TSTP Solution File: SET701+4 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET701+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 14:35:17 EDT 2023
% Result : Theorem 0.95s 1.02s
% Output : CNFRefutation 0.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 67 ( 6 unt; 19 typ; 0 def)
% Number of atoms : 130 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 135 ( 53 ~; 57 |; 15 &)
% ( 7 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 14 >; 10 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 78 ( 4 sgn; 35 !; 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,
esk1_2: ( $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_0: $i ).
tff(decl_38,type,
esk5_0: $i ).
tff(decl_39,type,
esk6_0: $i ).
tff(decl_40,type,
esk7_0: $i ).
fof(thI35,conjecture,
! [X1,X2,X6,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),intersection(X6,difference(X4,X6))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI35) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(intersection,axiom,
! [X3,X1,X2] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',intersection) ).
fof(difference,axiom,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).
fof(power_set,axiom,
! [X3,X1] :
( member(X3,power_set(X1))
<=> subset(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X6,X4] :
( ( subset(X1,X4)
& subset(X2,X4) )
=> ( subset(X1,X2)
<=> subset(intersection(X1,difference(X4,X2)),intersection(X6,difference(X4,X6))) ) ),
inference(assume_negation,[status(cth)],[thI35]) ).
fof(c_0_6,negated_conjecture,
( subset(esk4_0,esk7_0)
& subset(esk5_0,esk7_0)
& ( ~ subset(esk4_0,esk5_0)
| ~ subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) )
& ( subset(esk4_0,esk5_0)
| subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X7,X8,X9,X10,X11] :
( ( ~ subset(X7,X8)
| ~ member(X9,X7)
| member(X9,X8) )
& ( member(esk1_2(X10,X11),X10)
| subset(X10,X11) )
& ( ~ member(esk1_2(X10,X11),X11)
| subset(X10,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)],[subset])])])])])]) ).
fof(c_0_8,plain,
! [X17,X18,X19] :
( ( member(X17,X18)
| ~ member(X17,intersection(X18,X19)) )
& ( member(X17,X19)
| ~ member(X17,intersection(X18,X19)) )
& ( ~ member(X17,X18)
| ~ member(X17,X19)
| member(X17,intersection(X18,X19)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection])])]) ).
cnf(c_0_9,negated_conjecture,
( ~ subset(esk4_0,esk5_0)
| ~ subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X2,X1,X4] :
( member(X2,difference(X4,X1))
<=> ( member(X2,X4)
& ~ member(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[difference]) ).
cnf(c_0_12,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( subset(esk4_0,esk5_0)
| subset(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
( member(esk1_2(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),intersection(esk4_0,difference(esk7_0,esk5_0)))
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_16,plain,
! [X24,X25,X26] :
( ( member(X24,X26)
| ~ member(X24,difference(X26,X25)) )
& ( ~ member(X24,X25)
| ~ member(X24,difference(X26,X25)) )
& ( ~ member(X24,X26)
| member(X24,X25)
| member(X24,difference(X26,X25)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
cnf(c_0_17,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( member(X1,intersection(esk6_0,difference(esk7_0,esk6_0)))
| subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk7_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( member(esk1_2(X1,X2),X1)
| member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
( member(esk1_2(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),esk4_0)
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_21,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,difference(esk7_0,esk6_0))
| subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk7_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( member(X1,esk6_0)
| subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk7_0,esk5_0))) ),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
( member(esk1_2(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),difference(esk7_0,esk5_0))
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_15]) ).
cnf(c_0_25,negated_conjecture,
( member(esk1_2(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),X1)
| member(esk1_2(esk4_0,X1),esk4_0)
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(X1,intersection(esk4_0,difference(esk7_0,esk5_0))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_28,negated_conjecture,
( ~ member(esk1_2(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),esk5_0)
| ~ subset(esk4_0,esk5_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( member(esk1_2(intersection(esk4_0,difference(esk7_0,esk5_0)),intersection(esk6_0,difference(esk7_0,esk6_0))),X1)
| member(esk1_2(esk4_0,esk5_0),esk4_0)
| member(esk1_2(esk4_0,X1),esk4_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_10]) ).
fof(c_0_30,plain,
! [X15,X16] :
( ( ~ member(X15,power_set(X16))
| subset(X15,X16) )
& ( ~ subset(X15,X16)
| member(X15,power_set(X16)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[power_set])]) ).
cnf(c_0_31,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(X1,difference(esk7_0,esk5_0))
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,negated_conjecture,
member(esk1_2(esk4_0,esk5_0),esk4_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_10]) ).
cnf(c_0_33,negated_conjecture,
subset(esk4_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_34,plain,
( member(X1,power_set(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( subset(esk4_0,esk5_0)
| ~ member(esk1_2(esk4_0,esk5_0),difference(esk7_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( member(X1,esk7_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_12,c_0_33]) ).
cnf(c_0_37,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_38,plain,
( subset(X1,X2)
| ~ member(X1,power_set(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( member(esk4_0,power_set(esk5_0))
| ~ member(esk1_2(esk4_0,esk5_0),difference(esk7_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_41,negated_conjecture,
member(esk1_2(esk4_0,esk5_0),esk7_0),
inference(spm,[status(thm)],[c_0_36,c_0_32]) ).
cnf(c_0_42,plain,
( member(X1,power_set(X2))
| ~ member(esk1_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_37]) ).
cnf(c_0_43,plain,
( member(X1,X2)
| ~ member(X3,power_set(X2))
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
member(esk4_0,power_set(esk5_0)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,negated_conjecture,
~ subset(esk4_0,esk5_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_20]),c_0_28]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_38]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET701+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n012.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Sat Aug 26 09:08:55 EDT 2023
% 0.14/0.33 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.95/1.02 % Version : CSE_E---1.5
% 0.95/1.02 % Problem : theBenchmark.p
% 0.95/1.02 % Proof found
% 0.95/1.02 % SZS status Theorem for theBenchmark.p
% 0.95/1.02 % SZS output start Proof
% See solution above
% 0.95/1.03 % Total time : 0.478000 s
% 0.95/1.03 % SZS output end Proof
% 0.95/1.03 % Total time : 0.481000 s
%------------------------------------------------------------------------------