TSTP Solution File: SEU049+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU049+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 16:22:15 EDT 2023
% Result : Theorem 0.50s 0.77s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 35
% Syntax : Number of formulae : 61 ( 8 unt; 32 typ; 0 def)
% Number of atoms : 138 ( 48 equ)
% Maximal formula atoms : 44 ( 4 avg)
% Number of connectives : 183 ( 74 ~; 82 |; 18 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 21 >; 14 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 11 con; 0-4 aty)
% Number of variables : 65 ( 0 sgn; 26 !; 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,
relation_image: ( $i * $i ) > $i ).
tff(decl_28,type,
relation_dom: $i > $i ).
tff(decl_29,type,
apply: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
element: ( $i * $i ) > $o ).
tff(decl_32,type,
empty_set: $i ).
tff(decl_33,type,
relation_empty_yielding: $i > $o ).
tff(decl_34,type,
powerset: $i > $i ).
tff(decl_35,type,
subset: ( $i * $i ) > $o ).
tff(decl_36,type,
esk1_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_37,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk5_1: $i > $i ).
tff(decl_41,type,
esk6_0: $i ).
tff(decl_42,type,
esk7_0: $i ).
tff(decl_43,type,
esk8_1: $i > $i ).
tff(decl_44,type,
esk9_0: $i ).
tff(decl_45,type,
esk10_0: $i ).
tff(decl_46,type,
esk11_0: $i ).
tff(decl_47,type,
esk12_1: $i > $i ).
tff(decl_48,type,
esk13_0: $i ).
tff(decl_49,type,
esk14_0: $i ).
tff(decl_50,type,
esk15_0: $i ).
tff(decl_51,type,
esk16_0: $i ).
tff(decl_52,type,
esk17_0: $i ).
tff(decl_53,type,
esk18_2: ( $i * $i ) > $i ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(d12_funct_1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2,X3] :
( X3 = relation_image(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,relation_dom(X1))
& in(X5,X2)
& X4 = apply(X1,X5) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(t117_funct_1,conjecture,
! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t117_funct_1) ).
fof(c_0_3,plain,
! [X23,X24,X25,X26,X27,X28] :
( ( ~ in(X25,X24)
| X25 = X23
| X24 != singleton(X23) )
& ( X26 != X23
| in(X26,X24)
| X24 != singleton(X23) )
& ( ~ in(esk4_2(X27,X28),X28)
| esk4_2(X27,X28) != X27
| X28 = singleton(X27) )
& ( in(esk4_2(X27,X28),X28)
| esk4_2(X27,X28) = X27
| X28 = singleton(X27) ) ),
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)],[d1_tarski])])])])])]) ).
fof(c_0_4,plain,
! [X11,X12,X13,X14,X16,X17,X18,X19,X21] :
( ( in(esk1_4(X11,X12,X13,X14),relation_dom(X11))
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk1_4(X11,X12,X13,X14),X12)
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( X14 = apply(X11,esk1_4(X11,X12,X13,X14))
| ~ in(X14,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(X17,relation_dom(X11))
| ~ in(X17,X12)
| X16 != apply(X11,X17)
| in(X16,X13)
| X13 != relation_image(X11,X12)
| ~ relation(X11)
| ~ function(X11) )
& ( ~ in(esk2_3(X11,X18,X19),X19)
| ~ in(X21,relation_dom(X11))
| ~ in(X21,X18)
| esk2_3(X11,X18,X19) != apply(X11,X21)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk3_3(X11,X18,X19),relation_dom(X11))
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( in(esk3_3(X11,X18,X19),X18)
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) )
& ( esk2_3(X11,X18,X19) = apply(X11,esk3_3(X11,X18,X19))
| in(esk2_3(X11,X18,X19),X19)
| X19 = relation_image(X11,X18)
| ~ relation(X11)
| ~ function(X11) ) ),
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)],[d12_funct_1])])])])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X1,relation_dom(X2))
=> relation_image(X2,singleton(X1)) = singleton(apply(X2,X1)) ) ),
inference(assume_negation,[status(cth)],[t117_funct_1]) ).
cnf(c_0_6,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( in(esk1_4(X1,X2,X3,X4),X2)
| ~ in(X4,X3)
| X3 != relation_image(X1,X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
( relation(esk17_0)
& function(esk17_0)
& in(esk16_0,relation_dom(esk17_0))
& relation_image(esk17_0,singleton(esk16_0)) != singleton(apply(esk17_0,esk16_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(esk1_4(X1,X2,relation_image(X1,X2),X3),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
relation_image(esk17_0,singleton(esk16_0)) != singleton(apply(esk17_0,esk16_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( in(esk4_2(X1,X2),X2)
| esk4_2(X1,X2) = X1
| X2 = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_13,plain,
( X1 = apply(X2,esk1_4(X2,X3,X4,X1))
| ~ in(X1,X4)
| X4 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_14,plain,
( esk1_4(X1,singleton(X2),relation_image(X1,singleton(X2)),X3) = X2
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_image(X1,singleton(X2))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))) = apply(esk17_0,esk16_0)
| in(esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))),relation_image(esk17_0,singleton(esk16_0))) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12])]) ).
cnf(c_0_16,negated_conjecture,
relation(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
function(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,plain,
( apply(X1,esk1_4(X1,X2,relation_image(X1,X2),X3)) = X3
| ~ relation(X1)
| ~ function(X1)
| ~ in(X3,relation_image(X1,X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( esk1_4(esk17_0,singleton(esk16_0),relation_image(esk17_0,singleton(esk16_0)),esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0)))) = esk16_0
| esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))) = apply(esk17_0,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_20,plain,
( X2 = singleton(X1)
| ~ in(esk4_2(X1,X2),X2)
| esk4_2(X1,X2) != X1 ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_21,negated_conjecture,
esk4_2(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))) = apply(esk17_0,esk16_0),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_16]),c_0_17])]),c_0_15]) ).
cnf(c_0_22,plain,
( in(X4,X5)
| ~ in(X1,relation_dom(X2))
| ~ in(X1,X3)
| X4 != apply(X2,X1)
| X5 != relation_image(X2,X3)
| ~ relation(X2)
| ~ function(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_23,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_24,negated_conjecture,
~ in(apply(esk17_0,esk16_0),relation_image(esk17_0,singleton(esk16_0))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_11]) ).
cnf(c_0_25,plain,
( in(apply(X1,X2),relation_image(X1,X3))
| ~ relation(X1)
| ~ function(X1)
| ~ in(X2,relation_dom(X1))
| ~ in(X2,X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_22])]) ).
cnf(c_0_26,negated_conjecture,
in(esk16_0,relation_dom(esk17_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_23])]) ).
cnf(c_0_28,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_24,c_0_25]),c_0_16]),c_0_17]),c_0_26]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SEU049+1 : TPTP v8.1.2. Bugfixed v4.0.0.
% 0.10/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.32 % Computer : n024.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Wed Aug 23 17:23:09 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.16/0.59 start to proof: theBenchmark
% 0.50/0.77 % Version : CSE_E---1.5
% 0.50/0.77 % Problem : theBenchmark.p
% 0.50/0.77 % Proof found
% 0.50/0.77 % SZS status Theorem for theBenchmark.p
% 0.50/0.77 % SZS output start Proof
% See solution above
% 0.50/0.77 % Total time : 0.176000 s
% 0.50/0.77 % SZS output end Proof
% 0.50/0.77 % Total time : 0.178000 s
%------------------------------------------------------------------------------