TSTP Solution File: SET671+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET671+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 : n031.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 14:35:09 EDT 2023
% Result : Theorem 23.99s 24.10s
% Output : CNFRefutation 23.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 49
% Syntax : Number of formulae : 160 ( 18 unt; 31 typ; 0 def)
% Number of atoms : 567 ( 29 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 740 ( 302 ~; 319 |; 42 &)
% ( 12 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 24 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-4 aty)
% Number of variables : 308 ( 24 sgn; 109 !; 2 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
binary_relation_type: $i ).
tff(decl_23,type,
ilf_type: ( $i * $i ) > $o ).
tff(decl_24,type,
set_type: $i ).
tff(decl_25,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
member: ( $i * $i ) > $o ).
tff(decl_27,type,
restrict: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_29,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_30,type,
subset_type: $i > $i ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
relation_like: $i > $o ).
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_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk5_0: $i ).
tff(decl_42,type,
esk6_1: $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_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk11_1: $i > $i ).
tff(decl_48,type,
esk12_1: $i > $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_0: $i ).
tff(decl_52,type,
esk16_0: $i ).
fof(p19,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',p19) ).
fof(p18,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',p18) ).
fof(p27,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p27) ).
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/sandbox/benchmark/theBenchmark.p',p12) ).
fof(p17,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',p17) ).
fof(p4,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',p4) ).
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)
=> ilf_type(restrict4(X1,X2,X3,X4),relation_type(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p26) ).
fof(prove_relset_1_34,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(X2,X1))
=> ( subset(X2,X3)
=> restrict4(X2,X1,X4,X3) = X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_34) ).
fof(p23,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',p23) ).
fof(p22,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',p22) ).
fof(p2,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',p2) ).
fof(p21,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',p21) ).
fof(p25,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',p25) ).
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/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p6,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',p6) ).
fof(p9,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',p9) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,binary_relation_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( X1 = X2
<=> ! [X3] :
( ilf_type(X3,set_type)
=> ! [X4] :
( ilf_type(X4,set_type)
=> ( member(ordered_pair(X3,X4),X1)
<=> member(ordered_pair(X3,X4),X2) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
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(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)],[p19]) ).
fof(c_0_19,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( ~ empty(power_set(X1))
& ilf_type(power_set(X1),set_type) ) ),
inference(fof_simplification,[status(thm)],[p18]) ).
fof(c_0_20,plain,
! [X53,X54] :
( ( ~ ilf_type(X53,member_type(X54))
| member(X53,X54)
| empty(X54)
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) )
& ( ~ member(X53,X54)
| ilf_type(X53,member_type(X54))
| empty(X54)
| ~ ilf_type(X54,set_type)
| ~ ilf_type(X53,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])]) ).
fof(c_0_21,plain,
! [X79] : ilf_type(X79,set_type),
inference(variable_rename,[status(thm)],[p27]) ).
fof(c_0_22,plain,
! [X40,X41] :
( ( ~ ilf_type(X41,subset_type(X40))
| ilf_type(X41,member_type(power_set(X40)))
| ~ ilf_type(X41,set_type)
| ~ ilf_type(X40,set_type) )
& ( ~ ilf_type(X41,member_type(power_set(X40)))
| ilf_type(X41,subset_type(X40))
| ~ ilf_type(X41,set_type)
| ~ ilf_type(X40,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_23,plain,
! [X52] :
( ( ~ empty(power_set(X52))
| ~ ilf_type(X52,set_type) )
& ( ilf_type(power_set(X52),set_type)
| ~ ilf_type(X52,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_24,plain,
! [X48,X49,X50] :
( ( ~ member(X48,power_set(X49))
| ~ ilf_type(X50,set_type)
| ~ member(X50,X48)
| member(X50,X49)
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( ilf_type(esk7_2(X48,X49),set_type)
| member(X48,power_set(X49))
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( member(esk7_2(X48,X49),X48)
| member(X48,power_set(X49))
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) )
& ( ~ member(esk7_2(X48,X49),X49)
| member(X48,power_set(X49))
| ~ ilf_type(X49,set_type)
| ~ ilf_type(X48,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])])])]) ).
cnf(c_0_25,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_26,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
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_22]) ).
cnf(c_0_28,plain,
( ~ empty(power_set(X1))
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,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_24]) ).
cnf(c_0_30,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_25,c_0_26]),c_0_26])]) ).
cnf(c_0_31,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_26]),c_0_26])]) ).
cnf(c_0_32,plain,
~ empty(power_set(X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_26])]) ).
fof(c_0_33,plain,
! [X21,X22,X23,X24] :
( ( ~ ilf_type(X23,subset_type(cross_product(X21,X22)))
| ilf_type(X23,relation_type(X21,X22))
| ~ ilf_type(X22,set_type)
| ~ ilf_type(X21,set_type) )
& ( ~ ilf_type(X24,relation_type(X21,X22))
| ilf_type(X24,subset_type(cross_product(X21,X22)))
| ~ ilf_type(X22,set_type)
| ~ ilf_type(X21,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_34,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_29,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_35,plain,
( member(X1,power_set(X2))
| ~ ilf_type(X1,subset_type(X2)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_36,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_33]) ).
fof(c_0_37,plain,
! [X75,X76,X77,X78] :
( ~ ilf_type(X75,set_type)
| ~ ilf_type(X76,set_type)
| ~ ilf_type(X77,relation_type(X75,X76))
| ~ ilf_type(X78,set_type)
| ilf_type(restrict4(X75,X76,X77,X78),relation_type(X75,X76)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p26])])]) ).
cnf(c_0_38,plain,
( member(X1,X2)
| ~ member(X1,X3)
| ~ ilf_type(X3,subset_type(X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,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_36,c_0_26]),c_0_26])]) ).
cnf(c_0_40,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_37]) ).
cnf(c_0_41,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,X4)
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,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_40,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_43,plain,
( member(esk7_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_24]) ).
fof(c_0_44,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(X2,X1))
=> ( subset(X2,X3)
=> restrict4(X2,X1,X4,X3) = X4 ) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_34]) ).
fof(c_0_45,plain,
! [X1] :
( ilf_type(X1,set_type)
=> ( empty(X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ~ member(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[p23]) ).
cnf(c_0_46,plain,
( member(X1,cross_product(X2,X3))
| ~ member(X1,restrict4(X2,X3,X4,X5))
| ~ ilf_type(X4,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
( member(esk7_2(X1,X2),X1)
| member(X1,power_set(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_26]),c_0_26])]) ).
fof(c_0_48,negated_conjecture,
( ilf_type(esk13_0,set_type)
& ilf_type(esk14_0,set_type)
& ilf_type(esk15_0,set_type)
& ilf_type(esk16_0,relation_type(esk14_0,esk13_0))
& subset(esk14_0,esk15_0)
& restrict4(esk14_0,esk13_0,esk16_0,esk15_0) != esk16_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_44])])]) ).
fof(c_0_49,plain,
! [X67,X68] :
( ( ~ empty(X67)
| ~ ilf_type(X68,set_type)
| ~ member(X68,X67)
| ~ ilf_type(X67,set_type) )
& ( ilf_type(esk12_1(X67),set_type)
| empty(X67)
| ~ ilf_type(X67,set_type) )
& ( member(esk12_1(X67),X67)
| empty(X67)
| ~ ilf_type(X67,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_45])])])])]) ).
cnf(c_0_50,plain,
( member(X1,power_set(X2))
| ~ member(esk7_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_51,plain,
( member(esk7_2(restrict4(X1,X2,X3,X4),X5),cross_product(X1,X2))
| member(restrict4(X1,X2,X3,X4),power_set(X5))
| ~ ilf_type(X3,relation_type(X1,X2)) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
ilf_type(esk16_0,relation_type(esk14_0,esk13_0)),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_53,plain,
( ~ empty(X1)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X1)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
fof(c_0_54,plain,
! [X64,X65,X66] :
( ~ ilf_type(X64,set_type)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X66,subset_type(cross_product(X64,X65)))
| relation_like(X66) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p22])])]) ).
fof(c_0_55,plain,
! [X12,X13,X14,X15] :
( ( member(X13,X12)
| ~ member(ordered_pair(X13,X14),restrict(X15,X12))
| ~ ilf_type(X15,binary_relation_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X13,set_type)
| ~ ilf_type(X12,set_type) )
& ( member(ordered_pair(X13,X14),X15)
| ~ member(ordered_pair(X13,X14),restrict(X15,X12))
| ~ ilf_type(X15,binary_relation_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X13,set_type)
| ~ ilf_type(X12,set_type) )
& ( ~ member(X13,X12)
| ~ member(ordered_pair(X13,X14),X15)
| member(ordered_pair(X13,X14),restrict(X15,X12))
| ~ ilf_type(X15,binary_relation_type)
| ~ ilf_type(X14,set_type)
| ~ ilf_type(X13,set_type)
| ~ ilf_type(X12,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])]) ).
fof(c_0_56,plain,
! [X57,X58,X62,X63] :
( ( ilf_type(esk9_2(X57,X58),set_type)
| ~ member(X58,X57)
| ~ ilf_type(X58,set_type)
| ~ relation_like(X57)
| ~ ilf_type(X57,set_type) )
& ( ilf_type(esk10_2(X57,X58),set_type)
| ~ member(X58,X57)
| ~ ilf_type(X58,set_type)
| ~ relation_like(X57)
| ~ ilf_type(X57,set_type) )
& ( X58 = ordered_pair(esk9_2(X57,X58),esk10_2(X57,X58))
| ~ member(X58,X57)
| ~ ilf_type(X58,set_type)
| ~ relation_like(X57)
| ~ ilf_type(X57,set_type) )
& ( ilf_type(esk11_1(X57),set_type)
| relation_like(X57)
| ~ ilf_type(X57,set_type) )
& ( member(esk11_1(X57),X57)
| relation_like(X57)
| ~ ilf_type(X57,set_type) )
& ( ~ ilf_type(X62,set_type)
| ~ ilf_type(X63,set_type)
| esk11_1(X57) != ordered_pair(X62,X63)
| relation_like(X57)
| ~ ilf_type(X57,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)],[p21])])])])]) ).
cnf(c_0_57,plain,
( member(X1,power_set(X2))
| ~ member(esk7_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_26]),c_0_26])]) ).
cnf(c_0_58,negated_conjecture,
( member(esk7_2(restrict4(esk14_0,esk13_0,esk16_0,X1),X2),cross_product(esk14_0,esk13_0))
| member(restrict4(esk14_0,esk13_0,esk16_0,X1),power_set(X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
fof(c_0_59,plain,
! [X71,X72,X73,X74] :
( ~ ilf_type(X71,set_type)
| ~ ilf_type(X72,set_type)
| ~ ilf_type(X73,relation_type(X71,X72))
| ~ ilf_type(X74,set_type)
| restrict4(X71,X72,X73,X74) = restrict(X73,X74) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p25])])]) ).
cnf(c_0_60,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_61,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_62,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_26]),c_0_26])]) ).
fof(c_0_63,plain,
! [X38] :
( ( relation_like(X38)
| ~ ilf_type(X38,binary_relation_type)
| ~ ilf_type(X38,set_type) )
& ( ilf_type(X38,set_type)
| ~ ilf_type(X38,binary_relation_type)
| ~ ilf_type(X38,set_type) )
& ( ~ relation_like(X38)
| ~ ilf_type(X38,set_type)
| ilf_type(X38,binary_relation_type)
| ~ ilf_type(X38,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p10])])]) ).
cnf(c_0_64,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_54]) ).
cnf(c_0_65,plain,
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X3,X4))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_66,plain,
( X1 = ordered_pair(esk9_2(X2,X1),esk10_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_56]) ).
fof(c_0_67,plain,
! [X28,X29,X30] :
( ( ~ subset(X28,X29)
| ~ ilf_type(X30,set_type)
| ~ member(X30,X28)
| member(X30,X29)
| ~ ilf_type(X29,set_type)
| ~ ilf_type(X28,set_type) )
& ( ilf_type(esk4_2(X28,X29),set_type)
| subset(X28,X29)
| ~ ilf_type(X29,set_type)
| ~ ilf_type(X28,set_type) )
& ( member(esk4_2(X28,X29),X28)
| subset(X28,X29)
| ~ ilf_type(X29,set_type)
| ~ ilf_type(X28,set_type) )
& ( ~ member(esk4_2(X28,X29),X29)
| subset(X28,X29)
| ~ ilf_type(X29,set_type)
| ~ ilf_type(X28,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)],[p6])])])])]) ).
cnf(c_0_68,negated_conjecture,
member(restrict4(esk14_0,esk13_0,esk16_0,X1),power_set(cross_product(esk14_0,esk13_0))),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_69,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_59]) ).
cnf(c_0_70,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_60,c_0_26]),c_0_26])]) ).
cnf(c_0_71,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_61,c_0_26]),c_0_26])]),c_0_62]) ).
cnf(c_0_72,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_63]) ).
cnf(c_0_73,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_64,c_0_26]),c_0_26])]) ).
cnf(c_0_74,plain,
( member(ordered_pair(X1,X2),X3)
| ~ member(ordered_pair(X1,X2),restrict(X3,X4))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_75,plain,
( ordered_pair(esk9_2(X1,X2),esk10_2(X1,X2)) = X2
| ~ relation_like(X1)
| ~ member(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_26]),c_0_26])]) ).
cnf(c_0_76,plain,
( member(esk4_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_77,negated_conjecture,
( member(X1,cross_product(esk14_0,esk13_0))
| ~ member(X1,restrict4(esk14_0,esk13_0,esk16_0,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_68]) ).
cnf(c_0_78,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_69,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_79,plain,
( ilf_type(X1,subset_type(X2))
| ~ member(X1,power_set(X2)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_80,plain,
member(X1,power_set(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_47]) ).
cnf(c_0_81,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_72]) ).
cnf(c_0_82,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_73,c_0_39]) ).
fof(c_0_83,plain,
! [X36,X37] :
( ~ ilf_type(X36,binary_relation_type)
| ~ ilf_type(X37,set_type)
| ilf_type(restrict(X36,X37),binary_relation_type) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p9])])]) ).
cnf(c_0_84,plain,
( member(X1,X2)
| ~ relation_like(X3)
| ~ member(X1,restrict(X2,X4))
| ~ member(X1,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_85,plain,
( subset(X1,X2)
| member(esk4_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_26]),c_0_26])]) ).
cnf(c_0_86,negated_conjecture,
( member(X1,cross_product(esk14_0,esk13_0))
| ~ member(X1,restrict(esk16_0,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_52])]) ).
cnf(c_0_87,plain,
ilf_type(X1,subset_type(X1)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_88,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_26])]) ).
cnf(c_0_89,negated_conjecture,
relation_like(esk16_0),
inference(spm,[status(thm)],[c_0_82,c_0_52]) ).
fof(c_0_90,plain,
! [X6,X7,X8,X9] :
( ( ~ member(ordered_pair(X8,X9),X6)
| member(ordered_pair(X8,X9),X7)
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| X6 != X7
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,binary_relation_type) )
& ( ~ member(ordered_pair(X8,X9),X7)
| member(ordered_pair(X8,X9),X6)
| ~ ilf_type(X9,set_type)
| ~ ilf_type(X8,set_type)
| X6 != X7
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,binary_relation_type) )
& ( ilf_type(esk1_2(X6,X7),set_type)
| X6 = X7
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,binary_relation_type) )
& ( ilf_type(esk2_2(X6,X7),set_type)
| X6 = X7
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,binary_relation_type) )
& ( ~ member(ordered_pair(esk1_2(X6,X7),esk2_2(X6,X7)),X6)
| ~ member(ordered_pair(esk1_2(X6,X7),esk2_2(X6,X7)),X7)
| X6 = X7
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,binary_relation_type) )
& ( member(ordered_pair(esk1_2(X6,X7),esk2_2(X6,X7)),X6)
| member(ordered_pair(esk1_2(X6,X7),esk2_2(X6,X7)),X7)
| X6 = X7
| ~ ilf_type(X7,binary_relation_type)
| ~ ilf_type(X6,binary_relation_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_91,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_83]) ).
cnf(c_0_92,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_93,plain,
( subset(restrict(X1,X2),X3)
| member(esk4_2(restrict(X1,X2),X3),X1)
| ~ relation_like(X4)
| ~ member(esk4_2(restrict(X1,X2),X3),X4)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_94,negated_conjecture,
( subset(restrict(esk16_0,X1),X2)
| member(esk4_2(restrict(esk16_0,X1),X2),cross_product(esk14_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_86,c_0_85]) ).
cnf(c_0_95,plain,
relation_like(cross_product(X1,X2)),
inference(spm,[status(thm)],[c_0_73,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
ilf_type(esk16_0,binary_relation_type),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,plain,
( member(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X1)
| member(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| X1 = X2
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_98,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_91,c_0_26])]) ).
cnf(c_0_99,plain,
( member(X3,X2)
| ~ subset(X1,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_67]) ).
cnf(c_0_100,plain,
( subset(X1,X2)
| ~ member(esk4_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_26]),c_0_26])]) ).
cnf(c_0_101,negated_conjecture,
( subset(restrict(esk16_0,X1),X2)
| member(esk4_2(restrict(esk16_0,X1),X2),esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_94]),c_0_95]),c_0_96])]) ).
fof(c_0_102,plain,
! [X16,X17,X18,X19,X20] :
( ( member(X18,X16)
| ~ member(ordered_pair(X18,X19),X20)
| ~ ilf_type(X20,relation_type(X16,X17))
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type)
| ~ ilf_type(X16,set_type) )
& ( member(X19,X17)
| ~ member(ordered_pair(X18,X19),X20)
| ~ ilf_type(X20,relation_type(X16,X17))
| ~ ilf_type(X19,set_type)
| ~ ilf_type(X18,set_type)
| ~ 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)],[p3])])])]) ).
cnf(c_0_103,plain,
( member(ordered_pair(X1,X3),restrict(X4,X2))
| ~ member(X1,X2)
| ~ member(ordered_pair(X1,X3),X4)
| ~ 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_55]) ).
cnf(c_0_104,plain,
( X1 = restrict(X2,X3)
| member(ordered_pair(esk1_2(X1,restrict(X2,X3)),esk2_2(X1,restrict(X2,X3))),restrict(X2,X3))
| member(ordered_pair(esk1_2(X1,restrict(X2,X3)),esk2_2(X1,restrict(X2,X3))),X1)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
( member(X1,X2)
| ~ subset(X3,X2)
| ~ member(X1,X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_106,negated_conjecture,
subset(restrict(esk16_0,X1),esk16_0),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_107,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_102]) ).
cnf(c_0_108,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_33]) ).
cnf(c_0_109,plain,
( X1 = X2
| ~ member(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X1)
| ~ member(ordered_pair(esk1_2(X1,X2),esk2_2(X1,X2)),X2)
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,binary_relation_type) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_110,plain,
( member(ordered_pair(X1,X2),restrict(X3,X4))
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(X1,X4)
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_111,negated_conjecture,
( restrict(X1,X2) = esk16_0
| member(ordered_pair(esk1_2(esk16_0,restrict(X1,X2)),esk2_2(esk16_0,restrict(X1,X2))),restrict(X1,X2))
| member(ordered_pair(esk1_2(esk16_0,restrict(X1,X2)),esk2_2(esk16_0,restrict(X1,X2))),esk16_0)
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_104,c_0_96]) ).
cnf(c_0_112,negated_conjecture,
( member(X1,esk16_0)
| ~ member(X1,restrict(esk16_0,X2)) ),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_113,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_107,c_0_26]),c_0_26]),c_0_26]),c_0_26])]) ).
cnf(c_0_114,negated_conjecture,
( member(X1,cross_product(esk14_0,esk13_0))
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_41,c_0_52]) ).
cnf(c_0_115,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_108,c_0_26]),c_0_26])]) ).
cnf(c_0_116,plain,
( X1 = restrict(X2,X3)
| ~ member(ordered_pair(esk1_2(X1,restrict(X2,X3)),esk2_2(X1,restrict(X2,X3))),X1)
| ~ member(ordered_pair(esk1_2(X1,restrict(X2,X3)),esk2_2(X1,restrict(X2,X3))),X2)
| ~ member(esk1_2(X1,restrict(X2,X3)),X3)
| ~ ilf_type(X1,binary_relation_type)
| ~ ilf_type(X2,binary_relation_type) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_98]) ).
cnf(c_0_117,negated_conjecture,
( restrict(esk16_0,X1) = esk16_0
| member(ordered_pair(esk1_2(esk16_0,restrict(esk16_0,X1)),esk2_2(esk16_0,restrict(esk16_0,X1))),esk16_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_96]),c_0_112]) ).
cnf(c_0_118,negated_conjecture,
subset(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_119,negated_conjecture,
restrict4(esk14_0,esk13_0,esk16_0,esk15_0) != esk16_0,
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_120,negated_conjecture,
( member(X1,X2)
| ~ member(ordered_pair(X1,X3),esk16_0)
| ~ ilf_type(cross_product(esk14_0,esk13_0),relation_type(X2,X4)) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_121,plain,
ilf_type(cross_product(X1,X2),relation_type(X1,X2)),
inference(spm,[status(thm)],[c_0_115,c_0_87]) ).
cnf(c_0_122,negated_conjecture,
( restrict(esk16_0,X1) = esk16_0
| ~ member(esk1_2(esk16_0,restrict(esk16_0,X1)),X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_96])]),c_0_117]) ).
cnf(c_0_123,negated_conjecture,
( member(X1,esk15_0)
| ~ member(X1,esk14_0) ),
inference(spm,[status(thm)],[c_0_105,c_0_118]) ).
cnf(c_0_124,negated_conjecture,
restrict(esk16_0,esk15_0) != esk16_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_78]),c_0_52])]) ).
cnf(c_0_125,negated_conjecture,
( member(X1,esk14_0)
| ~ member(ordered_pair(X1,X2),esk16_0) ),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_126,negated_conjecture,
~ member(esk1_2(esk16_0,restrict(esk16_0,esk15_0)),esk14_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_123]),c_0_124]) ).
cnf(c_0_127,negated_conjecture,
( restrict(esk16_0,X1) = esk16_0
| member(esk1_2(esk16_0,restrict(esk16_0,X1)),esk14_0) ),
inference(spm,[status(thm)],[c_0_125,c_0_117]) ).
cnf(c_0_128,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_124]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET671+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
% 0.13/0.34 % Computer : n031.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 09:35:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 23.99/24.10 % Version : CSE_E---1.5
% 23.99/24.10 % Problem : theBenchmark.p
% 23.99/24.10 % Proof found
% 23.99/24.10 % SZS status Theorem for theBenchmark.p
% 23.99/24.10 % SZS output start Proof
% See solution above
% 23.99/24.11 % Total time : 23.509000 s
% 23.99/24.11 % SZS output end Proof
% 23.99/24.11 % Total time : 23.513000 s
%------------------------------------------------------------------------------