0,set_type)
& ~ empty(esk12_0)
& ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,relation_type(esk11_0,esk12_0))
& ilf_type(esk14_0,member_type(esk11_0))
& member(esk14_0,domain(esk11_0,esk12_0,esk13_0))
& ( ~ ilf_type(X68,member_type(esk12_0))
| ~ member(X68,range(esk11_0,esk12_0,esk13_0)) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])]) ).
cnf(c_0_47,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_36]) ).
cnf(c_0_48,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_37]) ).
cnf(c_0_49,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_38,c_0_22]),c_0_22])]) ).
cnf(c_0_50,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_39,c_0_22]),c_0_22])]) ).
cnf(c_0_51,plain,
( member(esk4_1(X1),X1)
| empty(X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_52,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
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_42,c_0_22]),c_0_22])]) ).
cnf(c_0_54,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_43]) ).
cnf(c_0_55,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_22]),c_0_22])]) ).
cnf(c_0_56,plain,
( member(esk1_2(X1,X2),range_of(X2))
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_22])]) ).
cnf(c_0_57,negated_conjecture,
member(esk14_0,domain(esk11_0,esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_58,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_22]),c_0_22])]) ).
cnf(c_0_59,negated_conjecture,
ilf_type(esk13_0,relation_type(esk11_0,esk12_0)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_60,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_48]) ).
cnf(c_0_61,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_62,negated_conjecture,
( ~ ilf_type(X1,member_type(esk12_0))
| ~ member(X1,range(esk11_0,esk12_0,esk13_0)) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_63,plain,
( empty(X1)
| member(esk4_1(X1),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_22])]) ).
cnf(c_0_64,plain,
( ilf_type(X1,member_type(X2))
| empty(X2)
| ~ member(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_65,plain,
( member(X1,X2)
| ~ member(X1,range(X3,X2,X4))
| ~ ilf_type(X4,relation_type(X3,X2)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_66,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_54,c_0_22]),c_0_22])]) ).
cnf(c_0_67,plain,
( ~ empty(range_of(X1))
| ~ member(X2,domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_68,negated_conjecture,
member(esk14_0,domain_of(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]) ).
cnf(c_0_69,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_22])]) ).
cnf(c_0_70,negated_conjecture,
relation_like(esk13_0),
inference(spm,[status(thm)],[c_0_61,c_0_59]) ).
cnf(c_0_71,negated_conjecture,
( empty(range(esk11_0,esk12_0,esk13_0))
| ~ ilf_type(esk4_1(range(esk11_0,esk12_0,esk13_0)),member_type(esk12_0)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_72,plain,
( ilf_type(X1,member_type(X2))
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_22]),c_0_22])]),c_0_55]) ).
cnf(c_0_73,plain,
( member(X1,X2)
| ~ member(X1,range_of(X3))
| ~ ilf_type(X3,relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_74,negated_conjecture,
( ~ empty(range_of(esk13_0))
| ~ ilf_type(esk13_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
ilf_type(esk13_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,negated_conjecture,
( empty(range(esk11_0,esk12_0,esk13_0))
| ~ member(esk4_1(range(esk11_0,esk12_0,esk13_0)),esk12_0) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( member(X1,esk12_0)
| ~ member(X1,range_of(esk13_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_59]) ).
cnf(c_0_78,negated_conjecture,
~ empty(range_of(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_75])]) ).
cnf(c_0_79,negated_conjecture,
( empty(range_of(esk13_0))
| ~ member(esk4_1(range_of(esk13_0)),esk12_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_66]),c_0_59])]) ).
cnf(c_0_80,negated_conjecture,
member(esk4_1(range_of(esk13_0)),esk12_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_63]),c_0_78]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79,c_0_80])]),c_0_78]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET682+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n025.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 16:28:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.019000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.023000 s
%------------------------------------------------------------------------------