TSTP Solution File: KLE059+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : KLE059+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 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 : Thu Aug 31 05:25:08 EDT 2023
% Result : Theorem 0.19s 0.61s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KLE059+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 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 : Tue Aug 29 11:25:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.19/0.60 %-------------------------------------------
% 0.19/0.60 % File :CSE---1.6
% 0.19/0.60 % Problem :theBenchmark
% 0.19/0.60 % Transform :cnf
% 0.19/0.60 % Format :tptp:raw
% 0.19/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.60
% 0.19/0.60 % Result :Theorem 0.000000s
% 0.19/0.60 % Output :CNFRefutation 0.000000s
% 0.19/0.60 %-------------------------------------------
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 % File : KLE059+1 : TPTP v8.1.2. Released v4.0.0.
% 0.19/0.61 % Domain : Kleene Algebra (Domain Semirings)
% 0.19/0.61 % Problem : Domain is isotone
% 0.19/0.61 % Version : [Hoe08] axioms.
% 0.19/0.61 % English :
% 0.19/0.61
% 0.19/0.61 % Refs : [DS08] Desharnais & Struth (2008), Modal Semirings Revisited
% 0.19/0.61 % : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.19/0.61 % Source : [Hoe08]
% 0.19/0.61 % Names :
% 0.19/0.61
% 0.19/0.61 % Status : Theorem
% 0.19/0.61 % Rating : 0.08 v8.1.0, 0.11 v7.5.0, 0.12 v7.4.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.04 v6.2.0, 0.12 v6.1.0, 0.20 v6.0.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.04 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0
% 0.19/0.61 % Syntax : Number of formulae : 18 ( 16 unt; 0 def)
% 0.19/0.61 % Number of atoms : 20 ( 19 equ)
% 0.19/0.61 % Maximal formula atoms : 2 ( 1 avg)
% 0.19/0.61 % Number of connectives : 2 ( 0 ~; 0 |; 0 &)
% 0.19/0.61 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.19/0.61 % Maximal formula depth : 4 ( 3 avg)
% 0.19/0.61 % Maximal term depth : 4 ( 2 avg)
% 0.19/0.61 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.19/0.61 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.19/0.61 % Number of variables : 30 ( 30 !; 0 ?)
% 0.19/0.61 % SPC : FOF_THM_RFO_SEQ
% 0.19/0.61
% 0.19/0.61 % Comments : Equational encoding
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 %---Include axioms for domain semiring
% 0.19/0.61 include('Axioms/KLE001+0.ax').
% 0.19/0.61 %---Include axioms for domain
% 0.19/0.61 include('Axioms/KLE001+5.ax').
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 fof(goals,conjecture,
% 0.19/0.61 ! [X0,X1] :
% 0.19/0.61 ( addition(X0,X1) = X1
% 0.19/0.61 => addition(domain(X0),domain(X1)) = domain(X1) ) ).
% 0.19/0.61
% 0.19/0.61 %------------------------------------------------------------------------------
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % Proof found
% 0.19/0.61 % SZS status Theorem for theBenchmark
% 0.19/0.61 % SZS output start Proof
% 0.19/0.61 %ClaNum:30(EqnAxiom:10)
% 0.19/0.61 %VarNum:65(SingletonVarNum:30)
% 0.19/0.61 %MaxLitNum:2
% 0.19/0.61 %MaxfuncDepth:3
% 0.19/0.61 %SharedTerms:12
% 0.19/0.61 %goalClause: 12 28
% 0.19/0.61 %singleGoalClaCount:2
% 0.19/0.61 [11]E(f2(a1),a1)
% 0.19/0.61 [12]E(f3(a4,a5),a5)
% 0.19/0.61 [28]~E(f3(f2(a4),f2(a5)),f2(a5))
% 0.19/0.61 [13]E(f6(x131,a1),a1)
% 0.19/0.61 [14]E(f6(a1,x141),a1)
% 0.19/0.61 [15]E(f3(x151,a1),x151)
% 0.19/0.61 [16]E(f6(x161,a7),x161)
% 0.19/0.61 [17]E(f6(a7,x171),x171)
% 0.19/0.61 [18]E(f3(x181,x181),x181)
% 0.19/0.61 [19]E(f3(f2(x191),a7),a7)
% 0.19/0.61 [23]E(f3(x231,f6(f2(x231),x231)),f6(f2(x231),x231))
% 0.19/0.61 [20]E(f3(x201,x202),f3(x202,x201))
% 0.19/0.61 [21]E(f2(f3(x211,x212)),f3(f2(x211),f2(x212)))
% 0.19/0.61 [22]E(f2(f6(x221,f2(x222))),f2(f6(x221,x222)))
% 0.19/0.61 [24]E(f3(f3(x241,x242),x243),f3(x241,f3(x242,x243)))
% 0.19/0.61 [25]E(f6(f6(x251,x252),x253),f6(x251,f6(x252,x253)))
% 0.19/0.61 [26]E(f3(f6(x261,x262),f6(x261,x263)),f6(x261,f3(x262,x263)))
% 0.19/0.61 [27]E(f3(f6(x271,x272),f6(x273,x272)),f6(f3(x271,x273),x272))
% 0.19/0.61 [29]~P1(x291,x292)+E(f3(x291,x292),x292)
% 0.19/0.61 [30]P1(x301,x302)+~E(f3(x301,x302),x302)
% 0.19/0.61 %EqnAxiom
% 0.19/0.61 [1]E(x11,x11)
% 0.19/0.61 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.61 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.19/0.61 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53))
% 0.19/0.61 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62))
% 0.19/0.61 [7]~E(x71,x72)+E(f6(x71,x73),f6(x72,x73))
% 0.19/0.61 [8]~E(x81,x82)+E(f6(x83,x81),f6(x83,x82))
% 0.19/0.61 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93)
% 0.19/0.61 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101)
% 0.19/0.61
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 cnf(31,plain,
% 0.19/0.61 (E(a5,f3(a4,a5))),
% 0.19/0.61 inference(scs_inference,[],[12,2])).
% 0.19/0.61 cnf(38,plain,
% 0.19/0.61 (E(f3(x381,x381),x381)),
% 0.19/0.61 inference(rename_variables,[],[18])).
% 0.19/0.61 cnf(44,plain,
% 0.19/0.61 (~P1(f3(f2(a4),f2(a4)),f2(a5))),
% 0.19/0.61 inference(scs_inference,[],[12,28,18,38,2,30,29,10,3,8,7,6,5,4,9])).
% 0.19/0.61 cnf(50,plain,
% 0.19/0.61 (~E(f2(a5),f3(f2(a4),f2(a5)))),
% 0.19/0.61 inference(scs_inference,[],[15,28,44,30,9,2])).
% 0.19/0.61 cnf(77,plain,
% 0.19/0.61 (~E(f2(a5),f2(f3(a4,a5)))),
% 0.19/0.61 inference(scs_inference,[],[13,21,23,50,30,9,3])).
% 0.19/0.61 cnf(89,plain,
% 0.19/0.61 ($false),
% 0.19/0.61 inference(scs_inference,[],[31,77,4]),
% 0.19/0.61 ['proof']).
% 0.19/0.61 % SZS output end Proof
% 0.19/0.61 % Total time :0.000000s
%------------------------------------------------------------------------------