TSTP Solution File: SET143+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET143+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 : n025.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 14:33:17 EDT 2023
% Result : Theorem 3.02s 3.08s
% Output : CNFRefutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 30 unt; 8 typ; 0 def)
% Number of atoms : 137 ( 35 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 114 ( 42 ~; 55 |; 11 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 178 ( 15 sgn; 37 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
intersection: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_26,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk3_0: $i ).
tff(decl_28,type,
esk4_0: $i ).
tff(decl_29,type,
esk5_0: $i ).
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(subset_defn,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
fof(commutativity_of_intersection,axiom,
! [X1,X2] : intersection(X1,X2) = intersection(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
fof(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
fof(prove_associativity_of_intersection,conjecture,
! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
fof(c_0_6,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_7,plain,
! [X18,X19,X20,X21,X22,X23] :
( ( ~ member(X20,X18)
| member(X20,X19)
| X18 != X19 )
& ( ~ member(X21,X19)
| member(X21,X18)
| X18 != X19 )
& ( ~ member(esk2_2(X22,X23),X22)
| ~ member(esk2_2(X22,X23),X23)
| X22 = X23 )
& ( member(esk2_2(X22,X23),X22)
| member(esk2_2(X22,X23),X23)
| X22 = X23 ) ),
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_8,plain,
! [X11,X12,X13,X14,X15] :
( ( ~ subset(X11,X12)
| ~ member(X13,X11)
| member(X13,X12) )
& ( member(esk1_2(X14,X15),X14)
| subset(X14,X15) )
& ( ~ member(esk1_2(X14,X15),X15)
| subset(X14,X15) ) ),
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_defn])])])])])]) ).
cnf(c_0_9,plain,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( member(esk2_2(X1,X2),X1)
| member(esk2_2(X1,X2),X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( member(X1,X2)
| ~ member(X1,intersection(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
( intersection(X1,X2) = X3
| member(esk2_2(intersection(X1,X2),X3),X3)
| member(esk2_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_16,plain,
( subset(X1,intersection(X2,X3))
| ~ member(esk1_2(X1,intersection(X2,X3)),X3)
| ~ member(esk1_2(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_19,plain,
( X1 = X2
| ~ member(esk2_2(X1,X2),X1)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,plain,
( intersection(X1,X2) = X1
| member(esk2_2(intersection(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( subset(intersection(X1,X2),intersection(X3,X2))
| ~ member(esk1_2(intersection(X1,X2),intersection(X3,X2)),X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( subset(intersection(intersection(X1,X2),X3),X4)
| member(esk1_2(intersection(intersection(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
fof(c_0_23,plain,
! [X9,X10] : intersection(X9,X10) = intersection(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_intersection]) ).
cnf(c_0_24,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,X3)),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
intersection(X1,X2) = intersection(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
( intersection(X1,X2) = X1
| ~ member(esk2_2(intersection(X1,X2),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_12]),c_0_20]) ).
fof(c_0_28,plain,
! [X7,X8] :
( ( subset(X7,X8)
| X7 != X8 )
& ( subset(X8,X7)
| X7 != X8 )
& ( ~ subset(X7,X8)
| ~ subset(X8,X7)
| X7 = X8 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_29,plain,
( subset(X1,intersection(X2,X1))
| ~ member(esk1_2(X1,intersection(X2,X1)),X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_30,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_17]) ).
cnf(c_0_31,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_32,plain,
intersection(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_33,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,intersection(X2,X3)))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
subset(intersection(X1,X2),X2),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_36,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_37,plain,
subset(intersection(X1,X2),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_39,plain,
intersection(X1,intersection(X2,intersection(X1,X3))) = intersection(X2,intersection(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_40,plain,
subset(intersection(intersection(X1,X2),X3),intersection(X1,intersection(intersection(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_34,c_0_26]) ).
cnf(c_0_41,plain,
( member(X1,intersection(X2,X3))
| ~ member(X1,intersection(X3,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( subset(intersection(X1,intersection(X2,X3)),X4)
| member(esk1_2(intersection(X1,intersection(X2,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_43,plain,
subset(intersection(X1,intersection(X2,intersection(X3,X4))),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
intersection(X1,intersection(intersection(X1,X2),X3)) = intersection(intersection(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_40]),c_0_35])]) ).
cnf(c_0_45,plain,
( subset(intersection(X1,X2),X3)
| member(esk1_2(intersection(X1,X2),X3),intersection(X2,X1)) ),
inference(spm,[status(thm)],[c_0_41,c_0_14]) ).
cnf(c_0_46,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X3,intersection(X1,intersection(X2,X3)))),
inference(spm,[status(thm)],[c_0_29,c_0_42]) ).
cnf(c_0_47,plain,
subset(intersection(intersection(X1,X2),intersection(X3,X4)),intersection(X3,X1)),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_48,plain,
subset(intersection(X1,X2),intersection(intersection(X2,X1),intersection(X1,X2))),
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_49,plain,
( intersection(X1,intersection(X2,X3)) = X1
| ~ member(esk2_2(intersection(X1,intersection(X2,X3)),X1),X3)
| ~ member(esk2_2(intersection(X1,intersection(X2,X3)),X1),X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_12]) ).
cnf(c_0_50,plain,
( intersection(intersection(X1,X2),X3) = intersection(X1,X2)
| member(esk2_2(intersection(intersection(X1,X2),X3),intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_51,plain,
intersection(X1,intersection(X2,intersection(X3,X1))) = intersection(X2,intersection(X3,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_46]),c_0_35])]) ).
fof(c_0_52,negated_conjecture,
~ ! [X1,X2,X3] : intersection(intersection(X1,X2),X3) = intersection(X1,intersection(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_intersection]) ).
cnf(c_0_53,plain,
subset(intersection(intersection(X1,X2),intersection(X3,intersection(X4,X5))),intersection(X4,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_39]) ).
cnf(c_0_54,plain,
intersection(intersection(X1,X2),intersection(X2,X1)) = intersection(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_48]),c_0_35])]) ).
cnf(c_0_55,plain,
( intersection(intersection(X1,X2),intersection(X3,X1)) = intersection(X1,X2)
| ~ member(esk2_2(intersection(intersection(X1,X2),intersection(X3,X1)),intersection(X1,X2)),X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,plain,
( intersection(intersection(X1,intersection(X2,X3)),X4) = intersection(X1,intersection(X2,X3))
| member(esk2_2(intersection(intersection(X1,intersection(X2,X3)),X4),intersection(X1,intersection(X2,X3))),X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
fof(c_0_57,negated_conjecture,
intersection(intersection(esk3_0,esk4_0),esk5_0) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])]) ).
cnf(c_0_58,plain,
subset(intersection(intersection(X1,X2),intersection(X3,intersection(X4,X5))),intersection(X4,intersection(X2,X1))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
intersection(intersection(X1,X2),intersection(X2,intersection(X3,X1))) = intersection(X2,intersection(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_26]) ).
cnf(c_0_60,negated_conjecture,
intersection(intersection(esk3_0,esk4_0),esk5_0) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_61,plain,
subset(intersection(X1,intersection(X2,X3)),intersection(X2,intersection(X1,X3))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_62,negated_conjecture,
intersection(esk5_0,intersection(esk3_0,esk4_0)) != intersection(esk3_0,intersection(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_60,c_0_26]) ).
cnf(c_0_63,plain,
intersection(X1,intersection(X2,X3)) = intersection(X2,intersection(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_61]),c_0_61])]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET143+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 15:10:08 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 3.02/3.08 % Version : CSE_E---1.5
% 3.02/3.08 % Problem : theBenchmark.p
% 3.02/3.08 % Proof found
% 3.02/3.08 % SZS status Theorem for theBenchmark.p
% 3.02/3.08 % SZS output start Proof
% See solution above
% 3.02/3.09 % Total time : 2.508000 s
% 3.02/3.09 % SZS output end Proof
% 3.02/3.09 % Total time : 2.511000 s
%------------------------------------------------------------------------------