TSTP Solution File: GRP165-2 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP165-2 : 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 : n007.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 00:11:21 EDT 2023
% Result : Unsatisfiable 0.57s 0.85s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP165-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.35 % Computer : n007.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 00:34:28 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.46/0.59 start to proof:theBenchmark
% 0.57/0.85 %-------------------------------------------
% 0.57/0.85 % File :CSE---1.6
% 0.57/0.85 % Problem :theBenchmark
% 0.57/0.85 % Transform :cnf
% 0.57/0.85 % Format :tptp:raw
% 0.57/0.85 % Command :java -jar mcs_scs.jar %d %s
% 0.57/0.85
% 0.57/0.85 % Result :Theorem 0.200000s
% 0.57/0.85 % Output :CNFRefutation 0.200000s
% 0.57/0.85 %-------------------------------------------
% 0.57/0.85 %--------------------------------------------------------------------------
% 0.57/0.85 % File : GRP165-2 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.57/0.85 % Domain : Group Theory (Lattice Ordered)
% 0.57/0.85 % Problem : An application of monotonicity
% 0.57/0.85 % Version : [Fuc94] (equality) axioms.
% 0.57/0.85 % Theorem formulation : Dual.
% 0.57/0.85 % English : Essentially a simple application of monotonicity, more
% 0.57/0.85 % difficult when proved from the equations replacing
% 0.57/0.85 % monotonicity.
% 0.57/0.85
% 0.57/0.85 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.57/0.85 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.57/0.85 % Source : [Sch95]
% 0.57/0.85 % Names : lat1b [Sch95]
% 0.57/0.85
% 0.57/0.85 % Status : Unsatisfiable
% 0.57/0.85 % Rating : 0.00 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.05 v7.1.0, 0.00 v7.0.0, 0.05 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 v5.1.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.1.0, 0.14 v2.0.0
% 0.57/0.85 % Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 2 RR)
% 0.57/0.85 % Number of literals : 17 ( 17 equ; 1 neg)
% 0.57/0.85 % Maximal clause size : 1 ( 1 avg)
% 0.57/0.85 % Maximal term depth : 3 ( 2 avg)
% 0.57/0.85 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.57/0.85 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.57/0.85 % Number of variables : 33 ( 2 sgn)
% 0.57/0.85 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.57/0.85
% 0.57/0.85 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.57/0.85 % least_upper_bound > identity > a
% 0.57/0.85 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.57/0.85 %--------------------------------------------------------------------------
% 0.57/0.85 %----Include equality group theory axioms
% 0.57/0.85 include('Axioms/GRP004-0.ax').
% 0.57/0.85 %----Include Lattice ordered group (equality) axioms
% 0.57/0.85 include('Axioms/GRP004-2.ax').
% 0.57/0.85 %--------------------------------------------------------------------------
% 0.57/0.85 cnf(lat1b_1,hypothesis,
% 0.57/0.85 greatest_lower_bound(a,identity) = identity ).
% 0.57/0.85
% 0.57/0.85 cnf(prove_lat1b,negated_conjecture,
% 0.57/0.85 greatest_lower_bound(a,multiply(a,a)) != a ).
% 0.57/0.85
% 0.57/0.85 %--------------------------------------------------------------------------
% 0.57/0.85 %-------------------------------------------
% 0.57/0.85 % Proof found
% 0.57/0.85 % SZS status Theorem for theBenchmark
% 0.57/0.85 % SZS output start Proof
% 0.57/0.85 %ClaNum:27(EqnAxiom:10)
% 0.57/0.85 %VarNum:72(SingletonVarNum:33)
% 0.57/0.85 %MaxLitNum:1
% 0.57/0.85 %MaxfuncDepth:2
% 0.57/0.85 %SharedTerms:7
% 0.57/0.85 %goalClause: 27
% 0.57/0.85 %singleGoalClaCount:1
% 0.57/0.85 [11]E(f3(a1,a2),a2)
% 0.57/0.85 [27]~E(f3(a1,f4(a1,a1)),a1)
% 0.57/0.85 [12]E(f4(a2,x121),x121)
% 0.57/0.85 [13]E(f3(x131,x131),x131)
% 0.57/0.85 [14]E(f5(x141,x141),x141)
% 0.57/0.85 [15]E(f4(f6(x151),x151),a2)
% 0.57/0.85 [16]E(f3(x161,x162),f3(x162,x161))
% 0.57/0.85 [17]E(f5(x171,x172),f5(x172,x171))
% 0.57/0.85 [18]E(f3(x181,f5(x181,x182)),x181)
% 0.57/0.85 [19]E(f5(x191,f3(x191,x192)),x191)
% 0.57/0.85 [20]E(f3(f3(x201,x202),x203),f3(x201,f3(x202,x203)))
% 0.57/0.85 [21]E(f5(f5(x211,x212),x213),f5(x211,f5(x212,x213)))
% 0.57/0.85 [22]E(f4(f4(x221,x222),x223),f4(x221,f4(x222,x223)))
% 0.57/0.85 [23]E(f3(f4(x231,x232),f4(x231,x233)),f4(x231,f3(x232,x233)))
% 0.57/0.85 [24]E(f5(f4(x241,x242),f4(x241,x243)),f4(x241,f5(x242,x243)))
% 0.57/0.85 [25]E(f3(f4(x251,x252),f4(x253,x252)),f4(f3(x251,x253),x252))
% 0.57/0.85 [26]E(f5(f4(x261,x262),f4(x263,x262)),f4(f5(x261,x263),x262))
% 0.57/0.85 %EqnAxiom
% 0.57/0.85 [1]E(x11,x11)
% 0.57/0.85 [2]E(x22,x21)+~E(x21,x22)
% 0.57/0.85 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.57/0.85 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.57/0.85 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.57/0.85 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.57/0.85 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.57/0.85 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 0.57/0.85 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 0.57/0.85 [10]~E(x101,x102)+E(f6(x101),f6(x102))
% 0.57/0.85
% 0.57/0.85 %-------------------------------------------
% 0.57/0.86 cnf(32,plain,
% 0.57/0.86 (E(f5(x321,f3(a1,a2)),f5(x321,a2))),
% 0.57/0.86 inference(scs_inference,[],[11,13,2,3,10,9])).
% 0.57/0.86 cnf(33,plain,
% 0.57/0.86 (E(f5(f3(a1,a2),x331),f5(a2,x331))),
% 0.57/0.86 inference(scs_inference,[],[11,13,2,3,10,9,8])).
% 0.57/0.86 cnf(35,plain,
% 0.57/0.86 (E(f4(f3(a1,a2),x351),f4(a2,x351))),
% 0.57/0.86 inference(scs_inference,[],[11,13,2,3,10,9,8,7,6])).
% 0.57/0.86 cnf(38,plain,
% 0.57/0.86 (~E(a1,f3(a1,f4(a1,a1)))),
% 0.57/0.86 inference(scs_inference,[],[27,2])).
% 0.57/0.86 cnf(39,plain,
% 0.57/0.86 (~E(f3(f4(a1,a1),a1),a1)),
% 0.57/0.86 inference(scs_inference,[],[27,16,2,3])).
% 0.57/0.86 cnf(41,plain,
% 0.57/0.86 (E(x411,f5(x411,x411))),
% 0.57/0.86 inference(scs_inference,[],[14,2])).
% 0.57/0.86 cnf(46,plain,
% 0.57/0.86 (~E(a1,f3(f4(a1,a1),a1))),
% 0.57/0.86 inference(scs_inference,[],[12,39,3,2])).
% 0.57/0.86 cnf(49,plain,
% 0.57/0.86 (E(x491,f4(a2,x491))),
% 0.57/0.86 inference(scs_inference,[],[12,41,46,3,2])).
% 0.57/0.86 cnf(54,plain,
% 0.57/0.86 (E(f3(x541,f4(a2,x542)),f3(x541,x542))),
% 0.57/0.86 inference(scs_inference,[],[12,41,46,3,2,10,9,8,7,5])).
% 0.57/0.86 cnf(95,plain,
% 0.57/0.86 (~E(f4(a2,a1),f3(a1,f4(a1,a1)))),
% 0.57/0.86 inference(scs_inference,[],[49,38,3])).
% 0.57/0.86 cnf(104,plain,
% 0.57/0.86 (~E(f3(a1,f4(a1,a1)),f4(a2,a1))),
% 0.57/0.86 inference(scs_inference,[],[17,24,95,3,2])).
% 0.57/0.86 cnf(119,plain,
% 0.57/0.86 (~E(f3(a1,f4(a1,a1)),f4(f3(a1,a2),a1))),
% 0.57/0.86 inference(scs_inference,[],[35,104,3])).
% 0.57/0.86 cnf(159,plain,
% 0.57/0.86 (~E(f5(a1,a1),f3(a1,f4(a1,a1)))),
% 0.57/0.86 inference(scs_inference,[],[38,41,5,3])).
% 0.57/0.86 cnf(166,plain,
% 0.57/0.86 (~E(f3(a1,f4(a1,a1)),f3(f4(a1,a1),f4(a2,a1)))),
% 0.57/0.86 inference(scs_inference,[],[25,159,119,2,3])).
% 0.57/0.86 cnf(181,plain,
% 0.57/0.86 (~E(f3(f4(a1,a1),f4(a2,a1)),f3(a1,f4(a1,a1)))),
% 0.57/0.86 inference(scs_inference,[],[33,32,166,3,2])).
% 0.57/0.86 cnf(263,plain,
% 0.57/0.86 ($false),
% 0.57/0.86 inference(scs_inference,[],[54,181,16,3]),
% 0.57/0.86 ['proof']).
% 0.57/0.86 % SZS output end Proof
% 0.57/0.86 % Total time :0.200000s
%------------------------------------------------------------------------------