TSTP Solution File: SEU243+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU243+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 16:23:44 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 33
% Syntax : Number of formulae : 76 ( 10 unt; 28 typ; 0 def)
% Number of atoms : 173 ( 28 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 211 ( 86 ~; 96 |; 20 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 21 >; 11 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn; 19 !; 1 ?; 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,
set_union2: ( $i * $i ) > $i ).
tff(decl_28,type,
well_founded_relation: $i > $o ).
tff(decl_29,type,
relation_field: $i > $i ).
tff(decl_30,type,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
empty_set: $i ).
tff(decl_32,type,
fiber: ( $i * $i ) > $i ).
tff(decl_33,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_34,type,
is_well_founded_in: ( $i * $i ) > $o ).
tff(decl_35,type,
relation_dom: $i > $i ).
tff(decl_36,type,
relation_rng: $i > $i ).
tff(decl_37,type,
element: ( $i * $i ) > $o ).
tff(decl_38,type,
powerset: $i > $i ).
tff(decl_39,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk2_1: $i > $i ).
tff(decl_41,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk5_1: $i > $i ).
tff(decl_44,type,
esk6_0: $i ).
tff(decl_45,type,
esk7_0: $i ).
tff(decl_46,type,
esk8_0: $i ).
tff(decl_47,type,
esk9_0: $i ).
tff(decl_48,type,
esk10_0: $i ).
tff(decl_49,type,
esk11_0: $i ).
fof(t5_wellord1,conjecture,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_wellord1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc2_funct_1,axiom,
? [X1] :
( relation(X1)
& empty(X1)
& function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(d3_wellord1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( is_well_founded_in(X1,X2)
<=> ! [X3] :
~ ( subset(X3,X2)
& X3 != empty_set
& ! [X4] :
~ ( in(X4,X3)
& disjoint(fiber(X1,X4),X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_wellord1) ).
fof(d2_wellord1,axiom,
! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> ! [X2] :
~ ( subset(X2,relation_field(X1))
& X2 != empty_set
& ! [X3] :
~ ( in(X3,X2)
& disjoint(fiber(X1,X3),X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_wellord1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( relation(X1)
=> ( well_founded_relation(X1)
<=> is_well_founded_in(X1,relation_field(X1)) ) ),
inference(assume_negation,[status(cth)],[t5_wellord1]) ).
fof(c_0_6,plain,
! [X53] :
( ~ empty(X53)
| X53 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_7,plain,
( relation(esk8_0)
& empty(esk8_0)
& function(esk8_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
fof(c_0_8,plain,
! [X16,X17,X18,X20,X22] :
( ( in(esk3_3(X16,X17,X18),X18)
| ~ subset(X18,X17)
| X18 = empty_set
| ~ is_well_founded_in(X16,X17)
| ~ relation(X16) )
& ( disjoint(fiber(X16,esk3_3(X16,X17,X18)),X18)
| ~ subset(X18,X17)
| X18 = empty_set
| ~ is_well_founded_in(X16,X17)
| ~ relation(X16) )
& ( subset(esk4_2(X16,X20),X20)
| is_well_founded_in(X16,X20)
| ~ relation(X16) )
& ( esk4_2(X16,X20) != empty_set
| is_well_founded_in(X16,X20)
| ~ relation(X16) )
& ( ~ in(X22,esk4_2(X16,X20))
| ~ disjoint(fiber(X16,X22),esk4_2(X16,X20))
| is_well_founded_in(X16,X20)
| ~ relation(X16) ) ),
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)],[d3_wellord1])])])])])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk11_0)
& ( ~ well_founded_relation(esk11_0)
| ~ is_well_founded_in(esk11_0,relation_field(esk11_0)) )
& ( well_founded_relation(esk11_0)
| is_well_founded_in(esk11_0,relation_field(esk11_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_10,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
empty(esk8_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_12,plain,
! [X11,X12,X15] :
( ( in(esk1_2(X11,X12),X12)
| ~ subset(X12,relation_field(X11))
| X12 = empty_set
| ~ well_founded_relation(X11)
| ~ relation(X11) )
& ( disjoint(fiber(X11,esk1_2(X11,X12)),X12)
| ~ subset(X12,relation_field(X11))
| X12 = empty_set
| ~ well_founded_relation(X11)
| ~ relation(X11) )
& ( subset(esk2_1(X11),relation_field(X11))
| well_founded_relation(X11)
| ~ relation(X11) )
& ( esk2_1(X11) != empty_set
| well_founded_relation(X11)
| ~ relation(X11) )
& ( ~ in(X15,esk2_1(X11))
| ~ disjoint(fiber(X11,X15),esk2_1(X11))
| well_founded_relation(X11)
| ~ relation(X11) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d2_wellord1])])])])]) ).
cnf(c_0_13,plain,
( subset(esk4_2(X1,X2),X2)
| is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( is_well_founded_in(X1,X2)
| esk4_2(X1,X2) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
empty_set = esk8_0,
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( disjoint(fiber(X1,esk1_2(X1,X2)),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
( ~ well_founded_relation(esk11_0)
| ~ is_well_founded_in(esk11_0,relation_field(esk11_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( is_well_founded_in(esk11_0,X1)
| subset(esk4_2(esk11_0,X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_20,plain,
( is_well_founded_in(X1,X2)
| esk4_2(X1,X2) != esk8_0
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,plain,
( in(esk1_2(X1,X2),X2)
| X2 = empty_set
| ~ subset(X2,relation_field(X1))
| ~ well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,plain,
( X1 = esk8_0
| disjoint(fiber(X2,esk1_2(X2,X1)),X1)
| ~ subset(X1,relation_field(X2))
| ~ well_founded_relation(X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( subset(esk4_2(esk11_0,relation_field(esk11_0)),relation_field(esk11_0))
| ~ well_founded_relation(esk11_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( esk4_2(esk11_0,relation_field(esk11_0)) != esk8_0
| ~ well_founded_relation(esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_20]),c_0_14])]) ).
cnf(c_0_25,plain,
( X1 = esk8_0
| in(esk1_2(X2,X1),X1)
| ~ subset(X1,relation_field(X2))
| ~ well_founded_relation(X2)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_26,plain,
( is_well_founded_in(X2,X3)
| ~ in(X1,esk4_2(X2,X3))
| ~ disjoint(fiber(X2,X1),esk4_2(X2,X3))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
( disjoint(fiber(esk11_0,esk1_2(esk11_0,esk4_2(esk11_0,relation_field(esk11_0)))),esk4_2(esk11_0,relation_field(esk11_0)))
| ~ well_founded_relation(esk11_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_14])]),c_0_24]) ).
cnf(c_0_28,negated_conjecture,
( in(esk1_2(esk11_0,esk4_2(esk11_0,relation_field(esk11_0))),esk4_2(esk11_0,relation_field(esk11_0)))
| ~ well_founded_relation(esk11_0) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_23]),c_0_14])]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( well_founded_relation(esk11_0)
| is_well_founded_in(esk11_0,relation_field(esk11_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,plain,
( disjoint(fiber(X1,esk3_3(X1,X2,X3)),X3)
| X3 = empty_set
| ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_31,plain,
( subset(esk2_1(X1),relation_field(X1))
| well_founded_relation(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_32,negated_conjecture,
is_well_founded_in(esk11_0,relation_field(esk11_0)),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14])]),c_0_28]),c_0_29]) ).
cnf(c_0_33,plain,
( well_founded_relation(X1)
| esk2_1(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_34,plain,
( in(esk3_3(X1,X2,X3),X3)
| X3 = empty_set
| ~ subset(X3,X2)
| ~ is_well_founded_in(X1,X2)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_35,plain,
( X1 = esk8_0
| disjoint(fiber(X2,esk3_3(X2,X3,X1)),X1)
| ~ is_well_founded_in(X2,X3)
| ~ subset(X1,X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_30,c_0_16]) ).
cnf(c_0_36,negated_conjecture,
( subset(esk2_1(esk11_0),relation_field(esk11_0))
| well_founded_relation(esk11_0) ),
inference(spm,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_37,negated_conjecture,
~ well_founded_relation(esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_32])]) ).
cnf(c_0_38,plain,
( well_founded_relation(X1)
| esk2_1(X1) != esk8_0
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_33,c_0_16]) ).
cnf(c_0_39,plain,
( X1 = esk8_0
| in(esk3_3(X2,X3,X1),X1)
| ~ is_well_founded_in(X2,X3)
| ~ subset(X1,X3)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_34,c_0_16]) ).
cnf(c_0_40,negated_conjecture,
( X1 = esk8_0
| disjoint(fiber(esk11_0,esk3_3(esk11_0,relation_field(esk11_0),X1)),X1)
| ~ subset(X1,relation_field(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_14])]) ).
cnf(c_0_41,negated_conjecture,
subset(esk2_1(esk11_0),relation_field(esk11_0)),
inference(sr,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
esk8_0 != esk2_1(esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_14])]) ).
cnf(c_0_43,negated_conjecture,
( X1 = esk8_0
| in(esk3_3(esk11_0,relation_field(esk11_0),X1),X1)
| ~ subset(X1,relation_field(esk11_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_32]),c_0_14])]) ).
cnf(c_0_44,plain,
( well_founded_relation(X2)
| ~ in(X1,esk2_1(X2))
| ~ disjoint(fiber(X2,X1),esk2_1(X2))
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_45,negated_conjecture,
disjoint(fiber(esk11_0,esk3_3(esk11_0,relation_field(esk11_0),esk2_1(esk11_0))),esk2_1(esk11_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
in(esk3_3(esk11_0,relation_field(esk11_0),esk2_1(esk11_0)),esk2_1(esk11_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_41]),c_0_42]) ).
cnf(c_0_47,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_44,c_0_45]),c_0_14]),c_0_46])]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU243+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 18:44:16 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.015000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.018000 s
%------------------------------------------------------------------------------