TSTP Solution File: SEU215+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU215+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 : 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 16:23:25 EDT 2023
% Result : Theorem 0.21s 0.63s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 33
% Syntax : Number of formulae : 63 ( 10 unt; 27 typ; 0 def)
% Number of atoms : 167 ( 25 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 207 ( 76 ~; 78 |; 29 &)
% ( 5 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 17 >; 7 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn; 35 !; 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,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
relation_dom: $i > $i ).
tff(decl_28,type,
apply: ( $i * $i ) > $i ).
tff(decl_29,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_30,type,
empty_set: $i ).
tff(decl_31,type,
singleton: $i > $i ).
tff(decl_32,type,
relation_composition: ( $i * $i ) > $i ).
tff(decl_33,type,
element: ( $i * $i ) > $o ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
powerset: $i > $i ).
tff(decl_36,type,
subset: ( $i * $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_1: $i > $i ).
tff(decl_41,type,
esk5_0: $i ).
tff(decl_42,type,
esk6_0: $i ).
tff(decl_43,type,
esk7_1: $i > $i ).
tff(decl_44,type,
esk8_0: $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_0: $i ).
fof(t23_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
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(dt_k5_relat_1,axiom,
! [X1,X2] :
( ( relation(X1)
& relation(X2) )
=> relation(relation_composition(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(fc1_funct_1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& relation(X2)
& function(X2) )
=> ( relation(relation_composition(X1,X2))
& function(relation_composition(X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_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/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
fof(t22_funct_1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(relation_composition(X3,X2)))
=> apply(relation_composition(X3,X2),X1) = apply(X2,apply(X3,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ! [X3] :
( ( relation(X3)
& function(X3) )
=> ( in(X1,relation_dom(X2))
=> apply(relation_composition(X2,X3),X1) = apply(X3,apply(X2,X1)) ) ) ),
inference(assume_negation,[status(cth)],[t23_funct_1]) ).
fof(c_0_7,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_8,plain,
! [X15,X16] :
( ~ relation(X15)
| ~ relation(X16)
| relation(relation_composition(X15,X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k5_relat_1])]) ).
fof(c_0_9,negated_conjecture,
( relation(esk11_0)
& function(esk11_0)
& relation(esk12_0)
& function(esk12_0)
& in(esk10_0,relation_dom(esk11_0))
& apply(relation_composition(esk11_0,esk12_0),esk10_0) != apply(esk12_0,apply(esk11_0,esk10_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X21,X22] :
( ( relation(relation_composition(X21,X22))
| ~ relation(X21)
| ~ function(X21)
| ~ relation(X22)
| ~ function(X22) )
& ( function(relation_composition(X21,X22))
| ~ relation(X21)
| ~ function(X21)
| ~ relation(X22)
| ~ function(X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc1_funct_1])])]) ).
fof(c_0_11,plain,
! [X10,X11,X12] :
( ( X12 != apply(X10,X11)
| in(ordered_pair(X11,X12),X10)
| ~ in(X11,relation_dom(X10))
| ~ relation(X10)
| ~ function(X10) )
& ( ~ in(ordered_pair(X11,X12),X10)
| X12 = apply(X10,X11)
| ~ in(X11,relation_dom(X10))
| ~ relation(X10)
| ~ function(X10) )
& ( X12 != apply(X10,X11)
| X12 = empty_set
| in(X11,relation_dom(X10))
| ~ relation(X10)
| ~ function(X10) )
& ( X12 != empty_set
| X12 = apply(X10,X11)
| in(X11,relation_dom(X10))
| ~ relation(X10)
| ~ function(X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
cnf(c_0_12,plain,
( relation(relation_composition(X1,X2))
| ~ relation(X1)
| ~ relation(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
relation(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( function(relation_composition(X1,X2))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
function(esk12_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
( X1 = empty_set
| in(X3,relation_dom(X2))
| X1 != apply(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( relation(relation_composition(X1,esk12_0))
| ~ relation(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
relation(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( function(relation_composition(X1,esk12_0))
| ~ relation(X1)
| ~ function(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15])]) ).
cnf(c_0_20,negated_conjecture,
function(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_21,plain,
( apply(X1,X2) = empty_set
| in(X2,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
relation(relation_composition(esk11_0,esk12_0)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
function(relation_composition(esk11_0,esk12_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
apply(relation_composition(esk11_0,esk12_0),esk10_0) != apply(esk12_0,apply(esk11_0,esk10_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
( apply(relation_composition(esk11_0,esk12_0),X1) = empty_set
| in(X1,relation_dom(relation_composition(esk11_0,esk12_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
fof(c_0_26,plain,
! [X46,X47,X48] :
( ( in(X46,relation_dom(X48))
| ~ in(X46,relation_dom(relation_composition(X48,X47)))
| ~ relation(X48)
| ~ function(X48)
| ~ relation(X47)
| ~ function(X47) )
& ( in(apply(X48,X46),relation_dom(X47))
| ~ in(X46,relation_dom(relation_composition(X48,X47)))
| ~ relation(X48)
| ~ function(X48)
| ~ relation(X47)
| ~ function(X47) )
& ( ~ in(X46,relation_dom(X48))
| ~ in(apply(X48,X46),relation_dom(X47))
| in(X46,relation_dom(relation_composition(X48,X47)))
| ~ relation(X48)
| ~ function(X48)
| ~ relation(X47)
| ~ function(X47) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_funct_1])])])]) ).
cnf(c_0_27,negated_conjecture,
( in(esk10_0,relation_dom(relation_composition(esk11_0,esk12_0)))
| apply(esk12_0,apply(esk11_0,esk10_0)) != empty_set ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( apply(esk12_0,X1) = empty_set
| in(X1,relation_dom(esk12_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_13]),c_0_15])]) ).
fof(c_0_29,plain,
! [X49,X50,X51] :
( ~ relation(X50)
| ~ function(X50)
| ~ relation(X51)
| ~ function(X51)
| ~ in(X49,relation_dom(relation_composition(X51,X50)))
| apply(relation_composition(X51,X50),X49) = apply(X50,apply(X51,X49)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t22_funct_1])])]) ).
cnf(c_0_30,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_26]) ).
cnf(c_0_31,negated_conjecture,
( in(apply(esk11_0,esk10_0),relation_dom(esk12_0))
| in(esk10_0,relation_dom(relation_composition(esk11_0,esk12_0))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
in(esk10_0,relation_dom(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_33,plain,
( apply(relation_composition(X2,X1),X3) = apply(X1,apply(X2,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ relation(X2)
| ~ function(X2)
| ~ in(X3,relation_dom(relation_composition(X2,X1))) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
in(esk10_0,relation_dom(relation_composition(esk11_0,esk12_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_13]),c_0_18]),c_0_15]),c_0_20]),c_0_32])]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(sr,[status(thm)],[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_33,c_0_34]),c_0_18]),c_0_13]),c_0_20]),c_0_15])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU215+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
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 16:06:02 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.63 % Version : CSE_E---1.5
% 0.21/0.63 % Problem : theBenchmark.p
% 0.21/0.63 % Proof found
% 0.21/0.63 % SZS status Theorem for theBenchmark.p
% 0.21/0.63 % SZS output start Proof
% See solution above
% 0.21/0.63 % Total time : 0.053000 s
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63 % Total time : 0.057000 s
%------------------------------------------------------------------------------