TSTP Solution File: SET015-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET015-1 : 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 : n025.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 14:32:05 EDT 2023
% Result : Unsatisfiable 0.81s 0.88s
% Output : CNFRefutation 0.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 18
% Syntax : Number of formulae : 32 ( 5 unt; 11 typ; 0 def)
% Number of atoms : 42 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 37 ( 16 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 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 ).
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(member_of_set1_is_member_of_union,axiom,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set1_is_member_of_union) ).
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(member_of_set2_is_member_of_union,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_set2_is_member_of_union) ).
cnf(subsets_are_set_equal_sets,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_are_set_equal_sets) ).
cnf(prove_commutativity,negated_conjecture,
~ equal_sets(union(as,bs),union(bs,as)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_commutativity) ).
cnf(c_0_7,axiom,
( subset(X1,X2)
| ~ member(member_of_1_not_of_2(X1,X2),X2) ),
subsets_axiom2 ).
cnf(c_0_8,axiom,
( member(X1,union(X2,X3))
| ~ member(X1,X2) ),
member_of_set1_is_member_of_union ).
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,axiom,
( member(X1,union(X3,X2))
| ~ member(X1,X2) ),
member_of_set2_is_member_of_union ).
cnf(c_0_12,plain,
( subset(X1,union(X2,X3))
| ~ member(member_of_1_not_of_2(X1,union(X2,X3)),X2) ),
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,plain,
( subset(X1,union(X2,X3))
| ~ member(member_of_1_not_of_2(X1,union(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_7,c_0_11]) ).
cnf(c_0_15,plain,
( subset(union(X1,X2),union(X2,X3))
| member(member_of_1_not_of_2(union(X1,X2),union(X2,X3)),X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_16,axiom,
( equal_sets(X2,X1)
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
subsets_are_set_equal_sets ).
cnf(c_0_17,plain,
subset(union(X1,X2),union(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
~ equal_sets(union(as,bs),union(bs,as)),
prove_commutativity ).
cnf(c_0_19,plain,
equal_sets(union(X1,X2),union(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_17])]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET015-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n025.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 12:33:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.81/0.88 % Version : CSE_E---1.5
% 0.81/0.88 % Problem : theBenchmark.p
% 0.81/0.88 % Proof found
% 0.81/0.88 % SZS status Theorem for theBenchmark.p
% 0.81/0.88 % SZS output start Proof
% See solution above
% 0.81/0.88 % Total time : 0.311000 s
% 0.81/0.88 % SZS output end Proof
% 0.81/0.88 % Total time : 0.314000 s
%------------------------------------------------------------------------------