TSTP Solution File: SYO680-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SYO680-1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 04:12:56 EDT 2023
% Result : Unsatisfiable 0.21s 0.65s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 26
% Syntax : Number of formulae : 73 ( 9 unt; 8 typ; 0 def)
% Number of atoms : 245 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 330 ( 150 ~; 180 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 6 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 106 ( 6 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
'0': $i ).
tff(decl_23,type,
f: $i > $i ).
tff(decl_24,type,
'E': ( $i * $i ) > $o ).
tff(decl_25,type,
suc: $i > $i ).
tff(decl_26,type,
iLEQ: ( $i * $i ) > $o ).
tff(decl_27,type,
s: $i > $i ).
tff(decl_28,type,
'LE': ( $i * $i ) > $o ).
tff(decl_29,type,
z: $i ).
cnf(clause_102,axiom,
( 'E'(s(s(s('0'))),f(suc(X1)))
| 'LE'(f(X1),s(s(s('0'))))
| ~ 'LE'(f(suc(X1)),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_102) ).
cnf(clause_104,axiom,
'LE'(f(X1),s(s(s(s('0'))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_104) ).
cnf(clause_127,axiom,
( 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0'))))
| ~ 'LE'(f(X1),s(s(s(s('0'))))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_127) ).
cnf(clause_71,axiom,
( ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_71) ).
cnf(clause_14,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_14) ).
cnf(clause_84,axiom,
( 'E'(s(s('0')),f(suc(X1)))
| 'LE'(f(X1),s(s('0')))
| ~ 'LE'(f(suc(X1)),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_84) ).
cnf(clause_51,axiom,
( 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0')))
| ~ 'LE'(f(X1),s(s(s('0')))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_51) ).
cnf(clause_20,axiom,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_20) ).
cnf(clause_5,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
cnf(clause_15,axiom,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(suc(X1)),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_15) ).
cnf(clause_6,axiom,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(X1),s(s('0'))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_21,axiom,
( ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_21) ).
cnf(clause_91,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_91) ).
cnf(clause_114,axiom,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(suc(X1)),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_114) ).
cnf(clause_96,axiom,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(X1),s('0')) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_96) ).
cnf(clause_144,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_144) ).
cnf(clause_109,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_109) ).
cnf(clause_66,axiom,
~ 'LE'(f(z),'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_66) ).
cnf(c_0_18,axiom,
( 'E'(s(s(s('0'))),f(suc(X1)))
| 'LE'(f(X1),s(s(s('0'))))
| ~ 'LE'(f(suc(X1)),s(s(s(s('0'))))) ),
clause_102 ).
cnf(c_0_19,axiom,
'LE'(f(X1),s(s(s(s('0'))))),
clause_104 ).
cnf(c_0_20,axiom,
( 'E'(s(s(s('0'))),f(X1))
| 'LE'(f(X1),s(s(s('0'))))
| ~ 'LE'(f(X1),s(s(s(s('0'))))) ),
clause_127 ).
cnf(c_0_21,axiom,
( ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s(s('0'))),f(X2))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(suc(X1)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(suc(X3))) ),
clause_71 ).
cnf(c_0_22,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(suc(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]) ).
cnf(c_0_23,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'E'(s(s(s('0'))),f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_19])]) ).
cnf(c_0_24,plain,
( 'LE'(f(X1),s(s(s('0'))))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(suc(X2)))
| ~ 'E'(s(s(s('0'))),f(X3))
| ~ 'E'(s(s(s('0'))),f(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_25,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X3)))
| ~ 'E'(s(s(s('0'))),f(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_22]),c_0_23]) ).
cnf(c_0_26,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| 'LE'(f(X3),s(s(s('0'))))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_23]) ).
cnf(c_0_27,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s(s(s('0'))),f(X1))
| ~ 'E'(s(s(s('0'))),f(suc(X1))) ),
clause_14 ).
cnf(c_0_28,plain,
( 'LE'(f(X1),s(s(s('0'))))
| 'LE'(f(X2),s(s(s('0'))))
| ~ iLEQ(suc(X2),suc(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),c_0_22]) ).
cnf(c_0_29,axiom,
( 'E'(s(s('0')),f(suc(X1)))
| 'LE'(f(X1),s(s('0')))
| ~ 'LE'(f(suc(X1)),s(s(s('0')))) ),
clause_84 ).
cnf(c_0_30,plain,
'LE'(f(X1),s(s(s('0')))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_23]),c_0_22]) ).
cnf(c_0_31,axiom,
( 'E'(s(s('0')),f(X1))
| 'LE'(f(X1),s(s('0')))
| ~ 'LE'(f(X1),s(s(s('0')))) ),
clause_51 ).
cnf(c_0_32,axiom,
( ~ 'E'(s(s('0')),f(suc(X1)))
| ~ 'E'(s(s('0')),f(X1))
| ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s('0')),f(X2))
| ~ 'E'(s(s('0')),f(X3)) ),
clause_20 ).
cnf(c_0_33,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(suc(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30])]) ).
cnf(c_0_34,plain,
( 'LE'(f(X1),s(s('0')))
| 'E'(s(s('0')),f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_30])]) ).
cnf(c_0_35,plain,
( 'LE'(f(X1),s(s('0')))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(suc(X2)))
| ~ 'E'(s(s('0')),f(X3))
| ~ 'E'(s(s('0')),f(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_36,plain,
( 'LE'(f(X1),s(s('0')))
| 'LE'(f(X2),s(s('0')))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s(s('0')),f(suc(X3)))
| ~ 'E'(s(s('0')),f(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_34]) ).
cnf(c_0_37,plain,
( 'LE'(f(X1),s(s('0')))
| 'LE'(f(X2),s(s('0')))
| 'LE'(f(X3),s(s('0')))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_34]) ).
cnf(c_0_38,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s(s('0')),f(X1))
| ~ 'E'(s(s('0')),f(suc(X1))) ),
clause_5 ).
cnf(c_0_39,plain,
( 'LE'(f(X1),s(s('0')))
| 'LE'(f(X2),s(s('0')))
| ~ iLEQ(suc(X2),suc(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_34]),c_0_33]) ).
cnf(c_0_40,axiom,
( 'E'(s('0'),f(suc(X1)))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(suc(X1)),s(s('0'))) ),
clause_15 ).
cnf(c_0_41,plain,
'LE'(f(X1),s(s('0'))),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_38]),c_0_34]),c_0_33]) ).
cnf(c_0_42,axiom,
( 'E'(s('0'),f(X1))
| 'LE'(f(X1),s('0'))
| ~ 'LE'(f(X1),s(s('0'))) ),
clause_6 ).
cnf(c_0_43,axiom,
( ~ iLEQ(suc(X1),suc(X2))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2))
| ~ 'E'(s('0'),f(suc(X1)))
| ~ 'E'(s('0'),f(X1)) ),
clause_21 ).
cnf(c_0_44,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(suc(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_41])]) ).
cnf(c_0_45,plain,
( 'LE'(f(X1),s('0'))
| 'E'(s('0'),f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_41])]) ).
cnf(c_0_46,plain,
( 'LE'(f(X1),s('0'))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(suc(X2)))
| ~ 'E'(s('0'),f(X3))
| ~ 'E'(s('0'),f(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_47,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'(s('0'),f(suc(X3)))
| ~ 'E'(s('0'),f(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_44]),c_0_45]) ).
cnf(c_0_48,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| 'LE'(f(X3),s('0'))
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_44]),c_0_45]) ).
cnf(c_0_49,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'(s('0'),f(X1))
| ~ 'E'(s('0'),f(suc(X1))) ),
clause_91 ).
cnf(c_0_50,plain,
( 'LE'(f(X1),s('0'))
| 'LE'(f(X2),s('0'))
| ~ iLEQ(suc(X2),suc(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_45]),c_0_44]) ).
cnf(c_0_51,axiom,
( 'E'('0',f(suc(X1)))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(suc(X1)),s('0')) ),
clause_114 ).
cnf(c_0_52,plain,
'LE'(f(X1),s('0')),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_49]),c_0_45]),c_0_44]) ).
cnf(c_0_53,axiom,
( 'E'('0',f(X1))
| 'LE'(f(X1),'0')
| ~ 'LE'(f(X1),s('0')) ),
clause_96 ).
cnf(c_0_54,axiom,
( ~ 'E'('0',f(suc(X1)))
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X2))
| ~ 'E'('0',f(X3)) ),
clause_144 ).
cnf(c_0_55,plain,
( 'LE'(f(X1),'0')
| 'E'('0',f(suc(X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_56,plain,
( 'LE'(f(X1),'0')
| 'E'('0',f(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_52])]) ).
cnf(c_0_57,plain,
( 'LE'(f(X1),'0')
| ~ iLEQ(suc(X1),suc(X2))
| ~ iLEQ(suc(X2),suc(X3))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(suc(X2)))
| ~ 'E'('0',f(X3))
| ~ 'E'('0',f(X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_56]) ).
cnf(c_0_58,plain,
( 'LE'(f(X1),'0')
| 'LE'(f(X2),'0')
| ~ iLEQ(suc(X2),suc(X3))
| ~ iLEQ(suc(X3),suc(X1))
| ~ 'E'('0',f(suc(X3)))
| ~ 'E'('0',f(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_55]),c_0_56]) ).
cnf(c_0_59,plain,
( 'LE'(f(X1),'0')
| 'LE'(f(X2),'0')
| 'LE'(f(X3),'0')
| ~ iLEQ(suc(X2),suc(X1))
| ~ iLEQ(suc(X1),suc(X3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_55]),c_0_56]) ).
cnf(c_0_60,axiom,
( iLEQ(suc(X1),suc(X1))
| ~ 'E'('0',f(X1))
| ~ 'E'('0',f(suc(X1))) ),
clause_109 ).
cnf(c_0_61,plain,
( 'LE'(f(X1),'0')
| 'LE'(f(X2),'0')
| ~ iLEQ(suc(X2),suc(X1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_56]),c_0_55]) ).
cnf(c_0_62,axiom,
~ 'LE'(f(z),'0'),
clause_66 ).
cnf(c_0_63,plain,
'LE'(f(X1),'0'),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_60]),c_0_56]),c_0_55]) ).
cnf(c_0_64,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SYO680-1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 06:45:14 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.63 start to proof: theBenchmark
% 0.21/0.65 % Version : CSE_E---1.5
% 0.21/0.65 % Problem : theBenchmark.p
% 0.21/0.65 % Proof found
% 0.21/0.65 % SZS status Theorem for theBenchmark.p
% 0.21/0.65 % SZS output start Proof
% See solution above
% 0.21/0.66 % Total time : 0.012000 s
% 0.21/0.66 % SZS output end Proof
% 0.21/0.66 % Total time : 0.015000 s
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