TSTP Solution File: SET767+4 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET767+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 14:35:29 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 45
% Syntax : Number of formulae : 56 ( 4 unt; 42 typ; 0 def)
% Number of atoms : 36 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 34 ( 12 ~; 11 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 75 ( 38 >; 37 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 4 con; 0-3 aty)
% Number of variables : 30 ( 2 sgn; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_35,type,
partition: ( $i * $i ) > $o ).
tff(decl_36,type,
equivalence: ( $i * $i ) > $o ).
tff(decl_37,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
equivalence_class: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
pre_order: ( $i * $i ) > $o ).
tff(decl_40,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_41,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_42,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk15_0: $i ).
tff(decl_56,type,
esk16_0: $i ).
tff(decl_57,type,
esk17_0: $i ).
tff(decl_58,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk23_2: ( $i * $i ) > $i ).
fof(thIII03,conjecture,
! [X4,X7,X1] :
( equivalence(X7,X4)
=> subset(equivalence_class(X1,X4,X7),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII03) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(equivalence_class,axiom,
! [X7,X4,X1,X3] :
( member(X3,equivalence_class(X1,X4,X7))
<=> ( member(X3,X4)
& apply(X7,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(c_0_3,negated_conjecture,
~ ! [X4,X7,X1] :
( equivalence(X7,X4)
=> subset(equivalence_class(X1,X4,X7),X4) ),
inference(assume_negation,[status(cth)],[thIII03]) ).
fof(c_0_4,negated_conjecture,
( equivalence(esk16_0,esk15_0)
& ~ subset(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X8,X9,X10,X11,X12] :
( ( ~ subset(X8,X9)
| ~ member(X10,X8)
| member(X10,X9) )
& ( member(esk1_2(X11,X12),X11)
| subset(X11,X12) )
& ( ~ member(esk1_2(X11,X12),X12)
| subset(X11,X12) ) ),
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)],[subset])])])])])]) ).
fof(c_0_6,plain,
! [X69,X70,X71,X72] :
( ( member(X72,X70)
| ~ member(X72,equivalence_class(X71,X70,X69)) )
& ( apply(X69,X71,X72)
| ~ member(X72,equivalence_class(X71,X70,X69)) )
& ( ~ member(X72,X70)
| ~ apply(X69,X71,X72)
| member(X72,equivalence_class(X71,X70,X69)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_class])])]) ).
cnf(c_0_7,negated_conjecture,
~ subset(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( member(X1,X2)
| ~ member(X1,equivalence_class(X3,X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
member(esk1_2(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0),equivalence_class(esk17_0,esk15_0,esk16_0)),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
member(esk1_2(equivalence_class(esk17_0,esk15_0,esk16_0),esk15_0),esk15_0),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_7]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET767+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 08:36:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.030000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.032000 s
%------------------------------------------------------------------------------