TSTP Solution File: KLE146+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n017.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 05:25:22 EDT 2023
% Result : Theorem 0.18s 0.70s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n017.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
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 12:05:43 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 % File :CSE---1.6
% 0.18/0.70 % Problem :theBenchmark
% 0.18/0.70 % Transform :cnf
% 0.18/0.70 % Format :tptp:raw
% 0.18/0.70 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.70
% 0.18/0.70 % Result :Theorem 0.100000s
% 0.18/0.70 % Output :CNFRefutation 0.100000s
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 %------------------------------------------------------------------------------
% 0.18/0.70 % File : KLE146+1 : TPTP v8.1.2. Released v4.0.0.
% 0.18/0.70 % Domain : Kleene Algebra (Demonic Refinement Algebra)
% 0.18/0.70 % Problem : Skip is part of strong iteration
% 0.18/0.70 % Version : [Hoe08] axioms.
% 0.18/0.70 % English :
% 0.18/0.70
% 0.18/0.70 % Refs : [vW02] von Wright (2002), From Kleene Algebra to Refinement A
% 0.18/0.70 % : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.18/0.70 % Source : [Hoe08]
% 0.18/0.70 % Names :
% 0.18/0.70
% 0.18/0.70 % Status : Theorem
% 0.18/0.70 % Rating : 0.19 v8.1.0, 0.22 v7.5.0, 0.25 v7.4.0, 0.10 v7.3.0, 0.21 v7.1.0, 0.13 v7.0.0, 0.17 v6.4.0, 0.23 v6.3.0, 0.25 v6.2.0, 0.28 v6.1.0, 0.33 v6.0.0, 0.26 v5.5.0, 0.33 v5.4.0, 0.43 v5.3.0, 0.48 v5.2.0, 0.35 v5.1.0, 0.38 v5.0.0, 0.33 v4.1.0, 0.35 v4.0.1, 0.30 v4.0.0
% 0.18/0.70 % Syntax : Number of formulae : 19 ( 15 unt; 0 def)
% 0.18/0.70 % Number of atoms : 23 ( 15 equ)
% 0.18/0.70 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.70 % Number of connectives : 4 ( 0 ~; 0 |; 0 &)
% 0.18/0.70 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.18/0.70 % Maximal formula depth : 5 ( 3 avg)
% 0.18/0.70 % Maximal term depth : 4 ( 2 avg)
% 0.18/0.70 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.18/0.70 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.18/0.70 % Number of variables : 35 ( 35 !; 0 ?)
% 0.18/0.70 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.70
% 0.18/0.70 % Comments :
% 0.18/0.70 %------------------------------------------------------------------------------
% 0.18/0.70 %---Include axioms for demonic refinement algebra
% 0.18/0.70 include('Axioms/KLE004+0.ax').
% 0.18/0.70 %------------------------------------------------------------------------------
% 0.18/0.70 fof(goals,conjecture,
% 0.18/0.70 ! [X0] : leq(one,strong_iteration(X0)) ).
% 0.18/0.70
% 0.18/0.70 %------------------------------------------------------------------------------
% 0.18/0.70 %-------------------------------------------
% 0.18/0.70 % Proof found
% 0.18/0.70 % SZS status Theorem for theBenchmark
% 0.18/0.70 % SZS output start Proof
% 0.18/0.71 %ClaNum:31(EqnAxiom:11)
% 0.18/0.71 %VarNum:83(SingletonVarNum:36)
% 0.18/0.71 %MaxLitNum:2
% 0.18/0.71 %MaxfuncDepth:3
% 0.18/0.71 %SharedTerms:5
% 0.18/0.71 %goalClause: 26
% 0.18/0.71 %singleGoalClaCount:1
% 0.18/0.71 [26]~P1(a5,f6(a4))
% 0.18/0.71 [12]E(f2(a1,x121),a1)
% 0.18/0.71 [13]E(f3(x131,a1),x131)
% 0.18/0.71 [14]E(f2(x141,a5),x141)
% 0.18/0.71 [15]E(f2(a5,x151),x151)
% 0.18/0.71 [16]E(f3(x161,x161),x161)
% 0.18/0.71 [18]E(f3(f2(x181,f6(x181)),a5),f6(x181))
% 0.18/0.71 [19]E(f3(a5,f2(x191,f7(x191))),f7(x191))
% 0.18/0.71 [20]E(f3(a5,f2(f7(x201),x201)),f7(x201))
% 0.18/0.71 [21]E(f3(f7(x211),f2(f6(x211),a1)),f6(x211))
% 0.18/0.71 [17]E(f3(x171,x172),f3(x172,x171))
% 0.18/0.71 [22]E(f3(f3(x221,x222),x223),f3(x221,f3(x222,x223)))
% 0.18/0.71 [23]E(f2(f2(x231,x232),x233),f2(x231,f2(x232,x233)))
% 0.18/0.71 [24]E(f3(f2(x241,x242),f2(x241,x243)),f2(x241,f3(x242,x243)))
% 0.18/0.71 [25]E(f3(f2(x251,x252),f2(x253,x252)),f2(f3(x251,x253),x252))
% 0.18/0.71 [27]~P1(x271,x272)+E(f3(x271,x272),x272)
% 0.18/0.71 [28]P1(x281,x282)+~E(f3(x281,x282),x282)
% 0.18/0.71 [29]~P1(x291,f3(f2(x292,x291),x293))+P1(x291,f2(f6(x292),x293))
% 0.18/0.71 [30]~P1(f3(f2(x303,x302),x301),x303)+P1(f2(x301,f7(x302)),x303)
% 0.18/0.71 [31]~P1(f3(f2(x311,x313),x312),x313)+P1(f2(f7(x311),x312),x313)
% 0.18/0.71 %EqnAxiom
% 0.18/0.71 [1]E(x11,x11)
% 0.18/0.71 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.71 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.18/0.71 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.18/0.71 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.18/0.71 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.18/0.71 [8]~E(x81,x82)+E(f6(x81),f6(x82))
% 0.18/0.71 [9]~E(x91,x92)+E(f7(x91),f7(x92))
% 0.18/0.71 [10]P1(x102,x103)+~E(x101,x102)+~P1(x101,x103)
% 0.18/0.71 [11]P1(x113,x112)+~E(x111,x112)+~P1(x113,x111)
% 0.18/0.71
% 0.18/0.71 %-------------------------------------------
% 0.18/0.71 cnf(32,plain,
% 0.18/0.71 (E(x321,f3(x321,x321))),
% 0.18/0.71 inference(scs_inference,[],[16,2])).
% 0.18/0.71 cnf(33,plain,
% 0.18/0.71 (P1(x331,x331)),
% 0.18/0.71 inference(scs_inference,[],[16,2,28])).
% 0.18/0.71 cnf(35,plain,
% 0.18/0.71 (~E(a5,f6(a4))),
% 0.18/0.71 inference(scs_inference,[],[26,16,2,28,11])).
% 0.18/0.71 cnf(37,plain,
% 0.18/0.71 (E(f3(f3(a5,a5),a1),a5)),
% 0.18/0.71 inference(scs_inference,[],[26,16,13,2,28,11,10,3])).
% 0.18/0.71 cnf(38,plain,
% 0.18/0.71 (E(f3(x381,x381),x381)),
% 0.18/0.71 inference(rename_variables,[],[16])).
% 0.18/0.71 cnf(42,plain,
% 0.18/0.71 (E(f3(x421,f3(x422,x422)),f3(x421,x422))),
% 0.18/0.71 inference(scs_inference,[],[26,16,38,13,2,28,11,10,3,9,8,7])).
% 0.18/0.71 cnf(49,plain,
% 0.18/0.71 (~E(f3(a5,f6(a4)),f6(a4))),
% 0.18/0.71 inference(scs_inference,[],[26,35,2,28])).
% 0.18/0.71 cnf(51,plain,
% 0.18/0.71 (~P1(a5,f2(f6(a4),a5))),
% 0.18/0.71 inference(scs_inference,[],[26,14,35,2,28,11])).
% 0.18/0.71 cnf(52,plain,
% 0.18/0.71 (E(f2(x521,a5),x521)),
% 0.18/0.71 inference(rename_variables,[],[14])).
% 0.18/0.71 cnf(53,plain,
% 0.18/0.71 (~E(f3(a5,a5),f6(a4))),
% 0.18/0.71 inference(scs_inference,[],[26,14,32,35,2,28,11,3])).
% 0.18/0.71 cnf(55,plain,
% 0.18/0.71 (~P1(f2(a5,a5),f6(a4))),
% 0.18/0.71 inference(scs_inference,[],[26,14,52,32,35,2,28,11,3,10])).
% 0.18/0.71 cnf(57,plain,
% 0.18/0.71 (~P1(a5,f3(f2(a4,a5),a5))),
% 0.18/0.71 inference(scs_inference,[],[26,14,52,32,35,2,28,11,3,10,29])).
% 0.18/0.71 cnf(60,plain,
% 0.18/0.71 (P1(x601,f3(x601,x601))),
% 0.18/0.71 inference(scs_inference,[],[12,42,2,28])).
% 0.18/0.71 cnf(70,plain,
% 0.18/0.71 (~E(f3(a5,a5),f3(f2(a4,a5),a5))),
% 0.18/0.71 inference(scs_inference,[],[60,49,57,2,11])).
% 0.18/0.71 cnf(72,plain,
% 0.18/0.71 (~E(f3(a5,f3(f2(a4,a5),a5)),f3(f2(a4,a5),a5))),
% 0.18/0.71 inference(scs_inference,[],[60,49,57,2,11,28])).
% 0.18/0.71 cnf(84,plain,
% 0.18/0.71 (E(f3(x841,a1),x841)),
% 0.18/0.71 inference(rename_variables,[],[13])).
% 0.18/0.71 cnf(87,plain,
% 0.18/0.71 (~E(f3(f3(f2(a4,a5),a5),a5),f3(f2(a4,a5),a5))),
% 0.18/0.71 inference(scs_inference,[],[13,84,17,72,55,6,2,11,10,3])).
% 0.18/0.71 cnf(98,plain,
% 0.18/0.71 (~E(f3(f2(a4,a5),a5),f2(a4,a5))),
% 0.18/0.71 inference(scs_inference,[],[87,6])).
% 0.18/0.71 cnf(99,plain,
% 0.18/0.71 (~E(f3(f2(a4,a5),a5),f3(a5,a5))),
% 0.18/0.71 inference(scs_inference,[],[70,87,6,2])).
% 0.18/0.71 cnf(114,plain,
% 0.18/0.71 (~E(f2(a4,a5),a5)),
% 0.18/0.71 inference(scs_inference,[],[99,6])).
% 0.18/0.71 cnf(115,plain,
% 0.18/0.71 (~E(f2(a4,a5),f3(f2(a4,a5),a5))),
% 0.18/0.71 inference(scs_inference,[],[99,98,6,2])).
% 0.18/0.71 cnf(148,plain,
% 0.18/0.71 (E(f3(x1481,x1481),x1481)),
% 0.18/0.71 inference(rename_variables,[],[16])).
% 0.18/0.71 cnf(152,plain,
% 0.18/0.71 (~P1(f3(a5,a5),f2(f6(a4),a5))),
% 0.18/0.71 inference(scs_inference,[],[16,148,37,32,114,51,6,11,3,2,10])).
% 0.18/0.71 cnf(157,plain,
% 0.18/0.71 (P1(x1571,x1571)),
% 0.18/0.71 inference(rename_variables,[],[33])).
% 0.18/0.71 cnf(161,plain,
% 0.18/0.71 (P1(f6(x1611),f3(f2(x1611,f6(x1611)),a5))),
% 0.18/0.71 inference(scs_inference,[],[16,18,32,33,157,53,11,3,2,10])).
% 0.18/0.71 cnf(167,plain,
% 0.18/0.71 (~E(f2(a4,a5),f3(a5,f2(a4,a5)))),
% 0.18/0.71 inference(scs_inference,[],[17,33,115,152,161,29,11,3])).
% 0.18/0.71 cnf(281,plain,
% 0.18/0.71 (P1(x2811,x2811)),
% 0.18/0.71 inference(rename_variables,[],[33])).
% 0.18/0.71 cnf(284,plain,
% 0.18/0.71 ($false),
% 0.18/0.71 inference(scs_inference,[],[22,42,33,281,167,87,2,11,10,3]),
% 0.18/0.71 ['proof']).
% 0.18/0.71 % SZS output end Proof
% 0.18/0.71 % Total time :0.100000s
%------------------------------------------------------------------------------