TSTP Solution File: SEU293+1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU293+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 : n008.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 16:24:10 EDT 2023
% Result : Theorem 0.21s 0.59s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 51
% Syntax : Number of formulae : 100 ( 18 unt; 41 typ; 0 def)
% Number of atoms : 214 ( 52 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 249 ( 94 ~; 99 |; 36 &)
% ( 7 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 25 >; 20 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 30 ( 30 usr; 16 con; 0-3 aty)
% Number of variables : 96 ( 4 sgn; 53 !; 2 ?; 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_inverse_image: ( $i * $i ) > $i ).
tff(decl_31,type,
relation_dom: $i > $i ).
tff(decl_32,type,
apply: ( $i * $i ) > $i ).
tff(decl_33,type,
relation_of2_as_subset: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
empty_set: $i ).
tff(decl_35,type,
quasi_total: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
relation_dom_as_subset: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
relation_of2: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
relation_empty_yielding: $i > $o ).
tff(decl_39,type,
subset: ( $i * $i ) > $o ).
tff(decl_40,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk3_1: $i > $i ).
tff(decl_43,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk5_0: $i ).
tff(decl_45,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_0: $i ).
tff(decl_48,type,
esk9_1: $i > $i ).
tff(decl_49,type,
esk10_0: $i ).
tff(decl_50,type,
esk11_0: $i ).
tff(decl_51,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk13_0: $i ).
tff(decl_53,type,
esk14_1: $i > $i ).
tff(decl_54,type,
esk15_0: $i ).
tff(decl_55,type,
esk16_0: $i ).
tff(decl_56,type,
esk17_0: $i ).
tff(decl_57,type,
esk18_0: $i ).
tff(decl_58,type,
esk19_0: $i ).
tff(decl_59,type,
esk20_0: $i ).
tff(decl_60,type,
esk21_0: $i ).
tff(decl_61,type,
esk22_0: $i ).
tff(decl_62,type,
esk23_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(t46_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( X2 != empty_set
=> ! [X5] :
( in(X5,relation_inverse_image(X4,X3))
<=> ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t46_funct_2) ).
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(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(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(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(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(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(c_0_10,plain,
! [X88] :
( ~ empty(X88)
| X88 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,plain,
( relation(esk11_0)
& empty(esk11_0)
& function(esk11_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
empty(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_14,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ( X2 != empty_set
=> ! [X5] :
( in(X5,relation_inverse_image(X4,X3))
<=> ( in(X5,X1)
& in(apply(X4,X5),X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t46_funct_2]) ).
cnf(c_0_15,plain,
empty_set = esk11_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,plain,
( relation(esk7_0)
& function(esk7_0)
& one_to_one(esk7_0)
& empty(esk7_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_partfun1])]) ).
fof(c_0_17,negated_conjecture,
( function(esk22_0)
& quasi_total(esk22_0,esk19_0,esk20_0)
& relation_of2_as_subset(esk22_0,esk19_0,esk20_0)
& esk20_0 != empty_set
& ( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| ~ in(apply(esk22_0,esk23_0),esk21_0) )
& ( in(esk23_0,esk19_0)
| in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) )
& ( in(apply(esk22_0,esk23_0),esk21_0)
| in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
fof(c_0_18,plain,
! [X22,X23,X24] :
( ( ~ quasi_total(X24,X22,X23)
| X22 = relation_dom_as_subset(X22,X23,X24)
| X23 = empty_set
| ~ relation_of2_as_subset(X24,X22,X23) )
& ( X22 != relation_dom_as_subset(X22,X23,X24)
| quasi_total(X24,X22,X23)
| X23 = empty_set
| ~ relation_of2_as_subset(X24,X22,X23) )
& ( ~ quasi_total(X24,X22,X23)
| X22 = relation_dom_as_subset(X22,X23,X24)
| X22 != empty_set
| ~ relation_of2_as_subset(X24,X22,X23) )
& ( X22 != relation_dom_as_subset(X22,X23,X24)
| quasi_total(X24,X22,X23)
| X22 != empty_set
| ~ relation_of2_as_subset(X24,X22,X23) )
& ( ~ quasi_total(X24,X22,X23)
| X24 = empty_set
| X22 = empty_set
| X23 != empty_set
| ~ relation_of2_as_subset(X24,X22,X23) )
& ( X24 != empty_set
| quasi_total(X24,X22,X23)
| X22 = empty_set
| X23 != empty_set
| ~ relation_of2_as_subset(X24,X22,X23) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_19,plain,
( X1 = esk11_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_20,plain,
empty(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk20_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X28,X29,X30] :
( ~ relation_of2_as_subset(X30,X28,X29)
| element(X30,powerset(cartesian_product2(X28,X29))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
cnf(c_0_23,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_18]) ).
cnf(c_0_24,plain,
esk11_0 = esk7_0,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
esk20_0 != esk11_0,
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_26,plain,
! [X14,X15,X16,X17,X18,X19,X20] :
( ( in(X17,relation_dom(X14))
| ~ in(X17,X16)
| X16 != relation_inverse_image(X14,X15)
| ~ relation(X14)
| ~ function(X14) )
& ( in(apply(X14,X17),X15)
| ~ in(X17,X16)
| X16 != relation_inverse_image(X14,X15)
| ~ relation(X14)
| ~ function(X14) )
& ( ~ in(X18,relation_dom(X14))
| ~ in(apply(X14,X18),X15)
| in(X18,X16)
| X16 != relation_inverse_image(X14,X15)
| ~ relation(X14)
| ~ function(X14) )
& ( ~ in(esk1_3(X14,X19,X20),X20)
| ~ in(esk1_3(X14,X19,X20),relation_dom(X14))
| ~ in(apply(X14,esk1_3(X14,X19,X20)),X19)
| X20 = relation_inverse_image(X14,X19)
| ~ relation(X14)
| ~ function(X14) )
& ( in(esk1_3(X14,X19,X20),relation_dom(X14))
| in(esk1_3(X14,X19,X20),X20)
| X20 = relation_inverse_image(X14,X19)
| ~ relation(X14)
| ~ function(X14) )
& ( in(apply(X14,esk1_3(X14,X19,X20)),X19)
| in(esk1_3(X14,X19,X20),X20)
| X20 = relation_inverse_image(X14,X19)
| ~ relation(X14)
| ~ function(X14) ) ),
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_27,plain,
! [X10,X11,X12] :
( ~ element(X12,powerset(cartesian_product2(X10,X11)))
| relation(X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_relset_1])]) ).
cnf(c_0_28,plain,
( element(X1,powerset(cartesian_product2(X2,X3)))
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
relation_of2_as_subset(esk22_0,esk19_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_30,plain,
! [X64,X65,X66] :
( ~ relation_of2(X66,X64,X65)
| relation_dom_as_subset(X64,X65,X66) = relation_dom(X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_k4_relset_1])]) ).
cnf(c_0_31,plain,
( relation_dom_as_subset(X1,X2,X3) = X1
| X2 = esk7_0
| ~ quasi_total(X3,X1,X2)
| ~ relation_of2_as_subset(X3,X1,X2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_15]),c_0_24]) ).
cnf(c_0_32,negated_conjecture,
quasi_total(esk22_0,esk19_0,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_33,negated_conjecture,
esk20_0 != esk7_0,
inference(rw,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_34,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X3 != relation_inverse_image(X2,X4)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_35,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_36,negated_conjecture,
element(esk22_0,powerset(cartesian_product2(esk19_0,esk20_0))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
relation_dom_as_subset(esk19_0,esk20_0,esk22_0) = esk19_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_29])]),c_0_33]) ).
fof(c_0_39,plain,
! [X67,X68,X69] :
( ( ~ relation_of2_as_subset(X69,X67,X68)
| relation_of2(X69,X67,X68) )
& ( ~ relation_of2(X69,X67,X68)
| relation_of2_as_subset(X69,X67,X68) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_m2_relset_1])]) ).
cnf(c_0_40,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2)
| ~ in(X1,relation_inverse_image(X2,X3)) ),
inference(er,[status(thm)],[c_0_34]) ).
cnf(c_0_41,negated_conjecture,
( in(esk23_0,esk19_0)
| in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
relation(esk22_0),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_43,negated_conjecture,
function(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_44,negated_conjecture,
( relation_dom(esk22_0) = esk19_0
| ~ relation_of2(esk22_0,esk19_0,esk20_0) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_46,negated_conjecture,
( in(esk23_0,relation_dom(esk22_0))
| in(esk23_0,esk19_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]),c_0_43])]) ).
cnf(c_0_47,negated_conjecture,
relation_dom(esk22_0) = esk19_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_29])]) ).
cnf(c_0_48,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_26]) ).
cnf(c_0_49,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(esk23_0,esk19_0)
| ~ in(apply(esk22_0,esk23_0),esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_50,negated_conjecture,
in(esk23_0,esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47])]) ).
cnf(c_0_51,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_48]) ).
cnf(c_0_52,negated_conjecture,
( in(apply(esk22_0,esk23_0),esk21_0)
| in(esk23_0,relation_inverse_image(esk22_0,esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_53,plain,
( in(apply(X1,X2),X3)
| ~ in(X2,X4)
| X4 != relation_inverse_image(X1,X3)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_54,negated_conjecture,
( ~ in(esk23_0,relation_inverse_image(esk22_0,esk21_0))
| ~ in(apply(esk22_0,esk23_0),esk21_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50])]) ).
cnf(c_0_55,negated_conjecture,
in(esk23_0,relation_inverse_image(esk22_0,esk21_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_42]),c_0_43]),c_0_47]),c_0_50])]) ).
cnf(c_0_56,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_inverse_image(X1,X3)) ),
inference(er,[status(thm)],[c_0_53]) ).
cnf(c_0_57,negated_conjecture,
~ in(apply(esk22_0,esk23_0),esk21_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55])]) ).
cnf(c_0_58,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_56,c_0_55]),c_0_42]),c_0_43])]),c_0_57]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU293+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n008.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 : Thu Aug 24 01:32:02 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.59 % Version : CSE_E---1.5
% 0.21/0.59 % Problem : theBenchmark.p
% 0.21/0.59 % Proof found
% 0.21/0.59 % SZS status Theorem for theBenchmark.p
% 0.21/0.59 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.019000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.023000 s
%------------------------------------------------------------------------------