TSTP Solution File: SEU212+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU212+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 : n015.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 16:23:22 EDT 2023
% Result : Theorem 0.12s 0.52s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 29
% Syntax : Number of formulae : 58 ( 9 unt; 25 typ; 0 def)
% Number of atoms : 135 ( 38 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 167 ( 65 ~; 67 |; 18 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 15 >; 9 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 57 ( 3 sgn; 29 !; 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,
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,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
relation_empty_yielding: $i > $o ).
tff(decl_34,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk3_2: ( $i * $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_0: $i ).
tff(decl_46,type,
esk13_0: $i ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t8_funct_1,conjecture,
! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_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/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(c_0_4,plain,
! [X14,X15,X16,X18,X19,X20,X22] :
( ( ~ in(X16,X15)
| in(ordered_pair(X16,esk1_3(X14,X15,X16)),X14)
| X15 != relation_dom(X14)
| ~ relation(X14) )
& ( ~ in(ordered_pair(X18,X19),X14)
| in(X18,X15)
| X15 != relation_dom(X14)
| ~ relation(X14) )
& ( ~ in(esk2_2(X14,X20),X20)
| ~ in(ordered_pair(esk2_2(X14,X20),X22),X14)
| X20 = relation_dom(X14)
| ~ relation(X14) )
& ( in(esk2_2(X14,X20),X20)
| in(ordered_pair(esk2_2(X14,X20),esk3_2(X14,X20)),X14)
| X20 = relation_dom(X14)
| ~ relation(X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d4_relat_1])])])])])]) ).
fof(c_0_5,plain,
! [X24,X25] : ordered_pair(X24,X25) = unordered_pair(unordered_pair(X24,X25),singleton(X24)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2,X3] :
( ( relation(X3)
& function(X3) )
=> ( in(ordered_pair(X1,X2),X3)
<=> ( in(X1,relation_dom(X3))
& X2 = apply(X3,X1) ) ) ),
inference(assume_negation,[status(cth)],[t8_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]) ).
cnf(c_0_8,plain,
( in(X1,X4)
| ~ in(ordered_pair(X1,X2),X3)
| X4 != relation_dom(X3)
| ~ relation(X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
( relation(esk13_0)
& function(esk13_0)
& ( ~ in(ordered_pair(esk11_0,esk12_0),esk13_0)
| ~ in(esk11_0,relation_dom(esk13_0))
| esk12_0 != apply(esk13_0,esk11_0) )
& ( in(esk11_0,relation_dom(esk13_0))
| in(ordered_pair(esk11_0,esk12_0),esk13_0) )
& ( esk12_0 = apply(esk13_0,esk11_0)
| in(ordered_pair(esk11_0,esk12_0),esk13_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_11,plain,
! [X11,X12,X13] :
( ( X13 != apply(X11,X12)
| in(ordered_pair(X12,X13),X11)
| ~ in(X12,relation_dom(X11))
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(ordered_pair(X12,X13),X11)
| X13 = apply(X11,X12)
| ~ in(X12,relation_dom(X11))
| ~ relation(X11)
| ~ function(X11) )
& ( X13 != apply(X11,X12)
| X13 = empty_set
| in(X12,relation_dom(X11))
| ~ relation(X11)
| ~ function(X11) )
& ( X13 != empty_set
| X13 = apply(X11,X12)
| in(X12,relation_dom(X11))
| ~ relation(X11)
| ~ function(X11) ) ),
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,
( in(X1,X4)
| X4 != relation_dom(X3)
| ~ relation(X3)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(ordered_pair(esk11_0,esk12_0),esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( X2 = apply(X3,X1)
| ~ in(ordered_pair(X1,X2),X3)
| ~ in(X1,relation_dom(X3))
| ~ relation(X3)
| ~ function(X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
( in(X1,relation_dom(X2))
| ~ relation(X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),X2) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( in(esk11_0,relation_dom(esk13_0))
| in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(rw,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_17,negated_conjecture,
relation(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
( X2 = apply(X3,X1)
| ~ function(X3)
| ~ relation(X3)
| ~ in(X1,relation_dom(X3))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X3) ),
inference(rw,[status(thm)],[c_0_14,c_0_9]) ).
cnf(c_0_19,negated_conjecture,
in(esk11_0,relation_dom(esk13_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
function(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( esk12_0 = apply(esk13_0,esk11_0)
| in(ordered_pair(esk11_0,esk12_0),esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( ~ in(ordered_pair(esk11_0,esk12_0),esk13_0)
| ~ in(esk11_0,relation_dom(esk13_0))
| esk12_0 != apply(esk13_0,esk11_0) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_23,plain,
( in(ordered_pair(X3,X1),X2)
| X1 != apply(X2,X3)
| ~ in(X3,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_24,negated_conjecture,
( X1 = apply(esk13_0,esk11_0)
| ~ in(unordered_pair(unordered_pair(esk11_0,X1),singleton(esk11_0)),esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]),c_0_20])]) ).
cnf(c_0_25,negated_conjecture,
( esk12_0 = apply(esk13_0,esk11_0)
| in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(rw,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_26,negated_conjecture,
( esk12_0 != apply(esk13_0,esk11_0)
| ~ in(esk11_0,relation_dom(esk13_0))
| ~ in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(rw,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_27,plain,
( in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),X2)
| X1 != apply(X2,X3)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X3,relation_dom(X2)) ),
inference(rw,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_28,negated_conjecture,
apply(esk13_0,esk11_0) = esk12_0,
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( apply(esk13_0,esk11_0) != esk12_0
| ~ in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_19])]) ).
cnf(c_0_30,negated_conjecture,
( in(unordered_pair(unordered_pair(esk11_0,X1),singleton(esk11_0)),esk13_0)
| X1 != esk12_0 ),
inference(cn,[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_17]),c_0_20]),c_0_19])]) ).
cnf(c_0_31,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk11_0,esk12_0),singleton(esk11_0)),esk13_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU212+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.07/0.28 % Computer : n015.cluster.edu
% 0.07/0.28 % Model : x86_64 x86_64
% 0.07/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28 % Memory : 8042.1875MB
% 0.07/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28 % CPULimit : 300
% 0.07/0.28 % WCLimit : 300
% 0.07/0.28 % DateTime : Wed Aug 23 18:22:50 EDT 2023
% 0.07/0.28 % CPUTime :
% 0.12/0.50 start to proof: theBenchmark
% 0.12/0.52 % Version : CSE_E---1.5
% 0.12/0.52 % Problem : theBenchmark.p
% 0.12/0.52 % Proof found
% 0.12/0.52 % SZS status Theorem for theBenchmark.p
% 0.12/0.52 % SZS output start Proof
% See solution above
% 0.12/0.52 % Total time : 0.010000 s
% 0.12/0.52 % SZS output end Proof
% 0.12/0.52 % Total time : 0.012000 s
%------------------------------------------------------------------------------