TSTP Solution File: SET674+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET674+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 : n014.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 14:35:10 EDT 2023
% Result : Theorem 3.36s 3.43s
% Output : CNFRefutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 56
% Syntax : Number of formulae : 149 ( 9 unt; 40 typ; 0 def)
% Number of atoms : 481 ( 44 equ)
% Maximal formula atoms : 22 ( 4 avg)
% Number of connectives : 656 ( 284 ~; 281 |; 34 &)
% ( 7 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 34 >; 31 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 6 con; 0-4 aty)
% Number of variables : 259 ( 17 sgn; 96 !; 4 ?; 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,
image: ( $i * $i ) > $i ).
tff(decl_30,type,
inverse2: ( $i * $i ) > $i ).
tff(decl_31,type,
relation_type: ( $i * $i ) > $i ).
tff(decl_32,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_33,type,
subset_type: $i > $i ).
tff(decl_34,type,
subset: ( $i * $i ) > $o ).
tff(decl_35,type,
relation_like: $i > $o ).
tff(decl_36,type,
power_set: $i > $i ).
tff(decl_37,type,
member_type: $i > $i ).
tff(decl_38,type,
empty: $i > $o ).
tff(decl_39,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
image4: ( $i * $i * $i * $i ) > $i ).
tff(decl_42,type,
inverse4: ( $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk7_0: $i ).
tff(decl_50,type,
esk8_1: $i > $i ).
tff(decl_51,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk12_1: $i > $i ).
tff(decl_55,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk15_1: $i > $i ).
tff(decl_58,type,
esk16_1: $i > $i ).
tff(decl_59,type,
esk17_0: $i ).
tff(decl_60,type,
esk18_0: $i ).
tff(decl_61,type,
esk19_0: $i ).
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(p40,axiom,
! [X1] : ilf_type(X1,set_type),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p40) ).
fof(prove_relset_1_38,conjecture,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( image4(X1,X2,X3,X1) = range(X1,X2,X3)
& inverse4(X1,X2,X3,X2) = domain(X1,X2,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_38) ).
fof(p5,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,inverse2(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X2,X4),X3)
& member(X4,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p5) ).
fof(p1,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,domain_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).
fof(p4,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,binary_relation_type)
=> ( member(X2,image(X3,X1))
<=> ? [X4] :
( ilf_type(X4,set_type)
& member(ordered_pair(X4,X2),X3)
& member(X4,X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4) ).
fof(p2,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,binary_relation_type)
=> ( member(X1,range_of(X2))
<=> ? [X3] :
( ilf_type(X3,set_type)
& member(ordered_pair(X3,X1),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).
fof(p38,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)
=> inverse4(X1,X2,X3,X4) = inverse2(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p38) ).
fof(p32,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/sandbox/benchmark/theBenchmark.p',p32) ).
fof(p22,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',p22) ).
fof(p36,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)
=> image4(X1,X2,X3,X4) = image(X3,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p36) ).
fof(p34,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/sandbox/benchmark/theBenchmark.p',p34) ).
fof(p10,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10) ).
fof(p29,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',p29) ).
fof(p8,axiom,
! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ( ! [X3] :
( ilf_type(X3,subset_type(cross_product(X1,X2)))
=> ilf_type(X3,relation_type(X1,X2)) )
& ! [X4] :
( ilf_type(X4,relation_type(X1,X2))
=> ilf_type(X4,subset_type(cross_product(X1,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8) ).
fof(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/sandbox/benchmark/theBenchmark.p',p17) ).
fof(c_0_16,plain,
! [X30,X31,X32,X33,X34] :
( ( member(X32,X30)
| ~ member(ordered_pair(X32,X33),X34)
| ~ ilf_type(X34,relation_type(X30,X31))
| ~ ilf_type(X33,set_type)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,set_type) )
& ( member(X33,X31)
| ~ member(ordered_pair(X32,X33),X34)
| ~ ilf_type(X34,relation_type(X30,X31))
| ~ ilf_type(X33,set_type)
| ~ ilf_type(X32,set_type)
| ~ ilf_type(X31,set_type)
| ~ ilf_type(X30,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_17,plain,
! [X120] : ilf_type(X120,set_type),
inference(variable_rename,[status(thm)],[p40]) ).
fof(c_0_18,negated_conjecture,
~ ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X1,X2))
=> ( image4(X1,X2,X3,X1) = range(X1,X2,X3)
& inverse4(X1,X2,X3,X2) = domain(X1,X2,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[prove_relset_1_38]) ).
fof(c_0_19,plain,
! [X22,X23,X24,X26] :
( ( ilf_type(esk4_3(X22,X23,X24),set_type)
| ~ member(X23,inverse2(X24,X22))
| ~ ilf_type(X24,binary_relation_type)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( member(ordered_pair(X23,esk4_3(X22,X23,X24)),X24)
| ~ member(X23,inverse2(X24,X22))
| ~ ilf_type(X24,binary_relation_type)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( member(esk4_3(X22,X23,X24),X22)
| ~ member(X23,inverse2(X24,X22))
| ~ ilf_type(X24,binary_relation_type)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,set_type) )
& ( ~ ilf_type(X26,set_type)
| ~ member(ordered_pair(X23,X26),X24)
| ~ member(X26,X22)
| member(X23,inverse2(X24,X22))
| ~ ilf_type(X24,binary_relation_type)
| ~ ilf_type(X23,set_type)
| ~ ilf_type(X22,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)],[p5])])])])]) ).
fof(c_0_20,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_21,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_16]) ).
cnf(c_0_22,plain,
ilf_type(X1,set_type),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_23,negated_conjecture,
( ilf_type(esk17_0,set_type)
& ilf_type(esk18_0,set_type)
& ilf_type(esk19_0,relation_type(esk17_0,esk18_0))
& ( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| inverse4(esk17_0,esk18_0,esk19_0,esk18_0) != domain(esk17_0,esk18_0,esk19_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_24,plain,
( member(X2,inverse2(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X2,X1),X3)
| ~ member(X1,X4)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,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_20]) ).
cnf(c_0_26,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_21,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
ilf_type(esk19_0,relation_type(esk17_0,esk18_0)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
fof(c_0_28,plain,
! [X17,X18,X19,X21] :
( ( ilf_type(esk3_3(X17,X18,X19),set_type)
| ~ member(X18,image(X19,X17))
| ~ ilf_type(X19,binary_relation_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) )
& ( member(ordered_pair(esk3_3(X17,X18,X19),X18),X19)
| ~ member(X18,image(X19,X17))
| ~ ilf_type(X19,binary_relation_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) )
& ( member(esk3_3(X17,X18,X19),X17)
| ~ member(X18,image(X19,X17))
| ~ ilf_type(X19,binary_relation_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,set_type) )
& ( ~ ilf_type(X21,set_type)
| ~ member(ordered_pair(X21,X18),X19)
| ~ member(X21,X17)
| member(X18,image(X19,X17))
| ~ ilf_type(X19,binary_relation_type)
| ~ ilf_type(X18,set_type)
| ~ ilf_type(X17,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)],[p4])])])])]) ).
fof(c_0_29,plain,
! [X10,X11,X13] :
( ( ilf_type(esk2_2(X10,X11),set_type)
| ~ member(X10,range_of(X11))
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,set_type) )
& ( member(ordered_pair(esk2_2(X10,X11),X10),X11)
| ~ member(X10,range_of(X11))
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,set_type) )
& ( ~ ilf_type(X13,set_type)
| ~ member(ordered_pair(X13,X10),X11)
| member(X10,range_of(X11))
| ~ ilf_type(X11,binary_relation_type)
| ~ ilf_type(X10,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p2])])])])]) ).
cnf(c_0_30,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_16]) ).
fof(c_0_31,plain,
! [X112,X113,X114,X115] :
( ~ ilf_type(X112,set_type)
| ~ ilf_type(X113,set_type)
| ~ ilf_type(X114,relation_type(X112,X113))
| ~ ilf_type(X115,set_type)
| inverse4(X112,X113,X114,X115) = inverse2(X114,X115) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p38])])]) ).
fof(c_0_32,plain,
! [X92,X93,X94] :
( ~ ilf_type(X92,set_type)
| ~ ilf_type(X93,set_type)
| ~ ilf_type(X94,relation_type(X92,X93))
| domain(X92,X93,X94) = domain_of(X94) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p32])])]) ).
fof(c_0_33,plain,
! [X64,X65,X66] :
( ( ~ subset(X64,X65)
| ~ ilf_type(X66,set_type)
| ~ member(X66,X64)
| member(X66,X65)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type) )
& ( ilf_type(esk10_2(X64,X65),set_type)
| subset(X64,X65)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type) )
& ( member(esk10_2(X64,X65),X64)
| subset(X64,X65)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,set_type) )
& ( ~ member(esk10_2(X64,X65),X65)
| subset(X64,X65)
| ~ ilf_type(X65,set_type)
| ~ ilf_type(X64,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_34,plain,
( member(X1,inverse2(X2,X3))
| ~ member(ordered_pair(X1,X4),X2)
| ~ member(X4,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_35,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_25,c_0_22])]) ).
cnf(c_0_36,negated_conjecture,
( member(X1,esk18_0)
| ~ member(ordered_pair(X2,X1),esk19_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_37,plain,
( member(X2,image(X3,X4))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ member(X1,X4)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X4,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_38,plain,
( member(ordered_pair(esk2_2(X1,X2),X1),X2)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_39,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_30,c_0_22]),c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_40,plain,
( inverse4(X1,X2,X3,X4) = inverse2(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_31]) ).
cnf(c_0_41,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_32]) ).
cnf(c_0_42,plain,
( subset(X1,X2)
| ~ member(esk10_2(X1,X2),X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
( member(X1,inverse2(X2,X3))
| ~ member(esk1_2(X1,X2),X3)
| ~ member(X1,domain_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,negated_conjecture,
( member(esk1_2(X1,esk19_0),esk18_0)
| ~ member(X1,domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_45,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_20]) ).
cnf(c_0_46,plain,
( member(ordered_pair(X1,esk4_3(X2,X1,X3)),X3)
| ~ member(X1,inverse2(X3,X2))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_47,plain,
( member(X1,image(X2,X3))
| ~ member(ordered_pair(X4,X1),X2)
| ~ member(X4,X3)
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_48,plain,
( member(ordered_pair(esk2_2(X1,X2),X1),X2)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_22])]) ).
cnf(c_0_49,negated_conjecture,
( member(X1,esk17_0)
| ~ member(ordered_pair(X1,X2),esk19_0) ),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_50,negated_conjecture,
( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| inverse4(esk17_0,esk18_0,esk19_0,esk18_0) != domain(esk17_0,esk18_0,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_51,plain,
( inverse4(X1,X2,X3,X4) = inverse2(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_40,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_52,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_41,c_0_22]),c_0_22])]) ).
fof(c_0_53,plain,
! [X104,X105,X106,X107] :
( ~ ilf_type(X104,set_type)
| ~ ilf_type(X105,set_type)
| ~ ilf_type(X106,relation_type(X104,X105))
| ~ ilf_type(X107,set_type)
| image4(X104,X105,X106,X107) = image(X106,X107) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p36])])]) ).
fof(c_0_54,plain,
! [X98,X99,X100] :
( ~ ilf_type(X98,set_type)
| ~ ilf_type(X99,set_type)
| ~ ilf_type(X100,relation_type(X98,X99))
| range(X98,X99,X100) = range_of(X100) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p34])])]) ).
fof(c_0_55,plain,
! [X42,X43] :
( ( subset(X42,X43)
| X42 != X43
| ~ ilf_type(X43,set_type)
| ~ ilf_type(X42,set_type) )
& ( subset(X43,X42)
| X42 != X43
| ~ ilf_type(X43,set_type)
| ~ ilf_type(X42,set_type) )
& ( ~ subset(X42,X43)
| ~ subset(X43,X42)
| X42 = X43
| ~ 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)],[p10])])])]) ).
cnf(c_0_56,plain,
( subset(X1,X2)
| ~ member(esk10_2(X1,X2),X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_22]),c_0_22])]) ).
cnf(c_0_57,negated_conjecture,
( member(X1,inverse2(esk19_0,esk18_0))
| ~ member(X1,domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_58,plain,
( member(esk10_2(X1,X2),X1)
| subset(X1,X2)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_59,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_45,c_0_22]),c_0_22])]) ).
cnf(c_0_60,plain,
( member(ordered_pair(X1,esk4_3(X2,X1,X3)),X3)
| ~ member(X1,inverse2(X3,X2))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_22]),c_0_22])]) ).
cnf(c_0_61,plain,
( member(X1,image(X2,X3))
| ~ member(esk2_2(X1,X2),X3)
| ~ member(X1,range_of(X2))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_62,negated_conjecture,
( member(esk2_2(X1,esk19_0),esk17_0)
| ~ member(X1,range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_49,c_0_48]) ).
cnf(c_0_63,plain,
( member(X2,range_of(X3))
| ~ ilf_type(X1,set_type)
| ~ member(ordered_pair(X1,X2),X3)
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_64,plain,
( member(ordered_pair(esk3_3(X1,X2,X3),X2),X3)
| ~ member(X2,image(X3,X1))
| ~ ilf_type(X3,binary_relation_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_65,negated_conjecture,
( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| domain(esk17_0,esk18_0,esk19_0) != inverse2(esk19_0,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_27])]) ).
cnf(c_0_66,negated_conjecture,
domain(esk17_0,esk18_0,esk19_0) = domain_of(esk19_0),
inference(spm,[status(thm)],[c_0_52,c_0_27]) ).
cnf(c_0_67,plain,
( image4(X1,X2,X3,X4) = image(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_53]) ).
cnf(c_0_68,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_54]) ).
cnf(c_0_69,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X1,set_type) ),
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_70,negated_conjecture,
( subset(X1,inverse2(esk19_0,esk18_0))
| ~ member(esk10_2(X1,inverse2(esk19_0,esk18_0)),domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_71,plain,
( subset(X1,X2)
| member(esk10_2(X1,X2),X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_22]),c_0_22])]) ).
cnf(c_0_72,plain,
( member(X1,domain_of(X2))
| ~ member(X1,inverse2(X2,X3))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_73,negated_conjecture,
( member(X1,image(esk19_0,esk17_0))
| ~ member(X1,range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_74,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_63,c_0_22]),c_0_22])]) ).
cnf(c_0_75,plain,
( member(ordered_pair(esk3_3(X1,X2,X3),X2),X3)
| ~ member(X2,image(X3,X1))
| ~ ilf_type(X3,binary_relation_type) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_22]),c_0_22])]) ).
cnf(c_0_76,negated_conjecture,
( image4(esk17_0,esk18_0,esk19_0,esk17_0) != range(esk17_0,esk18_0,esk19_0)
| inverse2(esk19_0,esk18_0) != domain_of(esk19_0) ),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_77,plain,
( image4(X1,X2,X3,X4) = image(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_67,c_0_22]),c_0_22]),c_0_22])]) ).
cnf(c_0_78,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_68,c_0_22]),c_0_22])]) ).
cnf(c_0_79,plain,
( X1 = X2
| ~ subset(X2,X1)
| ~ subset(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_69,c_0_22]),c_0_22])]) ).
cnf(c_0_80,negated_conjecture,
( subset(domain_of(esk19_0),inverse2(esk19_0,esk18_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_81,plain,
( subset(inverse2(X1,X2),X3)
| member(esk10_2(inverse2(X1,X2),X3),domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_72,c_0_71]) ).
fof(c_0_82,plain,
! [X85,X86,X87] :
( ~ ilf_type(X85,set_type)
| ~ ilf_type(X86,set_type)
| ~ ilf_type(X87,subset_type(cross_product(X85,X86)))
| relation_like(X87) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p29])])]) ).
fof(c_0_83,plain,
! [X35,X36,X37,X38] :
( ( ~ ilf_type(X37,subset_type(cross_product(X35,X36)))
| ilf_type(X37,relation_type(X35,X36))
| ~ ilf_type(X36,set_type)
| ~ ilf_type(X35,set_type) )
& ( ~ ilf_type(X38,relation_type(X35,X36))
| ilf_type(X38,subset_type(cross_product(X35,X36)))
| ~ ilf_type(X36,set_type)
| ~ ilf_type(X35,set_type) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p8])])])]) ).
cnf(c_0_84,negated_conjecture,
( subset(X1,image(esk19_0,esk17_0))
| ~ member(esk10_2(X1,image(esk19_0,esk17_0)),range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_56,c_0_73]) ).
cnf(c_0_85,plain,
( member(X1,range_of(X2))
| ~ member(X1,image(X2,X3))
| ~ ilf_type(X2,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( range(esk17_0,esk18_0,esk19_0) != image(esk19_0,esk17_0)
| inverse2(esk19_0,esk18_0) != domain_of(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_27])]) ).
cnf(c_0_87,negated_conjecture,
range(esk17_0,esk18_0,esk19_0) = range_of(esk19_0),
inference(spm,[status(thm)],[c_0_78,c_0_27]) ).
cnf(c_0_88,negated_conjecture,
( inverse2(esk19_0,esk18_0) = domain_of(esk19_0)
| ~ subset(inverse2(esk19_0,esk18_0),domain_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_89,plain,
( subset(inverse2(X1,X2),domain_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_56,c_0_81]) ).
fof(c_0_90,plain,
! [X54] :
( ( relation_like(X54)
| ~ ilf_type(X54,binary_relation_type)
| ~ ilf_type(X54,set_type) )
& ( ilf_type(X54,set_type)
| ~ ilf_type(X54,binary_relation_type)
| ~ ilf_type(X54,set_type) )
& ( ~ relation_like(X54)
| ~ ilf_type(X54,set_type)
| ilf_type(X54,binary_relation_type)
| ~ ilf_type(X54,set_type) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[p17])])]) ).
cnf(c_0_91,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_82]) ).
cnf(c_0_92,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_83]) ).
cnf(c_0_93,negated_conjecture,
( subset(range_of(esk19_0),image(esk19_0,esk17_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_84,c_0_71]) ).
cnf(c_0_94,plain,
( subset(image(X1,X2),X3)
| member(esk10_2(image(X1,X2),X3),range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_85,c_0_71]) ).
cnf(c_0_95,negated_conjecture,
( image(esk19_0,esk17_0) != range_of(esk19_0)
| inverse2(esk19_0,esk18_0) != domain_of(esk19_0) ),
inference(rw,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,negated_conjecture,
( inverse2(esk19_0,esk18_0) = domain_of(esk19_0)
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_97,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_90]) ).
cnf(c_0_98,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_91,c_0_22]),c_0_22])]) ).
cnf(c_0_99,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_92,c_0_22]),c_0_22])]) ).
cnf(c_0_100,negated_conjecture,
( image(esk19_0,esk17_0) = range_of(esk19_0)
| ~ subset(image(esk19_0,esk17_0),range_of(esk19_0))
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_79,c_0_93]) ).
cnf(c_0_101,plain,
( subset(image(X1,X2),range_of(X1))
| ~ ilf_type(X1,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_56,c_0_94]) ).
cnf(c_0_102,negated_conjecture,
( image(esk19_0,esk17_0) != range_of(esk19_0)
| ~ ilf_type(esk19_0,binary_relation_type) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_103,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1)
| ~ ilf_type(X1,set_type) ),
inference(cn,[status(thm)],[c_0_97]) ).
cnf(c_0_104,plain,
( relation_like(X1)
| ~ ilf_type(X1,relation_type(X2,X3)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_105,negated_conjecture,
~ ilf_type(esk19_0,binary_relation_type),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]) ).
cnf(c_0_106,plain,
( ilf_type(X1,binary_relation_type)
| ~ relation_like(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_103,c_0_22])]) ).
cnf(c_0_107,negated_conjecture,
relation_like(esk19_0),
inference(spm,[status(thm)],[c_0_104,c_0_27]) ).
cnf(c_0_108,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_107])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET674+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 14:01:02 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 3.36/3.43 % Version : CSE_E---1.5
% 3.36/3.43 % Problem : theBenchmark.p
% 3.36/3.43 % Proof found
% 3.36/3.43 % SZS status Theorem for theBenchmark.p
% 3.36/3.43 % SZS output start Proof
% See solution above
% 3.39/3.44 % Total time : 2.843000 s
% 3.39/3.44 % SZS output end Proof
% 3.39/3.44 % Total time : 2.848000 s
%------------------------------------------------------------------------------