TSTP Solution File: SET159+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET159+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 : n003.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 14:33:23 EDT 2023
% Result : Theorem 5.28s 5.42s
% Output : CNFRefutation 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 79 ( 41 unt; 8 typ; 0 def)
% Number of atoms : 124 ( 22 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 84 ( 31 ~; 42 |; 7 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 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 : 197 ( 26 sgn; 28 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
union: ( $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(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(union_defn,axiom,
! [X1,X2,X3] :
( member(X3,union(X1,X2))
<=> ( member(X3,X1)
| member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
fof(commutativity_of_union,axiom,
! [X1,X2] : union(X1,X2) = union(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
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_union,conjecture,
! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_union) ).
fof(c_0_5,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])])])])])]) ).
fof(c_0_6,plain,
! [X4,X5,X6] :
( ( ~ member(X6,union(X4,X5))
| member(X6,X4)
| member(X6,X5) )
& ( ~ member(X6,X4)
| member(X6,union(X4,X5)) )
& ( ~ member(X6,X5)
| member(X6,union(X4,X5)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_7,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_10,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
fof(c_0_14,plain,
! [X9,X10] : union(X9,X10) = union(X10,X9),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_15,plain,
( subset(X1,union(X2,X3))
| ~ member(esk1_2(X1,union(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_10]) ).
cnf(c_0_16,plain,
( subset(union(X1,X2),X3)
| member(esk1_2(union(X1,X2),X3),X1)
| member(esk1_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
subset(X1,union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_18,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_20,plain,
( subset(union(X1,X2),union(X3,X2))
| member(esk1_2(union(X1,X2),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
fof(c_0_21,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_22,plain,
( subset(union(X1,X1),X2)
| member(esk1_2(union(X1,X1),X2),X1) ),
inference(ef,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
subset(X1,union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
subset(union(X1,X2),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
subset(union(X1,X1),X1),
inference(spm,[status(thm)],[c_0_7,c_0_22]) ).
cnf(c_0_27,plain,
subset(X1,union(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_12]) ).
cnf(c_0_28,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_29,plain,
subset(X1,union(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_30,plain,
subset(union(X1,X2),union(X2,union(X3,X1))),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_31,plain,
union(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27])]) ).
cnf(c_0_32,plain,
( member(X1,union(union(X2,X3),X4))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( subset(X1,union(X2,union(X3,X4)))
| ~ member(esk1_2(X1,union(X2,union(X3,X4))),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_34,plain,
( subset(union(X1,X2),X2)
| member(esk1_2(union(X1,X2),X2),X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_16]) ).
cnf(c_0_35,plain,
subset(union(X1,X2),union(X2,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_36,plain,
( subset(X1,union(X2,union(union(X3,X4),X5)))
| ~ member(esk1_2(X1,union(X2,union(union(X3,X4),X5))),X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_32]) ).
cnf(c_0_37,plain,
( subset(union(X1,X2),union(X2,X3))
| member(esk1_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_38,plain,
subset(union(X1,union(X2,union(X1,X3))),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
subset(X1,union(X2,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_40,plain,
( member(X1,union(X2,X3))
| ~ member(X1,union(X3,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_35]) ).
cnf(c_0_41,plain,
subset(union(X1,X2),union(X2,union(union(X1,X3),X4))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
union(X1,union(X2,union(X1,X3))) = union(X2,union(X1,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_38]),c_0_39])]) ).
cnf(c_0_43,plain,
subset(union(X1,union(union(X1,X2),X3)),union(union(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_44,plain,
( subset(union(union(X1,X2),X3),X3)
| member(esk1_2(union(union(X1,X2),X3),X3),union(X2,X1)) ),
inference(spm,[status(thm)],[c_0_40,c_0_34]) ).
cnf(c_0_45,plain,
( subset(union(union(X1,X2),X3),X3)
| member(esk1_2(union(union(X1,X2),X3),X3),X1)
| member(esk1_2(union(union(X1,X2),X3),X3),X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_34]) ).
cnf(c_0_46,plain,
subset(union(X1,X2),union(union(X1,X3),union(X2,X4))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_47,plain,
union(X1,union(union(X1,X2),X3)) = union(union(X1,X2),X3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_43]),c_0_39])]) ).
cnf(c_0_48,plain,
subset(union(union(X1,X2),union(X2,X1)),union(X2,X1)),
inference(spm,[status(thm)],[c_0_7,c_0_44]) ).
cnf(c_0_49,plain,
( subset(union(union(X1,X2),union(X3,X2)),union(X3,X2))
| member(esk1_2(union(union(X1,X2),union(X3,X2)),union(X3,X2)),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_45]) ).
cnf(c_0_50,plain,
( subset(X1,union(union(X2,X3),X4))
| ~ member(esk1_2(X1,union(union(X2,X3),X4)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_51,plain,
subset(union(X1,X2),union(union(X1,X3),union(union(X2,X4),X5))),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
union(union(X1,X2),union(X2,X1)) = union(X2,X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_48]),c_0_39])]) ).
cnf(c_0_53,plain,
subset(union(union(X1,X2),union(union(X3,X1),X2)),union(union(X3,X1),X2)),
inference(spm,[status(thm)],[c_0_19,c_0_49]) ).
cnf(c_0_54,plain,
subset(union(X1,X2),union(union(X1,X3),X2)),
inference(spm,[status(thm)],[c_0_50,c_0_20]) ).
cnf(c_0_55,plain,
subset(union(union(X1,X2),X3),union(union(X2,X1),union(union(X3,X4),X5))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
union(union(X1,X2),union(union(X3,X1),X2)) = union(union(X3,X1),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_53]),c_0_39])]) ).
fof(c_0_57,negated_conjecture,
~ ! [X1,X2,X3] : union(union(X1,X2),X3) = union(X1,union(X2,X3)),
inference(assume_negation,[status(cth)],[prove_associativity_of_union]) ).
cnf(c_0_58,plain,
subset(union(X1,X2),union(X2,union(X1,X3))),
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_59,plain,
subset(union(X1,X2),union(union(X2,X3),X1)),
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_60,plain,
subset(union(union(X1,X2),X3),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
fof(c_0_61,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])]) ).
cnf(c_0_62,plain,
subset(union(union(X1,X2),X3),union(X3,union(X2,X1))),
inference(spm,[status(thm)],[c_0_58,c_0_52]) ).
cnf(c_0_63,plain,
subset(union(X1,union(X2,X3)),union(union(X3,X2),X1)),
inference(spm,[status(thm)],[c_0_59,c_0_52]) ).
cnf(c_0_64,plain,
union(union(X1,X2),X3) = union(union(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_60]),c_0_60])]) ).
cnf(c_0_65,negated_conjecture,
union(union(esk3_0,esk4_0),esk5_0) != union(esk3_0,union(esk4_0,esk5_0)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
union(X1,union(X2,X3)) = union(union(X3,X2),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_62]),c_0_63])]) ).
cnf(c_0_67,plain,
union(union(X1,X2),X3) = union(X1,union(X3,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_64]) ).
cnf(c_0_68,negated_conjecture,
union(esk5_0,union(esk3_0,esk4_0)) != union(esk3_0,union(esk4_0,esk5_0)),
inference(rw,[status(thm)],[c_0_65,c_0_18]) ).
cnf(c_0_69,plain,
union(X1,union(X2,X3)) = union(X3,union(X1,X2)),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET159+3 : 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
% 0.13/0.35 % Computer : n003.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 14:59:09 EDT 2023
% 0.20/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 5.28/5.41 % Version : CSE_E---1.5
% 5.28/5.41 % Problem : theBenchmark.p
% 5.28/5.42 % Proof found
% 5.28/5.42 % SZS status Theorem for theBenchmark.p
% 5.28/5.42 % SZS output start Proof
% See solution above
% 5.28/5.42 % Total time : 4.842000 s
% 5.28/5.42 % SZS output end Proof
% 5.28/5.42 % Total time : 4.845000 s
%------------------------------------------------------------------------------