TSTP Solution File: GRP155-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP155-1 : 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 : n023.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 0.55s 0.73s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP155-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.33 % Computer : n023.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 : Mon Aug 28 21:16:40 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.51/0.57 start to proof:theBenchmark
% 0.55/0.73 %-------------------------------------------
% 0.55/0.73 % File :CSE---1.6
% 0.55/0.73 % Problem :theBenchmark
% 0.55/0.73 % Transform :cnf
% 0.55/0.73 % Format :tptp:raw
% 0.55/0.73 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.73
% 0.55/0.73 % Result :Theorem 0.090000s
% 0.55/0.73 % Output :CNFRefutation 0.090000s
% 0.55/0.73 %-------------------------------------------
% 0.55/0.73 %--------------------------------------------------------------------------
% 0.55/0.73 % File : GRP155-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.55/0.73 % Domain : Group Theory (Lattice Ordered)
% 0.55/0.73 % Problem : Prove monotonicity axiom using the GLB transformation
% 0.55/0.73 % Version : [Fuc94] (equality) axioms.
% 0.55/0.73 % English : This problem proves the original monotonicity axiom from the
% 0.55/0.73 % equational axiomatization.
% 0.55/0.73
% 0.55/0.73 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.55/0.73 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.55/0.73 % Source : [Sch95]
% 0.55/0.73 % Names : ax_mono1b [Sch95]
% 0.55/0.73
% 0.55/0.73 % Status : Unsatisfiable
% 0.55/0.73 % 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
% 0.55/0.73 % Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 2 RR)
% 0.55/0.73 % Number of literals : 17 ( 17 equ; 1 neg)
% 0.55/0.73 % Maximal clause size : 1 ( 1 avg)
% 0.55/0.73 % Maximal term depth : 3 ( 2 avg)
% 0.55/0.73 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.55/0.73 % Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% 0.55/0.73 % Number of variables : 33 ( 2 sgn)
% 0.55/0.73 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.55/0.73
% 0.55/0.73 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.55/0.73 % least_upper_bound > identity > a > b > c
% 0.55/0.73 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.55/0.73 %--------------------------------------------------------------------------
% 0.55/0.73 %----Include equality group theory axioms
% 0.55/0.73 include('Axioms/GRP004-0.ax').
% 0.55/0.73 %----Include Lattice ordered group (equality) axioms
% 0.55/0.73 include('Axioms/GRP004-2.ax').
% 0.55/0.73 %--------------------------------------------------------------------------
% 0.55/0.73 cnf(ax_mono1b,hypothesis,
% 0.55/0.73 greatest_lower_bound(a,b) = a ).
% 0.55/0.73
% 0.55/0.73 cnf(prove_ax_mono1b,negated_conjecture,
% 0.55/0.73 greatest_lower_bound(multiply(a,c),multiply(b,c)) != multiply(a,c) ).
% 0.55/0.73
% 0.55/0.73 %--------------------------------------------------------------------------
% 0.55/0.73 %-------------------------------------------
% 0.55/0.73 % Proof found
% 0.55/0.73 % SZS status Theorem for theBenchmark
% 0.55/0.73 % SZS output start Proof
% 0.55/0.74 %ClaNum:27(EqnAxiom:10)
% 0.55/0.74 %VarNum:72(SingletonVarNum:33)
% 0.55/0.74 %MaxLitNum:1
% 0.55/0.74 %MaxfuncDepth:2
% 0.55/0.74 %SharedTerms:10
% 0.55/0.74 %goalClause: 27
% 0.55/0.74 %singleGoalClaCount:1
% 0.55/0.74 [11]E(f3(a1,a2),a1)
% 0.55/0.74 [27]~E(f3(f6(a1,a4),f6(a2,a4)),f6(a1,a4))
% 0.55/0.74 [12]E(f6(a5,x121),x121)
% 0.55/0.74 [13]E(f3(x131,x131),x131)
% 0.55/0.74 [14]E(f7(x141,x141),x141)
% 0.55/0.74 [15]E(f6(f8(x151),x151),a5)
% 0.55/0.74 [16]E(f3(x161,x162),f3(x162,x161))
% 0.55/0.74 [17]E(f7(x171,x172),f7(x172,x171))
% 0.55/0.74 [18]E(f3(x181,f7(x181,x182)),x181)
% 0.55/0.74 [19]E(f7(x191,f3(x191,x192)),x191)
% 0.55/0.74 [20]E(f3(f3(x201,x202),x203),f3(x201,f3(x202,x203)))
% 0.55/0.74 [21]E(f7(f7(x211,x212),x213),f7(x211,f7(x212,x213)))
% 0.55/0.74 [22]E(f6(f6(x221,x222),x223),f6(x221,f6(x222,x223)))
% 0.55/0.74 [23]E(f3(f6(x231,x232),f6(x231,x233)),f6(x231,f3(x232,x233)))
% 0.55/0.74 [24]E(f7(f6(x241,x242),f6(x241,x243)),f6(x241,f7(x242,x243)))
% 0.55/0.74 [25]E(f3(f6(x251,x252),f6(x253,x252)),f6(f3(x251,x253),x252))
% 0.55/0.74 [26]E(f7(f6(x261,x262),f6(x263,x262)),f6(f7(x261,x263),x262))
% 0.55/0.74 %EqnAxiom
% 0.55/0.74 [1]E(x11,x11)
% 0.55/0.74 [2]E(x22,x21)+~E(x21,x22)
% 0.55/0.74 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.55/0.74 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.55/0.74 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.55/0.74 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.55/0.74 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.55/0.74 [8]~E(x81,x82)+E(f7(x81,x83),f7(x82,x83))
% 0.55/0.74 [9]~E(x91,x92)+E(f7(x93,x91),f7(x93,x92))
% 0.55/0.74 [10]~E(x101,x102)+E(f8(x101),f8(x102))
% 0.55/0.74
% 0.55/0.74 %-------------------------------------------
% 0.55/0.74 cnf(28,plain,
% 0.55/0.74 (E(a1,f3(a1,a2))),
% 0.55/0.74 inference(scs_inference,[],[11,2])).
% 0.55/0.74 cnf(33,plain,
% 0.55/0.74 (E(f7(f3(a1,a2),x331),f7(a1,x331))),
% 0.55/0.74 inference(scs_inference,[],[11,13,2,3,10,9,8])).
% 0.55/0.74 cnf(38,plain,
% 0.55/0.74 (~E(f6(a1,a4),f3(f6(a1,a4),f6(a2,a4)))),
% 0.55/0.74 inference(scs_inference,[],[27,2])).
% 0.55/0.74 cnf(41,plain,
% 0.55/0.74 (E(x411,f7(x411,x411))),
% 0.55/0.74 inference(scs_inference,[],[14,2])).
% 0.55/0.74 cnf(76,plain,
% 0.55/0.74 (E(f7(a1,a1),f3(a1,a2))),
% 0.55/0.74 inference(scs_inference,[],[14,28,3])).
% 0.55/0.74 cnf(95,plain,
% 0.55/0.74 (~E(f7(f6(a1,a4),f6(a1,a4)),f3(f6(a1,a4),f6(a2,a4)))),
% 0.55/0.74 inference(scs_inference,[],[33,38,41,2,3])).
% 0.55/0.74 cnf(97,plain,
% 0.55/0.74 (~E(f3(f6(a1,a4),f6(a2,a4)),f7(f6(a1,a4),f6(a1,a4)))),
% 0.55/0.74 inference(scs_inference,[],[95,2])).
% 0.55/0.74 cnf(123,plain,
% 0.55/0.74 (~E(f6(f3(a1,a2),a4),f7(f6(a1,a4),f6(a1,a4)))),
% 0.55/0.74 inference(scs_inference,[],[19,25,97,2,3])).
% 0.55/0.74 cnf(125,plain,
% 0.55/0.74 (~E(f7(f6(a1,a4),f6(a1,a4)),f6(f3(a1,a2),a4))),
% 0.55/0.74 inference(scs_inference,[],[123,2])).
% 0.55/0.74 cnf(160,plain,
% 0.55/0.74 (~E(f6(f7(a1,a1),a4),f6(f3(a1,a2),a4))),
% 0.55/0.74 inference(scs_inference,[],[22,26,41,125,6,2,3])).
% 0.55/0.74 cnf(162,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(scs_inference,[],[160,76,6]),
% 0.55/0.74 ['proof']).
% 0.56/0.74 % SZS output end Proof
% 0.56/0.74 % Total time :0.090000s
%------------------------------------------------------------------------------