TSTP Solution File: SET014-4 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET014-4 : 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 : n032.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 14:32:04 EDT 2023
% Result : Unsatisfiable 23.29s 23.41s
% Output : CNFRefutation 23.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 82 ( 19 unt; 13 typ; 0 def)
% Number of atoms : 137 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 119 ( 51 ~; 68 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 111 ( 10 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,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
f17: ( $i * $i ) > $i ).
tff(decl_32,type,
as: $i ).
tff(decl_33,type,
cs: $i ).
tff(decl_34,type,
bs: $i ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset2) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
cnf(universal_set,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
cnf(extensionality1,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset1) ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset3) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
cnf(a_subset_of_c,hypothesis,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
cnf(b_subset_of_c,hypothesis,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
cnf(prove_a_union_b_subset_of_c,negated_conjecture,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
cnf(c_0_17,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_18,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_19,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_20,plain,
( subset(complement(X1),X2)
| ~ member(f17(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_22,plain,
( subset(X1,X2)
| little_set(f17(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_23,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_24,plain,
( subset(complement(complement(X1)),X2)
| member(f17(complement(complement(X1)),X2),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
universal_set ).
cnf(c_0_26,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
extensionality1 ).
cnf(c_0_27,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_28,plain,
subset(complement(complement(empty_set)),X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_30,plain,
( X1 = X2
| member(f1(X1,X2),universal_set) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
( member(X1,X2)
| ~ member(X1,complement(complement(empty_set))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
subset3 ).
cnf(c_0_33,plain,
( X1 = universal_set
| ~ member(f1(X1,universal_set),X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
( member(X1,complement(empty_set))
| ~ little_set(X1) ),
inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_21])]) ).
cnf(c_0_35,plain,
( subset(X1,complement(X2))
| member(f17(X1,complement(X2)),X2)
| ~ little_set(f17(X1,complement(X2))) ),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_36,plain,
complement(empty_set) = universal_set,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_26]) ).
cnf(c_0_37,plain,
subset(X1,universal_set),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_23]),c_0_22]) ).
cnf(c_0_38,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_39,plain,
( member(X1,universal_set)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_37]) ).
cnf(c_0_40,hypothesis,
subset(as,cs),
a_subset_of_c ).
cnf(c_0_41,plain,
( subset(X1,intersection(X2,X3))
| ~ member(f17(X1,intersection(X2,X3)),X3)
| ~ member(f17(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_42,plain,
( subset(X1,X2)
| member(f17(X1,X2),universal_set) ),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_43,hypothesis,
( member(X1,cs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_44,plain,
( subset(X1,intersection(X2,universal_set))
| ~ member(f17(X1,intersection(X2,universal_set)),X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,hypothesis,
( subset(as,X1)
| member(f17(as,X1),cs) ),
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
cnf(c_0_46,plain,
subset(X1,intersection(X1,universal_set)),
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_47,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_48,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_49,hypothesis,
subset(as,intersection(cs,universal_set)),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_50,plain,
( member(X1,intersection(X2,universal_set))
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_46]) ).
cnf(c_0_51,plain,
( X1 = intersection(X2,X3)
| member(f1(X1,intersection(X2,X3)),X1)
| member(f1(X1,intersection(X2,X3)),X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
( subset(complement(intersection(X1,X2)),X3)
| ~ member(f17(complement(intersection(X1,X2)),X3),X2)
| ~ member(f17(complement(intersection(X1,X2)),X3),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_38]) ).
cnf(c_0_53,hypothesis,
( member(X1,intersection(cs,universal_set))
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_27,c_0_49]) ).
cnf(c_0_54,plain,
( X1 = intersection(X2,universal_set)
| ~ member(f1(X1,intersection(X2,universal_set)),X1)
| ~ member(f1(X1,intersection(X2,universal_set)),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_50]) ).
cnf(c_0_55,plain,
( intersection(X1,X2) = X1
| member(f1(X1,intersection(X1,X2)),X1) ),
inference(ef,[status(thm)],[c_0_51]) ).
cnf(c_0_56,hypothesis,
subset(bs,cs),
b_subset_of_c ).
cnf(c_0_57,plain,
( subset(complement(intersection(X1,complement(X2))),X3)
| member(f17(complement(intersection(X1,complement(X2))),X3),X2)
| ~ member(f17(complement(intersection(X1,complement(X2))),X3),X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_21]),c_0_19]) ).
cnf(c_0_58,hypothesis,
( subset(X1,intersection(intersection(cs,universal_set),universal_set))
| ~ member(f17(X1,intersection(intersection(cs,universal_set),universal_set)),as) ),
inference(spm,[status(thm)],[c_0_44,c_0_53]) ).
cnf(c_0_59,plain,
intersection(X1,universal_set) = X1,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_60,hypothesis,
( member(X1,cs)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_27,c_0_56]) ).
cnf(c_0_61,plain,
( subset(complement(intersection(complement(X1),complement(X2))),X3)
| member(f17(complement(intersection(complement(X1),complement(X2))),X3),X1)
| member(f17(complement(intersection(complement(X1),complement(X2))),X3),X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_21]),c_0_22]) ).
cnf(c_0_62,negated_conjecture,
~ subset(union(as,bs),cs),
prove_a_union_b_subset_of_c ).
cnf(c_0_63,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_64,hypothesis,
( subset(X1,cs)
| ~ member(f17(X1,cs),as) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59]),c_0_59]),c_0_59]),c_0_59]) ).
cnf(c_0_65,hypothesis,
( subset(complement(intersection(complement(X1),complement(bs))),X2)
| member(f17(complement(intersection(complement(X1),complement(bs))),X2),cs)
| member(f17(complement(intersection(complement(X1),complement(bs))),X2),X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_66,negated_conjecture,
~ subset(complement(intersection(complement(as),complement(bs))),cs),
inference(rw,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_67,hypothesis,
member(f17(complement(intersection(complement(as),complement(bs))),cs),cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66]) ).
cnf(c_0_68,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_67]),c_0_66]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET014-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Sat Aug 26 11:14:43 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.49 start to proof: theBenchmark
% 23.29/23.41 % Version : CSE_E---1.5
% 23.29/23.41 % Problem : theBenchmark.p
% 23.29/23.41 % Proof found
% 23.29/23.41 % SZS status Theorem for theBenchmark.p
% 23.29/23.41 % SZS output start Proof
% See solution above
% 23.29/23.42 % Total time : 22.920000 s
% 23.29/23.42 % SZS output end Proof
% 23.29/23.42 % Total time : 22.924000 s
%------------------------------------------------------------------------------