TSTP Solution File: SEU225+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU225+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 16:23:32 EDT 2023
% Result : Theorem 5.53s 5.79s
% Output : CNFRefutation 5.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 40
% Syntax : Number of formulae : 73 ( 10 unt; 32 typ; 0 def)
% Number of atoms : 183 ( 44 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 230 ( 88 ~; 90 |; 29 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 20 >; 10 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 12 con; 0-3 aty)
% Number of variables : 71 ( 3 sgn; 39 !; 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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_29,type,
relation_dom: $i > $i ).
tff(decl_30,type,
apply: ( $i * $i ) > $i ).
tff(decl_31,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
singleton: $i > $i ).
tff(decl_34,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_35,type,
element: ( $i * $i ) > $o ).
tff(decl_36,type,
relation_empty_yielding: $i > $o ).
tff(decl_37,type,
powerset: $i > $i ).
tff(decl_38,type,
subset: ( $i * $i ) > $o ).
tff(decl_39,type,
esk1_1: $i > $i ).
tff(decl_40,type,
esk2_0: $i ).
tff(decl_41,type,
esk3_0: $i ).
tff(decl_42,type,
esk4_1: $i > $i ).
tff(decl_43,type,
esk5_0: $i ).
tff(decl_44,type,
esk6_0: $i ).
tff(decl_45,type,
esk7_0: $i ).
tff(decl_46,type,
esk8_1: $i > $i ).
tff(decl_47,type,
esk9_0: $i ).
tff(decl_48,type,
esk10_0: $i ).
tff(decl_49,type,
esk11_0: $i ).
tff(decl_50,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk13_0: $i ).
tff(decl_52,type,
esk14_0: $i ).
tff(decl_53,type,
esk15_0: $i ).
fof(d4_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
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(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_relat_1) ).
fof(fc4_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1) )
=> ( relation(relation_dom_restriction(X1,X2))
& function(relation_dom_restriction(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc4_funct_1) ).
fof(t72_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t72_funct_1) ).
fof(t68_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( X2 = relation_dom_restriction(X3,X1)
<=> ( relation_dom(X2) = set_intersection2(relation_dom(X3),X1)
& ! [X4] :
( in(X4,relation_dom(X2))
=> apply(X2,X4) = apply(X3,X4) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t68_funct_1) ).
fof(l82_funct_1,axiom,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_dom_restriction(X3,X1)))
<=> ( in(X2,relation_dom(X3))
& in(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l82_funct_1) ).
fof(c_0_8,plain,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( ( in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> in(ordered_pair(X2,X3),X1) ) )
& ( ~ in(X2,relation_dom(X1))
=> ( X3 = apply(X1,X2)
<=> X3 = empty_set ) ) ) ),
inference(fof_simplification,[status(thm)],[d4_funct_1]) ).
fof(c_0_9,plain,
! [X14,X15,X16] :
( ( X16 != apply(X14,X15)
| in(ordered_pair(X15,X16),X14)
| ~ in(X15,relation_dom(X14))
| ~ relation(X14)
| ~ function(X14) )
& ( ~ in(ordered_pair(X15,X16),X14)
| X16 = apply(X14,X15)
| ~ in(X15,relation_dom(X14))
| ~ relation(X14)
| ~ function(X14) )
& ( X16 != apply(X14,X15)
| X16 = empty_set
| in(X15,relation_dom(X14))
| ~ relation(X14)
| ~ function(X14) )
& ( X16 != empty_set
| X16 = apply(X14,X15)
| in(X15,relation_dom(X14))
| ~ relation(X14)
| ~ function(X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
fof(c_0_10,plain,
! [X72] :
( ~ empty(X72)
| X72 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,plain,
( relation(esk6_0)
& empty(esk6_0)
& function(esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc2_funct_1])]) ).
cnf(c_0_12,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
empty(esk6_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
empty_set = esk6_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_17,plain,
! [X19,X20] :
( ~ relation(X19)
| relation(relation_dom_restriction(X19,X20)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k7_relat_1])]) ).
cnf(c_0_18,plain,
( apply(X1,X2) = esk6_0
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( relation(relation_dom_restriction(X1,X2))
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X33,X34] :
( ( relation(relation_dom_restriction(X33,X34))
| ~ relation(X33)
| ~ function(X33) )
& ( function(relation_dom_restriction(X33,X34))
| ~ relation(X33)
| ~ function(X33) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc4_funct_1])])]) ).
fof(c_0_21,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,X1)
=> apply(relation_dom_restriction(X3,X1),X2) = apply(X3,X2) ) ),
inference(assume_negation,[status(cth)],[t72_funct_1]) ).
fof(c_0_22,plain,
! [X67,X68,X69,X70] :
( ( relation_dom(X68) = set_intersection2(relation_dom(X69),X67)
| X68 != relation_dom_restriction(X69,X67)
| ~ relation(X69)
| ~ function(X69)
| ~ relation(X68)
| ~ function(X68) )
& ( ~ in(X70,relation_dom(X68))
| apply(X68,X70) = apply(X69,X70)
| X68 != relation_dom_restriction(X69,X67)
| ~ relation(X69)
| ~ function(X69)
| ~ relation(X68)
| ~ function(X68) )
& ( in(esk12_3(X67,X68,X69),relation_dom(X68))
| relation_dom(X68) != set_intersection2(relation_dom(X69),X67)
| X68 = relation_dom_restriction(X69,X67)
| ~ relation(X69)
| ~ function(X69)
| ~ relation(X68)
| ~ function(X68) )
& ( apply(X68,esk12_3(X67,X68,X69)) != apply(X69,esk12_3(X67,X68,X69))
| relation_dom(X68) != set_intersection2(relation_dom(X69),X67)
| X68 = relation_dom_restriction(X69,X67)
| ~ relation(X69)
| ~ function(X69)
| ~ relation(X68)
| ~ function(X68) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t68_funct_1])])])])]) ).
cnf(c_0_23,plain,
( apply(relation_dom_restriction(X1,X2),X3) = esk6_0
| in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ function(relation_dom_restriction(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
( function(relation_dom_restriction(X1,X2))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_25,negated_conjecture,
( relation(esk15_0)
& function(esk15_0)
& in(esk14_0,esk13_0)
& apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_26,plain,
( apply(X2,X1) = apply(X3,X1)
| ~ in(X1,relation_dom(X2))
| X2 != relation_dom_restriction(X3,X4)
| ~ relation(X3)
| ~ function(X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( apply(relation_dom_restriction(X1,X2),X3) = esk6_0
| in(X3,relation_dom(relation_dom_restriction(X1,X2)))
| ~ relation(X1)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,negated_conjecture,
relation(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
function(esk15_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
apply(relation_dom_restriction(esk15_0,esk13_0),esk14_0) != apply(esk15_0,esk14_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
( apply(relation_dom_restriction(X1,X2),X3) = apply(X1,X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_dom(relation_dom_restriction(X1,X2))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_26]),c_0_24]),c_0_19]) ).
fof(c_0_32,plain,
! [X38,X39,X40] :
( ( in(X39,relation_dom(X40))
| ~ in(X39,relation_dom(relation_dom_restriction(X40,X38)))
| ~ relation(X40)
| ~ function(X40) )
& ( in(X39,X38)
| ~ in(X39,relation_dom(relation_dom_restriction(X40,X38)))
| ~ relation(X40)
| ~ function(X40) )
& ( ~ in(X39,relation_dom(X40))
| ~ in(X39,X38)
| in(X39,relation_dom(relation_dom_restriction(X40,X38)))
| ~ relation(X40)
| ~ function(X40) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l82_funct_1])])]) ).
cnf(c_0_33,negated_conjecture,
( apply(relation_dom_restriction(esk15_0,X1),X2) = esk6_0
| in(X2,relation_dom(relation_dom_restriction(esk15_0,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29])]) ).
cnf(c_0_34,negated_conjecture,
~ in(esk14_0,relation_dom(relation_dom_restriction(esk15_0,esk13_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_29])]) ).
cnf(c_0_35,plain,
( in(X1,relation_dom(relation_dom_restriction(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_36,negated_conjecture,
in(esk14_0,esk13_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,negated_conjecture,
apply(esk15_0,esk14_0) != esk6_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_34]) ).
cnf(c_0_38,negated_conjecture,
( apply(esk15_0,X1) = esk6_0
| in(X1,relation_dom(esk15_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_29])]) ).
cnf(c_0_39,negated_conjecture,
~ in(esk14_0,relation_dom(esk15_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28]),c_0_29]),c_0_36])]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU225+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.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 21:32:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 5.53/5.79 % Version : CSE_E---1.5
% 5.53/5.79 % Problem : theBenchmark.p
% 5.53/5.79 % Proof found
% 5.53/5.79 % SZS status Theorem for theBenchmark.p
% 5.53/5.79 % SZS output start Proof
% See solution above
% 5.53/5.79 % Total time : 5.202000 s
% 5.53/5.79 % SZS output end Proof
% 5.53/5.79 % Total time : 5.206000 s
%------------------------------------------------------------------------------