TSTP Solution File: GRP146-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP146-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 00:11:16 EDT 2023
% Result : Unsatisfiable 0.12s 0.58s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRP146-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.07 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.06/0.28 % Computer : n002.cluster.edu
% 0.06/0.28 % Model : x86_64 x86_64
% 0.06/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.28 % Memory : 8042.1875MB
% 0.06/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.28 % CPULimit : 300
% 0.06/0.28 % WCLimit : 300
% 0.06/0.28 % DateTime : Mon Aug 28 23:14:04 EDT 2023
% 0.06/0.28 % CPUTime :
% 0.12/0.51 start to proof:theBenchmark
% 0.12/0.57 %-------------------------------------------
% 0.12/0.57 % File :CSE---1.6
% 0.12/0.57 % Problem :theBenchmark
% 0.12/0.57 % Transform :cnf
% 0.12/0.57 % Format :tptp:raw
% 0.12/0.57 % Command :java -jar mcs_scs.jar %d %s
% 0.12/0.57
% 0.12/0.57 % Result :Theorem 0.010000s
% 0.12/0.57 % Output :CNFRefutation 0.010000s
% 0.12/0.57 %-------------------------------------------
% 0.12/0.57 %--------------------------------------------------------------------------
% 0.12/0.57 % File : GRP146-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.57 % Domain : Group Theory (Lattice Ordered)
% 0.12/0.57 % Problem : Prove least upper-bound axiom using the LUB transformation
% 0.12/0.57 % Version : [Fuc94] (equality) axioms.
% 0.12/0.57 % English : This problem proves the original least upper-bound axiom from
% 0.12/0.57 % the equational axiomatization.
% 0.12/0.57
% 0.12/0.57 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.12/0.57 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.12/0.57 % Source : [Sch95]
% 0.12/0.57 % Names : ax_lub1a [Sch95]
% 0.12/0.57
% 0.12/0.57 % Status : Unsatisfiable
% 0.12/0.57 % Rating : 0.04 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.00 v7.0.0, 0.11 v6.3.0, 0.06 v6.2.0, 0.07 v6.1.0, 0.06 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v3.4.0, 0.12 v3.3.0, 0.00 v2.0.0
% 0.12/0.57 % Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% 0.12/0.57 % Number of literals : 18 ( 18 equ; 1 neg)
% 0.12/0.57 % Maximal clause size : 1 ( 1 avg)
% 0.12/0.57 % Maximal term depth : 3 ( 2 avg)
% 0.12/0.57 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.12/0.57 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.12/0.57 % Number of variables : 33 ( 2 sgn)
% 0.12/0.57 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.12/0.57
% 0.12/0.57 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.12/0.58 % least_upper_bound > identity > a > b > c
% 0.12/0.58 % : ORDERING LPO greatest_lower_bound > least_upper_bound >
% 0.12/0.58 % inverse > product > identity > a > b > c
% 0.12/0.58 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.12/0.58 %--------------------------------------------------------------------------
% 0.12/0.58 %----Include equality group theory axioms
% 0.12/0.58 include('Axioms/GRP004-0.ax').
% 0.12/0.58 %----Include Lattice ordered group (equality) axioms
% 0.12/0.58 include('Axioms/GRP004-2.ax').
% 0.12/0.58 %--------------------------------------------------------------------------
% 0.12/0.58 cnf(ax_lub1a_1,hypothesis,
% 0.12/0.58 least_upper_bound(a,c) = c ).
% 0.12/0.58
% 0.12/0.58 cnf(ax_lub1a_2,hypothesis,
% 0.12/0.58 least_upper_bound(b,c) = c ).
% 0.12/0.58
% 0.12/0.58 cnf(prove_ax_lub1a,negated_conjecture,
% 0.12/0.58 least_upper_bound(least_upper_bound(a,b),c) != c ).
% 0.12/0.58
% 0.12/0.58 %--------------------------------------------------------------------------
% 0.12/0.58 %-------------------------------------------
% 0.12/0.58 % Proof found
% 0.12/0.58 % SZS status Theorem for theBenchmark
% 0.12/0.58 % SZS output start Proof
% 0.12/0.58 %ClaNum:28(EqnAxiom:10)
% 0.12/0.58 %VarNum:72(SingletonVarNum:33)
% 0.12/0.58 %MaxLitNum:1
% 0.12/0.58 %MaxfuncDepth:2
% 0.12/0.58 %SharedTerms:11
% 0.12/0.58 %goalClause: 28
% 0.12/0.58 %singleGoalClaCount:1
% 0.12/0.58 [11]E(f4(a1,a2),a2)
% 0.12/0.58 [12]E(f4(a3,a2),a2)
% 0.12/0.58 [28]~E(f4(f4(a1,a3),a2),a2)
% 0.12/0.58 [13]E(f8(a5,x131),x131)
% 0.12/0.58 [14]E(f6(x141,x141),x141)
% 0.12/0.58 [15]E(f4(x151,x151),x151)
% 0.12/0.58 [16]E(f8(f7(x161),x161),a5)
% 0.12/0.58 [17]E(f6(x171,x172),f6(x172,x171))
% 0.12/0.58 [18]E(f4(x181,x182),f4(x182,x181))
% 0.12/0.58 [19]E(f6(x191,f4(x191,x192)),x191)
% 0.12/0.58 [20]E(f4(x201,f6(x201,x202)),x201)
% 0.12/0.58 [21]E(f6(f6(x211,x212),x213),f6(x211,f6(x212,x213)))
% 0.12/0.58 [22]E(f4(f4(x221,x222),x223),f4(x221,f4(x222,x223)))
% 0.12/0.58 [23]E(f8(f8(x231,x232),x233),f8(x231,f8(x232,x233)))
% 0.12/0.58 [24]E(f6(f8(x241,x242),f8(x241,x243)),f8(x241,f6(x242,x243)))
% 0.12/0.58 [25]E(f4(f8(x251,x252),f8(x251,x253)),f8(x251,f4(x252,x253)))
% 0.12/0.58 [26]E(f6(f8(x261,x262),f8(x263,x262)),f8(f6(x261,x263),x262))
% 0.12/0.58 [27]E(f4(f8(x271,x272),f8(x273,x272)),f8(f4(x271,x273),x272))
% 0.12/0.58 %EqnAxiom
% 0.12/0.58 [1]E(x11,x11)
% 0.12/0.58 [2]E(x22,x21)+~E(x21,x22)
% 0.12/0.58 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.12/0.58 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.12/0.58 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.12/0.58 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63))
% 0.12/0.58 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72))
% 0.12/0.58 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.12/0.58 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.12/0.58 [10]~E(x101,x102)+E(f7(x101),f7(x102))
% 0.12/0.58
% 0.12/0.58 %-------------------------------------------
% 0.12/0.58 cnf(30,plain,
% 0.12/0.58 (~E(f4(f4(a1,a3),a2),f4(a1,a2))),
% 0.12/0.58 inference(scs_inference,[],[28,11,2,3])).
% 0.12/0.58 cnf(55,plain,
% 0.12/0.58 ($false),
% 0.12/0.58 inference(scs_inference,[],[12,14,22,30,3,2,9,7,10,8,6,5]),
% 0.12/0.58 ['proof']).
% 0.12/0.58 % SZS output end Proof
% 0.12/0.58 % Total time :0.010000s
%------------------------------------------------------------------------------