TSTP Solution File: SEU009+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 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 16:22:07 EDT 2023
% Result : Theorem 0.21s 0.67s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 31
% Syntax : Number of formulae : 56 ( 11 unt; 26 typ; 0 def)
% Number of atoms : 126 ( 15 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 162 ( 66 ~; 66 |; 20 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 16 >; 6 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn; 22 !; 0 ?; 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,
relation_composition: ( $i * $i ) > $i ).
tff(decl_27,type,
identity_relation: $i > $i ).
tff(decl_28,type,
element: ( $i * $i ) > $o ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
relation_empty_yielding: $i > $o ).
tff(decl_31,type,
powerset: $i > $i ).
tff(decl_32,type,
relation_dom: $i > $i ).
tff(decl_33,type,
subset: ( $i * $i ) > $o ).
tff(decl_34,type,
apply: ( $i * $i ) > $i ).
tff(decl_35,type,
esk1_1: $i > $i ).
tff(decl_36,type,
esk2_0: $i ).
tff(decl_37,type,
esk3_0: $i ).
tff(decl_38,type,
esk4_1: $i > $i ).
tff(decl_39,type,
esk5_0: $i ).
tff(decl_40,type,
esk6_0: $i ).
tff(decl_41,type,
esk7_1: $i > $i ).
tff(decl_42,type,
esk8_0: $i ).
tff(decl_43,type,
esk9_0: $i ).
tff(decl_44,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
fof(t40_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_funct_1) ).
fof(t34_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( X2 = identity_relation(X1)
<=> ( relation_dom(X2) = X1
& ! [X3] :
( in(X3,X1)
=> apply(X2,X3) = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(dt_k6_relat_1,axiom,
! [X1] : relation(identity_relation(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(t21_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
<=> ( in(X1,relation_dom(X3))
& in(apply(X3,X1),relation_dom(X2)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X2,relation_dom(relation_composition(X3,identity_relation(X1))))
<=> ( in(X2,relation_dom(X3))
& in(apply(X3,X2),X1) ) ) ),
inference(assume_negation,[status(cth)],[t40_funct_1]) ).
fof(c_0_6,plain,
! [X41,X42,X43] :
( ( relation_dom(X42) = X41
| X42 != identity_relation(X41)
| ~ relation(X42)
| ~ function(X42) )
& ( ~ in(X43,X41)
| apply(X42,X43) = X43
| X42 != identity_relation(X41)
| ~ relation(X42)
| ~ function(X42) )
& ( in(esk10_2(X41,X42),X41)
| relation_dom(X42) != X41
| X42 = identity_relation(X41)
| ~ relation(X42)
| ~ function(X42) )
& ( apply(X42,esk10_2(X41,X42)) != esk10_2(X41,X42)
| relation_dom(X42) != X41
| X42 = identity_relation(X41)
| ~ relation(X42)
| ~ function(X42) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t34_funct_1])])])])]) ).
fof(c_0_7,plain,
! [X10] : relation(identity_relation(X10)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_8,plain,
! [X18] :
( relation(identity_relation(X18))
& function(identity_relation(X18)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_9,plain,
! [X36,X37,X38] :
( ( in(X36,relation_dom(X38))
| ~ in(X36,relation_dom(relation_composition(X38,X37)))
| ~ relation(X38)
| ~ function(X38)
| ~ relation(X37)
| ~ function(X37) )
& ( in(apply(X38,X36),relation_dom(X37))
| ~ in(X36,relation_dom(relation_composition(X38,X37)))
| ~ relation(X38)
| ~ function(X38)
| ~ relation(X37)
| ~ function(X37) )
& ( ~ in(X36,relation_dom(X38))
| ~ in(apply(X38,X36),relation_dom(X37))
| in(X36,relation_dom(relation_composition(X38,X37)))
| ~ relation(X38)
| ~ function(X38)
| ~ relation(X37)
| ~ function(X37) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
fof(c_0_10,negated_conjecture,
( relation(esk13_0)
& function(esk13_0)
& ( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| ~ in(esk12_0,relation_dom(esk13_0))
| ~ in(apply(esk13_0,esk12_0),esk11_0) )
& ( in(esk12_0,relation_dom(esk13_0))
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) )
& ( in(apply(esk13_0,esk12_0),esk11_0)
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_11,plain,
( relation_dom(X1) = X2
| X1 != identity_relation(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(X1,relation_dom(X2))
| ~ in(X1,relation_dom(relation_composition(X2,X3)))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( in(esk12_0,relation_dom(esk13_0))
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( in(apply(X1,X2),relation_dom(X3))
| ~ in(X2,relation_dom(relation_composition(X1,X3)))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
relation_dom(identity_relation(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_11]),c_0_12]),c_0_13])]) ).
cnf(c_0_20,negated_conjecture,
( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| ~ in(esk12_0,relation_dom(esk13_0))
| ~ in(apply(esk13_0,esk12_0),esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_12]),c_0_16]),c_0_13]),c_0_17])]) ).
cnf(c_0_22,plain,
( in(apply(X1,X2),X3)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(relation_composition(X1,identity_relation(X3)))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_12]),c_0_13])]) ).
cnf(c_0_23,negated_conjecture,
( in(apply(esk13_0,esk12_0),esk11_0)
| in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_24,negated_conjecture,
( ~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0))))
| ~ in(apply(esk13_0,esk12_0),esk11_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]) ).
cnf(c_0_25,negated_conjecture,
in(apply(esk13_0,esk12_0),esk11_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_17])]) ).
cnf(c_0_26,plain,
( in(X1,relation_dom(relation_composition(X2,X3)))
| ~ in(X1,relation_dom(X2))
| ~ in(apply(X2,X1),relation_dom(X3))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_27,negated_conjecture,
~ in(esk12_0,relation_dom(relation_composition(esk13_0,identity_relation(esk11_0)))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_28,plain,
( in(X1,relation_dom(relation_composition(X2,identity_relation(X3))))
| ~ relation(X2)
| ~ function(X2)
| ~ in(apply(X2,X1),X3)
| ~ in(X1,relation_dom(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_12]),c_0_13])]) ).
cnf(c_0_29,negated_conjecture,
$false,
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_27,c_0_28]),c_0_16]),c_0_17]),c_0_25]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU009+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 14:52:02 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.67 % Version : CSE_E---1.5
% 0.21/0.67 % Problem : theBenchmark.p
% 0.21/0.67 % Proof found
% 0.21/0.67 % SZS status Theorem for theBenchmark.p
% 0.21/0.67 % SZS output start Proof
% See solution above
% 0.21/0.68 % Total time : 0.079000 s
% 0.21/0.68 % SZS output end Proof
% 0.21/0.68 % Total time : 0.082000 s
%------------------------------------------------------------------------------