TSTP Solution File: COL100-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : COL100-2 : 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 : n021.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 : Wed Aug 30 18:22:38 EDT 2023
% Result : Unsatisfiable 1.14s 1.22s
% Output : CNFRefutation 1.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 91
% Syntax : Number of formulae : 110 ( 11 unt; 80 typ; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 71 ( 38 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 147 ( 71 >; 76 *; 0 +; 0 <<)
% Number of predicates : 11 ( 10 usr; 1 prp; 0-8 aty)
% Number of functors : 70 ( 70 usr; 9 con; 0-4 aty)
% Number of variables : 47 ( 2 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,
cons_subsetI_sk1: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
subset: ( $i * $i ) > $o ).
tff(decl_31,type,
pair: ( $i * $i ) > $i ).
tff(decl_32,type,
converse: $i > $i ).
tff(decl_33,type,
eptset: $i ).
tff(decl_34,type,
diff: ( $i * $i ) > $i ).
tff(decl_35,type,
int: ( $i * $i ) > $i ).
tff(decl_36,type,
un: ( $i * $i ) > $i ).
tff(decl_37,type,
powI_sk1: ( $i * $i ) > $i ).
tff(decl_38,type,
pow: $i > $i ).
tff(decl_39,type,
interI_sk1: ( $i * $i ) > $i ).
tff(decl_40,type,
inter: $i > $i ).
tff(decl_41,type,
card_Union_sk1: $i > $i ).
tff(decl_42,type,
union: $i > $i ).
tff(decl_43,type,
card: $i > $o ).
tff(decl_44,type,
fin: $i > $i ).
tff(decl_45,type,
order_Inter_sk1: $i > $i ).
tff(decl_46,type,
ord: $i > $o ).
tff(decl_47,type,
order_Union_sk1: $i > $i ).
tff(decl_48,type,
comp: ( $i * $i ) > $i ).
tff(decl_49,type,
vimage: ( $i * $i ) > $i ).
tff(decl_50,type,
image: ( $i * $i ) > $i ).
tff(decl_51,type,
qInr: $i > $i ).
tff(decl_52,type,
qInl: $i > $i ).
tff(decl_53,type,
qsum: ( $i * $i ) > $i ).
tff(decl_54,type,
qsumE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
qsumE_sk2: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
qconverse: $i > $i ).
tff(decl_57,type,
qconverseE_sk2: ( $i * $i ) > $i ).
tff(decl_58,type,
qconverseE_sk1: ( $i * $i ) > $i ).
tff(decl_59,type,
qPair: ( $i * $i ) > $i ).
tff(decl_60,type,
rmult: ( $i * $i * $i * $i ) > $i ).
tff(decl_61,type,
rmultE_c1: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_62,type,
rmultE_c2: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).
tff(decl_63,type,
radd: ( $i * $i * $i * $i ) > $i ).
tff(decl_64,type,
le: ( $i * $i ) > $o ).
tff(decl_65,type,
lt: ( $i * $i ) > $o ).
tff(decl_66,type,
memrel: $i > $i ).
tff(decl_67,type,
compE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
compE_sk3: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
compE_sk2: ( $i * $i * $i ) > $i ).
tff(decl_70,type,
id: $i > $i ).
tff(decl_71,type,
idE_sk1: ( $i * $i ) > $i ).
tff(decl_72,type,
sumE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_73,type,
sumE_sk2: ( $i * $i * $i ) > $i ).
tff(decl_74,type,
vimageE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_75,type,
imageE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_76,type,
field: $i > $i ).
tff(decl_77,type,
fieldE_sk1: ( $i * $i ) > $i ).
tff(decl_78,type,
fieldE_sk2: ( $i * $i ) > $i ).
tff(decl_79,type,
range: $i > $i ).
tff(decl_80,type,
rangeE_sk1: ( $i * $i ) > $i ).
tff(decl_81,type,
domain: $i > $i ).
tff(decl_82,type,
domainE_sk1: ( $i * $i ) > $i ).
tff(decl_83,type,
cons_subsetE_sk1: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
converseE_sk2: ( $i * $i ) > $i ).
tff(decl_85,type,
converseE_sk1: ( $i * $i ) > $i ).
tff(decl_86,type,
unionE_sk1: ( $i * $i ) > $i ).
tff(decl_87,type,
subsetD_sk1: ( $i * $i * $i ) > $i ).
tff(decl_88,type,
subsetI_sk1: ( $i * $i ) > $i ).
tff(decl_89,type,
combK: $i ).
tff(decl_90,type,
combS: $i ).
tff(decl_91,type,
comb_app: ( $i * $i ) > $i ).
tff(decl_92,type,
trancl: $i > $i ).
tff(decl_93,type,
trans: $i > $o ).
tff(decl_94,type,
diamond: $i > $o ).
tff(decl_95,type,
diamond_strip_lemmaD_sk1: ( $i * $i * $i * $i ) > $i ).
tff(decl_96,type,
r: $i ).
tff(decl_97,type,
y: $i ).
tff(decl_98,type,
ya: $i ).
tff(decl_99,type,
z: $i ).
tff(decl_100,type,
sk1: $i > $i ).
tff(decl_101,type,
yp: $i ).
cnf(transD,axiom,
( member(pair(X2,X4),X1)
| ~ trans(X1)
| ~ member(pair(X2,X3),X1)
| ~ member(pair(X3,X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transD) ).
cnf(r_into_trancl,axiom,
( member(pair(X1,X2),trancl(X3))
| ~ member(pair(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r_into_trancl) ).
cnf(trans_trancl,axiom,
trans(trancl(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',trans_trancl) ).
cnf(diamond_trancl_2h5,hypothesis,
( member(pair(X1,sk1(X1)),trancl(r))
| ~ member(pair(y,X1),trancl(r)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h5) ).
cnf(diamond_trancl_2c1,negated_conjecture,
member(pair(y,yp),trancl(r)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2c1) ).
cnf(diamond_trancl_2c2,negated_conjecture,
( ~ member(pair(z,X1),trancl(r))
| ~ member(pair(yp,X1),trancl(r)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2c2) ).
cnf(diamond_strip_lemmaD1,axiom,
( member(pair(X4,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),trancl(X1))
| ~ diamond(X1)
| ~ member(pair(X2,X3),trancl(X1))
| ~ member(pair(X2,X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).
cnf(diamond_trancl_2h1,hypothesis,
diamond(r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h1) ).
cnf(diamond_strip_lemmaD2,axiom,
( member(pair(X3,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),X1)
| ~ diamond(X1)
| ~ member(pair(X2,X3),trancl(X1))
| ~ member(pair(X2,X4),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).
cnf(diamond_trancl_2h4,hypothesis,
( member(pair(ya,sk1(X1)),trancl(r))
| ~ member(pair(y,X1),trancl(r)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h4) ).
cnf(diamond_trancl_2h3,hypothesis,
member(pair(ya,z),r),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',diamond_trancl_2h3) ).
cnf(c_0_11,axiom,
( member(pair(X2,X4),X1)
| ~ trans(X1)
| ~ member(pair(X2,X3),X1)
| ~ member(pair(X3,X4),X1) ),
transD ).
cnf(c_0_12,axiom,
( member(pair(X1,X2),trancl(X3))
| ~ member(pair(X1,X2),X3) ),
r_into_trancl ).
cnf(c_0_13,axiom,
trans(trancl(X1)),
trans_trancl ).
cnf(c_0_14,hypothesis,
( member(pair(X1,sk1(X1)),trancl(r))
| ~ member(pair(y,X1),trancl(r)) ),
diamond_trancl_2h5 ).
cnf(c_0_15,negated_conjecture,
member(pair(y,yp),trancl(r)),
diamond_trancl_2c1 ).
cnf(c_0_16,plain,
( member(pair(X1,X2),trancl(X3))
| ~ member(pair(X1,X4),trancl(X3))
| ~ member(pair(X4,X2),X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_17,negated_conjecture,
member(pair(yp,sk1(yp)),trancl(r)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( ~ member(pair(z,X1),trancl(r))
| ~ member(pair(yp,X1),trancl(r)) ),
diamond_trancl_2c2 ).
cnf(c_0_19,negated_conjecture,
( member(pair(yp,X1),trancl(r))
| ~ member(pair(sk1(yp),X1),r) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( ~ member(pair(z,X1),trancl(r))
| ~ member(pair(sk1(yp),X1),r) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
( member(pair(X4,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),trancl(X1))
| ~ diamond(X1)
| ~ member(pair(X2,X3),trancl(X1))
| ~ member(pair(X2,X4),X1) ),
diamond_strip_lemmaD1 ).
cnf(c_0_22,hypothesis,
diamond(r),
diamond_trancl_2h1 ).
cnf(c_0_23,negated_conjecture,
( ~ member(pair(sk1(yp),diamond_strip_lemmaD_sk1(X1,X2,z,r)),r)
| ~ member(pair(X1,X2),trancl(r))
| ~ member(pair(X1,z),r) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]) ).
cnf(c_0_24,axiom,
( member(pair(X3,diamond_strip_lemmaD_sk1(X2,X3,X4,X1)),X1)
| ~ diamond(X1)
| ~ member(pair(X2,X3),trancl(X1))
| ~ member(pair(X2,X4),X1) ),
diamond_strip_lemmaD2 ).
cnf(c_0_25,hypothesis,
( member(pair(ya,sk1(X1)),trancl(r))
| ~ member(pair(y,X1),trancl(r)) ),
diamond_trancl_2h4 ).
cnf(c_0_26,negated_conjecture,
( ~ member(pair(X1,sk1(yp)),trancl(r))
| ~ member(pair(X1,z),r) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_22])]) ).
cnf(c_0_27,negated_conjecture,
member(pair(ya,sk1(yp)),trancl(r)),
inference(spm,[status(thm)],[c_0_25,c_0_15]) ).
cnf(c_0_28,hypothesis,
member(pair(ya,z),r),
diamond_trancl_2h3 ).
cnf(c_0_29,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COL100-2 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.16/0.33 % Computer : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Sun Aug 27 04:12:12 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 1.14/1.22 % Version : CSE_E---1.5
% 1.14/1.22 % Problem : theBenchmark.p
% 1.14/1.22 % Proof found
% 1.14/1.22 % SZS status Theorem for theBenchmark.p
% 1.14/1.22 % SZS output start Proof
% See solution above
% 1.14/1.22 % Total time : 0.650000 s
% 1.14/1.22 % SZS output end Proof
% 1.14/1.22 % Total time : 0.655000 s
%------------------------------------------------------------------------------