TSTP Solution File: GRP154-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP154-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n004.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 00:11:18 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP154-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.14/0.34 % Computer : n004.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 20:35:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.58 start to proof:theBenchmark
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % File :CSE---1.6
% 0.20/0.64 % Problem :theBenchmark
% 0.20/0.64 % Transform :cnf
% 0.20/0.64 % Format :tptp:raw
% 0.20/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.20/0.64
% 0.20/0.64 % Result :Theorem 0.020000s
% 0.20/0.64 % Output :CNFRefutation 0.020000s
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 % File : GRP154-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.20/0.64 % Domain : Group Theory (Lattice Ordered)
% 0.20/0.64 % Problem : Prove monotonicity axiom using the LUB transformation
% 0.20/0.64 % Version : [Fuc94] (equality) axioms.
% 0.20/0.64 % English : This problem proves the original mononicity axiom from the
% 0.20/0.64 % equational axiomatization.
% 0.20/0.64
% 0.20/0.64 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.20/0.64 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.20/0.64 % Source : [Sch95]
% 0.20/0.64 % Names : ax_mono1a [Sch95]
% 0.20/0.64
% 0.20/0.64 % Status : Unsatisfiable
% 0.20/0.64 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v7.0.0, 0.05 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.07 v5.0.0, 0.14 v4.1.0, 0.18 v4.0.1, 0.14 v4.0.0, 0.15 v3.7.0, 0.11 v3.4.0, 0.00 v2.0.0
% 0.20/0.64 % Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 2 RR)
% 0.20/0.64 % Number of literals : 17 ( 17 equ; 1 neg)
% 0.20/0.64 % Maximal clause size : 1 ( 1 avg)
% 0.20/0.64 % Maximal term depth : 3 ( 2 avg)
% 0.20/0.64 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.20/0.64 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.20/0.64 % Number of variables : 33 ( 2 sgn)
% 0.20/0.64 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.20/0.64
% 0.20/0.64 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.20/0.64 % least_upper_bound > identity > a > b > c
% 0.20/0.64 % : ORDERING LPO greatest_lower_bound > least_upper_bound >
% 0.20/0.64 % inverse > product > identity > a > b > c
% 0.20/0.64 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %----Include equality group theory axioms
% 0.20/0.64 include('Axioms/GRP004-0.ax').
% 0.20/0.64 %----Include Lattice ordered group (equality) axioms
% 0.20/0.64 include('Axioms/GRP004-2.ax').
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 cnf(ax_mono1a_1,hypothesis,
% 0.20/0.64 least_upper_bound(a,b) = b ).
% 0.20/0.64
% 0.20/0.64 cnf(prove_ax_mono1a,negated_conjecture,
% 0.20/0.64 least_upper_bound(multiply(a,c),multiply(b,c)) != multiply(b,c) ).
% 0.20/0.64
% 0.20/0.64 %--------------------------------------------------------------------------
% 0.20/0.64 %-------------------------------------------
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark
% 0.20/0.64 % SZS output start Proof
% 0.20/0.65 %ClaNum:27(EqnAxiom:10)
% 0.20/0.65 %VarNum:72(SingletonVarNum:33)
% 0.20/0.65 %MaxLitNum:1
% 0.20/0.65 %MaxfuncDepth:2
% 0.20/0.65 %SharedTerms:10
% 0.20/0.65 %goalClause: 27
% 0.20/0.65 %singleGoalClaCount:1
% 0.20/0.65 [11]E(f3(a1,a2),a2)
% 0.20/0.65 [27]~E(f3(f8(a1,a6),f8(a2,a6)),f8(a2,a6))
% 0.20/0.65 [12]E(f8(a4,x121),x121)
% 0.20/0.65 [13]E(f5(x131,x131),x131)
% 0.20/0.65 [14]E(f3(x141,x141),x141)
% 0.20/0.65 [15]E(f8(f7(x151),x151),a4)
% 0.20/0.65 [16]E(f5(x161,x162),f5(x162,x161))
% 0.20/0.65 [17]E(f3(x171,x172),f3(x172,x171))
% 0.20/0.65 [18]E(f5(x181,f3(x181,x182)),x181)
% 0.20/0.65 [19]E(f3(x191,f5(x191,x192)),x191)
% 0.20/0.65 [20]E(f5(f5(x201,x202),x203),f5(x201,f5(x202,x203)))
% 0.20/0.65 [21]E(f3(f3(x211,x212),x213),f3(x211,f3(x212,x213)))
% 0.20/0.65 [22]E(f8(f8(x221,x222),x223),f8(x221,f8(x222,x223)))
% 0.20/0.65 [23]E(f5(f8(x231,x232),f8(x231,x233)),f8(x231,f5(x232,x233)))
% 0.20/0.65 [24]E(f3(f8(x241,x242),f8(x241,x243)),f8(x241,f3(x242,x243)))
% 0.20/0.65 [25]E(f5(f8(x251,x252),f8(x253,x252)),f8(f5(x251,x253),x252))
% 0.20/0.65 [26]E(f3(f8(x261,x262),f8(x263,x262)),f8(f3(x261,x263),x262))
% 0.20/0.65 %EqnAxiom
% 0.20/0.65 [1]E(x11,x11)
% 0.20/0.65 [2]E(x22,x21)+~E(x21,x22)
% 0.20/0.65 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.20/0.65 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.20/0.65 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.20/0.65 [6]~E(x61,x62)+E(f8(x61,x63),f8(x62,x63))
% 0.20/0.65 [7]~E(x71,x72)+E(f8(x73,x71),f8(x73,x72))
% 0.20/0.65 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.20/0.65 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.20/0.65 [10]~E(x101,x102)+E(f7(x101),f7(x102))
% 0.20/0.65
% 0.20/0.65 %-------------------------------------------
% 0.20/0.65 cnf(35,plain,
% 0.20/0.65 (E(f8(f3(a1,a2),x351),f8(a2,x351))),
% 0.20/0.65 inference(scs_inference,[],[11,13,2,3,10,9,8,7,6])).
% 0.20/0.65 cnf(39,plain,
% 0.20/0.65 (~E(f3(f8(a2,a6),f8(a1,a6)),f8(a2,a6))),
% 0.20/0.65 inference(scs_inference,[],[27,17,2,3])).
% 0.20/0.65 cnf(123,plain,
% 0.20/0.65 (~E(f3(f8(a2,a6),f8(a1,a6)),f8(f3(a1,a2),a6))),
% 0.20/0.65 inference(scs_inference,[],[19,35,39,2,3])).
% 0.20/0.65 cnf(128,plain,
% 0.20/0.65 ($false),
% 0.20/0.65 inference(scs_inference,[],[26,123,17,2,3,6]),
% 0.20/0.65 ['proof']).
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time :0.020000s
%------------------------------------------------------------------------------