TSTP Solution File: SET670+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET670+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 : 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 14:35:08 EDT 2023
% Result : Theorem 224.89s 224.83s
% Output : CNFRefutation 224.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 47
% Syntax : Number of formulae : 137 ( 16 unt; 30 typ; 0 def)
% Number of atoms : 453 ( 11 equ)
% Maximal formula atoms : 26 ( 4 avg)
% Number of connectives : 591 ( 245 ~; 241 |; 36 &)
% ( 10 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 39 ( 23 >; 16 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 7 con; 0-4 aty)
% Number of variables : 254 ( 24 sgn; 103 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
binary_relation_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
set_type: $i ).
tff(decl_26,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
member: ( $i * $i ) > $o ).
tff(decl_28,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_29,type,
relation_like: $i > $o ).
tff(decl_30,type,
restrict: ( $i * $i ) > $i ).
tff(decl_31,type,
subset_type: $i > $i ).
tff(decl_32,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_33,type,
power_set: $i > $i ).
tff(decl_34,type,
member_type: $i > $i ).
tff(decl_35,type,
empty: $i > $o ).
tff(decl_36,type,
restrict4: ( $i * $i * $i * $i ) > $i ).
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_0: $i ).
tff(decl_41,type,
esk5_1: $i > $i ).
tff(decl_42,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk7_2: ( $i * $i ) > $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_1: $i > $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_0: $i ).
fof(p24,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p24) ).
fof(p22,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/sandbox/benchmark/theBenchmark.p',p22) ).
fof(p28,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).
fof(p21,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p21) ).
fof(p13,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/sandbox/benchmark/theBenchmark.p',p13) ).
fof(p5,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',p5) ).
fof(p11,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',p11) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ilf_type(restrict(X1,X2),binary_relation_type) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p19,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',p19) ).
fof(p7,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',p7) ).
fof(p27,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
fof(prove_relset_1_33,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ilf_type(restrict4(X1,X3,X4,X2),relation_type(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_33) ).
fof(p26,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ! [X4] :
( ilf_type(X4,set_type)
=> restrict4(X1,X2,X3,X4) = restrict(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(p20,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',p20) ).
fof(p18,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ( relation_like(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X1)
=> ? [X3] :
( ilf_type(X3,set_type)
& ? [X4] :
( ilf_type(X4,set_type)
& X2 = ordered_pair(X3,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p18) ).
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,binary_relation_type)
=> ( member(ordered_pair(X2,X3),restrict(X4,X1))
<=> ( member(X2,X1)
& member(ordered_pair(X2,X3),X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3) ).
fof(p4,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)
=> ( member(ordered_pair(X1,X2),cross_product(X3,X4))
<=> ( member(X1,X3)
& member(X2,X4) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(c_0_17,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p24]) ).
fof(c_0_18,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)],[p22]) ).
fof(c_0_19,plain,
! [X69,X70] :
( ( ~ empty(X69)
| ~ ilf_type(X70,set_type)
| ~ member(X70,X69)
| ~ ilf_type(X69,set_type) )
& ( ilf_type(esk11_1(X69),set_type)
| empty(X69)
| ~ ilf_type(X69,set_type) )
& ( member(esk11_1(X69),X69)
| empty(X69)
| ~ 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)],[c_0_17])])])])]) ).
fof(c_0_20,plain,
! [X81] : ilf_type(X81,set_type),
inference(variable_rename,[status(thm)],[p28]) ).
fof(c_0_21,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p21]) ).
fof(c_0_22,plain,
! [X42,X43] :
( ( ~ ilf_type(X43,subset_type(X42))
| ilf_type(X43,member_type(power_set(X42)))
| ~ ilf_type(X43,set_type)
| ~ ilf_type(X42,set_type) )
& ( ~ ilf_type(X43,member_type(power_set(X42)))
| ilf_type(X43,subset_type(X42))
| ~ ilf_type(X43,set_type)
| ~ ilf_type(X42,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p13])])])]) ).
fof(c_0_23,plain,
! [X65,X66] :
( ( ~ ilf_type(X65,member_type(X66))
| member(X65,X66)
| empty(X66)
| ~ ilf_type(X66,set_type)
| ~ ilf_type(X65,set_type) )
& ( ~ member(X65,X66)
| ilf_type(X65,member_type(X66))
| empty(X66)
| ~ ilf_type(X66,set_type)
| ~ ilf_type(X65,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
cnf(c_0_24,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_26,plain,
! [X64] :
( ( ~ empty(power_set(X64))
| ~ ilf_type(X64,set_type) )
& ( ilf_type(power_set(X64),set_type)
| ~ ilf_type(X64,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
fof(c_0_27,plain,
! [X22,X23,X24,X25] :
( ( ~ ilf_type(X24,subset_type(cross_product(X22,X23)))
| ilf_type(X24,relation_type(X22,X23))
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ~ ilf_type(X25,relation_type(X22,X23))
| ilf_type(X25,subset_type(cross_product(X22,X23)))
| ~ 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)],[p5])])])]) ).
cnf(c_0_28,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_22]) ).
cnf(c_0_29,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_23]) ).
cnf(c_0_30,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_25])]) ).
fof(c_0_31,plain,
! [X40] :
( ( relation_like(X40)
| ~ ilf_type(X40,binary_relation_type)
| ~ ilf_type(X40,set_type) )
& ( ilf_type(X40,set_type)
| ~ ilf_type(X40,binary_relation_type)
| ~ ilf_type(X40,set_type) )
& ( ~ relation_like(X40)
| ~ ilf_type(X40,set_type)
| ilf_type(X40,binary_relation_type)
| ~ ilf_type(X40,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p11])])]) ).
fof(c_0_32,plain,
! [X38,X39] :
( ~ ilf_type(X38,binary_relation_type)
| ~ ilf_type(X39,set_type)
| ilf_type(restrict(X38,X39),binary_relation_type) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])]) ).
fof(c_0_33,plain,
! [X57,X58,X59] :
( ~ ilf_type(X57,set_type)
| ~ ilf_type(X58,set_type)
| ~ ilf_type(X59,subset_type(cross_product(X57,X58)))
| relation_like(X59) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p19])])]) ).
fof(c_0_34,plain,
! [X29,X30,X31,X32,X33] :
( ( member(X31,X29)
| ~ member(ordered_pair(X31,X32),X33)
| ~ ilf_type(X33,relation_type(X29,X30))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,set_type)
| ~ ilf_type(X29,set_type) )
& ( member(X32,X30)
| ~ member(ordered_pair(X31,X32),X33)
| ~ ilf_type(X33,relation_type(X29,X30))
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type)
| ~ 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)],[p7])])])]) ).
fof(c_0_35,plain,
! [X77,X78,X79,X80] :
( ~ ilf_type(X77,set_type)
| ~ ilf_type(X78,set_type)
| ~ ilf_type(X79,relation_type(X77,X78))
| ~ ilf_type(X80,set_type)
| ilf_type(restrict4(X77,X78,X79,X80),relation_type(X77,X78)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p27])])]) ).
cnf(c_0_36,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_37,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_22]) ).
cnf(c_0_38,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_39,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,relation_type(X1,X3))
=> ilf_type(restrict4(X1,X3,X4,X2),relation_type(X2,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_33]) ).
cnf(c_0_40,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_27]) ).
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_28,c_0_25]),c_0_25])]) ).
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_29,c_0_25]),c_0_25])]),c_0_30]) ).
cnf(c_0_43,plain,
( relation_like(X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_44,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,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_31]) ).
fof(c_0_46,plain,
! [X73,X74,X75,X76] :
( ~ ilf_type(X73,set_type)
| ~ ilf_type(X74,set_type)
| ~ ilf_type(X75,relation_type(X73,X74))
| ~ ilf_type(X76,set_type)
| restrict4(X73,X74,X75,X76) = restrict(X75,X76) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])]) ).
cnf(c_0_47,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_33]) ).
cnf(c_0_48,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_49,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_34]) ).
cnf(c_0_50,plain,
( ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2))
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_51,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_36,c_0_25]),c_0_25])]) ).
cnf(c_0_52,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_37,c_0_25]),c_0_25])]) ).
cnf(c_0_53,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_25])]) ).
fof(c_0_54,negated_conjecture,
( ilf_type(esk12_0,set_type)
& ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,relation_type(esk12_0,esk14_0))
& ~ ilf_type(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),relation_type(esk13_0,esk14_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_39])])]) ).
cnf(c_0_55,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_40,c_0_25]),c_0_25])]) ).
cnf(c_0_56,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
fof(c_0_57,plain,
! [X60,X61,X62] :
( ( ~ member(X60,power_set(X61))
| ~ ilf_type(X62,set_type)
| ~ member(X62,X60)
| member(X62,X61)
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) )
& ( ilf_type(esk9_2(X60,X61),set_type)
| member(X60,power_set(X61))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) )
& ( member(esk9_2(X60,X61),X60)
| member(X60,power_set(X61))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,set_type) )
& ( ~ member(esk9_2(X60,X61),X61)
| member(X60,power_set(X61))
| ~ ilf_type(X61,set_type)
| ~ ilf_type(X60,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)],[p20])])])])]) ).
cnf(c_0_58,plain,
( relation_like(X1)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_25])]) ).
cnf(c_0_59,plain,
( ilf_type(restrict(X1,X2),binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_25])]) ).
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_45]) ).
cnf(c_0_61,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X1,X2))
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_62,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_47,c_0_25]),c_0_25])]) ).
cnf(c_0_63,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_48,c_0_25]),c_0_25])]) ).
cnf(c_0_64,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_49,c_0_25]),c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_65,plain,
( ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_66,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]) ).
fof(c_0_67,plain,
! [X50,X51,X55,X56] :
( ( ilf_type(esk6_2(X50,X51),set_type)
| ~ member(X51,X50)
| ~ ilf_type(X51,set_type)
| ~ relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( ilf_type(esk7_2(X50,X51),set_type)
| ~ member(X51,X50)
| ~ ilf_type(X51,set_type)
| ~ relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( X51 = ordered_pair(esk6_2(X50,X51),esk7_2(X50,X51))
| ~ member(X51,X50)
| ~ ilf_type(X51,set_type)
| ~ relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( ilf_type(esk8_1(X50),set_type)
| relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( member(esk8_1(X50),X50)
| relation_like(X50)
| ~ ilf_type(X50,set_type) )
& ( ~ ilf_type(X55,set_type)
| ~ ilf_type(X56,set_type)
| esk8_1(X50) != ordered_pair(X55,X56)
| relation_like(X50)
| ~ ilf_type(X50,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])])])])]) ).
cnf(c_0_68,negated_conjecture,
~ ilf_type(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),relation_type(esk13_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_69,plain,
( ilf_type(X1,relation_type(X2,X3))
| ~ member(X1,power_set(cross_product(X2,X3))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_70,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_57]) ).
cnf(c_0_71,plain,
( relation_like(restrict(X1,X2))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_72,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_25])]) ).
cnf(c_0_73,plain,
( restrict4(X1,X2,X3,X4) = restrict(X3,X4)
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_74,negated_conjecture,
ilf_type(esk15_0,relation_type(esk12_0,esk14_0)),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_75,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_76,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),restrict4(X4,X2,X5,X6))
| ~ ilf_type(X5,relation_type(X4,X2)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_77,plain,
( member(X1,power_set(cross_product(X2,X3)))
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
cnf(c_0_78,plain,
( X1 = ordered_pair(esk6_2(X2,X1),esk7_2(X2,X1))
| ~ member(X1,X2)
| ~ ilf_type(X1,set_type)
| ~ relation_like(X2)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_79,negated_conjecture,
~ member(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),power_set(cross_product(esk13_0,esk14_0))),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_80,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_70,c_0_25]),c_0_25])]) ).
cnf(c_0_81,plain,
( relation_like(restrict(X1,X2))
| ~ relation_like(X1) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_82,negated_conjecture,
restrict(esk15_0,X1) = restrict4(esk12_0,esk14_0,esk15_0,X1),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_83,negated_conjecture,
relation_like(esk15_0),
inference(spm,[status(thm)],[c_0_75,c_0_74]) ).
fof(c_0_84,plain,
! [X14,X15,X16,X17] :
( ( member(X15,X14)
| ~ member(ordered_pair(X15,X16),restrict(X17,X14))
| ~ ilf_type(X17,binary_relation_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) )
& ( member(ordered_pair(X15,X16),X17)
| ~ member(ordered_pair(X15,X16),restrict(X17,X14))
| ~ ilf_type(X17,binary_relation_type)
| ~ ilf_type(X16,set_type)
| ~ ilf_type(X15,set_type)
| ~ ilf_type(X14,set_type) )
& ( ~ member(X15,X14)
| ~ member(ordered_pair(X15,X16),X17)
| member(ordered_pair(X15,X16),restrict(X17,X14))
| ~ ilf_type(X17,binary_relation_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_85,plain,
! [X18,X19,X20,X21] :
( ( member(X18,X20)
| ~ member(ordered_pair(X18,X19),cross_product(X20,X21))
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( member(X19,X21)
| ~ member(ordered_pair(X18,X19),cross_product(X20,X21))
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) )
& ( ~ member(X18,X20)
| ~ member(X19,X21)
| member(ordered_pair(X18,X19),cross_product(X20,X21))
| ~ ilf_type(X21,set_type)
| ~ ilf_type(X20,set_type)
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p4])])])]) ).
cnf(c_0_86,plain,
( member(X1,X2)
| ~ member(ordered_pair(X3,X1),restrict4(X4,X2,X5,X6))
| ~ member(X5,power_set(cross_product(X4,X2))) ),
inference(spm,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_87,negated_conjecture,
member(esk15_0,power_set(cross_product(esk12_0,esk14_0))),
inference(spm,[status(thm)],[c_0_77,c_0_74]) ).
cnf(c_0_88,plain,
( ordered_pair(esk6_2(X1,X2),esk7_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_25]),c_0_25])]) ).
cnf(c_0_89,negated_conjecture,
member(esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0)),restrict4(esk12_0,esk14_0,esk15_0,esk13_0)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
relation_like(restrict4(esk12_0,esk14_0,esk15_0,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83])]) ).
cnf(c_0_91,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),restrict(X4,X2))
| ~ ilf_type(X4,binary_relation_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_92,plain,
( member(ordered_pair(X1,X3),cross_product(X2,X4))
| ~ member(X1,X2)
| ~ member(X3,X4)
| ~ ilf_type(X4,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_93,negated_conjecture,
( member(X1,esk14_0)
| ~ member(ordered_pair(X2,X1),restrict4(esk12_0,esk14_0,esk15_0,X3)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_94,negated_conjecture,
ordered_pair(esk6_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),esk7_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0)))) = esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_90])]) ).
cnf(c_0_95,plain,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),restrict(X4,X2))
| ~ ilf_type(X4,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_96,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_57]) ).
cnf(c_0_97,plain,
( member(ordered_pair(X1,X2),cross_product(X3,X4))
| ~ member(X2,X4)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_25]),c_0_25]),c_0_25]),c_0_25])]) ).
cnf(c_0_98,negated_conjecture,
( member(esk7_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),esk14_0)
| ~ member(esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0)),restrict4(esk12_0,esk14_0,esk15_0,X1)) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,plain,
( member(X1,X2)
| ~ relation_like(X3)
| ~ member(ordered_pair(X1,X4),restrict(X3,X2)) ),
inference(spm,[status(thm)],[c_0_95,c_0_72]) ).
cnf(c_0_100,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_96,c_0_25]),c_0_25])]) ).
cnf(c_0_101,negated_conjecture,
( member(esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0)),cross_product(X1,X2))
| ~ member(esk7_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),X2)
| ~ member(esk6_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),X1) ),
inference(spm,[status(thm)],[c_0_97,c_0_94]) ).
cnf(c_0_102,negated_conjecture,
member(esk7_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),esk14_0),
inference(spm,[status(thm)],[c_0_98,c_0_89]) ).
cnf(c_0_103,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),restrict4(esk12_0,esk14_0,esk15_0,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_82]),c_0_83])]) ).
cnf(c_0_104,negated_conjecture,
~ member(esk6_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),esk13_0),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102])]),c_0_79]) ).
cnf(c_0_105,negated_conjecture,
( member(esk6_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0))),X1)
| ~ member(esk9_2(restrict4(esk12_0,esk14_0,esk15_0,esk13_0),cross_product(esk13_0,esk14_0)),restrict4(esk12_0,esk14_0,esk15_0,X1)) ),
inference(spm,[status(thm)],[c_0_103,c_0_94]) ).
cnf(c_0_106,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_89])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET670+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/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 10:53:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 224.89/224.83 % Version : CSE_E---1.5
% 224.89/224.83 % Problem : theBenchmark.p
% 224.89/224.83 % Proof found
% 224.89/224.83 % SZS status Theorem for theBenchmark.p
% 224.89/224.83 % SZS output start Proof
% See solution above
% 224.89/224.84 % Total time : 224.273000 s
% 224.89/224.84 % SZS output end Proof
% 224.89/224.84 % Total time : 224.286000 s
%------------------------------------------------------------------------------