TSTP Solution File: SET018-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET018-3 : 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 : n016.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 14:32:10 EDT 2023
% Result : Unsatisfiable 2.81s 2.91s
% Output : CNFRefutation 2.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 89
% Syntax : Number of formulae : 129 ( 28 unt; 76 typ; 0 def)
% Number of atoms : 100 ( 59 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 84 ( 37 ~; 47 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 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 : 63 ( 63 usr; 10 con; 0-5 aty)
% Number of variables : 57 ( 17 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: $i ).
tff(decl_95,type,
b: $i ).
tff(decl_96,type,
c: $i ).
tff(decl_97,type,
d: $i ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(equal_ordered_pair,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pair) ).
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(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
cnf(d_little_set,hypothesis,
little_set(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_little_set) ).
cnf(first_components_are_equal,axiom,
( X1 = X2
| ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_components_are_equal) ).
cnf(prove_second_components_equal,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).
cnf(c_little_set,hypothesis,
little_set(c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_little_set) ).
cnf(b_little_set,hypothesis,
little_set(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_little_set) ).
cnf(a_little_set,hypothesis,
little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_little_set) ).
cnf(left_cancellation,axiom,
( X1 = X2
| ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_cancellation) ).
cnf(c_0_13,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_14,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_15,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
equal_ordered_pair ).
cnf(c_0_16,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_18,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_19,hypothesis,
non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)) = non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]) ).
cnf(c_0_20,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,axiom,
little_set(non_ordered_pair(X1,X2)),
non_ordered_pair4 ).
cnf(c_0_22,hypothesis,
little_set(d),
d_little_set ).
cnf(c_0_23,hypothesis,
( X1 = non_ordered_pair(c,c)
| X1 = non_ordered_pair(c,d)
| ~ member(X1,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,plain,
member(non_ordered_pair(X1,X2),non_ordered_pair(X3,non_ordered_pair(X1,X2))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,hypothesis,
member(d,non_ordered_pair(X1,d)),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_26,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,b)
| non_ordered_pair(c,c) = non_ordered_pair(a,b) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,axiom,
( X1 = X2
| ~ little_set(X1)
| ~ little_set(X2)
| ordered_pair(X1,X3) != ordered_pair(X2,X4) ),
first_components_are_equal ).
cnf(c_0_28,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,b)
| member(d,non_ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,negated_conjecture,
b != d,
prove_second_components_equal ).
cnf(c_0_30,plain,
( X1 = X2
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X3)) != non_ordered_pair(non_ordered_pair(X2,X2),non_ordered_pair(X2,X4))
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_16]),c_0_16]) ).
cnf(c_0_31,hypothesis,
little_set(c),
c_little_set ).
cnf(c_0_32,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,b)
| d = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_28]),c_0_29]) ).
cnf(c_0_33,hypothesis,
little_set(b),
b_little_set ).
cnf(c_0_34,hypothesis,
( X1 = c
| non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))
| ~ little_set(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_19]),c_0_31])]) ).
cnf(c_0_35,hypothesis,
little_set(a),
a_little_set ).
cnf(c_0_36,hypothesis,
( d = a
| X1 = c
| ~ member(X1,non_ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_18,c_0_32]) ).
cnf(c_0_37,hypothesis,
member(b,non_ordered_pair(X1,b)),
inference(spm,[status(thm)],[c_0_20,c_0_33]) ).
cnf(c_0_38,hypothesis,
c = a,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_34]),c_0_35])]) ).
cnf(c_0_39,hypothesis,
( b = c
| d = a ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,hypothesis,
( non_ordered_pair(a,b) = non_ordered_pair(a,a)
| non_ordered_pair(a,d) = non_ordered_pair(a,b) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_38]),c_0_38]),c_0_38]) ).
cnf(c_0_41,hypothesis,
( d = a
| b = a ),
inference(rw,[status(thm)],[c_0_39,c_0_38]) ).
cnf(c_0_42,hypothesis,
( non_ordered_pair(a,b) = non_ordered_pair(a,a)
| b = a ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,hypothesis,
( b = a
| member(b,non_ordered_pair(a,a)) ),
inference(spm,[status(thm)],[c_0_37,c_0_42]) ).
cnf(c_0_44,axiom,
( X1 = X2
| ~ little_set(X1)
| ~ little_set(X2)
| non_ordered_pair(X3,X1) != non_ordered_pair(X3,X2) ),
left_cancellation ).
cnf(c_0_45,hypothesis,
b = a,
inference(spm,[status(thm)],[c_0_18,c_0_43]) ).
cnf(c_0_46,hypothesis,
( X1 = non_ordered_pair(c,d)
| non_ordered_pair(non_ordered_pair(c,c),X1) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))
| ~ little_set(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_19]),c_0_21])]) ).
cnf(c_0_47,hypothesis,
( d = a
| c = X1
| non_ordered_pair(c,X1) != non_ordered_pair(a,b)
| ~ little_set(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_32]),c_0_31])]) ).
cnf(c_0_48,negated_conjecture,
d != a,
inference(rw,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_49,hypothesis,
( X1 = non_ordered_pair(a,d)
| non_ordered_pair(non_ordered_pair(a,a),X1) != non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,a))
| ~ little_set(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_38]),c_0_38]),c_0_38]),c_0_45]) ).
cnf(c_0_50,hypothesis,
( a = X1
| non_ordered_pair(a,X1) != non_ordered_pair(a,a)
| ~ little_set(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_38]),c_0_38]),c_0_45]),c_0_48]) ).
cnf(c_0_51,hypothesis,
non_ordered_pair(a,d) = non_ordered_pair(a,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_49]),c_0_21])]) ).
cnf(c_0_52,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_22])]),c_0_48]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET018-3 : 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
% 0.12/0.33 % Computer : n016.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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 13:10:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 2.81/2.91 % Version : CSE_E---1.5
% 2.81/2.91 % Problem : theBenchmark.p
% 2.81/2.91 % Proof found
% 2.81/2.91 % SZS status Theorem for theBenchmark.p
% 2.81/2.91 % SZS output start Proof
% See solution above
% 2.87/2.92 % Total time : 2.348000 s
% 2.87/2.92 % SZS output end Proof
% 2.87/2.92 % Total time : 2.353000 s
%------------------------------------------------------------------------------