TSTP Solution File: SYO620-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SYO620-1 : TPTP v8.1.2. Released v7.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n002.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 : Fri Sep 1 04:12:06 EDT 2023
% Result : Unsatisfiable 0.76s 0.81s
% Output : CNFRefutation 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 17
% Syntax : Number of formulae : 104 ( 23 unt; 9 typ; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 247 ( 128 ~; 119 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 276 ( 167 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
le: ( $i * $i ) > $o ).
tff(decl_23,type,
max: ( $i * $i ) > $i ).
tff(decl_24,type,
f: $i > $i ).
tff(decl_25,type,
a0: $i ).
tff(decl_26,type,
eq: ( $i * $i ) > $o ).
tff(decl_27,type,
a1: $i ).
tff(decl_28,type,
a2: $i ).
tff(decl_29,type,
a3: $i ).
tff(decl_30,type,
s: $i > $i ).
cnf(sos_02,axiom,
( le(X1,X3)
| ~ le(max(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).
cnf(sos_01,axiom,
le(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_01) ).
cnf(sos_03,axiom,
( le(X2,X3)
| ~ le(max(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
cnf(sos_08,axiom,
( ~ eq(f(X1),a3)
| ~ eq(f(X2),a3)
| ~ le(s(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
cnf(sos_07,axiom,
( ~ eq(f(X1),a2)
| ~ eq(f(X2),a2)
| ~ le(s(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
cnf(sos_04,axiom,
( eq(f(X1),a0)
| eq(f(X1),a1)
| eq(f(X1),a2)
| eq(f(X1),a3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_04) ).
cnf(sos_06,axiom,
( ~ eq(f(X1),a1)
| ~ eq(f(X2),a1)
| ~ le(s(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).
cnf(sos_05,axiom,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a0)
| ~ le(s(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
cnf(c_0_8,axiom,
( le(X1,X3)
| ~ le(max(X1,X2),X3) ),
sos_02 ).
cnf(c_0_9,axiom,
le(X1,X1),
sos_01 ).
cnf(c_0_10,axiom,
( le(X2,X3)
| ~ le(max(X1,X2),X3) ),
sos_03 ).
cnf(c_0_11,plain,
le(X1,max(X1,X2)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,axiom,
( ~ eq(f(X1),a3)
| ~ eq(f(X2),a3)
| ~ le(s(X1),X2) ),
sos_08 ).
cnf(c_0_13,plain,
le(X1,max(X2,X1)),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_14,plain,
le(X1,max(max(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_15,axiom,
( ~ eq(f(X1),a2)
| ~ eq(f(X2),a2)
| ~ le(s(X1),X2) ),
sos_07 ).
cnf(c_0_16,plain,
le(X1,max(max(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_17,plain,
( ~ eq(f(max(X1,s(X2))),a3)
| ~ eq(f(X2),a3) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_18,axiom,
( eq(f(X1),a0)
| eq(f(X1),a1)
| eq(f(X1),a2)
| eq(f(X1),a3) ),
sos_04 ).
cnf(c_0_19,axiom,
( ~ eq(f(X1),a1)
| ~ eq(f(X2),a1)
| ~ le(s(X1),X2) ),
sos_06 ).
cnf(c_0_20,plain,
le(X1,max(max(max(X2,X1),X3),X4)),
inference(spm,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_21,plain,
( ~ eq(f(max(max(X1,s(X2)),X3)),a2)
| ~ eq(f(X2),a2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
( eq(f(max(X1,s(X2))),a2)
| eq(f(max(X1,s(X2))),a1)
| eq(f(max(X1,s(X2))),a0)
| ~ eq(f(X2),a3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
le(X1,max(X2,max(X1,X3))),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_24,axiom,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a0)
| ~ le(s(X1),X2) ),
sos_05 ).
cnf(c_0_25,plain,
le(X1,max(max(max(X1,X2),X3),X4)),
inference(spm,[status(thm)],[c_0_8,c_0_14]) ).
cnf(c_0_26,plain,
( ~ eq(f(max(max(max(X1,s(X2)),X3),X4)),a1)
| ~ eq(f(X2),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_27,plain,
( eq(f(max(max(X1,s(X2)),s(X3))),a0)
| eq(f(max(max(X1,s(X2)),s(X3))),a1)
| ~ eq(f(X2),a2)
| ~ eq(f(X3),a3) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,plain,
le(X1,max(X2,max(max(X1,X3),X4))),
inference(spm,[status(thm)],[c_0_8,c_0_23]) ).
cnf(c_0_29,plain,
( ~ eq(f(max(max(max(s(X1),X2),X3),X4)),a0)
| ~ eq(f(X1),a0) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( eq(f(max(max(max(X1,s(X2)),s(X3)),s(X4))),a0)
| ~ eq(f(X2),a1)
| ~ eq(f(X3),a2)
| ~ eq(f(X4),a3) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
le(X1,max(X2,max(max(max(X1,X3),X4),X5))),
inference(spm,[status(thm)],[c_0_8,c_0_28]) ).
cnf(c_0_32,plain,
( ~ eq(f(max(s(X1),X2)),a3)
| ~ eq(f(X1),a3) ),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_33,plain,
( ~ eq(f(max(max(max(s(X1),X2),X3),X4)),a1)
| ~ eq(f(X1),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_34,plain,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a1)
| ~ eq(f(X3),a2)
| ~ eq(f(X4),a3) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
le(X1,max(X2,max(X3,X1))),
inference(spm,[status(thm)],[c_0_10,c_0_13]) ).
cnf(c_0_36,plain,
( ~ eq(f(max(X1,max(max(max(s(X2),X3),X4),X5))),a2)
| ~ eq(f(X2),a2) ),
inference(spm,[status(thm)],[c_0_15,c_0_31]) ).
cnf(c_0_37,plain,
( eq(f(max(s(X1),X2)),a2)
| eq(f(max(s(X1),X2)),a1)
| eq(f(max(s(X1),X2)),a0)
| ~ eq(f(X1),a3) ),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_38,plain,
( ~ eq(f(X1),a1)
| ~ eq(f(X2),a2)
| ~ eq(f(X3),a3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_27]),c_0_34]) ).
cnf(c_0_39,plain,
( ~ eq(f(max(X1,max(X2,s(X3)))),a3)
| ~ eq(f(X3),a3) ),
inference(spm,[status(thm)],[c_0_12,c_0_35]) ).
cnf(c_0_40,plain,
( ~ eq(f(max(X1,max(X2,s(X3)))),a0)
| ~ eq(f(X3),a0) ),
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_41,plain,
( eq(f(max(s(X1),max(max(max(s(X2),X3),X4),X5))),a0)
| ~ eq(f(X2),a2)
| ~ eq(f(X1),a3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_42,plain,
( eq(f(max(X1,max(X2,s(X3)))),a2)
| eq(f(max(X1,max(X2,s(X3)))),a1)
| eq(f(max(X1,max(X2,s(X3)))),a0)
| ~ eq(f(X3),a3) ),
inference(spm,[status(thm)],[c_0_39,c_0_18]) ).
cnf(c_0_43,plain,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a2)
| ~ eq(f(X3),a3) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,plain,
( ~ eq(f(max(X1,max(max(max(s(X2),X3),X4),X5))),a3)
| ~ eq(f(X2),a3) ),
inference(spm,[status(thm)],[c_0_12,c_0_31]) ).
cnf(c_0_45,plain,
( ~ eq(f(X1),a2)
| ~ eq(f(X2),a3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_42]),c_0_43]),c_0_38]) ).
cnf(c_0_46,plain,
( ~ eq(f(max(s(X1),X2)),a1)
| ~ eq(f(X1),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_11]) ).
cnf(c_0_47,plain,
( eq(f(max(X1,max(max(max(s(X2),X3),X4),X5))),a1)
| eq(f(max(X1,max(max(max(s(X2),X3),X4),X5))),a0)
| ~ eq(f(X2),a3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_18]),c_0_45]) ).
cnf(c_0_48,plain,
le(X1,max(max(X2,max(X1,X3)),X4)),
inference(spm,[status(thm)],[c_0_8,c_0_16]) ).
cnf(c_0_49,plain,
( eq(f(max(s(X1),max(max(max(s(X2),X3),X4),X5))),a0)
| ~ eq(f(X1),a1)
| ~ eq(f(X2),a3) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
le(X1,max(max(X2,max(max(X1,X3),X4)),X5)),
inference(spm,[status(thm)],[c_0_8,c_0_48]) ).
cnf(c_0_51,plain,
( ~ eq(f(max(X1,max(X2,s(X3)))),a1)
| ~ eq(f(X3),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_52,plain,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a1)
| ~ eq(f(X3),a3) ),
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_53,plain,
( ~ eq(f(max(max(X1,max(max(s(X2),X3),X4)),X5)),a3)
| ~ eq(f(X2),a3) ),
inference(spm,[status(thm)],[c_0_12,c_0_50]) ).
cnf(c_0_54,plain,
( ~ eq(f(X1),a1)
| ~ eq(f(X2),a3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_47]),c_0_52]) ).
cnf(c_0_55,plain,
le(X1,max(max(max(X2,max(X3,X1)),X4),X5)),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_56,plain,
( ~ eq(f(max(X1,s(X2))),a0)
| ~ eq(f(X2),a0) ),
inference(spm,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_57,plain,
( eq(f(max(max(X1,max(max(s(X2),X3),X4)),X5)),a0)
| ~ eq(f(X2),a3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_18]),c_0_45]),c_0_54]) ).
cnf(c_0_58,plain,
( ~ eq(f(max(max(max(X1,max(X2,s(X3))),X4),X5)),a3)
| ~ eq(f(X3),a3) ),
inference(spm,[status(thm)],[c_0_12,c_0_55]) ).
cnf(c_0_59,plain,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a3) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
~ eq(f(X1),a3),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_18]),c_0_45]),c_0_54]),c_0_59]) ).
cnf(c_0_61,plain,
( ~ eq(f(max(X1,s(X2))),a2)
| ~ eq(f(X2),a2) ),
inference(spm,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_62,plain,
( eq(f(X1),a2)
| eq(f(X1),a1)
| eq(f(X1),a0) ),
inference(sr,[status(thm)],[c_0_18,c_0_60]) ).
cnf(c_0_63,plain,
( ~ eq(f(max(max(X1,s(X2)),X3)),a1)
| ~ eq(f(X2),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_64,plain,
( eq(f(max(X1,s(X2))),a0)
| eq(f(max(X1,s(X2))),a1)
| ~ eq(f(X2),a2) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,plain,
( ~ eq(f(max(max(s(X1),X2),X3)),a0)
| ~ eq(f(X1),a0) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_66,plain,
( eq(f(max(max(X1,s(X2)),s(X3))),a0)
| ~ eq(f(X2),a1)
| ~ eq(f(X3),a2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
( ~ eq(f(max(max(s(X1),X2),X3)),a1)
| ~ eq(f(X1),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_68,plain,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a1)
| ~ eq(f(X3),a2) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
( ~ eq(f(X1),a1)
| ~ eq(f(X2),a2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_64]),c_0_68]) ).
cnf(c_0_70,plain,
( ~ eq(f(s(X1)),a2)
| ~ eq(f(X1),a2) ),
inference(spm,[status(thm)],[c_0_15,c_0_9]) ).
cnf(c_0_71,plain,
( eq(f(max(X1,s(X2))),a0)
| ~ eq(f(X3),a2)
| ~ eq(f(X2),a2) ),
inference(spm,[status(thm)],[c_0_69,c_0_64]) ).
cnf(c_0_72,plain,
( eq(f(s(X1)),a0)
| eq(f(s(X1)),a1)
| ~ eq(f(X1),a2) ),
inference(spm,[status(thm)],[c_0_70,c_0_62]) ).
cnf(c_0_73,plain,
( eq(f(max(X1,s(X2))),a0)
| eq(f(X3),a0)
| ~ eq(f(X2),a2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_62]),c_0_69]) ).
cnf(c_0_74,plain,
( eq(f(s(X1)),a0)
| ~ eq(f(X2),a2)
| ~ eq(f(X1),a2) ),
inference(spm,[status(thm)],[c_0_69,c_0_72]) ).
cnf(c_0_75,plain,
( eq(f(max(X1,s(X2))),a0)
| eq(f(X2),a0)
| eq(f(X2),a1)
| eq(f(X3),a0) ),
inference(spm,[status(thm)],[c_0_73,c_0_62]) ).
cnf(c_0_76,plain,
( eq(f(s(X1)),a0)
| eq(f(X2),a0)
| ~ eq(f(X1),a2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_62]),c_0_69]) ).
cnf(c_0_77,plain,
( ~ eq(f(max(s(X1),X2)),a0)
| ~ eq(f(X1),a0) ),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_78,plain,
( eq(f(max(X1,s(X2))),a0)
| eq(f(X2),a1)
| eq(f(X2),a0) ),
inference(ef,[status(thm)],[c_0_75]) ).
cnf(c_0_79,plain,
( eq(f(s(X1)),a0)
| eq(f(X1),a0)
| eq(f(X1),a1)
| eq(f(X2),a0) ),
inference(spm,[status(thm)],[c_0_76,c_0_62]) ).
cnf(c_0_80,plain,
( eq(f(X1),a0)
| eq(f(X1),a1)
| ~ eq(f(X2),a0) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
( eq(f(s(X1)),a0)
| eq(f(X1),a1)
| eq(f(X1),a0) ),
inference(ef,[status(thm)],[c_0_79]) ).
cnf(c_0_82,plain,
( eq(f(X1),a1)
| eq(f(X2),a1)
| eq(f(X2),a0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_80]) ).
cnf(c_0_83,plain,
le(X1,max(X2,max(max(max(X3,X1),X4),X5))),
inference(spm,[status(thm)],[c_0_10,c_0_28]) ).
cnf(c_0_84,plain,
( ~ eq(f(max(X1,s(X2))),a1)
| ~ eq(f(X2),a1) ),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_85,plain,
( eq(f(X1),a0)
| eq(f(X1),a1) ),
inference(ef,[status(thm)],[c_0_82]) ).
cnf(c_0_86,plain,
le(X1,max(X2,max(max(max(X3,max(X4,X1)),X5),X6))),
inference(spm,[status(thm)],[c_0_10,c_0_83]) ).
cnf(c_0_87,plain,
( eq(f(max(X1,s(X2))),a0)
| ~ eq(f(X2),a1) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,plain,
le(X1,max(X2,max(max(max(X3,max(X4,max(X1,X5))),X6),X7))),
inference(spm,[status(thm)],[c_0_8,c_0_86]) ).
cnf(c_0_89,plain,
( ~ eq(f(X1),a0)
| ~ eq(f(X2),a1) ),
inference(spm,[status(thm)],[c_0_77,c_0_87]) ).
cnf(c_0_90,plain,
le(X1,max(X2,max(max(max(X3,max(X4,max(max(X5,X1),X6))),X7),X8))),
inference(spm,[status(thm)],[c_0_10,c_0_88]) ).
cnf(c_0_91,plain,
~ eq(f(X1),a1),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_85]),c_0_89]) ).
cnf(c_0_92,plain,
( ~ eq(f(max(X1,max(max(max(X2,max(X3,max(max(X4,s(X5)),X6))),X7),X8))),a0)
| ~ eq(f(X5),a0) ),
inference(spm,[status(thm)],[c_0_24,c_0_90]) ).
cnf(c_0_93,plain,
eq(f(X1),a0),
inference(sr,[status(thm)],[c_0_85,c_0_91]) ).
cnf(c_0_94,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_92,c_0_93]),c_0_93])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO620-1 : TPTP v8.1.2. Released v7.1.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n002.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 05:58:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.76/0.81 % Version : CSE_E---1.5
% 0.76/0.81 % Problem : theBenchmark.p
% 0.76/0.81 % Proof found
% 0.76/0.81 % SZS status Theorem for theBenchmark.p
% 0.76/0.81 % SZS output start Proof
% See solution above
% 0.76/0.82 % Total time : 0.245000 s
% 0.76/0.82 % SZS output end Proof
% 0.76/0.82 % Total time : 0.248000 s
%------------------------------------------------------------------------------