TSTP Solution File: SEU078+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU078+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n004.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 16:22:22 EDT 2023
% Result : Theorem 23.59s 23.67s
% Output : CNFRefutation 23.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 57
% Syntax : Number of formulae : 141 ( 28 unt; 37 typ; 0 def)
% Number of atoms : 347 ( 78 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 409 ( 166 ~; 179 |; 39 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 40 ( 26 >; 14 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 28 ( 28 usr; 11 con; 0-3 aty)
% Number of variables : 183 ( 14 sgn; 91 !; 7 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
one_to_one: $i > $o ).
tff(decl_27,type,
relation_inverse_image: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
relation_rng: $i > $i ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
subset: ( $i * $i ) > $o ).
tff(decl_37,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_38,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk6_1: $i > $i ).
tff(decl_44,type,
esk7_0: $i ).
tff(decl_45,type,
esk8_0: $i ).
tff(decl_46,type,
esk9_1: $i > $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_1: $i > $i ).
tff(decl_51,type,
esk14_0: $i ).
tff(decl_52,type,
esk15_0: $i ).
tff(decl_53,type,
esk16_0: $i ).
tff(decl_54,type,
esk17_1: $i > $i ).
tff(decl_55,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk19_0: $i ).
tff(decl_57,type,
esk20_0: $i ).
tff(decl_58,type,
esk21_1: $i > $i ).
fof(rc1_subset_1,axiom,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(fc2_subset_1,axiom,
! [X1] : ~ empty(singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_subset_1) ).
fof(t56_zfmisc_1,axiom,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t56_zfmisc_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_subset_1,axiom,
! [X1] :
? [X2] :
( element(X2,powerset(X1))
& empty(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(t39_zfmisc_1,axiom,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(t159_funct_1,conjecture,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t159_funct_1) ).
fof(symmetry_r1_xboole_0,axiom,
! [X1,X2] :
( disjoint(X1,X2)
=> disjoint(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
fof(t173_relat_1,axiom,
! [X1,X2] :
( relation(X2)
=> ( relation_inverse_image(X2,X1) = empty_set
<=> disjoint(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t173_relat_1) ).
fof(t144_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ! [X2] :
~ ( in(X2,relation_rng(X1))
& ! [X3] : relation_inverse_image(X1,singleton(X2)) != singleton(X3) )
<=> one_to_one(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t144_funct_1) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(d13_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_inverse_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,relation_dom(X1))
& in(apply(X1,X4),X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_funct_1) ).
fof(d5_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( X2 = relation_rng(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X1))
& X3 = apply(X1,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(c_0_20,plain,
! [X1] :
( ~ empty(X1)
=> ? [X2] :
( element(X2,powerset(X1))
& ~ empty(X2) ) ),
inference(fof_simplification,[status(thm)],[rc1_subset_1]) ).
fof(c_0_21,plain,
! [X77,X78] :
( ( ~ element(X77,powerset(X78))
| subset(X77,X78) )
& ( ~ subset(X77,X78)
| element(X77,powerset(X78)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_22,plain,
! [X45] :
( ( element(esk9_1(X45),powerset(X45))
| empty(X45) )
& ( ~ empty(esk9_1(X45))
| empty(X45) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
fof(c_0_23,plain,
! [X1] : ~ empty(singleton(X1)),
inference(fof_simplification,[status(thm)],[fc2_subset_1]) ).
fof(c_0_24,plain,
! [X1,X2] :
( ~ in(X1,X2)
=> disjoint(singleton(X1),X2) ),
inference(fof_simplification,[status(thm)],[t56_zfmisc_1]) ).
fof(c_0_25,plain,
! [X87] :
( ~ empty(X87)
| X87 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_26,plain,
! [X50] :
( element(esk13_1(X50),powerset(X50))
& empty(esk13_1(X50)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_subset_1])]) ).
fof(c_0_27,plain,
! [X75,X76] :
( ( ~ subset(X75,singleton(X76))
| X75 = empty_set
| X75 = singleton(X76) )
& ( X75 != empty_set
| subset(X75,singleton(X76)) )
& ( X75 != singleton(X76)
| subset(X75,singleton(X76)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t39_zfmisc_1])])]) ).
cnf(c_0_28,plain,
( subset(X1,X2)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
( element(esk9_1(X1),powerset(X1))
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_30,plain,
! [X38] : ~ empty(singleton(X38)),
inference(variable_rename,[status(thm)],[c_0_23]) ).
fof(c_0_31,negated_conjecture,
~ ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( one_to_one(X1)
<=> ! [X2] :
? [X3] : subset(relation_inverse_image(X1,singleton(X2)),singleton(X3)) ) ),
inference(assume_negation,[status(cth)],[t159_funct_1]) ).
fof(c_0_32,plain,
! [X56,X57] :
( ~ disjoint(X56,X57)
| disjoint(X57,X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[symmetry_r1_xboole_0])]) ).
fof(c_0_33,plain,
! [X82,X83] :
( in(X82,X83)
| disjoint(singleton(X82),X83) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])]) ).
cnf(c_0_34,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_35,plain,
empty(esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_36,plain,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_37,plain,
( subset(esk9_1(X1),X1)
| empty(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_38,plain,
~ empty(singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_39,negated_conjecture,
! [X65,X66] :
( relation(esk19_0)
& function(esk19_0)
& ( ~ one_to_one(esk19_0)
| ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X65)) )
& ( one_to_one(esk19_0)
| subset(relation_inverse_image(esk19_0,singleton(X66)),singleton(esk21_1(X66))) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_31])])])]) ).
fof(c_0_40,plain,
! [X68,X69] :
( ( relation_inverse_image(X69,X68) != empty_set
| disjoint(relation_rng(X69),X68)
| ~ relation(X69) )
& ( ~ disjoint(relation_rng(X69),X68)
| relation_inverse_image(X69,X68) = empty_set
| ~ relation(X69) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t173_relat_1])])]) ).
cnf(c_0_41,plain,
( disjoint(X2,X1)
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_42,plain,
( in(X1,X2)
| disjoint(singleton(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_43,plain,
! [X58,X60,X61] :
( ( in(esk17_1(X58),relation_rng(X58))
| one_to_one(X58)
| ~ relation(X58)
| ~ function(X58) )
& ( relation_inverse_image(X58,singleton(esk17_1(X58))) != singleton(X60)
| one_to_one(X58)
| ~ relation(X58)
| ~ function(X58) )
& ( ~ one_to_one(X58)
| ~ in(X61,relation_rng(X58))
| relation_inverse_image(X58,singleton(X61)) = singleton(esk18_2(X58,X61))
| ~ relation(X58)
| ~ function(X58) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t144_funct_1])])])])]) ).
fof(c_0_44,plain,
! [X84,X85,X86] :
( ~ in(X84,X85)
| ~ element(X85,powerset(X86))
| ~ empty(X86) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_45,plain,
element(esk13_1(X1),powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_46,plain,
esk13_1(X1) = empty_set,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_47,plain,
( esk9_1(singleton(X1)) = singleton(X1)
| esk9_1(singleton(X1)) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_48,negated_conjecture,
( one_to_one(esk19_0)
| subset(relation_inverse_image(esk19_0,singleton(X1)),singleton(esk21_1(X1))) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,plain,
( relation_inverse_image(X1,X2) = empty_set
| ~ disjoint(relation_rng(X1),X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,plain,
( disjoint(X1,singleton(X2))
| in(X2,X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,negated_conjecture,
( ~ one_to_one(esk19_0)
| ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),singleton(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_52,plain,
( relation_inverse_image(X1,singleton(X2)) = singleton(esk18_2(X1,X2))
| ~ one_to_one(X1)
| ~ in(X2,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
fof(c_0_53,plain,
! [X55] : subset(X55,X55),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_54,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,plain,
element(empty_set,powerset(X1)),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
fof(c_0_56,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( ~ in(X20,X19)
| X20 = X18
| X19 != singleton(X18) )
& ( X21 != X18
| in(X21,X19)
| X19 != singleton(X18) )
& ( ~ in(esk2_2(X22,X23),X23)
| esk2_2(X22,X23) != X22
| X23 = singleton(X22) )
& ( in(esk2_2(X22,X23),X23)
| esk2_2(X22,X23) = X22
| X23 = singleton(X22) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_tarski])])])])])]) ).
cnf(c_0_57,plain,
( empty(X1)
| ~ empty(esk9_1(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_58,plain,
( esk9_1(singleton(X1)) = empty_set
| singleton(X1) != empty_set ),
inference(ef,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
fof(c_0_60,plain,
! [X10,X11,X12,X13,X14,X15,X16] :
( ( in(X13,relation_dom(X10))
| ~ in(X13,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( in(apply(X10,X13),X11)
| ~ in(X13,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(X14,relation_dom(X10))
| ~ in(apply(X10,X14),X11)
| in(X14,X12)
| X12 != relation_inverse_image(X10,X11)
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(esk1_3(X10,X15,X16),X16)
| ~ in(esk1_3(X10,X15,X16),relation_dom(X10))
| ~ in(apply(X10,esk1_3(X10,X15,X16)),X15)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) )
& ( in(esk1_3(X10,X15,X16),relation_dom(X10))
| in(esk1_3(X10,X15,X16),X16)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) )
& ( in(apply(X10,esk1_3(X10,X15,X16)),X15)
| in(esk1_3(X10,X15,X16),X16)
| X16 = relation_inverse_image(X10,X15)
| ~ relation(X10)
| ~ function(X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d13_funct_1])])])])])]) ).
fof(c_0_61,plain,
! [X25,X26,X27,X29,X30,X31,X33] :
( ( in(esk3_3(X25,X26,X27),relation_dom(X25))
| ~ in(X27,X26)
| X26 != relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( X27 = apply(X25,esk3_3(X25,X26,X27))
| ~ in(X27,X26)
| X26 != relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( ~ in(X30,relation_dom(X25))
| X29 != apply(X25,X30)
| in(X29,X26)
| X26 != relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( ~ in(esk4_2(X25,X31),X31)
| ~ in(X33,relation_dom(X25))
| esk4_2(X25,X31) != apply(X25,X33)
| X31 = relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( in(esk5_2(X25,X31),relation_dom(X25))
| in(esk4_2(X25,X31),X31)
| X31 = relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) )
& ( esk4_2(X25,X31) = apply(X25,esk5_2(X25,X31))
| in(esk4_2(X25,X31),X31)
| X31 = relation_rng(X25)
| ~ relation(X25)
| ~ function(X25) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_funct_1])])])])])]) ).
cnf(c_0_62,plain,
( one_to_one(X1)
| relation_inverse_image(X1,singleton(esk17_1(X1))) != singleton(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_63,negated_conjecture,
( singleton(esk21_1(X1)) = relation_inverse_image(esk19_0,singleton(X1))
| relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| one_to_one(esk19_0) ),
inference(spm,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_64,plain,
( relation_inverse_image(X1,singleton(X2)) = empty_set
| in(X2,relation_rng(X1))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_65,negated_conjecture,
relation(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
fof(c_0_66,plain,
! [X74] : subset(empty_set,X74),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_67,negated_conjecture,
( ~ subset(relation_inverse_image(esk19_0,singleton(esk20_0)),relation_inverse_image(X1,singleton(X2)))
| ~ one_to_one(esk19_0)
| ~ one_to_one(X1)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_68,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_69,negated_conjecture,
function(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_70,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_71,plain,
( in(esk2_2(X1,X2),X2)
| esk2_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_72,plain,
singleton(X1) != empty_set,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_59])]),c_0_38]) ).
cnf(c_0_73,plain,
( in(X1,X4)
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),X3)
| X4 != relation_inverse_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_74,plain,
( X1 = apply(X2,esk3_3(X2,X3,X1))
| ~ in(X1,X3)
| X3 != relation_rng(X2)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_75,plain,
( in(esk3_3(X1,X2,X3),relation_dom(X1))
| ~ in(X3,X2)
| X2 != relation_rng(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_76,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| one_to_one(esk19_0)
| one_to_one(X2)
| relation_inverse_image(X2,singleton(esk17_1(X2))) != relation_inverse_image(esk19_0,singleton(X1))
| ~ relation(X2)
| ~ function(X2) ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_77,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(X1)) = empty_set
| in(X1,relation_rng(esk19_0)) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_78,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_79,negated_conjecture,
( ~ one_to_one(esk19_0)
| ~ in(esk20_0,relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_65]),c_0_69])]) ).
cnf(c_0_80,plain,
( esk2_2(X1,empty_set) = X1
| ~ empty(X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
fof(c_0_81,plain,
! [X72,X73] :
( ~ element(X72,X73)
| empty(X73)
| in(X72,X73) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_82,plain,
! [X35] : element(esk6_1(X35),X35),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_83,plain,
( in(X1,relation_inverse_image(X2,X3))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(er,[status(thm)],[c_0_73]) ).
cnf(c_0_84,plain,
( apply(X1,esk3_3(X1,relation_rng(X1),X2)) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_74]) ).
cnf(c_0_85,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_dom(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1)) ),
inference(er,[status(thm)],[c_0_75]) ).
cnf(c_0_86,negated_conjecture,
( relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set
| one_to_one(esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_76]),c_0_65]),c_0_69])]) ).
cnf(c_0_87,negated_conjecture,
~ one_to_one(esk19_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_77]),c_0_78])]),c_0_79]) ).
cnf(c_0_88,plain,
( X2 = singleton(X1)
| ~ in(esk2_2(X1,X2),X2)
| esk2_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_89,plain,
esk2_2(X1,empty_set) = X1,
inference(spm,[status(thm)],[c_0_80,c_0_59]) ).
cnf(c_0_90,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_91,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_92,plain,
element(esk6_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_82]) ).
cnf(c_0_93,plain,
( in(esk17_1(X1),relation_rng(X1))
| one_to_one(X1)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_43]) ).
cnf(c_0_94,plain,
( in(esk3_3(X1,relation_rng(X1),X2),relation_inverse_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_rng(X1))
| ~ in(X2,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_95,negated_conjecture,
relation_inverse_image(esk19_0,singleton(esk17_1(esk19_0))) = empty_set,
inference(sr,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,plain,
~ in(X1,empty_set),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_72]) ).
cnf(c_0_97,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_90]) ).
cnf(c_0_98,plain,
( empty(X1)
| in(esk6_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_99,negated_conjecture,
( one_to_one(esk19_0)
| in(esk17_1(esk19_0),relation_rng(esk19_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_65]),c_0_69])]) ).
cnf(c_0_100,negated_conjecture,
( ~ in(X1,singleton(esk17_1(esk19_0)))
| ~ in(X1,relation_rng(esk19_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_65]),c_0_69])]),c_0_96]) ).
cnf(c_0_101,plain,
esk6_1(singleton(X1)) = X1,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_38]) ).
cnf(c_0_102,negated_conjecture,
in(esk17_1(esk19_0),relation_rng(esk19_0)),
inference(sr,[status(thm)],[c_0_99,c_0_87]) ).
cnf(c_0_103,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_98]),c_0_101]),c_0_102])]),c_0_38]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU078+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 17:03:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 23.59/23.67 % Version : CSE_E---1.5
% 23.59/23.67 % Problem : theBenchmark.p
% 23.59/23.67 % Proof found
% 23.59/23.67 % SZS status Theorem for theBenchmark.p
% 23.59/23.67 % SZS output start Proof
% See solution above
% 23.67/23.68 % Total time : 23.100000 s
% 23.67/23.68 % SZS output end Proof
% 23.67/23.68 % Total time : 23.105000 s
%------------------------------------------------------------------------------