TSTP Solution File: SET013-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET013-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n017.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 14:32:02 EDT 2023
% Result : Unsatisfiable 2.78s 2.85s
% Output : CNFRefutation 2.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 107 ( 20 unt; 13 typ; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 182 ( 91 ~; 91 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 8 >; 7 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 121 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
empty_set: $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(decl_26,type,
complement: $i > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
intersection: ( $i * $i ) > $i ).
tff(decl_29,type,
equal_sets: ( $i * $i ) > $o ).
tff(decl_30,type,
equal_elements: ( $i * $i ) > $o ).
tff(decl_31,type,
as: $i ).
tff(decl_32,type,
bs: $i ).
tff(decl_33,type,
cs: $i ).
tff(decl_34,type,
ds: $i ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
cnf(member_of_set_or_complement,axiom,
( member(X1,X2)
| member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_set_or_complement) ).
cnf(not_member_of_set_and_complement,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',not_member_of_set_and_complement) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
cnf(symmetry_for_set_equal,axiom,
( equal_sets(X2,X1)
| ~ equal_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',symmetry_for_set_equal) ).
cnf(intersection_of_a_and_b_is_c,hypothesis,
equal_sets(intersection(as,bs),cs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_a_and_b_is_c) ).
cnf(transitivity_for_set_equal,axiom,
( equal_sets(X1,X3)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',transitivity_for_set_equal) ).
cnf(intersection_of_b_and_a_is_d,hypothesis,
equal_sets(intersection(bs,as),ds),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_of_b_and_a_is_d) ).
cnf(subsets_are_set_equal_sets,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
cnf(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
cnf(set_equal_sets_are_subsets2,axiom,
( subset(X2,X1)
| ~ equal_sets(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',set_equal_sets_are_subsets2) ).
cnf(member_of_both_is_member_of_intersection,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_both_is_member_of_intersection) ).
cnf(member_of_intersection_is_member_of_set1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set1) ).
cnf(member_of_intersection_is_member_of_set2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET002-0.ax',member_of_intersection_is_member_of_set2) ).
cnf(prove_c_equals_d,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_equals_d) ).
cnf(c_0_15,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_16,axiom,
( member(X1,X2)
| member(X1,complement(X2)) ),
member_of_set_or_complement ).
cnf(c_0_17,axiom,
( ~ member(X1,X2)
| ~ member(X1,complement(X2)) ),
not_member_of_set_and_complement ).
cnf(c_0_18,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_19,axiom,
( equal_sets(X2,X1)
| ~ equal_sets(X1,X2) ),
symmetry_for_set_equal ).
cnf(c_0_20,hypothesis,
equal_sets(intersection(as,bs),cs),
intersection_of_a_and_b_is_c ).
cnf(c_0_21,plain,
( subset(X1,complement(X2))
| member(member_of_1_not_of_2(X1,complement(X2)),X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( subset(complement(X1),X2)
| ~ member(member_of_1_not_of_2(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
( equal_sets(X1,X3)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X2,X3) ),
transitivity_for_set_equal ).
cnf(c_0_24,hypothesis,
equal_sets(cs,intersection(as,bs)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
( subset(X1,complement(complement(X2)))
| ~ member(member_of_1_not_of_2(X1,complement(complement(X2))),X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_26,plain,
( subset(complement(complement(X1)),X2)
| member(member_of_1_not_of_2(complement(complement(X1)),X2),X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_27,hypothesis,
( equal_sets(X1,intersection(as,bs))
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
equal_sets(intersection(bs,as),ds),
intersection_of_b_and_a_is_d ).
cnf(c_0_29,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
subsets_are_set_equal_sets ).
cnf(c_0_30,plain,
subset(X1,complement(complement(X1))),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_31,plain,
subset(complement(complement(X1)),X1),
inference(spm,[status(thm)],[c_0_15,c_0_26]) ).
cnf(c_0_32,hypothesis,
( equal_sets(intersection(as,bs),X1)
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_33,hypothesis,
equal_sets(ds,intersection(bs,as)),
inference(spm,[status(thm)],[c_0_19,c_0_28]) ).
cnf(c_0_34,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_35,axiom,
( subset(X2,X1)
| ~ equal_sets(X1,X2) ),
set_equal_sets_are_subsets2 ).
cnf(c_0_36,plain,
equal_sets(X1,complement(complement(X1))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).
cnf(c_0_37,hypothesis,
( equal_sets(X1,X2)
| ~ equal_sets(X1,intersection(as,bs))
| ~ equal_sets(X2,cs) ),
inference(spm,[status(thm)],[c_0_23,c_0_32]) ).
cnf(c_0_38,plain,
( equal_sets(complement(complement(X1)),X1)
| ~ subset(X1,complement(complement(X1))) ),
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_39,hypothesis,
( equal_sets(X1,intersection(bs,as))
| ~ equal_sets(X1,ds) ),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_40,plain,
( member(X1,X2)
| ~ equal_sets(X2,X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( equal_sets(X1,complement(complement(X2)))
| ~ equal_sets(X1,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_36]) ).
cnf(c_0_42,hypothesis,
( equal_sets(X1,X2)
| ~ equal_sets(X2,cs)
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_37,c_0_27]) ).
cnf(c_0_43,plain,
equal_sets(complement(complement(X1)),X1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_30])]) ).
cnf(c_0_44,hypothesis,
( equal_sets(X1,cs)
| ~ equal_sets(X1,intersection(as,bs)) ),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_45,hypothesis,
( equal_sets(intersection(bs,as),X1)
| ~ equal_sets(X1,ds) ),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_46,hypothesis,
( member(X1,cs)
| ~ member(X1,intersection(as,bs)) ),
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_47,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
member_of_both_is_member_of_intersection ).
cnf(c_0_48,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
member_of_intersection_is_member_of_set1 ).
cnf(c_0_49,hypothesis,
( member(X1,intersection(bs,as))
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_50,plain,
( equal_sets(X1,complement(complement(X2)))
| ~ equal_sets(X1,X3)
| ~ equal_sets(X3,X2) ),
inference(spm,[status(thm)],[c_0_23,c_0_41]) ).
cnf(c_0_51,hypothesis,
( equal_sets(X1,complement(complement(cs)))
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_52,hypothesis,
( equal_sets(intersection(bs,as),cs)
| ~ equal_sets(intersection(as,bs),ds) ),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_53,hypothesis,
( member(X1,cs)
| ~ member(X1,bs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,hypothesis,
( member(X1,bs)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_55,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
member_of_intersection_is_member_of_set2 ).
cnf(c_0_56,plain,
( equal_sets(X1,complement(complement(X2)))
| ~ equal_sets(complement(complement(X1)),X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_36]) ).
cnf(c_0_57,hypothesis,
( equal_sets(complement(complement(cs)),X1)
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_19,c_0_51]) ).
cnf(c_0_58,hypothesis,
( equal_sets(X1,ds)
| ~ equal_sets(X1,intersection(bs,as)) ),
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_59,hypothesis,
( equal_sets(cs,intersection(bs,as))
| ~ equal_sets(intersection(as,bs),ds) ),
inference(spm,[status(thm)],[c_0_19,c_0_52]) ).
cnf(c_0_60,hypothesis,
( subset(X1,cs)
| ~ member(member_of_1_not_of_2(X1,cs),bs)
| ~ member(member_of_1_not_of_2(X1,cs),as) ),
inference(spm,[status(thm)],[c_0_15,c_0_53]) ).
cnf(c_0_61,hypothesis,
( subset(ds,X1)
| member(member_of_1_not_of_2(ds,X1),bs) ),
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_62,hypothesis,
( member(X1,as)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_55,c_0_49]) ).
cnf(c_0_63,hypothesis,
( equal_sets(cs,complement(complement(X1)))
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_64,hypothesis,
( equal_sets(complement(complement(cs)),ds)
| ~ equal_sets(intersection(bs,as),cs) ),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_65,hypothesis,
( equal_sets(cs,intersection(bs,as))
| ~ equal_sets(ds,cs) ),
inference(spm,[status(thm)],[c_0_59,c_0_32]) ).
cnf(c_0_66,negated_conjecture,
~ equal_sets(cs,ds),
prove_c_equals_d ).
cnf(c_0_67,hypothesis,
( subset(ds,cs)
| ~ member(member_of_1_not_of_2(ds,cs),as) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_68,hypothesis,
( subset(ds,X1)
| member(member_of_1_not_of_2(ds,X1),as) ),
inference(spm,[status(thm)],[c_0_62,c_0_18]) ).
cnf(c_0_69,hypothesis,
( equal_sets(complement(complement(X1)),cs)
| ~ equal_sets(X1,cs) ),
inference(spm,[status(thm)],[c_0_19,c_0_63]) ).
cnf(c_0_70,plain,
( equal_sets(X1,X2)
| ~ equal_sets(X1,complement(complement(X2))) ),
inference(spm,[status(thm)],[c_0_23,c_0_43]) ).
cnf(c_0_71,hypothesis,
( equal_sets(ds,complement(complement(cs)))
| ~ equal_sets(intersection(bs,as),cs) ),
inference(spm,[status(thm)],[c_0_19,c_0_64]) ).
cnf(c_0_72,hypothesis,
~ equal_sets(ds,cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_65]),c_0_66]) ).
cnf(c_0_73,hypothesis,
subset(ds,cs),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,hypothesis,
( equal_sets(X1,cs)
| ~ equal_sets(X1,complement(complement(X2)))
| ~ equal_sets(X2,cs) ),
inference(spm,[status(thm)],[c_0_23,c_0_69]) ).
cnf(c_0_75,hypothesis,
~ equal_sets(intersection(bs,as),cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_76,hypothesis,
( member(X1,cs)
| ~ member(X1,ds) ),
inference(spm,[status(thm)],[c_0_34,c_0_73]) ).
cnf(c_0_77,hypothesis,
( ~ equal_sets(complement(complement(X1)),ds)
| ~ equal_sets(X1,cs) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_45]),c_0_75]) ).
cnf(c_0_78,plain,
( equal_sets(complement(complement(X1)),X2)
| ~ equal_sets(X2,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_41]) ).
cnf(c_0_79,hypothesis,
( member(X1,ds)
| ~ member(X1,intersection(bs,as)) ),
inference(spm,[status(thm)],[c_0_40,c_0_33]) ).
cnf(c_0_80,hypothesis,
( member(X1,intersection(as,bs))
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_40,c_0_20]) ).
cnf(c_0_81,hypothesis,
( subset(ds,X1)
| member(member_of_1_not_of_2(ds,X1),cs) ),
inference(spm,[status(thm)],[c_0_76,c_0_18]) ).
cnf(c_0_82,hypothesis,
( ~ equal_sets(X1,cs)
| ~ equal_sets(ds,X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,hypothesis,
( member(X1,ds)
| ~ member(X1,as)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_79,c_0_47]) ).
cnf(c_0_84,hypothesis,
( member(X1,bs)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_55,c_0_80]) ).
cnf(c_0_85,hypothesis,
subset(ds,complement(complement(cs))),
inference(spm,[status(thm)],[c_0_25,c_0_81]) ).
cnf(c_0_86,hypothesis,
~ equal_sets(ds,complement(complement(cs))),
inference(spm,[status(thm)],[c_0_82,c_0_43]) ).
cnf(c_0_87,hypothesis,
( subset(X1,ds)
| ~ member(member_of_1_not_of_2(X1,ds),as)
| ~ member(member_of_1_not_of_2(X1,ds),bs) ),
inference(spm,[status(thm)],[c_0_15,c_0_83]) ).
cnf(c_0_88,hypothesis,
( subset(complement(complement(cs)),X1)
| member(member_of_1_not_of_2(complement(complement(cs)),X1),bs) ),
inference(spm,[status(thm)],[c_0_84,c_0_26]) ).
cnf(c_0_89,hypothesis,
~ subset(complement(complement(cs)),ds),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_85]),c_0_86]) ).
cnf(c_0_90,hypothesis,
( member(X1,as)
| ~ member(X1,cs) ),
inference(spm,[status(thm)],[c_0_48,c_0_80]) ).
cnf(c_0_91,hypothesis,
~ member(member_of_1_not_of_2(complement(complement(cs)),ds),as),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_89]) ).
cnf(c_0_92,hypothesis,
( subset(complement(complement(cs)),X1)
| member(member_of_1_not_of_2(complement(complement(cs)),X1),as) ),
inference(spm,[status(thm)],[c_0_90,c_0_26]) ).
cnf(c_0_93,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_89]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET013-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n017.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 10:50:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 2.78/2.85 % Version : CSE_E---1.5
% 2.78/2.85 % Problem : theBenchmark.p
% 2.78/2.85 % Proof found
% 2.78/2.85 % SZS status Theorem for theBenchmark.p
% 2.78/2.85 % SZS output start Proof
% See solution above
% 2.78/2.85 % Total time : 2.270000 s
% 2.78/2.85 % SZS output end Proof
% 2.78/2.85 % Total time : 2.273000 s
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