TSTP Solution File: SET787-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET787-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 14:35:33 EDT 2023
% Result : Unsatisfiable 0.42s 0.67s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 78
% Syntax : Number of formulae : 97 ( 8 unt; 69 typ; 0 def)
% Number of atoms : 54 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 25 ~; 26 |; 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 : 129 ( 64 >; 65 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 61 ( 61 usr; 5 con; 0-4 aty)
% Number of variables : 46 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
cons: ( $i * $i ) > $i ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
nat: $i ).
tff(decl_25,type,
succ: $i > $i ).
tff(decl_26,type,
inr: $i > $i ).
tff(decl_27,type,
inl: $i > $i ).
tff(decl_28,type,
disjsum: ( $i * $i ) > $i ).
tff(decl_29,type,
eptset: $i ).
tff(decl_30,type,
diff: ( $i * $i ) > $i ).
tff(decl_31,type,
int: ( $i * $i ) > $i ).
tff(decl_32,type,
un: ( $i * $i ) > $i ).
tff(decl_33,type,
powI_sk1: ( $i * $i ) > $i ).
tff(decl_34,type,
pow: $i > $i ).
tff(decl_35,type,
interI_sk1: ( $i * $i ) > $i ).
tff(decl_36,type,
inter: $i > $i ).
tff(decl_37,type,
card_Union_sk1: $i > $i ).
tff(decl_38,type,
union: $i > $i ).
tff(decl_39,type,
card: $i > $o ).
tff(decl_40,type,
fin: $i > $i ).
tff(decl_41,type,
order_Inter_sk1: $i > $i ).
tff(decl_42,type,
ord: $i > $o ).
tff(decl_43,type,
order_Union_sk1: $i > $i ).
tff(decl_44,type,
pair: ( $i * $i ) > $i ).
tff(decl_45,type,
comp: ( $i * $i ) > $i ).
tff(decl_46,type,
vimage: ( $i * $i ) > $i ).
tff(decl_47,type,
image: ( $i * $i ) > $i ).
tff(decl_48,type,
qInr: $i > $i ).
tff(decl_49,type,
qInl: $i > $i ).
tff(decl_50,type,
qsum: ( $i * $i ) > $i ).
tff(decl_51,type,
qsumE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
qsumE_sk2: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
qconverse: $i > $i ).
tff(decl_54,type,
qconverseE_sk2: ( $i * $i ) > $i ).
tff(decl_55,type,
qconverseE_sk1: ( $i * $i ) > $i ).
tff(decl_56,type,
qPair: ( $i * $i ) > $i ).
tff(decl_57,type,
rmult: ( $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
rmultE_c1: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_59,type,
rmultE_c2: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_60,type,
radd: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
le: ( $i * $i ) > $o ).
tff(decl_62,type,
lt: ( $i * $i ) > $o ).
tff(decl_63,type,
memrel: $i > $i ).
tff(decl_64,type,
compE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_65,type,
compE_sk3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
compE_sk2: ( $i * $i * $i ) > $i ).
tff(decl_67,type,
id: $i > $i ).
tff(decl_68,type,
idE_sk1: ( $i * $i ) > $i ).
tff(decl_69,type,
sumE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
sumE_sk2: ( $i * $i * $i ) > $i ).
tff(decl_71,type,
unionE_sk1: ( $i * $i ) > $i ).
tff(decl_72,type,
subsetD_sk1: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
subset: ( $i * $i ) > $o ).
tff(decl_74,type,
field: $i > $i ).
tff(decl_75,type,
subsetI_sk1: ( $i * $i ) > $i ).
tff(decl_76,type,
upair: ( $i * $i ) > $i ).
tff(decl_77,type,
sigma: ( $i * $i ) > $i ).
tff(decl_78,type,
sigmaE_sk1x: ( $i * $i * $i ) > $i ).
tff(decl_79,type,
sigmaE_sk1y: ( $i * $i * $i ) > $i ).
tff(decl_80,type,
apply: ( $i * $i ) > $i ).
tff(decl_81,type,
fst: $i > $i ).
tff(decl_82,type,
snd: $i > $i ).
tff(decl_83,type,
converse: $i > $i ).
tff(decl_84,type,
converseE_sk2: $i > $i ).
tff(decl_85,type,
converseE_sk1: $i > $i ).
tff(decl_86,type,
converse_sk1: $i > $i ).
tff(decl_87,type,
converse_sk2: $i > $i ).
tff(decl_88,type,
sk2: $i ).
tff(decl_89,type,
a: $i ).
tff(decl_90,type,
b: $i ).
cnf(clause112,axiom,
( X1 = X2
| member(X1,X3)
| ~ member(X1,cons(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause112) ).
cnf(clause120,axiom,
( member(unionE_sk1(X1,X2),X2)
| ~ member(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause120) ).
cnf(clause143,axiom,
( member(X3,union(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause143) ).
cnf(clause119,axiom,
( member(X1,unionE_sk1(X1,X2))
| ~ member(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause119) ).
cnf(un_eq_Union_2_c1,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c1) ).
cnf(clause111,axiom,
( X1 = X2
| ~ member(X1,cons(X2,eptset)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause111) ).
cnf(un_eq_Union_2_c2,negated_conjecture,
~ member(sk2,un(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',un_eq_Union_2_c2) ).
cnf(clause20,axiom,
( member(X1,un(X2,X3))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause20) ).
cnf(clause19,axiom,
( member(X1,un(X3,X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause19) ).
cnf(c_0_9,axiom,
( X1 = X2
| member(X1,X3)
| ~ member(X1,cons(X2,X3)) ),
clause112 ).
cnf(c_0_10,axiom,
( member(unionE_sk1(X1,X2),X2)
| ~ member(X1,union(X2)) ),
clause120 ).
cnf(c_0_11,axiom,
( member(X3,union(X2))
| ~ member(X1,X2)
| ~ member(X3,X1) ),
clause143 ).
cnf(c_0_12,axiom,
( member(X1,unionE_sk1(X1,X2))
| ~ member(X1,union(X2)) ),
clause119 ).
cnf(c_0_13,plain,
( unionE_sk1(X1,cons(X2,X3)) = X2
| member(unionE_sk1(X1,cons(X2,X3)),X3)
| ~ member(X1,union(cons(X2,X3))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
member(sk2,union(cons(a,cons(b,eptset)))),
un_eq_Union_2_c1 ).
cnf(c_0_15,axiom,
( X1 = X2
| ~ member(X1,cons(X2,eptset)) ),
clause111 ).
cnf(c_0_16,plain,
( member(X1,union(X2))
| ~ member(unionE_sk1(X1,X3),X2)
| ~ member(X1,union(X3)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
| member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
~ member(sk2,un(a,b)),
un_eq_Union_2_c2 ).
cnf(c_0_19,axiom,
( member(X1,un(X2,X3))
| ~ member(X1,X2) ),
clause20 ).
cnf(c_0_20,plain,
( unionE_sk1(X1,cons(X2,eptset)) = X2
| ~ member(X1,union(cons(X2,eptset))) ),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_21,negated_conjecture,
( unionE_sk1(sk2,cons(a,cons(b,eptset))) = a
| member(sk2,union(cons(b,eptset))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_14])]) ).
cnf(c_0_22,negated_conjecture,
~ member(sk2,a),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
( member(X1,un(X3,X2))
| ~ member(X1,X2) ),
clause19 ).
cnf(c_0_24,plain,
( member(X1,X2)
| ~ member(X1,union(cons(X2,eptset))) ),
inference(spm,[status(thm)],[c_0_12,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
member(sk2,union(cons(b,eptset))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_14])]),c_0_22]) ).
cnf(c_0_26,negated_conjecture,
~ member(sk2,b),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SET787-2 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.15 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8042.1875MB
% 0.11/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Aug 26 13:17:05 EDT 2023
% 0.11/0.36 % CPUTime :
% 0.16/0.57 start to proof: theBenchmark
% 0.42/0.67 % Version : CSE_E---1.5
% 0.42/0.67 % Problem : theBenchmark.p
% 0.42/0.67 % Proof found
% 0.42/0.67 % SZS status Theorem for theBenchmark.p
% 0.42/0.67 % SZS output start Proof
% See solution above
% 0.42/0.67 % Total time : 0.086000 s
% 0.42/0.67 % SZS output end Proof
% 0.42/0.67 % Total time : 0.089000 s
%------------------------------------------------------------------------------