TSTP Solution File: SET014-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET014-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 14:32:03 EDT 2023
% Result : Unsatisfiable 5.61s 5.74s
% Output : CNFRefutation 5.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 19
% Syntax : Number of formulae : 32 ( 7 unt; 12 typ; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 12 ~; 19 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 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,
cs: $i ).
tff(decl_33,type,
bs: $i ).
cnf(membership_in_subsets,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
cnf(b_subset_of_c,hypothesis,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
cnf(member_of_union_is_member_of_one_set,axiom,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_union_is_member_of_one_set) ).
cnf(subsets_axiom1,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
cnf(a_subset_of_c,hypothesis,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
cnf(subsets_axiom2,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom2) ).
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(c_0_7,axiom,
( member(X1,X3)
| ~ member(X1,X2)
| ~ subset(X2,X3) ),
membership_in_subsets ).
cnf(c_0_8,hypothesis,
subset(bs,cs),
b_subset_of_c ).
cnf(c_0_9,axiom,
( member(X1,X2)
| member(X1,X3)
| ~ member(X1,union(X2,X3)) ),
member_of_union_is_member_of_one_set ).
cnf(c_0_10,axiom,
( subset(X1,X2)
| member(member_of_1_not_of_2(X1,X2),X1) ),
subsets_axiom1 ).
cnf(c_0_11,hypothesis,
subset(as,cs),
a_subset_of_c ).
cnf(c_0_12,hypothesis,
( member(X1,cs)
| ~ member(X1,bs) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,plain,
( subset(union(X1,X2),X3)
| member(member_of_1_not_of_2(union(X1,X2),X3),X1)
| member(member_of_1_not_of_2(union(X1,X2),X3),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,hypothesis,
( member(X1,cs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_15,hypothesis,
( subset(union(X1,bs),X2)
| member(member_of_1_not_of_2(union(X1,bs),X2),cs)
| member(member_of_1_not_of_2(union(X1,bs),X2),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_17,hypothesis,
( subset(union(as,bs),X1)
| member(member_of_1_not_of_2(union(as,bs),X1),cs) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
~ subset(union(as,bs),cs),
prove_a_union_b_subset_of_c ).
cnf(c_0_19,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET014-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 16:34:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 5.61/5.74 % Version : CSE_E---1.5
% 5.61/5.74 % Problem : theBenchmark.p
% 5.61/5.74 % Proof found
% 5.61/5.74 % SZS status Theorem for theBenchmark.p
% 5.61/5.74 % SZS output start Proof
% See solution above
% 5.61/5.74 % Total time : 5.176000 s
% 5.61/5.74 % SZS output end Proof
% 5.61/5.74 % Total time : 5.179000 s
%------------------------------------------------------------------------------