%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : KLE057+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 09:59:57 EDT 2024
% Result : Theorem 0.54s 0.72s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE057+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 20 22:08:24 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.46/0.57 start to proof:theBenchmark
% 0.54/0.71 %-------------------------------------------
% 0.54/0.71 % File :CSE---1.7
% 0.54/0.71 % Problem :theBenchmark
% 0.54/0.71 % Transform :cnf
% 0.54/0.71 % Format :tptp:raw
% 0.54/0.71 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.71
% 0.54/0.71 % Result :Theorem 0.100000s
% 0.54/0.71 % Output :CNFRefutation 0.100000s
% 0.54/0.71 %-------------------------------------------
% 0.54/0.72 %------------------------------------------------------------------------------
% 0.54/0.72 % File : KLE057+1 : TPTP v8.2.0. Released v4.0.0.
% 0.54/0.72 % Domain : Kleene Algebra (Domain Semirings)
% 0.54/0.72 % Problem : Domain is very strict
% 0.54/0.72 % Version : [Hoe08] axioms.
% 0.54/0.72 % English :
% 0.54/0.72
% 0.54/0.72 % Refs : [DS08] Desharnais & Struth (2008), Modal Semirings Revisited
% 0.54/0.72 % : [Hoe08] Hoefner (2008), Email to G. Sutcliffe
% 0.54/0.72 % Source : [Hoe08]
% 0.54/0.72 % Names :
% 0.54/0.72
% 0.54/0.72 % Status : Theorem
% 0.54/0.72 % Rating : 0.06 v8.1.0, 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, 0.08 v6.1.0, 0.10 v6.0.0, 0.09 v5.5.0, 0.07 v5.3.0, 0.15 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.08 v4.1.0, 0.04 v4.0.1, 0.09 v4.0.0
% 0.54/0.72 % Syntax : Number of formulae : 18 ( 16 unt; 0 def)
% 0.54/0.72 % Number of atoms : 20 ( 19 equ)
% 0.54/0.72 % Maximal formula atoms : 2 ( 1 avg)
% 0.54/0.72 % Number of connectives : 2 ( 0 ~; 0 |; 0 &)
% 0.54/0.72 % ( 1 <=>; 0 =>; 1 <=; 0 <~>)
% 0.54/0.72 % Maximal formula depth : 4 ( 3 avg)
% 0.54/0.72 % Maximal term depth : 4 ( 2 avg)
% 0.54/0.72 % Number of predicates : 2 ( 1 usr; 0 prp; 2-2 aty)
% 0.54/0.72 % Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.54/0.72 % Number of variables : 29 ( 29 !; 0 ?)
% 0.54/0.72 % SPC : FOF_THM_RFO_SEQ
% 0.54/0.72
% 0.54/0.72 % Comments : % encoding
% 0.54/0.72 %------------------------------------------------------------------------------
% 0.54/0.72 %---Include axioms for domain semiring
% 0.54/0.72 include('Axioms/KLE001+0.ax').
% 0.54/0.72 %---Include axioms for domain
% 0.54/0.72 include('Axioms/KLE001+5.ax').
% 0.54/0.72 %------------------------------------------------------------------------------
% 0.54/0.72 fof(goals,conjecture,
% 0.54/0.72 ! [X0] :
% 0.54/0.72 ( domain(X0) = zero
% 0.54/0.72 <= X0 = zero ) ).
% 0.54/0.72
% 0.54/0.72 %------------------------------------------------------------------------------
% 0.54/0.72 %-------------------------------------------
% 0.54/0.72 % Proof found
% 0.54/0.72 % SZS status Theorem for theBenchmark
% 0.54/0.72 % SZS output start Proof
% 0.54/0.72 %ClaNum:30(EqnAxiom:10)
% 0.54/0.72 %VarNum:65(SingletonVarNum:30)
% 0.54/0.72 %MaxLitNum:2
% 0.54/0.72 %MaxfuncDepth:3
% 0.54/0.72 %SharedTerms:8
% 0.54/0.72 %goalClause: 11 28
% 0.54/0.72 %singleGoalClaCount:2
% 0.54/0.72 [11]E(a1,a4)
% 0.54/0.72 [12]E(f2(a4),a4)
% 0.54/0.72 [28]~E(f2(a1),a4)
% 0.54/0.72 [13]E(f5(x131,a4),a4)
% 0.54/0.72 [14]E(f5(a4,x141),a4)
% 0.54/0.72 [15]E(f3(x151,a4),x151)
% 0.54/0.72 [16]E(f5(x161,a6),x161)
% 0.54/0.72 [17]E(f5(a6,x171),x171)
% 0.54/0.72 [18]E(f3(x181,x181),x181)
% 0.54/0.72 [19]E(f3(f2(x191),a6),a6)
% 0.54/0.72 [23]E(f3(x231,f5(f2(x231),x231)),f5(f2(x231),x231))
% 0.54/0.72 [20]E(f3(x201,x202),f3(x202,x201))
% 0.54/0.72 [21]E(f2(f3(x211,x212)),f3(f2(x211),f2(x212)))
% 0.54/0.72 [22]E(f2(f5(x221,f2(x222))),f2(f5(x221,x222)))
% 0.54/0.72 [24]E(f3(f3(x241,x242),x243),f3(x241,f3(x242,x243)))
% 0.54/0.72 [25]E(f5(f5(x251,x252),x253),f5(x251,f5(x252,x253)))
% 0.54/0.72 [26]E(f3(f5(x261,x262),f5(x261,x263)),f5(x261,f3(x262,x263)))
% 0.54/0.72 [27]E(f3(f5(x271,x272),f5(x273,x272)),f5(f3(x271,x273),x272))
% 0.54/0.72 [29]~P1(x291,x292)+E(f3(x291,x292),x292)
% 0.54/0.72 [30]P1(x301,x302)+~E(f3(x301,x302),x302)
% 0.54/0.72 %EqnAxiom
% 0.54/0.72 [1]E(x11,x11)
% 0.54/0.72 [2]E(x22,x21)+~E(x21,x22)
% 0.54/0.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.54/0.72 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 0.54/0.72 [5]~E(x51,x52)+E(f5(x51,x53),f5(x52,x53))
% 0.54/0.72 [6]~E(x61,x62)+E(f5(x63,x61),f5(x63,x62))
% 0.54/0.72 [7]~E(x71,x72)+E(f3(x71,x73),f3(x72,x73))
% 0.54/0.72 [8]~E(x81,x82)+E(f3(x83,x81),f3(x83,x82))
% 0.54/0.72 [9]P1(x92,x93)+~E(x91,x92)+~P1(x91,x93)
% 0.54/0.72 [10]P1(x103,x102)+~E(x101,x102)+~P1(x103,x101)
% 0.54/0.72
% 0.54/0.72 %-------------------------------------------
% 0.54/0.73 cnf(34,plain,
% 0.54/0.73 (~E(f2(a1),a1)),
% 0.54/0.73 inference(scs_inference,[],[11,28,18,2,30,3])).
% 0.54/0.73 cnf(54,plain,
% 0.54/0.73 (E(x541,f5(a6,x541))),
% 0.54/0.73 inference(scs_inference,[],[17,2])).
% 0.54/0.73 cnf(61,plain,
% 0.54/0.73 (E(f5(x611,f3(x612,x613)),f3(f5(x611,x612),f5(x611,x613)))),
% 0.54/0.73 inference(scs_inference,[],[26,2])).
% 0.54/0.73 cnf(62,plain,
% 0.54/0.73 (E(f3(f5(x621,x622),f5(x621,x623)),f5(x621,f3(x623,x622)))),
% 0.54/0.73 inference(scs_inference,[],[20,26,2,3])).
% 0.54/0.73 cnf(67,plain,
% 0.54/0.73 (E(f5(x671,f3(x672,x673)),f3(f5(x671,x673),f5(x671,x672)))),
% 0.54/0.73 inference(scs_inference,[],[62,2])).
% 0.54/0.73 cnf(68,plain,
% 0.54/0.73 (E(f3(x681,x682),f3(f5(a6,x681),f5(a6,x682)))),
% 0.54/0.73 inference(scs_inference,[],[61,54,62,2,3])).
% 0.54/0.73 cnf(75,plain,
% 0.54/0.73 (E(f3(x751,x752),f3(f5(a6,x752),f5(a6,x751)))),
% 0.54/0.73 inference(scs_inference,[],[67,54,68,2,3])).
% 0.54/0.73 cnf(81,plain,
% 0.54/0.73 (E(f3(f5(a6,x811),f5(a6,x812)),f3(x812,x811))),
% 0.54/0.73 inference(scs_inference,[],[75,2])).
% 0.54/0.73 cnf(94,plain,
% 0.54/0.73 (E(f3(f2(x941),f2(x942)),f2(f3(x941,x942)))),
% 0.54/0.73 inference(scs_inference,[],[21,2])).
% 0.54/0.73 cnf(146,plain,
% 0.54/0.73 (E(f2(a4),f2(a1))),
% 0.54/0.73 inference(scs_inference,[],[11,4,2])).
% 0.54/0.73 cnf(154,plain,
% 0.54/0.73 (E(f2(a1),f2(a4))),
% 0.54/0.73 inference(scs_inference,[],[146,2])).
% 0.54/0.73 cnf(155,plain,
% 0.54/0.73 (E(f3(f5(a6,f2(x1551)),f5(a6,f2(x1552))),f2(f3(x1552,x1551)))),
% 0.54/0.73 inference(scs_inference,[],[94,81,146,2,3])).
% 0.54/0.73 cnf(162,plain,
% 0.54/0.73 (E(f3(f2(a1),f2(a1)),f2(a4))),
% 0.54/0.73 inference(scs_inference,[],[154,155,18,2,3])).
% 0.54/0.73 cnf(168,plain,
% 0.54/0.73 (E(f2(a4),f3(f2(a1),f2(a1)))),
% 0.54/0.73 inference(scs_inference,[],[162,2])).
% 0.54/0.73 cnf(181,plain,
% 0.54/0.73 (E(a4,f2(a4))),
% 0.54/0.73 inference(scs_inference,[],[12,2])).
% 0.54/0.73 cnf(182,plain,
% 0.54/0.73 (E(f2(a4),f2(f3(a1,a1)))),
% 0.54/0.73 inference(scs_inference,[],[168,94,12,2,3])).
% 0.54/0.73 cnf(189,plain,
% 0.54/0.73 (E(a1,f2(a4))),
% 0.54/0.73 inference(scs_inference,[],[11,181,182,2,3])).
% 0.54/0.73 cnf(194,plain,
% 0.54/0.73 (E(f2(a4),a1)),
% 0.54/0.73 inference(scs_inference,[],[189,2])).
% 0.54/0.73 cnf(202,plain,
% 0.54/0.73 ($false),
% 0.54/0.73 inference(scs_inference,[],[194,154,34,22,2,3]),
% 0.54/0.73 ['proof']).
% 0.54/0.73 % SZS output end Proof
% 0.54/0.73 % Total time :0.100000s
%------------------------------------------------------------------------------