TSTP Solution File: GRP165-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP165-1 : 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 : n014.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 00:11:20 EDT 2023
% Result : Unsatisfiable 0.19s 0.75s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP165-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:10:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 % File :CSE---1.6
% 0.19/0.74 % Problem :theBenchmark
% 0.19/0.74 % Transform :cnf
% 0.19/0.74 % Format :tptp:raw
% 0.19/0.74 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.74
% 0.19/0.74 % Result :Theorem 0.120000s
% 0.19/0.74 % Output :CNFRefutation 0.120000s
% 0.19/0.74 %-------------------------------------------
% 0.19/0.74 %--------------------------------------------------------------------------
% 0.19/0.74 % File : GRP165-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.19/0.74 % Domain : Group Theory (Lattice Ordered)
% 0.19/0.74 % Problem : An application of monotonicity
% 0.19/0.74 % Version : [Fuc94] (equality) axioms.
% 0.19/0.74 % English : Essentially a simple application of monotonicity, more
% 0.19/0.74 % difficult when proved from the equations replacing
% 0.19/0.74 % monotonicity.
% 0.19/0.74
% 0.19/0.74 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.19/0.74 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.19/0.75 % Source : [Sch95]
% 0.19/0.75 % Names : lat1a [Sch95]
% 0.19/0.75
% 0.19/0.75 % Status : Unsatisfiable
% 0.19/0.75 % 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 v2.0.0
% 0.19/0.75 % Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 2 RR)
% 0.19/0.75 % Number of literals : 17 ( 17 equ; 1 neg)
% 0.19/0.75 % Maximal clause size : 1 ( 1 avg)
% 0.19/0.75 % Maximal term depth : 3 ( 2 avg)
% 0.19/0.75 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.19/0.75 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 0.19/0.75 % Number of variables : 33 ( 2 sgn)
% 0.19/0.75 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.19/0.75
% 0.19/0.75 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.19/0.75 % least_upper_bound > identity > a
% 0.19/0.75 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.19/0.75 %--------------------------------------------------------------------------
% 0.19/0.75 %----Include equality group theory axioms
% 0.19/0.75 include('Axioms/GRP004-0.ax').
% 0.19/0.75 %----Include Lattice ordered group (equality) axioms
% 0.19/0.75 include('Axioms/GRP004-2.ax').
% 0.19/0.75 %--------------------------------------------------------------------------
% 0.19/0.75 cnf(lat1a_1,hypothesis,
% 0.19/0.75 least_upper_bound(a,identity) = a ).
% 0.19/0.75
% 0.19/0.75 cnf(prove_lat1a,negated_conjecture,
% 0.19/0.75 least_upper_bound(a,multiply(a,a)) != multiply(a,a) ).
% 0.19/0.75
% 0.19/0.75 %--------------------------------------------------------------------------
% 0.19/0.75 %-------------------------------------------
% 0.19/0.75 % Proof found
% 0.19/0.75 % SZS status Theorem for theBenchmark
% 0.19/0.75 % SZS output start Proof
% 0.19/0.75 %ClaNum:27(EqnAxiom:10)
% 0.19/0.75 %VarNum:72(SingletonVarNum:33)
% 0.19/0.75 %MaxLitNum:1
% 0.19/0.75 %MaxfuncDepth:2
% 0.19/0.75 %SharedTerms:7
% 0.19/0.75 %goalClause: 27
% 0.19/0.75 %singleGoalClaCount:1
% 0.19/0.75 [11]E(f4(a1,a2),a1)
% 0.19/0.75 [27]~E(f4(a1,f6(a1,a1)),f6(a1,a1))
% 0.19/0.75 [12]E(f6(a2,x121),x121)
% 0.19/0.75 [13]E(f3(x131,x131),x131)
% 0.19/0.75 [14]E(f4(x141,x141),x141)
% 0.19/0.75 [15]E(f6(f5(x151),x151),a2)
% 0.19/0.75 [16]E(f3(x161,x162),f3(x162,x161))
% 0.19/0.75 [17]E(f4(x171,x172),f4(x172,x171))
% 0.19/0.75 [18]E(f3(x181,f4(x181,x182)),x181)
% 0.19/0.75 [19]E(f4(x191,f3(x191,x192)),x191)
% 0.19/0.75 [20]E(f3(f3(x201,x202),x203),f3(x201,f3(x202,x203)))
% 0.19/0.75 [21]E(f4(f4(x211,x212),x213),f4(x211,f4(x212,x213)))
% 0.19/0.75 [22]E(f6(f6(x221,x222),x223),f6(x221,f6(x222,x223)))
% 0.19/0.75 [23]E(f3(f6(x231,x232),f6(x231,x233)),f6(x231,f3(x232,x233)))
% 0.19/0.75 [24]E(f4(f6(x241,x242),f6(x241,x243)),f6(x241,f4(x242,x243)))
% 0.19/0.75 [25]E(f3(f6(x251,x252),f6(x253,x252)),f6(f3(x251,x253),x252))
% 0.19/0.75 [26]E(f4(f6(x261,x262),f6(x263,x262)),f6(f4(x261,x263),x262))
% 0.19/0.75 %EqnAxiom
% 0.19/0.75 [1]E(x11,x11)
% 0.19/0.75 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.75 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.75 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 0.19/0.75 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 0.19/0.75 [6]~E(x61,x62)+E(f6(x61,x63),f6(x62,x63))
% 0.19/0.75 [7]~E(x71,x72)+E(f6(x73,x71),f6(x73,x72))
% 0.19/0.75 [8]~E(x81,x82)+E(f3(x81,x83),f3(x82,x83))
% 0.19/0.75 [9]~E(x91,x92)+E(f3(x93,x91),f3(x93,x92))
% 0.19/0.75 [10]~E(x101,x102)+E(f5(x101),f5(x102))
% 0.19/0.75
% 0.19/0.75 %-------------------------------------------
% 0.19/0.75 cnf(35,plain,
% 0.19/0.75 (E(f6(f4(a1,a2),x351),f6(a1,x351))),
% 0.19/0.75 inference(scs_inference,[],[11,13,2,3,10,9,8,7,6])).
% 0.19/0.75 cnf(37,plain,
% 0.19/0.75 (E(f4(f4(a1,a2),x371),f4(a1,x371))),
% 0.19/0.75 inference(scs_inference,[],[11,13,2,3,10,9,8,7,6,5,4])).
% 0.19/0.75 cnf(38,plain,
% 0.19/0.75 (~E(f4(f6(a1,a1),a1),f6(a1,a1))),
% 0.19/0.75 inference(scs_inference,[],[27,17,3])).
% 0.19/0.75 cnf(40,plain,
% 0.19/0.75 (~E(f6(a1,a1),f4(a1,f6(a1,a1)))),
% 0.19/0.75 inference(scs_inference,[],[27,17,3,2])).
% 0.19/0.75 cnf(41,plain,
% 0.19/0.75 (E(x411,f4(x411,x411))),
% 0.19/0.75 inference(scs_inference,[],[14,2])).
% 0.19/0.75 cnf(42,plain,
% 0.19/0.75 (E(f4(f4(a1,a2),f4(a1,a2)),a1)),
% 0.19/0.75 inference(scs_inference,[],[11,14,2,3])).
% 0.19/0.75 cnf(46,plain,
% 0.19/0.75 (~E(f6(a1,a1),f4(f6(a1,a1),a1))),
% 0.19/0.75 inference(scs_inference,[],[12,40,38,3,2])).
% 0.19/0.75 cnf(47,plain,
% 0.19/0.75 (~E(f4(f6(a1,a1),f6(a1,a1)),f4(f6(a1,a1),a1))),
% 0.19/0.75 inference(scs_inference,[],[41,46,3])).
% 0.19/0.75 cnf(49,plain,
% 0.19/0.75 (E(x491,f6(a2,x491))),
% 0.19/0.75 inference(scs_inference,[],[12,41,46,3,2])).
% 0.19/0.75 cnf(57,plain,
% 0.19/0.75 (~E(f6(a1,a1),a1)),
% 0.19/0.75 inference(scs_inference,[],[47,5])).
% 0.19/0.75 cnf(122,plain,
% 0.19/0.75 (~E(f6(a1,a1),f4(f4(a1,a2),f6(a1,a1)))),
% 0.19/0.75 inference(scs_inference,[],[37,40,3])).
% 0.19/0.75 cnf(125,plain,
% 0.19/0.75 (~E(f4(f4(a1,a2),f6(a1,a1)),f6(a1,a1))),
% 0.19/0.75 inference(scs_inference,[],[122,2])).
% 0.19/0.75 cnf(143,plain,
% 0.19/0.75 (~E(f4(a1,f4(a2,f6(a1,a1))),f6(a1,a1))),
% 0.19/0.75 inference(scs_inference,[],[21,125,3])).
% 0.19/0.75 cnf(160,plain,
% 0.19/0.75 (~E(f4(f6(a1,a1),f6(a1,a1)),f4(a1,f6(a1,a1)))),
% 0.19/0.75 inference(scs_inference,[],[40,41,143,2,3])).
% 0.19/0.75 cnf(166,plain,
% 0.19/0.75 (~E(f6(a1,a1),f4(f4(a1,a2),f4(a1,a2)))),
% 0.19/0.75 inference(scs_inference,[],[42,160,57,2,3])).
% 0.19/0.75 cnf(167,plain,
% 0.19/0.75 (~E(f4(f6(a1,a1),f6(a1,a1)),f4(f4(a1,a2),f4(a1,a2)))),
% 0.19/0.75 inference(scs_inference,[],[41,166,3])).
% 0.19/0.75 cnf(180,plain,
% 0.19/0.75 (~E(f4(f6(a1,a1),a1),f6(f4(a1,a2),a1))),
% 0.19/0.75 inference(scs_inference,[],[38,35,3])).
% 0.19/0.75 cnf(184,plain,
% 0.19/0.75 (~E(f6(f4(a1,a1),a1),f4(f4(a1,a2),f4(a1,a2)))),
% 0.19/0.75 inference(scs_inference,[],[26,167,2,3])).
% 0.19/0.75 cnf(200,plain,
% 0.19/0.75 ($false),
% 0.19/0.75 inference(scs_inference,[],[26,184,180,49,2,3,5]),
% 0.19/0.75 ['proof']).
% 0.19/0.75 % SZS output end Proof
% 0.19/0.75 % Total time :0.120000s
%------------------------------------------------------------------------------