%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : KLE001+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n025.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 : Mon Jun 24 09:59:45 EDT 2024
% Result : Theorem 0.18s 0.56s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE001+1 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n025.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 20 22:52:54 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.18/0.54 start to proof:theBenchmark
% 0.18/0.56 %-------------------------------------------
% 0.18/0.56 % File :CSE---1.7
% 0.18/0.56 % Problem :theBenchmark
% 0.18/0.56 % Transform :cnf
% 0.18/0.56 % Format :tptp:raw
% 0.18/0.56 % Command :java -jar mcs_scs.jar %d %s
% 0.18/0.56
% 0.18/0.56 % Result :Theorem 0.000000s
% 0.18/0.56 % Output :CNFRefutation 0.000000s
% 0.18/0.56 %-------------------------------------------
% 0.18/0.56 %------------------------------------------------------------------------------
% 0.18/0.56 % File : KLE001+1 : TPTP v8.2.0. Released v4.0.0.
% 0.18/0.56 % Domain : Kleene Algebra (Idempotent Semirings)
% 0.18/0.56 % Problem : Addition is isotone
% 0.18/0.56 % Version : [Hoe08] axioms.
% 0.18/0.56 % English :
% 0.18/0.56
% 0.18/0.56 % Refs : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.18/0.56 % Source : [Hoe08]
% 0.18/0.56 % Names :
% 0.18/0.56
% 0.18/0.56 % Status : Theorem
% 0.18/0.56 % Rating : 0.00 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.12 v6.3.0, 0.08 v6.1.0, 0.13 v6.0.0, 0.09 v5.5.0, 0.04 v5.4.0, 0.07 v5.3.0, 0.11 v5.2.0, 0.05 v5.0.0, 0.04 v4.1.0, 0.09 v4.0.0
% 0.18/0.56 % Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% 0.18/0.56 % Number of atoms : 15 ( 12 equ)
% 0.18/0.56 % Maximal formula atoms : 2 ( 1 avg)
% 0.18/0.56 % Number of connectives : 2 ( 0 ~; 0 |; 0 &)
% 0.18/0.56 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.18/0.56 % Maximal formula depth : 5 ( 3 avg)
% 0.18/0.56 % Maximal term depth : 3 ( 1 avg)
% 0.18/0.56 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.18/0.56 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.18/0.56 % Number of variables : 25 ( 25 !; 0 ?)
% 0.18/0.56 % SPC : FOF_THM_RFO_SEQ
% 0.18/0.56
% 0.18/0.56 % Comments : Inequational axioms
% 0.18/0.56 %------------------------------------------------------------------------------
% 0.18/0.56 %---Include axioms for idempotent semiring
% 0.18/0.56 include('Axioms/KLE001+0.ax').
% 0.18/0.56 %------------------------------------------------------------------------------
% 0.18/0.56 fof(goals,conjecture,
% 0.18/0.56 ! [X0,X1,X2] :
% 0.18/0.56 ( leq(X0,X1)
% 0.18/0.56 => leq(addition(X0,X2),addition(X0,X2)) ) ).
% 0.18/0.56
% 0.18/0.56 %------------------------------------------------------------------------------
% 0.18/0.56 %-------------------------------------------
% 0.18/0.56 % Proof found
% 0.18/0.56 % SZS status Theorem for theBenchmark
% 0.18/0.56 % SZS output start Proof
% 0.18/0.56 %ClaNum:24(EqnAxiom:9)
% 0.18/0.56 %VarNum:51(SingletonVarNum:24)
% 0.18/0.56 %MaxLitNum:2
% 0.18/0.56 %MaxfuncDepth:2
% 0.18/0.56 %SharedTerms:8
% 0.18/0.56 %goalClause: 10 22
% 0.18/0.56 %singleGoalClaCount:2
% 0.18/0.56 [10]P1(a1,a3)
% 0.18/0.56 [22]~P1(f2(a1,a6),f2(a1,a6))
% 0.18/0.57 [11]E(f5(x111,a4),a4)
% 0.18/0.57 [12]E(f5(a4,x121),a4)
% 0.18/0.57 [13]E(f2(x131,a4),x131)
% 0.18/0.57 [14]E(f5(x141,a7),x141)
% 0.18/0.57 [15]E(f5(a7,x151),x151)
% 0.18/0.57 [16]E(f2(x161,x161),x161)
% 0.18/0.57 [17]E(f2(x171,x172),f2(x172,x171))
% 0.18/0.57 [18]E(f2(f2(x181,x182),x183),f2(x181,f2(x182,x183)))
% 0.18/0.57 [19]E(f5(f5(x191,x192),x193),f5(x191,f5(x192,x193)))
% 0.18/0.57 [20]E(f2(f5(x201,x202),f5(x201,x203)),f5(x201,f2(x202,x203)))
% 0.18/0.57 [21]E(f2(f5(x211,x212),f5(x213,x212)),f5(f2(x211,x213),x212))
% 0.18/0.57 [23]~P1(x231,x232)+E(f2(x231,x232),x232)
% 0.18/0.57 [24]P1(x241,x242)+~E(f2(x241,x242),x242)
% 0.18/0.57 %EqnAxiom
% 0.18/0.57 [1]E(x11,x11)
% 0.18/0.57 [2]E(x22,x21)+~E(x21,x22)
% 0.18/0.57 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.18/0.57 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.18/0.57 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.18/0.57 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 0.18/0.57 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 0.18/0.57 [8]P1(x82,x83)+~E(x81,x82)+~P1(x81,x83)
% 0.18/0.57 [9]P1(x93,x92)+~E(x91,x92)+~P1(x93,x91)
% 0.18/0.57
% 0.18/0.57 %-------------------------------------------
% 0.18/0.57 cnf(25,plain,
% 0.18/0.57 ($false),
% 0.18/0.57 inference(scs_inference,[],[22,16,24]),
% 0.18/0.57 ['proof']).
% 0.18/0.57 % SZS output end Proof
% 0.18/0.57 % Total time :0.000000s
%------------------------------------------------------------------------------