TSTP Solution File: SET028-3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET028-3 : 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 14:32:21 EDT 2023
% Result : Unsatisfiable 239.36s 239.40s
% Output : CNFRefutation 239.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 87
% Syntax : Number of formulae : 115 ( 14 unt; 74 typ; 0 def)
% Number of atoms : 84 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 89 ( 46 ~; 43 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 7 ( 2 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 : 61 ( 61 usr; 8 con; 0-5 aty)
% Number of variables : 70 ( 4 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,
a_function: $i ).
tff(decl_95,type,
element: $i ).
cnf(prove_property_of_image_and_apply1,negated_conjecture,
~ subset(apply(a_function,element),sigma(image(singleton_set(element),a_function))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_property_of_image_and_apply1) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(subset2,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset2) ).
cnf(subset3,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset3) ).
cnf(sigma3,axiom,
( member(X1,sigma(X2))
| ~ member(X3,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',sigma3) ).
cnf(apply1,axiom,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',apply1) ).
cnf(apply3,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',apply3) ).
cnf(apply4,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',apply4) ).
cnf(image_and_substitution5,axiom,
( member(X1,image(X2,X3))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X4)
| ~ member(X4,X3)
| ~ member(first(X4),X2)
| second(X4) != X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',image_and_substitution5) ).
cnf(second_component_is_small,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_component_is_small) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(first_component_is_small,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_component_is_small) ).
cnf(apply2,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',apply2) ).
cnf(c_0_13,negated_conjecture,
~ subset(apply(a_function,element),sigma(image(singleton_set(element),a_function))),
prove_property_of_image_and_apply1 ).
cnf(c_0_14,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_15,negated_conjecture,
~ subset(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
( subset(X1,X2)
| member(f17(X1,X2),X1) ),
subset2 ).
cnf(c_0_17,axiom,
( subset(X1,X2)
| ~ member(f17(X1,X2),X2) ),
subset3 ).
cnf(c_0_18,axiom,
( member(X1,sigma(X2))
| ~ member(X3,X2)
| ~ member(X1,X3) ),
sigma3 ).
cnf(c_0_19,axiom,
( ordered_pair_predicate(f28(X1,X2,X3))
| ~ member(X1,apply(X2,X3)) ),
apply1 ).
cnf(c_0_20,negated_conjecture,
member(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),apply(a_function,element)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,axiom,
( first(f28(X1,X2,X3)) = X3
| ~ member(X1,apply(X2,X3)) ),
apply3 ).
cnf(c_0_22,plain,
( subset(X1,sigma(X2))
| ~ member(f17(X1,sigma(X2)),X3)
| ~ member(X3,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
( member(X1,second(f28(X1,X2,X3)))
| ~ member(X1,apply(X2,X3)) ),
apply4 ).
cnf(c_0_24,axiom,
( member(X1,image(X2,X3))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X4)
| ~ member(X4,X3)
| ~ member(first(X4),X2)
| second(X4) != X1 ),
image_and_substitution5 ).
cnf(c_0_25,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
second_component_is_small ).
cnf(c_0_26,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_27,axiom,
( little_set(first(X1))
| ~ ordered_pair_predicate(X1) ),
first_component_is_small ).
cnf(c_0_28,negated_conjecture,
ordered_pair_predicate(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
first(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element)) = element,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ member(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),X1)
| ~ member(X1,image(non_ordered_pair(element,element),a_function)) ),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_31,negated_conjecture,
member(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),second(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element))),
inference(spm,[status(thm)],[c_0_23,c_0_20]) ).
cnf(c_0_32,plain,
( member(second(X1),image(X2,X3))
| ~ ordered_pair_predicate(X1)
| ~ member(first(X1),X2)
| ~ member(X1,X3) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_24]),c_0_25]) ).
cnf(c_0_33,axiom,
( member(f28(X1,X2,X3),X2)
| ~ member(X1,apply(X2,X3)) ),
apply2 ).
cnf(c_0_34,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_35,negated_conjecture,
little_set(element),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_36,negated_conjecture,
~ member(second(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element)),image(non_ordered_pair(element,element),a_function)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_37,negated_conjecture,
( member(second(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element)),image(X1,X2))
| ~ member(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element),X2)
| ~ member(element,X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_28]),c_0_29]) ).
cnf(c_0_38,negated_conjecture,
member(f28(f17(apply(a_function,element),sigma(image(non_ordered_pair(element,element),a_function))),a_function,element),a_function),
inference(spm,[status(thm)],[c_0_33,c_0_20]) ).
cnf(c_0_39,negated_conjecture,
member(element,non_ordered_pair(X1,element)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.17 % Problem : SET028-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.17 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.17/0.36 % Computer : n028.cluster.edu
% 0.17/0.36 % Model : x86_64 x86_64
% 0.17/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.36 % Memory : 8042.1875MB
% 0.17/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.36 % CPULimit : 300
% 0.17/0.36 % WCLimit : 300
% 0.17/0.36 % DateTime : Sat Aug 26 10:48:37 EDT 2023
% 0.17/0.37 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 239.36/239.40 % Version : CSE_E---1.5
% 239.36/239.40 % Problem : theBenchmark.p
% 239.36/239.40 % Proof found
% 239.36/239.40 % SZS status Theorem for theBenchmark.p
% 239.36/239.40 % SZS output start Proof
% See solution above
% 239.36/239.41 % Total time : 238.815000 s
% 239.36/239.41 % SZS output end Proof
% 239.36/239.41 % Total time : 238.828000 s
%------------------------------------------------------------------------------