TSTP Solution File: SET680+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET680+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 : n012.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 0.19s 0.60s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 49
% Syntax : Number of formulae : 145 ( 16 unt; 34 typ; 0 def)
% Number of atoms : 407 ( 8 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 505 ( 209 ~; 203 |; 36 &)
% ( 10 <=>; 47 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 26 >; 16 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 30 ( 30 usr; 8 con; 0-3 aty)
% Number of variables : 219 ( 16 sgn; 81 !; 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,
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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
singleton: $i > $i ).
tff(decl_32,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_33,type,
subset_type: $i > $i ).
tff(decl_34,type,
empty: $i > $o ).
tff(decl_35,type,
member_type: $i > $i ).
tff(decl_36,type,
relation_like: $i > $o ).
tff(decl_37,type,
power_set: $i > $i ).
tff(decl_38,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk3_1: $i > $i ).
tff(decl_43,type,
esk4_1: $i > $i ).
tff(decl_44,type,
esk5_0: $i ).
tff(decl_45,type,
esk6_1: $i > $i ).
tff(decl_46,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk11_1: $i > $i ).
tff(decl_51,type,
esk12_0: $i ).
tff(decl_52,type,
esk13_0: $i ).
tff(decl_53,type,
esk14_0: $i ).
tff(decl_54,type,
esk15_0: $i ).
tff(decl_55,type,
esk16_0: $i ).
fof(p10,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',p10) ).
fof(p8,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',p8) ).
fof(p23,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',p23) ).
fof(p31,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p31) ).
fof(p19,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',p19) ).
fof(p22,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',p22) ).
fof(p26,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',p26) ).
fof(p6,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',p6) ).
fof(p17,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',p17) ).
fof(prove_relset_1_47,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(ordered_pair(X4,X5),X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_47) ).
fof(p30,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',p30) ).
fof(p27,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',p27) ).
fof(p29,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',p29) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(ordered_pair(X1,X2),X3)
=> ( member(X1,domain_of(X3))
& member(X2,range_of(X3)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).
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/sandbox2/benchmark/theBenchmark.p',p1) ).
fof(c_0_15,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p10]) ).
fof(c_0_16,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)],[p8]) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
fof(c_0_18,plain,
! [X36,X37] :
( ( ~ empty(X36)
| ~ ilf_type(X37,set_type)
| ~ member(X37,X36)
| ~ ilf_type(X36,set_type) )
& ( ilf_type(esk4_1(X36),set_type)
| empty(X36)
| ~ ilf_type(X36,set_type) )
& ( member(esk4_1(X36),X36)
| empty(X36)
| ~ 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)],[c_0_15])])])])]) ).
fof(c_0_19,plain,
! [X86] : ilf_type(X86,set_type),
inference(variable_rename,[status(thm)],[p31]) ).
fof(c_0_20,plain,
! [X32,X33] :
( ( ~ ilf_type(X32,member_type(X33))
| member(X32,X33)
| empty(X33)
| ~ ilf_type(X33,set_type)
| ~ ilf_type(X32,set_type) )
& ( ~ member(X32,X33)
| ilf_type(X32,member_type(X33))
| empty(X33)
| ~ ilf_type(X33,set_type)
| ~ ilf_type(X32,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_21,plain,
! [X50,X51] :
( ( ~ ilf_type(X51,subset_type(X50))
| ilf_type(X51,member_type(power_set(X50)))
| ~ ilf_type(X51,set_type)
| ~ ilf_type(X50,set_type) )
& ( ~ ilf_type(X51,member_type(power_set(X50)))
| ilf_type(X51,subset_type(X50))
| ~ ilf_type(X51,set_type)
| ~ ilf_type(X50,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])])]) ).
fof(c_0_22,plain,
! [X62] :
( ( ~ empty(power_set(X62))
| ~ ilf_type(X62,set_type) )
& ( ilf_type(power_set(X62),set_type)
| ~ ilf_type(X62,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_23,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_24,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_25,plain,
! [X58,X59,X60] :
( ( ~ member(X58,power_set(X59))
| ~ ilf_type(X60,set_type)
| ~ member(X60,X58)
| member(X60,X59)
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) )
& ( ilf_type(esk8_2(X58,X59),set_type)
| member(X58,power_set(X59))
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) )
& ( member(esk8_2(X58,X59),X58)
| member(X58,power_set(X59))
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,set_type) )
& ( ~ member(esk8_2(X58,X59),X59)
| member(X58,power_set(X59))
| ~ ilf_type(X59,set_type)
| ~ ilf_type(X58,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)],[p22])])])])]) ).
cnf(c_0_26,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_20]) ).
cnf(c_0_27,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_21]) ).
cnf(c_0_28,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_30,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_20]) ).
cnf(c_0_31,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24])]) ).
cnf(c_0_32,plain,
( member(X1,power_set(X2))
| ~ member(esk8_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_33,plain,
( member(esk8_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_25]) ).
fof(c_0_34,plain,
! [X71,X72,X73] :
( ~ ilf_type(X71,set_type)
| ~ ilf_type(X72,set_type)
| ~ ilf_type(X73,subset_type(cross_product(X71,X72)))
| relation_like(X73) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])]) ).
fof(c_0_35,plain,
! [X25,X26,X27,X28] :
( ( ~ ilf_type(X27,subset_type(cross_product(X25,X26)))
| ilf_type(X27,relation_type(X25,X26))
| ~ ilf_type(X26,set_type)
| ~ ilf_type(X25,set_type) )
& ( ~ ilf_type(X28,relation_type(X25,X26))
| ilf_type(X28,subset_type(cross_product(X25,X26)))
| ~ ilf_type(X26,set_type)
| ~ ilf_type(X25,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p6])])])]) ).
cnf(c_0_36,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_25]) ).
cnf(c_0_37,plain,
( empty(X1)
| member(X2,X1)
| ~ ilf_type(X2,member_type(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_24]),c_0_24])]) ).
cnf(c_0_38,plain,
( ilf_type(X1,member_type(power_set(X2)))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_24])]) ).
cnf(c_0_39,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_24])]) ).
fof(c_0_40,plain,
! [X48] :
( ( relation_like(X48)
| ~ ilf_type(X48,binary_relation_type)
| ~ ilf_type(X48,set_type) )
& ( ilf_type(X48,set_type)
| ~ ilf_type(X48,binary_relation_type)
| ~ ilf_type(X48,set_type) )
& ( ~ relation_like(X48)
| ~ ilf_type(X48,set_type)
| ilf_type(X48,binary_relation_type)
| ~ ilf_type(X48,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])]) ).
cnf(c_0_41,plain,
( ilf_type(X1,subset_type(X2))
| ~ ilf_type(X1,member_type(power_set(X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_24]),c_0_24])]) ).
cnf(c_0_42,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_30,c_0_24]),c_0_24])]),c_0_31]) ).
cnf(c_0_43,plain,
( member(X1,power_set(X2))
| ~ member(esk8_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_32,c_0_24]),c_0_24])]) ).
cnf(c_0_44,plain,
( member(esk8_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_24]),c_0_24])]) ).
cnf(c_0_45,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_34]) ).
cnf(c_0_46,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_35]) ).
fof(c_0_47,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(ordered_pair(X4,X5),X3) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[prove_relset_1_47])]) ).
fof(c_0_48,plain,
! [X83,X84,X85] :
( ~ ilf_type(X83,set_type)
| ~ ilf_type(X84,set_type)
| ~ ilf_type(X85,relation_type(X83,X84))
| ilf_type(range(X83,X84,X85),subset_type(X84)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p30])])]) ).
cnf(c_0_49,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_24]),c_0_24]),c_0_24])]) ).
cnf(c_0_50,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_51,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_40]) ).
cnf(c_0_52,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_53,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_54,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_45,c_0_24]),c_0_24])]) ).
cnf(c_0_55,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_46,c_0_24]),c_0_24])]) ).
fof(c_0_56,negated_conjecture,
! [X91] :
( ~ empty(esk12_0)
& ilf_type(esk12_0,set_type)
& ~ empty(esk13_0)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,relation_type(esk12_0,esk13_0))
& ilf_type(esk15_0,member_type(esk12_0))
& ( ~ member(esk15_0,domain(esk12_0,esk13_0,esk14_0))
| ~ ilf_type(X91,member_type(esk13_0))
| ~ member(ordered_pair(esk15_0,X91),esk14_0) )
& ( ilf_type(esk16_0,member_type(esk13_0))
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) )
& ( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) ) ),
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_47])])])])]) ).
fof(c_0_57,plain,
! [X74,X75,X76] :
( ~ ilf_type(X74,set_type)
| ~ ilf_type(X75,set_type)
| ~ ilf_type(X76,relation_type(X74,X75))
| domain(X74,X75,X76) = domain_of(X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
cnf(c_0_58,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_48]) ).
fof(c_0_59,plain,
! [X80,X81,X82] :
( ~ ilf_type(X80,set_type)
| ~ ilf_type(X81,set_type)
| ~ ilf_type(X82,relation_type(X80,X81))
| range(X80,X81,X82) = range_of(X82) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])]) ).
fof(c_0_60,plain,
! [X10,X11,X12] :
( ( member(X10,domain_of(X12))
| ~ member(ordered_pair(X10,X11),X12)
| ~ ilf_type(X12,binary_relation_type)
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,set_type) )
& ( member(X11,range_of(X12))
| ~ member(ordered_pair(X10,X11),X12)
| ~ ilf_type(X12,binary_relation_type)
| ~ ilf_type(X11,set_type)
| ~ ilf_type(X10,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_61,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_62,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_51]) ).
cnf(c_0_63,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
fof(c_0_64,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_65,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_66,negated_conjecture,
ilf_type(esk14_0,relation_type(esk12_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_67,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_57]) ).
cnf(c_0_68,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_58,c_0_24]),c_0_24])]) ).
cnf(c_0_69,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_59]) ).
cnf(c_0_70,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3)))
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_71,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X3,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_72,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_61,c_0_55]) ).
cnf(c_0_73,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_24])]) ).
cnf(c_0_74,plain,
relation_like(cross_product(X1,X2)),
inference(spm,[status(thm)],[c_0_54,c_0_63]) ).
cnf(c_0_75,negated_conjecture,
( ~ member(esk15_0,domain(esk12_0,esk13_0,esk14_0))
| ~ ilf_type(X1,member_type(esk13_0))
| ~ member(ordered_pair(esk15_0,X1),esk14_0) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_76,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_77,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_64]) ).
cnf(c_0_78,negated_conjecture,
relation_like(esk14_0),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_79,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_67,c_0_24]),c_0_24])]) ).
cnf(c_0_80,plain,
( member(X1,X2)
| ~ member(X1,range(X3,X2,X4))
| ~ ilf_type(X4,relation_type(X3,X2)) ),
inference(spm,[status(thm)],[c_0_61,c_0_68]) ).
cnf(c_0_81,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_69,c_0_24]),c_0_24])]) ).
cnf(c_0_82,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ ilf_type(X1,subset_type(cross_product(X2,X3))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_24]),c_0_24])]) ).
cnf(c_0_83,plain,
( member(X1,range_of(X2))
| ~ member(ordered_pair(X3,X1),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_24]),c_0_24])]) ).
cnf(c_0_84,negated_conjecture,
( member(X1,cross_product(esk12_0,esk13_0))
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_72,c_0_66]) ).
cnf(c_0_85,plain,
ilf_type(cross_product(X1,X2),binary_relation_type),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_86,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_87,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_77,c_0_24])]) ).
cnf(c_0_88,negated_conjecture,
ilf_type(esk14_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_73,c_0_78]) ).
cnf(c_0_89,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| member(esk15_0,domain_of(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_79]),c_0_66])]) ).
cnf(c_0_90,plain,
( member(X1,X2)
| ~ member(X1,range_of(X3))
| ~ ilf_type(X3,relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_91,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_63]) ).
cnf(c_0_92,negated_conjecture,
( member(X1,range_of(cross_product(esk12_0,esk13_0)))
| ~ member(ordered_pair(X2,X1),esk14_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85])]) ).
cnf(c_0_93,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| ~ ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88])]),c_0_89]) ).
cnf(c_0_94,plain,
( member(X1,X2)
| ~ member(X1,range_of(cross_product(X3,X2))) ),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_95,negated_conjecture,
( member(esk1_2(X1,esk14_0),range_of(cross_product(esk12_0,esk13_0)))
| ~ member(X1,domain_of(esk14_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_87]),c_0_88])]) ).
cnf(c_0_96,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| member(esk15_0,domain(esk12_0,esk13_0,esk14_0)) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_97,plain,
( member(X2,domain_of(X3))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_98,negated_conjecture,
( member(ordered_pair(esk15_0,esk16_0),esk14_0)
| ~ member(esk1_2(esk15_0,esk14_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_93,c_0_42]) ).
cnf(c_0_99,negated_conjecture,
( member(esk1_2(X1,esk14_0),esk13_0)
| ~ member(X1,domain_of(esk14_0)) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_100,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(spm,[status(thm)],[c_0_75,c_0_96]) ).
cnf(c_0_101,negated_conjecture,
( member(esk15_0,domain_of(esk14_0))
| ilf_type(esk16_0,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_79]),c_0_66])]) ).
cnf(c_0_102,plain,
( member(X1,domain_of(X2))
| ~ member(ordered_pair(X1,X3),X2)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_24]),c_0_24])]) ).
cnf(c_0_103,negated_conjecture,
member(ordered_pair(esk15_0,esk16_0),esk14_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_89]) ).
cnf(c_0_104,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ~ ilf_type(esk1_2(esk15_0,esk14_0),member_type(esk13_0)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_87]),c_0_88])]),c_0_101]) ).
cnf(c_0_105,negated_conjecture,
( ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ member(esk15_0,domain_of(esk14_0))
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_79]),c_0_66])]) ).
cnf(c_0_106,negated_conjecture,
member(esk15_0,domain_of(esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_88])]) ).
cnf(c_0_107,negated_conjecture,
( ilf_type(esk16_0,member_type(esk13_0))
| ~ member(esk1_2(esk15_0,esk14_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_104,c_0_42]) ).
cnf(c_0_108,negated_conjecture,
( ~ member(ordered_pair(esk15_0,X1),esk14_0)
| ~ ilf_type(X1,member_type(esk13_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_106])]) ).
cnf(c_0_109,negated_conjecture,
ilf_type(esk16_0,member_type(esk13_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_99]),c_0_101]) ).
cnf(c_0_110,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_103]),c_0_109])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET680+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 : n012.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 09:32:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.60 % Version : CSE_E---1.5
% 0.19/0.60 % Problem : theBenchmark.p
% 0.19/0.60 % Proof found
% 0.19/0.60 % SZS status Theorem for theBenchmark.p
% 0.19/0.60 % SZS output start Proof
% See solution above
% 0.19/0.61 % Total time : 0.029000 s
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time : 0.033000 s
%------------------------------------------------------------------------------