%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : KLE003+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n022.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 09:59:46 EDT 2024
% Result : Theorem 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : KLE003+1 : TPTP v8.2.0. Released v4.0.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.28 % Computer : n022.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu Jun 20 22:32:08 EDT 2024
% 0.09/0.28 % CPUTime :
% 0.13/0.45 start to proof:theBenchmark
% 0.13/0.48 %-------------------------------------------
% 0.13/0.48 % File :CSE---1.7
% 0.13/0.48 % Problem :theBenchmark
% 0.13/0.48 % Transform :cnf
% 0.13/0.48 % Format :tptp:raw
% 0.13/0.48 % Command :java -jar mcs_scs.jar %d %s
% 0.13/0.48
% 0.13/0.48 % Result :Theorem 0.000000s
% 0.13/0.48 % Output :CNFRefutation 0.000000s
% 0.13/0.48 %-------------------------------------------
% 0.13/0.48 %------------------------------------------------------------------------------
% 0.13/0.48 % File : KLE003+1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.48 % Domain : Kleene Algebra (Idempotent Semirings)
% 0.13/0.48 % Problem : A semiring is idempotent iff 1 is idempotent
% 0.13/0.48 % Version : [Hoe08] axioms.
% 0.13/0.48 % English :
% 0.13/0.48
% 0.13/0.48 % Refs : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.13/0.48 % Source : [Hoe08]
% 0.13/0.48 % Names :
% 0.13/0.48
% 0.13/0.48 % Status : Theorem
% 0.13/0.48 % Rating : 0.00 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.04 v6.2.0, 0.08 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.4.0, 0.11 v5.3.0, 0.15 v5.2.0, 0.05 v5.0.0, 0.00 v4.1.0, 0.04 v4.0.0
% 0.13/0.48 % Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% 0.13/0.48 % Number of atoms : 15 ( 14 equ)
% 0.13/0.48 % Maximal formula atoms : 2 ( 1 avg)
% 0.13/0.48 % Number of connectives : 2 ( 0 ~; 0 |; 0 &)
% 0.13/0.48 % ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% 0.13/0.48 % Maximal formula depth : 4 ( 3 avg)
% 0.13/0.48 % Maximal term depth : 3 ( 1 avg)
% 0.13/0.48 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.13/0.48 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.13/0.48 % Number of variables : 23 ( 23 !; 0 ?)
% 0.13/0.48 % SPC : FOF_THM_RFO_SEQ
% 0.13/0.48
% 0.13/0.48 % Comments : Inequational axioms
% 0.13/0.48 %------------------------------------------------------------------------------
% 0.13/0.48 %---Include axioms for idempotent semiring
% 0.13/0.48 include('Axioms/KLE001+0.ax').
% 0.13/0.48 %------------------------------------------------------------------------------
% 0.13/0.48 fof(goals,conjecture,
% 0.13/0.48 ( ! [X0] : addition(X0,X0) = X0
% 0.13/0.48 <=> addition(one,one) = one ) ).
% 0.13/0.48
% 0.13/0.48 %------------------------------------------------------------------------------
% 0.13/0.48 %-------------------------------------------
% 0.13/0.48 % Proof found
% 0.13/0.48 % SZS status Theorem for theBenchmark
% 0.13/0.48 % SZS output start Proof
% 0.13/0.48 %ClaNum:24(EqnAxiom:9)
% 0.13/0.48 %VarNum:51(SingletonVarNum:24)
% 0.13/0.48 %MaxLitNum:2
% 0.13/0.48 %MaxfuncDepth:2
% 0.13/0.48 %SharedTerms:8
% 0.13/0.48 %goalClause: 22
% 0.13/0.48 [10]E(f2(x101,a1),a1)
% 0.13/0.48 [11]E(f2(a1,x111),a1)
% 0.13/0.48 [12]E(f3(x121,a1),x121)
% 0.13/0.48 [13]E(f2(x131,a5),x131)
% 0.13/0.48 [14]E(f2(a5,x141),x141)
% 0.13/0.48 [15]E(f3(x151,x151),x151)
% 0.13/0.48 [16]E(f3(x161,x162),f3(x162,x161))
% 0.13/0.48 [17]E(f3(f3(x171,x172),x173),f3(x171,f3(x172,x173)))
% 0.13/0.48 [18]E(f2(f2(x181,x182),x183),f2(x181,f2(x182,x183)))
% 0.13/0.48 [19]E(f3(f2(x191,x192),f2(x191,x193)),f2(x191,f3(x192,x193)))
% 0.13/0.48 [20]E(f3(f2(x201,x202),f2(x203,x202)),f2(f3(x201,x203),x202))
% 0.13/0.48 [22]~E(f3(a5,a5),a5)+~E(f3(a4,a4),a4)
% 0.13/0.48 [23]~P1(x231,x232)+E(f3(x231,x232),x232)
% 0.13/0.48 [24]P1(x241,x242)+~E(f3(x241,x242),x242)
% 0.13/0.48 %EqnAxiom
% 0.13/0.48 [1]E(x11,x11)
% 0.13/0.48 [2]E(x22,x21)+~E(x21,x22)
% 0.13/0.48 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.13/0.48 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.13/0.48 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.13/0.48 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.13/0.48 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.13/0.48 [8]P1(x82,x83)+~E(x81,x82)+~P1(x81,x83)
% 0.13/0.48 [9]P1(x93,x92)+~E(x91,x92)+~P1(x93,x91)
% 0.13/0.48
% 0.13/0.48 %-------------------------------------------
% 0.13/0.49 cnf(26,plain,
% 0.13/0.49 (E(f3(x261,x261),x261)),
% 0.13/0.49 inference(rename_variables,[],[15])).
% 0.13/0.49 cnf(30,plain,
% 0.13/0.49 ($false),
% 0.13/0.49 inference(scs_inference,[],[10,15,26,22,23,2,24]),
% 0.13/0.49 ['proof']).
% 0.13/0.49 % SZS output end Proof
% 0.13/0.49 % Total time :0.000000s
%------------------------------------------------------------------------------