TSTP Solution File: SEU291+1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 16:24:09 EDT 2023
% Result : Theorem 0.13s 0.61s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 56
% Syntax : Number of formulae : 157 ( 37 unt; 37 typ; 0 def)
% Number of atoms : 301 ( 74 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 296 ( 115 ~; 115 |; 43 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 22 >; 16 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 15 con; 0-3 aty)
% Number of variables : 186 ( 18 sgn; 84 !; 4 ?; 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,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_27,type,
powerset: $i > $i ).
tff(decl_28,type,
element: ( $i * $i ) > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_33,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(decl_34,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_35,type,
relation_empty_yielding: $i > $o ).
tff(decl_36,type,
relation_dom: $i > $i ).
tff(decl_37,type,
subset: ( $i * $i ) > $o ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_1: $i > $i ).
tff(decl_40,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk4_0: $i ).
tff(decl_42,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk6_0: $i ).
tff(decl_44,type,
esk7_0: $i ).
tff(decl_45,type,
esk8_1: $i > $i ).
tff(decl_46,type,
esk9_0: $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_2: ( $i * $i ) > $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_0: $i ).
tff(decl_55,type,
esk18_0: $i ).
tff(decl_56,type,
esk19_0: $i ).
tff(decl_57,type,
esk20_0: $i ).
tff(decl_58,type,
esk21_0: $i ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(rc1_partfun1,axiom,
? [X1] :
( relation(X1)
& function(X1)
& one_to_one(X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_partfun1) ).
fof(d1_funct_2,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> ( ( ( X2 = empty_set
=> X1 = empty_set )
=> ( quasi_total(X3,X1,X2)
<=> X1 = relation_dom_as_subset(X1,X2,X3) ) )
& ( X2 = empty_set
=> ( X1 = empty_set
| ( quasi_total(X3,X1,X2)
<=> X3 = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
fof(t9_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_funct_2) ).
fof(fc1_subset_1,axiom,
! [X1] : ~ empty(powerset(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(redefinition_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> relation_dom_as_subset(X1,X2,X3) = relation_dom(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_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(dt_k4_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2(X3,X1,X2)
=> element(relation_dom_as_subset(X1,X2,X3),powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_relset_1) ).
fof(redefinition_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
<=> relation_of2(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(t16_relset_1,axiom,
! [X1,X2,X3,X4] :
( relation_of2_as_subset(X4,X3,X1)
=> ( subset(X1,X2)
=> relation_of2_as_subset(X4,X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_relset_1) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
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(existence_m1_subset_1,axiom,
! [X1] :
? [X2] : element(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(cc1_relset_1,axiom,
! [X1,X2,X3] :
( element(X3,powerset(cartesian_product2(X1,X2)))
=> relation(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
fof(dt_m2_relset_1,axiom,
! [X1,X2,X3] :
( relation_of2_as_subset(X3,X1,X2)
=> element(X3,powerset(cartesian_product2(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(fc5_relat_1,axiom,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(rc1_funct_2,axiom,
! [X1,X2] :
? [X3] :
( relation_of2(X3,X1,X2)
& relation(X3)
& function(X3)
& quasi_total(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_2) ).
fof(c_0_19,plain,
! [X79] :
( ~ empty(X79)
| X79 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_20,plain,
( relation(esk10_0)
& empty(esk10_0)
& function(esk10_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
cnf(c_0_21,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
empty(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
empty_set = esk10_0,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
fof(c_0_24,plain,
( relation(esk6_0)
& function(esk6_0)
& one_to_one(esk6_0)
& empty(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])]) ).
fof(c_0_25,plain,
! [X13,X14,X15] :
( ( ~ quasi_total(X15,X13,X14)
| X13 = relation_dom_as_subset(X13,X14,X15)
| X14 = empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( X13 != relation_dom_as_subset(X13,X14,X15)
| quasi_total(X15,X13,X14)
| X14 = empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( ~ quasi_total(X15,X13,X14)
| X13 = relation_dom_as_subset(X13,X14,X15)
| X13 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( X13 != relation_dom_as_subset(X13,X14,X15)
| quasi_total(X15,X13,X14)
| X13 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( ~ quasi_total(X15,X13,X14)
| X15 = empty_set
| X13 = empty_set
| X14 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) )
& ( X15 != empty_set
| quasi_total(X15,X13,X14)
| X13 = empty_set
| X14 != empty_set
| ~ relation_of2_as_subset(X15,X13,X14) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_26,plain,
( X1 = esk10_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_27,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_28,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( subset(X2,X3)
=> ( ( X2 = empty_set
& X1 != empty_set )
| ( function(X4)
& quasi_total(X4,X1,X3)
& relation_of2_as_subset(X4,X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t9_funct_2]) ).
fof(c_0_29,plain,
! [X1] : ~ empty(powerset(X1)),
inference(fof_simplification,[status(thm)],[fc1_subset_1]) ).
cnf(c_0_30,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| X3 = empty_set
| ~ quasi_total(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
esk10_0 = esk6_0,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_32,negated_conjecture,
( function(esk21_0)
& quasi_total(esk21_0,esk18_0,esk19_0)
& relation_of2_as_subset(esk21_0,esk18_0,esk19_0)
& subset(esk19_0,esk20_0)
& ( esk19_0 != empty_set
| esk18_0 = empty_set )
& ( ~ function(esk21_0)
| ~ quasi_total(esk21_0,esk18_0,esk20_0)
| ~ relation_of2_as_subset(esk21_0,esk18_0,esk20_0) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
fof(c_0_33,plain,
! [X55,X56,X57] :
( ~ relation_of2(X57,X55,X56)
| relation_dom_as_subset(X55,X56,X57) = relation_dom(X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
fof(c_0_34,plain,
! [X68,X69] :
( ~ element(X68,X69)
| empty(X69)
| in(X68,X69) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_35,plain,
! [X16,X17,X18] :
( ~ relation_of2(X18,X16,X17)
| element(relation_dom_as_subset(X16,X17,X18),powerset(X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k4_relset_1])]) ).
fof(c_0_36,plain,
! [X30] : ~ empty(powerset(X30)),
inference(variable_rename,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( relation_dom_as_subset(X1,X2,X3) = X1
| X2 = esk6_0
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_23]),c_0_31]) ).
cnf(c_0_38,negated_conjecture,
quasi_total(esk21_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_39,negated_conjecture,
relation_of2_as_subset(esk21_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
( element(relation_dom_as_subset(X2,X3,X1),powerset(X2))
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
~ empty(powerset(X1)),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( relation_dom_as_subset(esk18_0,esk19_0,esk21_0) = esk18_0
| esk19_0 = esk6_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39])]) ).
cnf(c_0_45,plain,
( relation_dom_as_subset(X1,X2,X3) = relation_dom_as_subset(X4,X5,X3)
| ~ relation_of2(X3,X1,X2)
| ~ relation_of2(X3,X4,X5) ),
inference(spm,[status(thm)],[c_0_40,c_0_40]) ).
fof(c_0_46,plain,
! [X58,X59,X60] :
( ( ~ relation_of2_as_subset(X60,X58,X59)
| relation_of2(X60,X58,X59) )
& ( ~ relation_of2(X60,X58,X59)
| relation_of2_as_subset(X60,X58,X59) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
fof(c_0_47,plain,
! [X62,X63,X64,X65] :
( ~ relation_of2_as_subset(X65,X64,X62)
| ~ subset(X62,X63)
| relation_of2_as_subset(X65,X64,X63) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t16_relset_1])]) ).
cnf(c_0_48,plain,
( in(relation_dom_as_subset(X1,X2,X3),powerset(X1))
| ~ relation_of2(X3,X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]) ).
fof(c_0_49,plain,
! [X70,X71] :
( ( ~ element(X70,powerset(X71))
| subset(X70,X71) )
& ( ~ subset(X70,X71)
| element(X70,powerset(X71)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_50,negated_conjecture,
( relation_dom_as_subset(X1,X2,esk21_0) = esk18_0
| esk19_0 = esk6_0
| ~ relation_of2(esk21_0,esk18_0,esk19_0)
| ~ relation_of2(esk21_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_51,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_52,plain,
( relation_of2_as_subset(X1,X2,X4)
| ~ relation_of2_as_subset(X1,X2,X3)
| ~ subset(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_53,plain,
( in(relation_dom(X1),powerset(X2))
| ~ relation_of2(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_40]) ).
fof(c_0_54,plain,
! [X76,X77,X78] :
( ~ in(X76,X77)
| ~ element(X77,powerset(X78))
| ~ empty(X78) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_55,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_56,negated_conjecture,
subset(esk19_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_57,plain,
! [X25] : element(esk2_1(X25),X25),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[existence_m1_subset_1])]) ).
cnf(c_0_58,negated_conjecture,
( relation_dom_as_subset(X1,X2,esk21_0) = esk18_0
| esk19_0 = esk6_0
| ~ relation_of2(esk21_0,X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_39])]) ).
cnf(c_0_59,negated_conjecture,
( relation_of2_as_subset(esk21_0,esk18_0,X1)
| ~ subset(esk19_0,X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_60,negated_conjecture,
( ~ function(esk21_0)
| ~ quasi_total(esk21_0,esk18_0,esk20_0)
| ~ relation_of2_as_subset(esk21_0,esk18_0,esk20_0) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_61,negated_conjecture,
function(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_62,plain,
( X2 = relation_dom_as_subset(X2,X3,X1)
| ~ quasi_total(X1,X2,X3)
| X2 != empty_set
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
fof(c_0_63,plain,
! [X66,X67] :
( ~ in(X66,X67)
| element(X66,X67) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
cnf(c_0_64,plain,
( in(relation_dom(X1),powerset(X2))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_51]) ).
cnf(c_0_65,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_54]) ).
cnf(c_0_66,negated_conjecture,
element(esk19_0,powerset(esk20_0)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_67,plain,
element(esk2_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_68,plain,
( quasi_total(X3,X1,X2)
| X2 = empty_set
| X1 != relation_dom_as_subset(X1,X2,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_69,negated_conjecture,
( relation_dom_as_subset(X1,X2,esk21_0) = esk18_0
| esk19_0 = esk6_0
| ~ relation_of2_as_subset(esk21_0,X1,X2) ),
inference(spm,[status(thm)],[c_0_58,c_0_51]) ).
cnf(c_0_70,negated_conjecture,
relation_of2_as_subset(esk21_0,esk18_0,esk20_0),
inference(spm,[status(thm)],[c_0_59,c_0_56]) ).
cnf(c_0_71,negated_conjecture,
( ~ quasi_total(esk21_0,esk18_0,esk20_0)
| ~ relation_of2_as_subset(esk21_0,esk18_0,esk20_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_61])]) ).
cnf(c_0_72,plain,
( relation_dom_as_subset(empty_set,X1,X2) = empty_set
| ~ quasi_total(X2,empty_set,X1)
| ~ relation_of2_as_subset(X2,empty_set,X1) ),
inference(er,[status(thm)],[c_0_62]) ).
cnf(c_0_73,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_74,negated_conjecture,
in(relation_dom(esk21_0),powerset(esk18_0)),
inference(spm,[status(thm)],[c_0_64,c_0_39]) ).
fof(c_0_75,plain,
! [X9,X10,X11] :
( ~ element(X11,powerset(cartesian_product2(X9,X10)))
| relation(X11) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
fof(c_0_76,plain,
! [X19,X20,X21] :
( ~ relation_of2_as_subset(X21,X19,X20)
| element(X21,powerset(cartesian_product2(X19,X20))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_77,negated_conjecture,
( esk18_0 = empty_set
| esk19_0 != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_78,negated_conjecture,
( ~ empty(esk20_0)
| ~ in(X1,esk19_0) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_79,plain,
( empty(X1)
| in(esk2_1(X1),X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_67]) ).
cnf(c_0_80,plain,
( X1 = esk6_0
| quasi_total(X2,X3,X1)
| relation_dom_as_subset(X3,X1,X2) != X3
| ~ relation_of2_as_subset(X2,X3,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_23]),c_0_31]) ).
cnf(c_0_81,negated_conjecture,
( relation_dom_as_subset(esk18_0,esk20_0,esk21_0) = esk18_0
| esk19_0 = esk6_0 ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_82,negated_conjecture,
~ quasi_total(esk21_0,esk18_0,esk20_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_70])]) ).
fof(c_0_83,plain,
! [X1] :
( ( ~ empty(X1)
& relation(X1) )
=> ~ empty(relation_dom(X1)) ),
inference(fof_simplification,[status(thm)],[fc5_relat_1]) ).
cnf(c_0_84,plain,
( relation_dom_as_subset(esk6_0,X1,X2) = esk6_0
| ~ quasi_total(X2,esk6_0,X1)
| ~ relation_of2_as_subset(X2,esk6_0,X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_23]),c_0_31]),c_0_23]),c_0_31]),c_0_23]),c_0_31]),c_0_23]),c_0_31]) ).
cnf(c_0_85,plain,
( relation_of2_as_subset(X1,X2,X3)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
fof(c_0_86,plain,
! [X36,X37] :
( relation_of2(esk5_2(X36,X37),X36,X37)
& relation(esk5_2(X36,X37))
& function(esk5_2(X36,X37))
& quasi_total(esk5_2(X36,X37),X36,X37) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_funct_2])]) ).
cnf(c_0_87,negated_conjecture,
element(relation_dom(esk21_0),powerset(esk18_0)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_88,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_89,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_90,negated_conjecture,
( esk10_0 = esk18_0
| esk10_0 != esk19_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_23]),c_0_23]) ).
cnf(c_0_91,negated_conjecture,
( empty(esk19_0)
| ~ empty(esk20_0) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_92,negated_conjecture,
( esk19_0 = esk6_0
| esk20_0 = esk6_0 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_70])]),c_0_82]) ).
cnf(c_0_93,plain,
( X1 = esk6_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_26,c_0_31]) ).
fof(c_0_94,plain,
! [X33] :
( empty(X33)
| ~ relation(X33)
| ~ empty(relation_dom(X33)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_83])]) ).
cnf(c_0_95,plain,
( relation_dom(X1) = esk6_0
| ~ relation_of2(X1,esk6_0,X2)
| ~ quasi_total(X1,esk6_0,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_84]),c_0_85]) ).
cnf(c_0_96,plain,
relation_of2(esk5_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_97,plain,
quasi_total(esk5_2(X1,X2),X1,X2),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_98,negated_conjecture,
( ~ empty(esk18_0)
| ~ in(X1,relation_dom(esk21_0)) ),
inference(spm,[status(thm)],[c_0_65,c_0_87]) ).
cnf(c_0_99,plain,
( relation(X1)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_100,negated_conjecture,
( esk6_0 = esk18_0
| esk19_0 != esk6_0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_31]),c_0_31]) ).
cnf(c_0_101,negated_conjecture,
esk19_0 = esk6_0,
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_27])]),c_0_93]) ).
cnf(c_0_102,plain,
( empty(X1)
| ~ relation(X1)
| ~ empty(relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_103,plain,
relation_dom(esk5_2(esk6_0,X1)) = esk6_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97])]) ).
cnf(c_0_104,plain,
relation(esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_86]) ).
cnf(c_0_105,negated_conjecture,
( empty(relation_dom(esk21_0))
| ~ empty(esk18_0) ),
inference(spm,[status(thm)],[c_0_98,c_0_79]) ).
cnf(c_0_106,negated_conjecture,
relation(esk21_0),
inference(spm,[status(thm)],[c_0_99,c_0_39]) ).
cnf(c_0_107,negated_conjecture,
esk6_0 = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_101])]) ).
cnf(c_0_108,plain,
empty(esk5_2(esk6_0,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_27])]) ).
cnf(c_0_109,negated_conjecture,
( empty(esk21_0)
| ~ empty(esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_105]),c_0_106])]) ).
cnf(c_0_110,plain,
empty(esk18_0),
inference(rw,[status(thm)],[c_0_27,c_0_107]) ).
cnf(c_0_111,plain,
esk5_2(esk6_0,X1) = esk6_0,
inference(spm,[status(thm)],[c_0_93,c_0_108]) ).
cnf(c_0_112,plain,
( X1 = esk18_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_93,c_0_107]) ).
cnf(c_0_113,negated_conjecture,
empty(esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109,c_0_110])]) ).
cnf(c_0_114,plain,
quasi_total(esk6_0,esk6_0,X1),
inference(spm,[status(thm)],[c_0_97,c_0_111]) ).
cnf(c_0_115,negated_conjecture,
esk18_0 = esk21_0,
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,plain,
quasi_total(esk18_0,esk18_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_107]),c_0_107]) ).
cnf(c_0_117,negated_conjecture,
~ quasi_total(esk21_0,esk21_0,esk20_0),
inference(rw,[status(thm)],[c_0_82,c_0_115]) ).
cnf(c_0_118,plain,
quasi_total(esk21_0,esk21_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_116,c_0_115]),c_0_115]) ).
cnf(c_0_119,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_117,c_0_118])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU291+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.08/0.32 % Computer : n019.cluster.edu
% 0.08/0.32 % Model : x86_64 x86_64
% 0.08/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.32 % Memory : 8042.1875MB
% 0.08/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.32 % CPULimit : 300
% 0.08/0.32 % WCLimit : 300
% 0.08/0.32 % DateTime : Wed Aug 23 16:42:14 EDT 2023
% 0.08/0.32 % CPUTime :
% 0.13/0.55 start to proof: theBenchmark
% 0.13/0.61 % Version : CSE_E---1.5
% 0.13/0.61 % Problem : theBenchmark.p
% 0.13/0.61 % Proof found
% 0.13/0.61 % SZS status Theorem for theBenchmark.p
% 0.13/0.61 % SZS output start Proof
% See solution above
% 0.13/0.63 % Total time : 0.052000 s
% 0.13/0.63 % SZS output end Proof
% 0.13/0.63 % Total time : 0.055000 s
%------------------------------------------------------------------------------