TSTP Solution File: SEU225+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU225+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 : n007.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 16:23:31 EDT 2023
% Result : Theorem 2.51s 2.67s
% Output : CNFRefutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 36
% Syntax : Number of formulae : 69 ( 10 unt; 28 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 : 25 ( 16 >; 9 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 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,
esk1_1: $i > $i ).
tff(decl_38,type,
esk2_0: $i ).
tff(decl_39,type,
esk3_0: $i ).
tff(decl_40,type,
esk4_0: $i ).
tff(decl_41,type,
esk5_0: $i ).
tff(decl_42,type,
esk6_0: $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_0: $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
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(dt_k7_relat_1,axiom,
! [X1,X2] :
( relation(X1)
=> relation(relation_dom_restriction(X1,X2)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,
! [X58] :
( ~ empty(X58)
| X58 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_11,plain,
( relation(esk5_0)
& empty(esk5_0)
& function(esk5_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(esk5_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 = esk5_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) = esk5_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,
! [X32,X33] :
( ( relation(relation_dom_restriction(X32,X33))
| ~ relation(X32)
| ~ function(X32) )
& ( function(relation_dom_restriction(X32,X33))
| ~ relation(X32)
| ~ function(X32) ) ),
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,
! [X53,X54,X55,X56] :
( ( relation_dom(X54) = set_intersection2(relation_dom(X55),X53)
| X54 != relation_dom_restriction(X55,X53)
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) )
& ( ~ in(X56,relation_dom(X54))
| apply(X54,X56) = apply(X55,X56)
| X54 != relation_dom_restriction(X55,X53)
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) )
& ( in(esk10_3(X53,X54,X55),relation_dom(X54))
| relation_dom(X54) != set_intersection2(relation_dom(X55),X53)
| X54 = relation_dom_restriction(X55,X53)
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) )
& ( apply(X54,esk10_3(X53,X54,X55)) != apply(X55,esk10_3(X53,X54,X55))
| relation_dom(X54) != set_intersection2(relation_dom(X55),X53)
| X54 = relation_dom_restriction(X55,X53)
| ~ relation(X55)
| ~ function(X55)
| ~ relation(X54)
| ~ function(X54) ) ),
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) = esk5_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(esk13_0)
& function(esk13_0)
& in(esk12_0,esk11_0)
& apply(relation_dom_restriction(esk13_0,esk11_0),esk12_0) != apply(esk13_0,esk12_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) = esk5_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(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
apply(relation_dom_restriction(esk13_0,esk11_0),esk12_0) != apply(esk13_0,esk12_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,
! [X37,X38,X39] :
( ( in(X38,relation_dom(X39))
| ~ in(X38,relation_dom(relation_dom_restriction(X39,X37)))
| ~ relation(X39)
| ~ function(X39) )
& ( in(X38,X37)
| ~ in(X38,relation_dom(relation_dom_restriction(X39,X37)))
| ~ relation(X39)
| ~ function(X39) )
& ( ~ in(X38,relation_dom(X39))
| ~ in(X38,X37)
| in(X38,relation_dom(relation_dom_restriction(X39,X37)))
| ~ relation(X39)
| ~ function(X39) ) ),
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(esk13_0,X1),X2) = esk5_0
| in(X2,relation_dom(relation_dom_restriction(esk13_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(esk12_0,relation_dom(relation_dom_restriction(esk13_0,esk11_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(esk12_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_37,negated_conjecture,
apply(esk13_0,esk12_0) != esk5_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(esk13_0,X1) = esk5_0
| in(X1,relation_dom(esk13_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(esk12_0,relation_dom(esk13_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
% 0.00/0.14 % Problem : SEU225+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Aug 23 20:23:39 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.20/0.60 start to proof: theBenchmark
% 2.51/2.67 % Version : CSE_E---1.5
% 2.51/2.67 % Problem : theBenchmark.p
% 2.51/2.67 % Proof found
% 2.51/2.67 % SZS status Theorem for theBenchmark.p
% 2.51/2.67 % SZS output start Proof
% See solution above
% 2.51/2.68 % Total time : 1.994000 s
% 2.51/2.68 % SZS output end Proof
% 2.51/2.68 % Total time : 1.997000 s
%------------------------------------------------------------------------------