TSTP Solution File: SEU217+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU217+3 : 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 : 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 16:23:27 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 28
% Syntax : Number of formulae : 40 ( 7 unt; 24 typ; 0 def)
% Number of atoms : 49 ( 19 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 55 ( 22 ~; 20 |; 8 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 15 >; 5 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn; 14 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
empty_set: $i ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
relation: $i > $o ).
tff(decl_26,type,
relation_empty_yielding: $i > $o ).
tff(decl_27,type,
element: ( $i * $i ) > $o ).
tff(decl_28,type,
function: $i > $o ).
tff(decl_29,type,
powerset: $i > $i ).
tff(decl_30,type,
relation_dom: $i > $i ).
tff(decl_31,type,
in: ( $i * $i ) > $o ).
tff(decl_32,type,
identity_relation: $i > $i ).
tff(decl_33,type,
apply: ( $i * $i ) > $i ).
tff(decl_34,type,
esk1_1: $i > $i ).
tff(decl_35,type,
esk2_0: $i ).
tff(decl_36,type,
esk3_1: $i > $i ).
tff(decl_37,type,
esk4_1: $i > $i ).
tff(decl_38,type,
esk5_0: $i ).
tff(decl_39,type,
esk6_0: $i ).
tff(decl_40,type,
esk7_0: $i ).
tff(decl_41,type,
esk8_0: $i ).
tff(decl_42,type,
esk9_0: $i ).
tff(decl_43,type,
esk10_0: $i ).
tff(decl_44,type,
esk11_0: $i ).
tff(decl_45,type,
esk12_2: ( $i * $i ) > $i ).
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(fc2_funct_1,axiom,
! [X1] :
( relation(identity_relation(X1))
& function(identity_relation(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_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(t35_funct_1,conjecture,
! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(c_0_4,plain,
! [X45,X46,X47] :
( ( relation_dom(X46) = X45
| X46 != identity_relation(X45)
| ~ relation(X46)
| ~ function(X46) )
& ( ~ in(X47,X45)
| apply(X46,X47) = X47
| X46 != identity_relation(X45)
| ~ relation(X46)
| ~ function(X46) )
& ( in(esk12_2(X45,X46),X45)
| relation_dom(X46) != X45
| X46 = identity_relation(X45)
| ~ relation(X46)
| ~ function(X46) )
& ( apply(X46,esk12_2(X45,X46)) != esk12_2(X45,X46)
| relation_dom(X46) != X45
| X46 = identity_relation(X45)
| ~ relation(X46)
| ~ function(X46) ) ),
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_5,plain,
! [X28] :
( relation(identity_relation(X28))
& function(identity_relation(X28)) ),
inference(variable_rename,[status(thm)],[fc2_funct_1]) ).
fof(c_0_6,plain,
! [X27] : relation(identity_relation(X27)),
inference(variable_rename,[status(thm)],[dt_k6_relat_1]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( in(X2,X1)
=> apply(identity_relation(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[t35_funct_1]) ).
cnf(c_0_8,plain,
( apply(X3,X1) = X1
| ~ in(X1,X2)
| X3 != identity_relation(X2)
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
function(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
relation(identity_relation(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( in(esk11_0,esk10_0)
& apply(identity_relation(esk10_0),esk11_0) != esk11_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_12,plain,
( apply(identity_relation(X1),X2) = X2
| ~ in(X2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_8]),c_0_9]),c_0_10])]) ).
cnf(c_0_13,negated_conjecture,
in(esk11_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_14,negated_conjecture,
apply(identity_relation(esk10_0),esk11_0) != esk11_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n023.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 18:51:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 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
% 0.20/0.60 % Total time : 0.009000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.012000 s
%------------------------------------------------------------------------------