TSTP Solution File: SET015-4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET015-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 14:32:06 EDT 2023
% Result : Unsatisfiable 4.25s 4.32s
% Output : CNFRefutation 4.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 25
% Syntax : Number of formulae : 108 ( 27 unt; 12 typ; 0 def)
% Number of atoms : 195 ( 65 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 174 ( 75 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 146 ( 12 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
little_set: $i > $o ).
tff(decl_24,type,
f1: ( $i * $i ) > $i ).
tff(decl_25,type,
intersection: ( $i * $i ) > $i ).
tff(decl_26,type,
complement: $i > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
universal_set: $i ).
tff(decl_30,type,
as: $i ).
tff(decl_31,type,
bs: $i ).
tff(decl_32,type,
cs: $i ).
tff(decl_33,type,
ds: $i ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
cnf(extensionality1,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
cnf(b_union_a_is_d,hypothesis,
union(bs,as) = ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
cnf(a_union_b_is_c,hypothesis,
union(as,bs) = cs,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).
cnf(prove_c_equals_d,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_13,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_14,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_15,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_16,plain,
( empty_set = X1
| member(f1(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_18,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_19,plain,
( intersection(X1,X2) = empty_set
| member(f1(empty_set,intersection(X1,X2)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,plain,
( intersection(X1,X2) = empty_set
| member(f1(empty_set,intersection(X1,X2)),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
( intersection(X1,complement(X2)) = empty_set
| ~ member(f1(empty_set,intersection(X1,complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
( intersection(intersection(X1,X2),X3) = empty_set
| member(f1(empty_set,intersection(intersection(X1,X2),X3)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_23,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_24,plain,
intersection(intersection(X1,X2),complement(X2)) = empty_set,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_26,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
extensionality1 ).
cnf(c_0_27,plain,
( ~ member(X1,intersection(X2,X3))
| ~ member(X1,complement(X3)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_13]) ).
cnf(c_0_28,plain,
( intersection(complement(X1),X2) = empty_set
| ~ member(f1(empty_set,intersection(complement(X1),X2)),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_29,plain,
( X1 = X2
| member(f1(X1,X2),complement(X3))
| member(f1(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( complement(X1) = X2
| member(f1(complement(X1),X2),X2)
| ~ member(f1(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_31,plain,
( intersection(X1,X2) = empty_set
| ~ member(f1(empty_set,intersection(X1,X2)),complement(X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_32,plain,
( intersection(complement(complement(X1)),X2) = empty_set
| member(f1(empty_set,intersection(complement(complement(X1)),X2)),X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,plain,
( complement(complement(X1)) = X2
| member(f1(complement(complement(X1)),X2),X1)
| member(f1(complement(complement(X1)),X2),X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,plain,
intersection(complement(complement(complement(X1))),X1) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_36,plain,
( complement(complement(X1)) = X1
| member(f1(complement(complement(X1)),X1),X1) ),
inference(ef,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
( ~ member(X1,complement(complement(complement(X2))))
| ~ member(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_34]),c_0_13]) ).
cnf(c_0_38,plain,
( intersection(X1,X2) = X3
| member(f1(intersection(X1,X2),X3),X3)
| member(f1(intersection(X1,X2),X3),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_39,hypothesis,
union(bs,as) = ds,
b_union_a_is_d ).
cnf(c_0_40,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_41,plain,
( intersection(intersection(X1,X2),X3) = empty_set
| member(f1(empty_set,intersection(intersection(X1,X2),X3)),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_42,hypothesis,
union(as,bs) = cs,
a_union_b_is_c ).
cnf(c_0_43,plain,
( complement(complement(X1)) = X1
| ~ member(f1(complement(complement(X1)),X1),complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,plain,
( X1 = X2
| member(f1(X1,X2),complement(complement(X3)))
| ~ member(f1(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_45,plain,
( intersection(X1,X2) = X1
| member(f1(intersection(X1,X2),X1),X1) ),
inference(ef,[status(thm)],[c_0_38]) ).
cnf(c_0_46,plain,
intersection(intersection(X1,complement(X2)),X2) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_22]) ).
cnf(c_0_47,hypothesis,
complement(intersection(complement(bs),complement(as))) = ds,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
intersection(intersection(complement(X1),X2),X1) = empty_set,
inference(spm,[status(thm)],[c_0_31,c_0_41]) ).
cnf(c_0_49,hypothesis,
complement(intersection(complement(as),complement(bs))) = cs,
inference(rw,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_50,plain,
complement(complement(X1)) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_36]) ).
cnf(c_0_51,plain,
( intersection(X1,X2) = X1
| ~ member(f1(intersection(X1,X2),X1),intersection(X1,X2)) ),
inference(spm,[status(thm)],[c_0_35,c_0_45]) ).
cnf(c_0_52,plain,
( ~ member(X1,intersection(X2,complement(X3)))
| ~ member(X1,X3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_13]) ).
cnf(c_0_53,hypothesis,
( X1 = X2
| member(f1(X1,X2),intersection(complement(bs),complement(as)))
| member(f1(X1,X2),ds) ),
inference(spm,[status(thm)],[c_0_29,c_0_47]) ).
cnf(c_0_54,plain,
( ~ member(X1,intersection(complement(X2),X3))
| ~ member(X1,X2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_48]),c_0_13]) ).
cnf(c_0_55,hypothesis,
( X1 = X2
| member(f1(X1,X2),intersection(complement(as),complement(bs)))
| member(f1(X1,X2),cs) ),
inference(spm,[status(thm)],[c_0_29,c_0_49]) ).
cnf(c_0_56,hypothesis,
( ~ member(X1,intersection(complement(bs),complement(as)))
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_18,c_0_47]) ).
cnf(c_0_57,hypothesis,
intersection(complement(as),complement(bs)) = complement(cs),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_58,plain,
( intersection(X1,X2) = X1
| ~ member(f1(intersection(X1,X2),X1),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_23]),c_0_45]) ).
cnf(c_0_59,hypothesis,
( X1 = X2
| member(f1(X1,X2),ds)
| ~ member(f1(X1,X2),as) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,hypothesis,
( X1 = X2
| member(f1(X1,X2),cs)
| ~ member(f1(X1,X2),as) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,hypothesis,
( X1 = X2
| member(f1(X1,X2),ds)
| ~ member(f1(X1,X2),bs) ),
inference(spm,[status(thm)],[c_0_54,c_0_53]) ).
cnf(c_0_62,hypothesis,
( X1 = X2
| member(f1(X1,X2),cs)
| ~ member(f1(X1,X2),bs) ),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
cnf(c_0_63,hypothesis,
( ~ member(X1,complement(as))
| ~ member(X1,complement(bs))
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_56,c_0_23]) ).
cnf(c_0_64,hypothesis,
( member(X1,complement(as))
| ~ member(X1,complement(cs)) ),
inference(spm,[status(thm)],[c_0_17,c_0_57]) ).
cnf(c_0_65,hypothesis,
( member(X1,complement(bs))
| ~ member(X1,complement(cs)) ),
inference(spm,[status(thm)],[c_0_15,c_0_57]) ).
cnf(c_0_66,plain,
( X1 = complement(X2)
| member(f1(X1,complement(X2)),X2)
| ~ member(f1(X1,complement(X2)),X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_29]) ).
cnf(c_0_67,hypothesis,
( intersection(X1,ds) = X1
| ~ member(f1(intersection(X1,ds),X1),as) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_68,hypothesis,
( intersection(as,X1) = empty_set
| member(f1(empty_set,intersection(as,X1)),cs) ),
inference(spm,[status(thm)],[c_0_60,c_0_20]) ).
cnf(c_0_69,hypothesis,
( ~ member(X1,intersection(complement(as),complement(bs)))
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_18,c_0_49]) ).
cnf(c_0_70,hypothesis,
( intersection(X1,ds) = X1
| ~ member(f1(intersection(X1,ds),X1),bs) ),
inference(spm,[status(thm)],[c_0_58,c_0_61]) ).
cnf(c_0_71,hypothesis,
( intersection(X1,cs) = X1
| ~ member(f1(intersection(X1,cs),X1),bs) ),
inference(spm,[status(thm)],[c_0_58,c_0_62]) ).
cnf(c_0_72,hypothesis,
( ~ member(X1,complement(cs))
| ~ member(X1,ds) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_65]) ).
cnf(c_0_73,hypothesis,
( X1 = cs
| member(f1(X1,cs),intersection(complement(as),complement(bs)))
| ~ member(f1(X1,cs),X1) ),
inference(spm,[status(thm)],[c_0_66,c_0_49]) ).
cnf(c_0_74,hypothesis,
intersection(as,ds) = as,
inference(spm,[status(thm)],[c_0_67,c_0_45]) ).
cnf(c_0_75,hypothesis,
intersection(as,complement(cs)) = empty_set,
inference(spm,[status(thm)],[c_0_21,c_0_68]) ).
cnf(c_0_76,hypothesis,
( ~ member(X1,complement(bs))
| ~ member(X1,complement(as))
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_69,c_0_23]) ).
cnf(c_0_77,hypothesis,
intersection(bs,ds) = bs,
inference(spm,[status(thm)],[c_0_70,c_0_45]) ).
cnf(c_0_78,hypothesis,
intersection(bs,cs) = bs,
inference(spm,[status(thm)],[c_0_71,c_0_45]) ).
cnf(c_0_79,hypothesis,
( X1 = X2
| member(f1(X1,X2),cs)
| ~ member(f1(X1,X2),ds) ),
inference(spm,[status(thm)],[c_0_72,c_0_29]) ).
cnf(c_0_80,hypothesis,
( X1 = cs
| member(f1(X1,cs),complement(cs))
| ~ member(f1(X1,cs),X1) ),
inference(rw,[status(thm)],[c_0_73,c_0_57]) ).
cnf(c_0_81,hypothesis,
( member(X1,ds)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_15,c_0_74]) ).
cnf(c_0_82,negated_conjecture,
cs != ds,
prove_c_equals_d ).
cnf(c_0_83,hypothesis,
( ~ member(X1,complement(cs))
| ~ member(X1,as) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_75]),c_0_13]) ).
cnf(c_0_84,hypothesis,
( X1 = X2
| member(f1(X1,X2),as)
| ~ member(f1(X1,X2),complement(bs))
| ~ member(f1(X1,X2),cs) ),
inference(spm,[status(thm)],[c_0_76,c_0_29]) ).
cnf(c_0_85,hypothesis,
( member(X1,ds)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_15,c_0_77]) ).
cnf(c_0_86,hypothesis,
( ~ member(X1,complement(cs))
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_27,c_0_78]) ).
cnf(c_0_87,plain,
( intersection(X1,X2) = X3
| member(f1(intersection(X1,X2),X3),X3)
| member(f1(intersection(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_88,hypothesis,
( intersection(ds,X1) = ds
| member(f1(intersection(ds,X1),ds),cs) ),
inference(spm,[status(thm)],[c_0_79,c_0_45]) ).
cnf(c_0_89,hypothesis,
~ member(f1(ds,cs),as),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_83]) ).
cnf(c_0_90,hypothesis,
( X1 = X2
| member(f1(X1,X2),bs)
| member(f1(X1,X2),as)
| ~ member(f1(X1,X2),cs) ),
inference(spm,[status(thm)],[c_0_84,c_0_29]) ).
cnf(c_0_91,hypothesis,
~ member(f1(ds,cs),bs),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_85]),c_0_82]),c_0_86]) ).
cnf(c_0_92,plain,
( intersection(X1,X2) = X2
| member(f1(intersection(X1,X2),X2),X2) ),
inference(ef,[status(thm)],[c_0_87]) ).
cnf(c_0_93,hypothesis,
intersection(ds,cs) = ds,
inference(spm,[status(thm)],[c_0_58,c_0_88]) ).
cnf(c_0_94,hypothesis,
~ member(f1(ds,cs),cs),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_82]),c_0_91]) ).
cnf(c_0_95,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_82]),c_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET015-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n016.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 14:47:11 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 4.25/4.32 % Version : CSE_E---1.5
% 4.25/4.32 % Problem : theBenchmark.p
% 4.25/4.32 % Proof found
% 4.25/4.32 % SZS status Theorem for theBenchmark.p
% 4.25/4.32 % SZS output start Proof
% See solution above
% 4.25/4.32 % Total time : 3.757000 s
% 4.25/4.32 % SZS output end Proof
% 4.25/4.32 % Total time : 3.759000 s
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