TSTP Solution File: SET008+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET008+3 : 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 : n023.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 14:31:58 EDT 2023
% Result : Theorem 0.54s 0.59s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 47 ( 15 unt; 11 typ; 0 def)
% Number of atoms : 84 ( 17 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 84 ( 36 ~; 30 |; 11 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 72 ( 7 sgn; 42 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersection: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
empty_set: $i ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_1: $i > $i ).
tff(decl_30,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
fof(empty_defn,axiom,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_defn) ).
fof(empty_set_defn,axiom,
! [X1] : ~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).
fof(difference_defn,axiom,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
fof(intersection_defn,axiom,
! [X1,X2,X3] :
( member(X3,intersection(X1,X2))
<=> ( member(X3,X1)
& member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
fof(equal_member_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ! [X3] :
( member(X3,X1)
<=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
fof(prove_intersection_difference_empty_set,conjecture,
! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_intersection_difference_empty_set) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(c_0_7,plain,
! [X1] :
( empty(X1)
<=> ! [X2] : ~ member(X2,X1) ),
inference(fof_simplification,[status(thm)],[empty_defn]) ).
fof(c_0_8,plain,
! [X1] : ~ member(X1,empty_set),
inference(fof_simplification,[status(thm)],[empty_set_defn]) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( member(X3,difference(X1,X2))
<=> ( member(X3,X1)
& ~ member(X3,X2) ) ),
inference(fof_simplification,[status(thm)],[difference_defn]) ).
fof(c_0_10,plain,
! [X4,X5,X6] :
( ( member(X6,X4)
| ~ member(X6,intersection(X4,X5)) )
& ( member(X6,X5)
| ~ member(X6,intersection(X4,X5)) )
& ( ~ member(X6,X4)
| ~ member(X6,X5)
| member(X6,intersection(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[intersection_defn])])]) ).
fof(c_0_11,plain,
! [X22,X23,X24] :
( ( ~ empty(X22)
| ~ member(X23,X22) )
& ( member(esk2_1(X24),X24)
| empty(X24) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])])]) ).
fof(c_0_12,plain,
! [X10] : ~ member(X10,empty_set),
inference(variable_rename,[status(thm)],[c_0_8]) ).
fof(c_0_13,plain,
! [X26,X27,X28,X29,X30,X31] :
( ( ~ member(X28,X26)
| member(X28,X27)
| X26 != X27 )
& ( ~ member(X29,X27)
| member(X29,X26)
| X26 != X27 )
& ( ~ member(esk3_2(X30,X31),X30)
| ~ member(esk3_2(X30,X31),X31)
| X30 = X31 )
& ( member(esk3_2(X30,X31),X30)
| member(esk3_2(X30,X31),X31)
| X30 = X31 ) ),
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)],[equal_member_defn])])])])])]) ).
fof(c_0_14,plain,
! [X7,X8,X9] :
( ( member(X9,X7)
| ~ member(X9,difference(X7,X8)) )
& ( ~ member(X9,X8)
| ~ member(X9,difference(X7,X8)) )
& ( ~ member(X9,X7)
| member(X9,X8)
| member(X9,difference(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( member(esk2_1(X1),X1)
| empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_17,negated_conjecture,
~ ! [X1,X2] : intersection(difference(X1,X2),X2) = empty_set,
inference(assume_negation,[status(cth)],[prove_intersection_difference_empty_set]) ).
cnf(c_0_18,plain,
~ member(X1,empty_set),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( member(esk3_2(X1,X2),X1)
| member(esk3_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,plain,
( empty(intersection(X1,X2))
| member(esk2_1(intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_23,negated_conjecture,
intersection(difference(esk4_0,esk5_0),esk5_0) != empty_set,
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
fof(c_0_24,plain,
! [X13,X14] : intersection(X13,X14) = intersection(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_25,plain,
( ~ empty(X1)
| ~ member(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_26,plain,
( empty_set = X1
| member(esk3_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_27,plain,
( empty(intersection(X1,difference(X2,X3)))
| ~ member(esk2_1(intersection(X1,difference(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
( empty(intersection(X1,X2))
| member(esk2_1(intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_29,negated_conjecture,
intersection(difference(esk4_0,esk5_0),esk5_0) != empty_set,
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_30,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_31,plain,
( empty_set = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
empty(intersection(X1,difference(X2,X1))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,negated_conjecture,
intersection(esk5_0,difference(esk4_0,esk5_0)) != empty_set,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
intersection(X1,difference(X2,X1)) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET008+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n023.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 15:08:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.54/0.59 % Version : CSE_E---1.5
% 0.54/0.59 % Problem : theBenchmark.p
% 0.54/0.59 % Proof found
% 0.54/0.59 % SZS status Theorem for theBenchmark.p
% 0.54/0.59 % SZS output start Proof
% See solution above
% 0.54/0.60 % Total time : 0.019000 s
% 0.54/0.60 % SZS output end Proof
% 0.54/0.60 % Total time : 0.022000 s
%------------------------------------------------------------------------------