TSTP Solution File: SET595+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET595+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 : n014.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 14:34:41 EDT 2023
% Result : Theorem 2.02s 2.16s
% Output : CNFRefutation 2.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 85 ( 27 unt; 9 typ; 0 def)
% Number of atoms : 157 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 129 ( 48 ~; 61 |; 12 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 7 >; 7 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 173 ( 24 sgn; 35 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
union: ( $i * $i ) > $i ).
tff(decl_24,type,
difference: ( $i * $i ) > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_27,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
fof(prove_th54,conjecture,
! [X1,X2] :
( subset(X1,X2)
=> X2 = union(X1,difference(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th54) ).
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(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(equal_defn,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subset(X1,X2)
& subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_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(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,X2)
=> X2 = union(X1,difference(X2,X1)) ),
inference(assume_negation,[status(cth)],[prove_th54]) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17] :
( ( ~ subset(X13,X14)
| ~ member(X15,X13)
| member(X15,X14) )
& ( member(esk2_2(X16,X17),X16)
| subset(X16,X17) )
& ( ~ member(esk2_2(X16,X17),X17)
| subset(X16,X17) ) ),
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_8,negated_conjecture,
( subset(esk4_0,esk5_0)
& esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
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]) ).
cnf(c_0_10,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,negated_conjecture,
subset(esk4_0,esk5_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X10,X11,X12] :
( ( member(X12,X10)
| ~ member(X12,difference(X10,X11)) )
& ( ~ member(X12,X11)
| ~ member(X12,difference(X10,X11)) )
& ( ~ member(X12,X10)
| member(X12,X11)
| member(X12,difference(X10,X11)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ member(esk2_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,esk4_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( member(X1,X2)
| ~ member(X1,difference(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( member(esk2_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_17,negated_conjecture,
( subset(X1,esk5_0)
| ~ member(esk2_2(X1,esk5_0),esk4_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( subset(difference(X1,X2),X3)
| member(esk2_2(difference(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
subset(difference(esk4_0,X1),esk5_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_20,plain,
! [X19,X20] :
( ( subset(X19,X20)
| X19 != X20 )
& ( subset(X20,X19)
| X19 != X20 )
& ( ~ subset(X19,X20)
| ~ subset(X20,X19)
| X19 = X20 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equal_defn])])]) ).
cnf(c_0_21,plain,
( ~ member(X1,X2)
| ~ member(X1,difference(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( member(X1,esk5_0)
| ~ member(X1,difference(esk4_0,X2)) ),
inference(spm,[status(thm)],[c_0_10,c_0_19]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
subset(difference(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_25,plain,
( subset(difference(X1,X2),X3)
| ~ member(esk2_2(difference(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_26,negated_conjecture,
( subset(difference(esk4_0,X1),X2)
| member(esk2_2(difference(esk4_0,X1),X2),esk5_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
fof(c_0_27,plain,
! [X7,X8,X9] :
( ( ~ member(X9,union(X7,X8))
| member(X9,X7)
| member(X9,X8) )
& ( ~ member(X9,X7)
| member(X9,union(X7,X8)) )
& ( ~ member(X9,X8)
| member(X9,union(X7,X8)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[union_defn])])]) ).
cnf(c_0_28,plain,
( member(X1,X3)
| member(X1,difference(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_29,plain,
( difference(X1,X2) = X1
| ~ subset(X1,difference(X1,X2)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
subset(difference(esk4_0,esk5_0),X1),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
( subset(X1,difference(X2,X3))
| member(esk2_2(X1,difference(X2,X3)),X3)
| ~ member(esk2_2(X1,difference(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_33,plain,
( subset(difference(difference(X1,X2),X3),X4)
| member(esk2_2(difference(difference(X1,X2),X3),X4),X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_34,plain,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_35,negated_conjecture,
difference(difference(esk4_0,esk5_0),X1) = difference(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
( subset(difference(difference(X1,X2),X3),X4)
| ~ member(esk2_2(difference(difference(X1,X2),X3),X4),X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_37,plain,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
( subset(difference(X1,difference(X2,X3)),X4)
| member(esk2_2(difference(X1,difference(X2,X3)),X4),X3)
| ~ member(esk2_2(difference(X1,difference(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_39,negated_conjecture,
( subset(difference(difference(esk4_0,X1),X2),X3)
| member(esk2_2(difference(difference(esk4_0,X1),X2),X3),esk5_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_40,plain,
( subset(difference(X1,union(X2,X3)),X4)
| ~ member(esk2_2(difference(X1,union(X2,X3)),X4),X2) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_41,plain,
( subset(X1,difference(X1,X2))
| member(esk2_2(X1,difference(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_16]) ).
cnf(c_0_42,plain,
subset(difference(difference(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_13,c_0_33]) ).
cnf(c_0_43,plain,
( subset(union(X1,X2),X3)
| member(esk2_2(union(X1,X2),X3),X1)
| member(esk2_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_16]) ).
fof(c_0_44,plain,
! [X21,X22] : union(X21,X22) = union(X22,X21),
inference(variable_rename,[status(thm)],[commutativity_of_union]) ).
cnf(c_0_45,negated_conjecture,
( ~ member(X1,difference(esk4_0,esk5_0))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_35]) ).
cnf(c_0_46,plain,
( subset(difference(difference(X1,union(X2,X3)),X4),X5)
| ~ member(esk2_2(difference(difference(X1,union(X2,X3)),X4),X5),X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_47,negated_conjecture,
( subset(difference(difference(esk4_0,X1),difference(esk5_0,X2)),X3)
| member(esk2_2(difference(difference(esk4_0,X1),difference(esk5_0,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_48,plain,
subset(difference(X1,union(X2,X3)),difference(difference(X1,union(X2,X3)),X2)),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_49,plain,
( member(X1,X2)
| ~ member(X1,difference(difference(X2,X3),X4)) ),
inference(spm,[status(thm)],[c_0_10,c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( subset(union(X1,esk4_0),esk5_0)
| member(esk2_2(union(X1,esk4_0),esk5_0),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_43]) ).
cnf(c_0_51,plain,
union(X1,X2) = union(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,negated_conjecture,
~ member(X1,difference(esk4_0,esk5_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_30]),c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( subset(difference(esk4_0,X1),difference(esk5_0,X2))
| member(esk2_2(difference(esk4_0,X1),difference(esk5_0,X2)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_54,negated_conjecture,
subset(difference(difference(esk4_0,union(X1,X2)),difference(esk5_0,X2)),X3),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_55,plain,
difference(difference(X1,union(X2,X3)),X2) = difference(X1,union(X2,X3)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_48]),c_0_24])]) ).
cnf(c_0_56,plain,
( subset(difference(difference(X1,X2),difference(X1,X3)),X4)
| member(esk2_2(difference(difference(X1,X2),difference(X1,X3)),X4),X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_57,negated_conjecture,
( subset(union(esk4_0,difference(difference(X1,X2),X3)),esk5_0)
| member(esk2_2(union(esk4_0,difference(difference(X1,X2),X3)),esk5_0),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_51]) ).
cnf(c_0_58,negated_conjecture,
subset(X1,difference(X1,difference(esk4_0,esk5_0))),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
cnf(c_0_59,negated_conjecture,
subset(difference(esk4_0,X1),difference(esk5_0,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( X1 = difference(esk4_0,esk5_0)
| ~ subset(X1,difference(esk4_0,esk5_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_61,negated_conjecture,
subset(difference(esk4_0,union(X1,difference(esk5_0,X1))),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51]) ).
cnf(c_0_62,plain,
subset(difference(difference(X1,union(X2,X3)),difference(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_46,c_0_56]) ).
cnf(c_0_63,negated_conjecture,
subset(union(esk4_0,difference(difference(esk5_0,X1),X2)),esk5_0),
inference(spm,[status(thm)],[c_0_13,c_0_57]) ).
cnf(c_0_64,negated_conjecture,
difference(X1,difference(esk4_0,esk5_0)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_58]),c_0_24])]) ).
cnf(c_0_65,plain,
( subset(difference(X1,difference(X1,X2)),X3)
| member(esk2_2(difference(X1,difference(X1,X2)),X3),X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_66,negated_conjecture,
( difference(esk5_0,X1) = difference(esk4_0,X1)
| ~ subset(difference(esk5_0,X1),difference(esk4_0,X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_59]) ).
cnf(c_0_67,negated_conjecture,
difference(esk4_0,union(X1,difference(esk5_0,X1))) = difference(esk4_0,esk5_0),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,plain,
subset(difference(X1,union(X2,difference(X1,X2))),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_55]),c_0_51]) ).
cnf(c_0_69,negated_conjecture,
subset(union(esk4_0,difference(esk5_0,X1)),esk5_0),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_70,plain,
subset(difference(X1,difference(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_13,c_0_65]) ).
cnf(c_0_71,negated_conjecture,
difference(esk5_0,union(X1,difference(esk5_0,X1))) = difference(esk4_0,esk5_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68])]) ).
cnf(c_0_72,negated_conjecture,
( union(esk4_0,difference(esk5_0,X1)) = esk5_0
| ~ subset(esk5_0,union(esk4_0,difference(esk5_0,X1))) ),
inference(spm,[status(thm)],[c_0_23,c_0_69]) ).
cnf(c_0_73,negated_conjecture,
subset(esk5_0,union(X1,difference(esk5_0,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_64]) ).
cnf(c_0_74,negated_conjecture,
esk5_0 != union(esk4_0,difference(esk5_0,esk4_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET595+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 : n014.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 12:16:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 2.02/2.16 % Version : CSE_E---1.5
% 2.02/2.16 % Problem : theBenchmark.p
% 2.02/2.16 % Proof found
% 2.02/2.16 % SZS status Theorem for theBenchmark.p
% 2.02/2.16 % SZS output start Proof
% See solution above
% 2.02/2.17 % Total time : 1.571000 s
% 2.02/2.17 % SZS output end Proof
% 2.02/2.17 % Total time : 1.574000 s
%------------------------------------------------------------------------------