TSTP Solution File: KLE002+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : KLE002+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 : n029.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 05:24:54 EDT 2023
% Result : Theorem 0.56s 0.76s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n029.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 : Tue Aug 29 12:16:56 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.56/0.76 %-------------------------------------------
% 0.56/0.76 % File :CSE---1.6
% 0.56/0.76 % Problem :theBenchmark
% 0.56/0.76 % Transform :cnf
% 0.56/0.76 % Format :tptp:raw
% 0.56/0.76 % Command :java -jar mcs_scs.jar %d %s
% 0.56/0.76
% 0.56/0.76 % Result :Theorem 0.130000s
% 0.56/0.76 % Output :CNFRefutation 0.130000s
% 0.56/0.76 %-------------------------------------------
% 0.56/0.76 %------------------------------------------------------------------------------
% 0.56/0.76 % File : KLE002+1 : TPTP v8.1.2. Released v4.0.0.
% 0.56/0.76 % Domain : Kleene Algebra (Idempotent Semirings)
% 0.56/0.76 % Problem : Multiplication is isotone
% 0.56/0.76 % Version : [Hoe08] axioms.
% 0.56/0.76 % English :
% 0.56/0.76
% 0.56/0.76 % Refs : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.56/0.76 % Source : [Hoe08]
% 0.56/0.76 % Names :
% 0.56/0.76
% 0.56/0.76 % Status : Theorem
% 0.56/0.76 % Rating : 0.08 v8.1.0, 0.14 v7.5.0, 0.16 v7.4.0, 0.07 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.23 v6.0.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.26 v5.2.0, 0.15 v5.1.0, 0.14 v5.0.0, 0.12 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0
% 0.56/0.76 % Syntax : Number of formulae : 13 ( 11 unt; 0 def)
% 0.56/0.76 % Number of atoms : 15 ( 12 equ)
% 0.56/0.76 % Maximal formula atoms : 2 ( 1 avg)
% 0.56/0.76 % Number of connectives : 2 ( 0 ~; 0 |; 0 &)
% 0.56/0.76 % ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% 0.56/0.76 % Maximal formula depth : 5 ( 3 avg)
% 0.56/0.76 % Maximal term depth : 3 ( 1 avg)
% 0.56/0.76 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.56/0.76 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.56/0.76 % Number of variables : 25 ( 25 !; 0 ?)
% 0.56/0.76 % SPC : FOF_THM_RFO_SEQ
% 0.56/0.76
% 0.56/0.76 % Comments : Inequational axioms
% 0.56/0.76 %------------------------------------------------------------------------------
% 0.56/0.76 %---Include axioms for idempotent semiring
% 0.56/0.76 include('Axioms/KLE001+0.ax').
% 0.56/0.76 %------------------------------------------------------------------------------
% 0.56/0.76 fof(goals,conjecture,
% 0.56/0.76 ! [X0,X1,X2] :
% 0.56/0.76 ( leq(X0,X1)
% 0.56/0.76 => leq(multiplication(X0,X2),multiplication(X1,X2)) ) ).
% 0.56/0.76
% 0.56/0.76 %------------------------------------------------------------------------------
% 0.56/0.76 %-------------------------------------------
% 0.56/0.76 % Proof found
% 0.56/0.76 % SZS status Theorem for theBenchmark
% 0.56/0.76 % SZS output start Proof
% 0.56/0.76 %ClaNum:24(EqnAxiom:9)
% 0.56/0.76 %VarNum:51(SingletonVarNum:24)
% 0.56/0.76 %MaxLitNum:2
% 0.56/0.76 %MaxfuncDepth:2
% 0.56/0.76 %SharedTerms:9
% 0.56/0.76 %goalClause: 10 22
% 0.56/0.76 %singleGoalClaCount:2
% 0.56/0.76 [10]P1(a1,a3)
% 0.56/0.76 [22]~P1(f5(a1,a6),f5(a3,a6))
% 0.56/0.76 [11]E(f5(x111,a4),a4)
% 0.56/0.76 [12]E(f5(a4,x121),a4)
% 0.56/0.76 [13]E(f2(x131,a4),x131)
% 0.56/0.76 [14]E(f5(x141,a7),x141)
% 0.56/0.76 [15]E(f5(a7,x151),x151)
% 0.56/0.76 [16]E(f2(x161,x161),x161)
% 0.56/0.76 [17]E(f2(x171,x172),f2(x172,x171))
% 0.56/0.76 [18]E(f2(f2(x181,x182),x183),f2(x181,f2(x182,x183)))
% 0.56/0.76 [19]E(f5(f5(x191,x192),x193),f5(x191,f5(x192,x193)))
% 0.56/0.76 [20]E(f2(f5(x201,x202),f5(x201,x203)),f5(x201,f2(x202,x203)))
% 0.56/0.76 [21]E(f2(f5(x211,x212),f5(x213,x212)),f5(f2(x211,x213),x212))
% 0.56/0.76 [23]~P1(x231,x232)+E(f2(x231,x232),x232)
% 0.56/0.76 [24]P1(x241,x242)+~E(f2(x241,x242),x242)
% 0.56/0.76 %EqnAxiom
% 0.56/0.76 [1]E(x11,x11)
% 0.56/0.76 [2]E(x22,x21)+~E(x21,x22)
% 0.56/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.56/0.76 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.56/0.76 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.56/0.76 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 0.56/0.76 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 0.56/0.76 [8]P1(x82,x83)+~E(x81,x82)+~P1(x81,x83)
% 0.56/0.76 [9]P1(x93,x92)+~E(x91,x92)+~P1(x93,x91)
% 0.56/0.76
% 0.56/0.76 %-------------------------------------------
% 0.56/0.77 cnf(25,plain,
% 0.56/0.77 (E(x251,f2(x251,x251))),
% 0.56/0.77 inference(scs_inference,[],[16,2])).
% 0.56/0.77 cnf(26,plain,
% 0.56/0.77 (P1(x261,x261)),
% 0.56/0.77 inference(scs_inference,[],[16,2,24])).
% 0.56/0.77 cnf(31,plain,
% 0.56/0.77 (E(f2(x311,x311),x311)),
% 0.56/0.77 inference(rename_variables,[],[16])).
% 0.56/0.77 cnf(33,plain,
% 0.56/0.77 (E(f2(x331,f2(x332,x332)),f2(x331,x332))),
% 0.56/0.77 inference(scs_inference,[],[10,16,31,13,2,24,9,8,3,7])).
% 0.56/0.77 cnf(34,plain,
% 0.56/0.77 (E(f2(f2(x341,x341),x342),f2(x341,x342))),
% 0.56/0.77 inference(scs_inference,[],[10,16,31,13,2,24,9,8,3,7,6])).
% 0.56/0.77 cnf(36,plain,
% 0.56/0.77 (E(f5(f2(x361,x361),x362),f5(x361,x362))),
% 0.56/0.77 inference(scs_inference,[],[10,16,31,13,2,24,9,8,3,7,6,5,4])).
% 0.56/0.77 cnf(37,plain,
% 0.56/0.77 (E(f2(a1,a3),a3)),
% 0.56/0.77 inference(scs_inference,[],[10,16,31,13,2,24,9,8,3,7,6,5,4,23])).
% 0.56/0.77 cnf(39,plain,
% 0.56/0.77 (~E(f2(f5(a1,a6),f5(a3,a6)),f5(a3,a6))),
% 0.56/0.77 inference(scs_inference,[],[22,24])).
% 0.56/0.77 cnf(44,plain,
% 0.56/0.77 (~P1(f5(a1,a6),f5(f5(a3,a6),a7))),
% 0.56/0.77 inference(scs_inference,[],[22,14,17,24,2,3,9])).
% 0.56/0.77 cnf(45,plain,
% 0.56/0.77 (E(f5(x451,a7),x451)),
% 0.56/0.77 inference(rename_variables,[],[14])).
% 0.56/0.77 cnf(46,plain,
% 0.56/0.77 (~P1(f5(f5(a1,a6),a7),f5(a3,a6))),
% 0.56/0.77 inference(scs_inference,[],[22,14,45,17,24,2,3,9,8])).
% 0.56/0.77 cnf(70,plain,
% 0.56/0.77 (~P1(f5(a1,a6),f2(f5(f5(a3,a6),a7),a4))),
% 0.56/0.77 inference(scs_inference,[],[11,13,44,2,9])).
% 0.56/0.77 cnf(157,plain,
% 0.56/0.77 (~P1(f5(f5(a1,a6),a7),f5(a7,f5(a3,a6)))),
% 0.56/0.77 inference(scs_inference,[],[15,46,9])).
% 0.56/0.77 cnf(178,plain,
% 0.56/0.77 (~P1(f5(f5(a1,a6),a7),f5(f2(a7,a7),f5(a3,a6)))),
% 0.56/0.77 inference(scs_inference,[],[36,157,9])).
% 0.56/0.77 cnf(191,plain,
% 0.56/0.77 (P1(f2(f2(x1911,x1911),x1912),f2(x1911,x1912))),
% 0.56/0.77 inference(scs_inference,[],[34,26,9])).
% 0.56/0.77 cnf(206,plain,
% 0.56/0.77 (~P1(f5(f5(a1,a6),a7),f5(f2(f2(a7,a7),f2(a7,a7)),f5(a3,a6)))),
% 0.56/0.77 inference(scs_inference,[],[36,178,9])).
% 0.56/0.77 cnf(214,plain,
% 0.56/0.77 (P1(x2141,x2141)),
% 0.56/0.77 inference(rename_variables,[],[26])).
% 0.56/0.77 cnf(225,plain,
% 0.56/0.77 (E(f5(f2(a1,a3),x2251),f5(a3,x2251))),
% 0.56/0.77 inference(scs_inference,[],[19,37,25,26,214,191,206,9,2,3,8,23,5,7,6,4])).
% 0.56/0.77 cnf(238,plain,
% 0.56/0.77 ($false),
% 0.56/0.77 inference(scs_inference,[],[20,39,21,33,225,70,9,2,3]),
% 0.56/0.77 ['proof']).
% 0.56/0.77 % SZS output end Proof
% 0.56/0.77 % Total time :0.130000s
%------------------------------------------------------------------------------