TSTP Solution File: SET012-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET012-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 14:32:01 EDT 2023
% Result : Unsatisfiable 2.64s 2.69s
% Output : CNFRefutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 84
% Syntax : Number of formulae : 104 ( 11 unt; 75 typ; 0 def)
% Number of atoms : 58 ( 16 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 49 ( 20 ~; 29 |; 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 : 122 ( 66 >; 56 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-5 aty)
% Number of functors : 62 ( 62 usr; 9 con; 0-5 aty)
% Number of variables : 34 ( 2 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,
non_ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton_set: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
ordered_pair_predicate: $i > $o ).
tff(decl_29,type,
f2: $i > $i ).
tff(decl_30,type,
f3: $i > $i ).
tff(decl_31,type,
first: $i > $i ).
tff(decl_32,type,
f4: ( $i * $i ) > $i ).
tff(decl_33,type,
f5: ( $i * $i ) > $i ).
tff(decl_34,type,
second: $i > $i ).
tff(decl_35,type,
f6: ( $i * $i ) > $i ).
tff(decl_36,type,
f7: ( $i * $i ) > $i ).
tff(decl_37,type,
estin: $i ).
tff(decl_38,type,
intersection: ( $i * $i ) > $i ).
tff(decl_39,type,
complement: $i > $i ).
tff(decl_40,type,
union: ( $i * $i ) > $i ).
tff(decl_41,type,
domain_of: $i > $i ).
tff(decl_42,type,
f8: ( $i * $i ) > $i ).
tff(decl_43,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_44,type,
converse: $i > $i ).
tff(decl_45,type,
rotate_right: $i > $i ).
tff(decl_46,type,
f9: ( $i * $i ) > $i ).
tff(decl_47,type,
f10: ( $i * $i ) > $i ).
tff(decl_48,type,
f11: ( $i * $i ) > $i ).
tff(decl_49,type,
flip_range_of: $i > $i ).
tff(decl_50,type,
f12: ( $i * $i ) > $i ).
tff(decl_51,type,
f13: ( $i * $i ) > $i ).
tff(decl_52,type,
f14: ( $i * $i ) > $i ).
tff(decl_53,type,
successor: $i > $i ).
tff(decl_54,type,
empty_set: $i ).
tff(decl_55,type,
universal_set: $i ).
tff(decl_56,type,
infinity: $i ).
tff(decl_57,type,
sigma: $i > $i ).
tff(decl_58,type,
f16: ( $i * $i ) > $i ).
tff(decl_59,type,
subset: ( $i * $i ) > $o ).
tff(decl_60,type,
f17: ( $i * $i ) > $i ).
tff(decl_61,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_62,type,
powerset: $i > $i ).
tff(decl_63,type,
relation: $i > $o ).
tff(decl_64,type,
f18: $i > $i ).
tff(decl_65,type,
single_valued_set: $i > $o ).
tff(decl_66,type,
f19: $i > $i ).
tff(decl_67,type,
f20: $i > $i ).
tff(decl_68,type,
f21: $i > $i ).
tff(decl_69,type,
function: $i > $o ).
tff(decl_70,type,
image: ( $i * $i ) > $i ).
tff(decl_71,type,
f22: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_73,type,
f23: ( $i * $i ) > $i ).
tff(decl_74,type,
f24: $i > $i ).
tff(decl_75,type,
f25: $i ).
tff(decl_76,type,
f26: $i > $i ).
tff(decl_77,type,
range_of: $i > $i ).
tff(decl_78,type,
f27: ( $i * $i ) > $i ).
tff(decl_79,type,
identity_relation: $i ).
tff(decl_80,type,
restrict: ( $i * $i ) > $i ).
tff(decl_81,type,
one_to_one_function: $i > $o ).
tff(decl_82,type,
apply: ( $i * $i ) > $i ).
tff(decl_83,type,
f28: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
apply_to_two_arguments: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
maps: ( $i * $i * $i ) > $o ).
tff(decl_86,type,
closed: ( $i * $i ) > $o ).
tff(decl_87,type,
compose: ( $i * $i ) > $i ).
tff(decl_88,type,
f29: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
f30: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
f31: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
homomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_92,type,
f32: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
f33: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
as: $i ).
tff(decl_95,type,
bs: $i ).
tff(decl_96,type,
cs: $i ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',complement1) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',extensionality2) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',complement2) ).
cnf(extensionality1,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',extensionality1) ).
cnf(complement_of_a_is_b,hypothesis,
complement(as) = bs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_a_is_b) ).
cnf(complement_of_b_is_c,hypothesis,
complement(bs) = cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement_of_b_is_c) ).
cnf(prove_a_equals_c,negated_conjecture,
as != cs,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_equals_c) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(extensionality3,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',extensionality3) ).
cnf(c_0_9,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_10,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_11,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_12,axiom,
( little_set(f1(X1,X2))
| X1 = X2 ),
extensionality1 ).
cnf(c_0_13,plain,
( complement(X1) = X2
| member(f1(complement(X1),X2),X2)
| ~ member(f1(complement(X1),X2),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( X1 = X2
| member(f1(X1,X2),complement(X3))
| member(f1(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,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_13,c_0_14]) ).
cnf(c_0_16,hypothesis,
complement(as) = bs,
complement_of_a_is_b ).
cnf(c_0_17,hypothesis,
complement(bs) = cs,
complement_of_b_is_c ).
cnf(c_0_18,hypothesis,
( cs = X1
| member(f1(cs,X1),as)
| member(f1(cs,X1),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_19,negated_conjecture,
as != cs,
prove_a_equals_c ).
cnf(c_0_20,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_21,hypothesis,
member(f1(cs,as),as),
inference(sr,[status(thm)],[inference(ef,[status(thm)],[c_0_18]),c_0_19]) ).
cnf(c_0_22,hypothesis,
( ~ member(X1,bs)
| ~ member(X1,as) ),
inference(spm,[status(thm)],[c_0_9,c_0_16]) ).
cnf(c_0_23,axiom,
( X1 = X2
| ~ member(f1(X1,X2),X1)
| ~ member(f1(X1,X2),X2) ),
extensionality3 ).
cnf(c_0_24,hypothesis,
( member(X1,bs)
| member(X1,cs)
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_25,hypothesis,
little_set(f1(cs,as)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,hypothesis,
~ member(f1(cs,as),bs),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_27,hypothesis,
~ member(f1(cs,as),cs),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_21]),c_0_19]) ).
cnf(c_0_28,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET012-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n028.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 13:17:52 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 2.64/2.69 % Version : CSE_E---1.5
% 2.64/2.69 % Problem : theBenchmark.p
% 2.64/2.69 % Proof found
% 2.64/2.69 % SZS status Theorem for theBenchmark.p
% 2.64/2.69 % SZS output start Proof
% See solution above
% 2.64/2.69 % Total time : 2.103000 s
% 2.64/2.69 % SZS output end Proof
% 2.64/2.69 % Total time : 2.108000 s
%------------------------------------------------------------------------------