TSTP Solution File: SEU292+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU292+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 : n023.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 2.16s 2.24s
% Output : CNFRefutation 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 50
% Syntax : Number of formulae : 91 ( 19 unt; 40 typ; 0 def)
% Number of atoms : 164 ( 49 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 173 ( 60 ~; 61 |; 32 &)
% ( 3 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 24 >; 18 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 16 con; 0-3 aty)
% Number of variables : 80 ( 2 sgn; 48 !; 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_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_composition: ( $i * $i ) > $i ).
tff(decl_36,type,
relation_empty_yielding: $i > $o ).
tff(decl_37,type,
relation_dom: $i > $i ).
tff(decl_38,type,
subset: ( $i * $i ) > $o ).
tff(decl_39,type,
apply: ( $i * $i ) > $i ).
tff(decl_40,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk2_1: $i > $i ).
tff(decl_42,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk4_0: $i ).
tff(decl_44,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk6_0: $i ).
tff(decl_46,type,
esk7_0: $i ).
tff(decl_47,type,
esk8_1: $i > $i ).
tff(decl_48,type,
esk9_0: $i ).
tff(decl_49,type,
esk10_0: $i ).
tff(decl_50,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk12_0: $i ).
tff(decl_52,type,
esk13_1: $i > $i ).
tff(decl_53,type,
esk14_0: $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 ).
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(t21_funct_2,conjecture,
! [X1,X2,X3,X4] :
( ( function(X4)
& quasi_total(X4,X1,X2)
& relation_of2_as_subset(X4,X1,X2) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_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(t23_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_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(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_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,
! [X91] :
( ~ empty(X91)
| X91 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,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_12,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
empty(esk10_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) )
=> ! [X5] :
( ( relation(X5)
& function(X5) )
=> ( in(X3,X1)
=> ( X2 = empty_set
| apply(relation_composition(X4,X5),X3) = apply(X5,apply(X4,X3)) ) ) ) ),
inference(assume_negation,[status(cth)],[t21_funct_2]) ).
cnf(c_0_15,plain,
empty_set = esk10_0,
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_16,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_17,negated_conjecture,
( function(esk21_0)
& quasi_total(esk21_0,esk18_0,esk19_0)
& relation_of2_as_subset(esk21_0,esk18_0,esk19_0)
& relation(esk22_0)
& function(esk22_0)
& in(esk20_0,esk18_0)
& esk19_0 != empty_set
& apply(relation_composition(esk21_0,esk22_0),esk20_0) != apply(esk22_0,apply(esk21_0,esk20_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])]) ).
fof(c_0_18,plain,
! [X14,X15,X16] :
( ( ~ quasi_total(X16,X14,X15)
| X14 = relation_dom_as_subset(X14,X15,X16)
| X15 = empty_set
| ~ relation_of2_as_subset(X16,X14,X15) )
& ( X14 != relation_dom_as_subset(X14,X15,X16)
| quasi_total(X16,X14,X15)
| X15 = empty_set
| ~ relation_of2_as_subset(X16,X14,X15) )
& ( ~ quasi_total(X16,X14,X15)
| X14 = relation_dom_as_subset(X14,X15,X16)
| X14 != empty_set
| ~ relation_of2_as_subset(X16,X14,X15) )
& ( X14 != relation_dom_as_subset(X14,X15,X16)
| quasi_total(X16,X14,X15)
| X14 != empty_set
| ~ relation_of2_as_subset(X16,X14,X15) )
& ( ~ quasi_total(X16,X14,X15)
| X16 = empty_set
| X14 = empty_set
| X15 != empty_set
| ~ relation_of2_as_subset(X16,X14,X15) )
& ( X16 != empty_set
| quasi_total(X16,X14,X15)
| X14 = empty_set
| X15 != empty_set
| ~ relation_of2_as_subset(X16,X14,X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_2])])]) ).
cnf(c_0_19,plain,
( X1 = esk10_0
| ~ empty(X1) ),
inference(rw,[status(thm)],[c_0_12,c_0_15]) ).
cnf(c_0_20,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
esk19_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X22,X23,X24] :
( ~ relation_of2_as_subset(X24,X22,X23)
| element(X24,powerset(cartesian_product2(X22,X23))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m2_relset_1])]) ).
fof(c_0_23,plain,
! [X78,X79,X80] :
( ~ relation(X79)
| ~ function(X79)
| ~ relation(X80)
| ~ function(X80)
| ~ in(X78,relation_dom(X79))
| apply(relation_composition(X79,X80),X78) = apply(X80,apply(X79,X78)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t23_funct_1])])]) ).
fof(c_0_24,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_25,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_26,plain,
esk10_0 = esk6_0,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
esk19_0 != esk10_0,
inference(rw,[status(thm)],[c_0_21,c_0_15]) ).
fof(c_0_28,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_29,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_30,negated_conjecture,
relation_of2_as_subset(esk21_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_31,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_32,plain,
( relation_dom_as_subset(X2,X3,X1) = relation_dom(X1)
| ~ relation_of2(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,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_25,c_0_15]),c_0_26]) ).
cnf(c_0_34,negated_conjecture,
quasi_total(esk21_0,esk18_0,esk19_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_35,negated_conjecture,
esk19_0 != esk6_0,
inference(rw,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_36,plain,
( relation(X1)
| ~ element(X1,powerset(cartesian_product2(X2,X3))) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,negated_conjecture,
element(esk21_0,powerset(cartesian_product2(esk18_0,esk19_0))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,plain,
( apply(relation_composition(X1,X2),X3) = apply(X2,apply(X1,X3))
| ~ relation_of2(X1,X4,X5)
| ~ relation(X2)
| ~ relation(X1)
| ~ function(X2)
| ~ function(X1)
| ~ in(X3,relation_dom_as_subset(X4,X5,X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
relation_dom_as_subset(esk18_0,esk19_0,esk21_0) = esk18_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30])]),c_0_35]) ).
cnf(c_0_40,negated_conjecture,
relation(esk21_0),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
function(esk21_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_42,negated_conjecture,
apply(relation_composition(esk21_0,esk22_0),esk20_0) != apply(esk22_0,apply(esk21_0,esk20_0)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_43,negated_conjecture,
( apply(relation_composition(esk21_0,X1),X2) = apply(X1,apply(esk21_0,X2))
| ~ relation_of2(esk21_0,esk18_0,esk19_0)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41])]) ).
cnf(c_0_44,negated_conjecture,
relation(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_45,negated_conjecture,
function(esk22_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_46,negated_conjecture,
in(esk20_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_47,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_48,negated_conjecture,
~ relation_of2(esk21_0,esk18_0,esk19_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]),c_0_45]),c_0_46])]) ).
cnf(c_0_49,plain,
( relation_of2(X1,X2,X3)
| ~ relation_of2_as_subset(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_30])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU292+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n023.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 23 20:14:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 2.16/2.24 % Version : CSE_E---1.5
% 2.16/2.24 % Problem : theBenchmark.p
% 2.16/2.24 % Proof found
% 2.16/2.24 % SZS status Theorem for theBenchmark.p
% 2.16/2.24 % SZS output start Proof
% See solution above
% 2.16/2.25 % Total time : 1.689000 s
% 2.16/2.25 % SZS output end Proof
% 2.16/2.25 % Total time : 1.693000 s
%------------------------------------------------------------------------------