TSTP Solution File: GRP182-3 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP182-3 : 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 : n032.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 00:11:27 EDT 2023
% Result : Unsatisfiable 7.58s 7.72s
% Output : CNFRefutation 7.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : GRP182-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.05/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Tue Aug 29 02:08:01 EDT 2023
% 0.10/0.30 % CPUTime :
% 0.14/0.48 start to proof:theBenchmark
% 7.58/7.71 %-------------------------------------------
% 7.58/7.71 % File :CSE---1.6
% 7.58/7.71 % Problem :theBenchmark
% 7.58/7.71 % Transform :cnf
% 7.58/7.71 % Format :tptp:raw
% 7.58/7.71 % Command :java -jar mcs_scs.jar %d %s
% 7.58/7.71
% 7.58/7.71 % Result :Theorem 7.190000s
% 7.58/7.71 % Output :CNFRefutation 7.190000s
% 7.58/7.71 %-------------------------------------------
% 7.58/7.72 %--------------------------------------------------------------------------
% 7.58/7.72 % File : GRP182-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 7.58/7.72 % Domain : Group Theory (Lattice Ordered)
% 7.58/7.72 % Problem : Positive part of the negative part is identity
% 7.58/7.72 % Version : [Fuc94] (equality) axioms.
% 7.58/7.72 % Theorem formulation : Dual.
% 7.58/7.72 % English :
% 7.58/7.72
% 7.58/7.72 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 7.58/7.72 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 7.58/7.72 % Source : [TPTP]
% 7.58/7.72 % Names :
% 7.58/7.72
% 7.58/7.72 % Status : Unsatisfiable
% 7.58/7.72 % 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 v6.4.0, 0.11 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, 0.07 v5.3.0, 0.00 v2.0.0
% 7.58/7.72 % Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 1 RR)
% 7.58/7.72 % Number of literals : 16 ( 16 equ; 1 neg)
% 7.58/7.72 % Maximal clause size : 1 ( 1 avg)
% 7.58/7.72 % Maximal term depth : 3 ( 2 avg)
% 7.58/7.72 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 7.58/7.72 % Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% 7.58/7.72 % Number of variables : 33 ( 2 sgn)
% 7.58/7.72 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 7.58/7.72
% 7.58/7.72 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 7.58/7.72 % least_upper_bound > identity > a
% 7.58/7.72 % : ORDERING LPO greatest_lower_bound > least_upper_bound >
% 7.58/7.72 % inverse > product > identity > a
% 7.58/7.72 % : This is a standardized version of the problem that appears in
% 7.58/7.72 % [Sch95].
% 7.58/7.72 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 7.58/7.72 %--------------------------------------------------------------------------
% 7.58/7.72 %----Include equality group theory axioms
% 7.58/7.72 include('Axioms/GRP004-0.ax').
% 7.58/7.72 %----Include Lattice ordered group (equality) axioms
% 7.58/7.72 include('Axioms/GRP004-2.ax').
% 7.58/7.72 %--------------------------------------------------------------------------
% 7.58/7.72 cnf(prove_p17b,negated_conjecture,
% 7.58/7.72 greatest_lower_bound(identity,least_upper_bound(a,identity)) != identity ).
% 7.58/7.72
% 7.58/7.72 %--------------------------------------------------------------------------
% 7.58/7.72 %-------------------------------------------
% 7.58/7.72 % Proof found
% 7.58/7.72 % SZS status Theorem for theBenchmark
% 7.58/7.72 % SZS output start Proof
% 7.58/7.72 %ClaNum:26(EqnAxiom:10)
% 7.58/7.72 %VarNum:72(SingletonVarNum:33)
% 7.58/7.72 %MaxLitNum:1
% 7.58/7.72 %MaxfuncDepth:2
% 7.58/7.72 %SharedTerms:5
% 7.58/7.72 %goalClause: 26
% 7.58/7.72 %singleGoalClaCount:1
% 7.58/7.72 [26]~E(f2(a1,f5(a3,a1)),a1)
% 7.58/7.72 [11]E(f4(a1,x111),x111)
% 7.58/7.72 [12]E(f2(x121,x121),x121)
% 7.58/7.72 [13]E(f5(x131,x131),x131)
% 7.58/7.72 [14]E(f4(f6(x141),x141),a1)
% 7.58/7.72 [15]E(f2(x151,x152),f2(x152,x151))
% 7.58/7.72 [16]E(f5(x161,x162),f5(x162,x161))
% 7.58/7.72 [17]E(f2(x171,f5(x171,x172)),x171)
% 7.58/7.72 [18]E(f5(x181,f2(x181,x182)),x181)
% 7.58/7.72 [19]E(f2(f2(x191,x192),x193),f2(x191,f2(x192,x193)))
% 7.58/7.72 [20]E(f5(f5(x201,x202),x203),f5(x201,f5(x202,x203)))
% 7.58/7.72 [21]E(f4(f4(x211,x212),x213),f4(x211,f4(x212,x213)))
% 7.58/7.72 [22]E(f2(f4(x221,x222),f4(x221,x223)),f4(x221,f2(x222,x223)))
% 7.58/7.72 [23]E(f5(f4(x231,x232),f4(x231,x233)),f4(x231,f5(x232,x233)))
% 7.58/7.72 [24]E(f2(f4(x241,x242),f4(x243,x242)),f4(f2(x241,x243),x242))
% 7.58/7.72 [25]E(f5(f4(x251,x252),f4(x253,x252)),f4(f5(x251,x253),x252))
% 7.58/7.72 %EqnAxiom
% 7.58/7.72 [1]E(x11,x11)
% 7.58/7.72 [2]E(x22,x21)+~E(x21,x22)
% 7.58/7.72 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 7.58/7.72 [4]~E(x41,x42)+E(f4(x41,x43),f4(x42,x43))
% 7.58/7.72 [5]~E(x51,x52)+E(f4(x53,x51),f4(x53,x52))
% 7.58/7.72 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 7.58/7.72 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 7.58/7.72 [8]~E(x81,x82)+E(f5(x81,x83),f5(x82,x83))
% 7.58/7.72 [9]~E(x91,x92)+E(f5(x93,x91),f5(x93,x92))
% 7.58/7.72 [10]~E(x101,x102)+E(f6(x101),f6(x102))
% 7.58/7.72
% 7.58/7.72 %-------------------------------------------
% 7.58/7.73 cnf(27,plain,
% 7.58/7.73 (E(x271,f2(x271,x271))),
% 7.58/7.73 inference(scs_inference,[],[12,2])).
% 7.58/7.73 cnf(28,plain,
% 7.58/7.73 (~E(f2(a1,f5(a3,a1)),f2(a1,a1))),
% 7.58/7.73 inference(scs_inference,[],[26,12,2,3])).
% 7.58/7.73 cnf(29,plain,
% 7.58/7.73 (E(f2(x291,x291),x291)),
% 7.58/7.73 inference(rename_variables,[],[12])).
% 7.58/7.73 cnf(31,plain,
% 7.58/7.73 (E(f5(x311,f2(x312,x312)),f5(x311,x312))),
% 7.58/7.73 inference(scs_inference,[],[26,12,29,2,3,10,9])).
% 7.58/7.73 cnf(32,plain,
% 7.58/7.73 (E(f5(f2(x321,x321),x322),f5(x321,x322))),
% 7.58/7.73 inference(scs_inference,[],[26,12,29,2,3,10,9,8])).
% 7.58/7.73 cnf(33,plain,
% 7.58/7.73 (E(f2(x331,f2(x332,x332)),f2(x331,x332))),
% 7.58/7.73 inference(scs_inference,[],[26,12,29,2,3,10,9,8,7])).
% 7.58/7.73 cnf(34,plain,
% 7.58/7.73 (E(f2(f2(x341,x341),x342),f2(x341,x342))),
% 7.58/7.73 inference(scs_inference,[],[26,12,29,2,3,10,9,8,7,6])).
% 7.58/7.73 cnf(37,plain,
% 7.58/7.73 (~E(f5(a3,a1),a1)),
% 7.58/7.73 inference(scs_inference,[],[28,7])).
% 7.58/7.73 cnf(38,plain,
% 7.58/7.73 (~E(a1,f2(a1,f5(a3,a1)))),
% 7.58/7.73 inference(scs_inference,[],[26,28,7,2])).
% 7.58/7.73 cnf(39,plain,
% 7.58/7.73 (~E(f2(f5(a3,a1),a1),a1)),
% 7.58/7.73 inference(scs_inference,[],[26,15,28,7,2,3])).
% 7.58/7.73 cnf(46,plain,
% 7.58/7.73 (~E(f2(f5(a3,a1),a1),f4(a1,a1))),
% 7.58/7.73 inference(scs_inference,[],[11,39,2,3])).
% 7.58/7.73 cnf(48,plain,
% 7.58/7.73 (E(x481,f5(x481,x481))),
% 7.58/7.73 inference(scs_inference,[],[13,2])).
% 7.58/7.73 cnf(49,plain,
% 7.58/7.73 (~E(f5(a1,a3),a1)),
% 7.58/7.73 inference(scs_inference,[],[13,16,37,2,3])).
% 7.58/7.73 cnf(56,plain,
% 7.58/7.73 (E(f4(f5(x561,x561),x562),f4(x561,x562))),
% 7.58/7.73 inference(scs_inference,[],[13,16,37,2,3,10,9,8,5,6,4])).
% 7.58/7.73 cnf(57,plain,
% 7.58/7.73 (E(f2(f2(x571,x571),f5(f2(x571,x571),x572)),x571)),
% 7.58/7.73 inference(scs_inference,[],[12,17,3])).
% 7.58/7.73 cnf(60,plain,
% 7.58/7.73 (~E(a1,f5(a3,a1))),
% 7.58/7.73 inference(scs_inference,[],[12,17,28,3,2,7])).
% 7.58/7.73 cnf(61,plain,
% 7.58/7.73 (E(f2(x611,f5(x612,x612)),f2(x611,x612))),
% 7.58/7.73 inference(scs_inference,[],[13,7])).
% 7.58/7.73 cnf(66,plain,
% 7.58/7.73 (~E(f2(a1,a1),f5(a3,a1))),
% 7.58/7.73 inference(scs_inference,[],[27,46,60,2,3])).
% 7.58/7.73 cnf(69,plain,
% 7.58/7.73 (E(a1,f4(f6(x691),x691))),
% 7.58/7.73 inference(scs_inference,[],[14,7,2])).
% 7.58/7.73 cnf(77,plain,
% 7.58/7.73 (E(f2(f4(f6(x771),x771),x772),f2(a1,x772))),
% 7.58/7.73 inference(scs_inference,[],[14,27,7,2,3,10,9,8,5,4,6])).
% 7.58/7.73 cnf(79,plain,
% 7.58/7.73 (~E(f5(a3,a1),f2(a1,a1))),
% 7.58/7.73 inference(scs_inference,[],[14,66,49,3,2])).
% 7.58/7.73 cnf(87,plain,
% 7.58/7.73 (E(f2(x871,f2(x872,x872)),f2(x871,x872))),
% 7.58/7.73 inference(rename_variables,[],[33])).
% 7.58/7.73 cnf(90,plain,
% 7.58/7.73 (E(f5(x901,f5(x902,x903)),f5(x901,f5(x903,x902)))),
% 7.58/7.73 inference(scs_inference,[],[16,33,87,28,3,2,10,9])).
% 7.58/7.73 cnf(91,plain,
% 7.58/7.73 (E(f5(f5(x911,x912),x913),f5(f5(x912,x911),x913))),
% 7.58/7.73 inference(scs_inference,[],[16,33,87,28,3,2,10,9,8])).
% 7.58/7.73 cnf(92,plain,
% 7.58/7.73 (E(f4(x921,f5(x922,x923)),f4(x921,f5(x923,x922)))),
% 7.58/7.73 inference(scs_inference,[],[16,33,87,28,3,2,10,9,8,5])).
% 7.58/7.73 cnf(95,plain,
% 7.58/7.73 (E(f2(x951,f5(x952,x953)),f2(x951,f5(x953,x952)))),
% 7.58/7.73 inference(scs_inference,[],[16,33,87,28,3,2,10,9,8,5,4,6,7])).
% 7.58/7.73 cnf(101,plain,
% 7.58/7.73 (E(x1011,f2(x1011,f5(x1011,x1012)))),
% 7.58/7.73 inference(scs_inference,[],[17,34,3,2])).
% 7.58/7.73 cnf(212,plain,
% 7.58/7.73 (~E(f5(f5(a3,a1),f5(a3,a1)),a1)),
% 7.58/7.73 inference(scs_inference,[],[37,48,3])).
% 7.58/7.73 cnf(217,plain,
% 7.58/7.73 (E(x2171,f2(f2(x2171,x2171),f5(f2(x2171,x2171),x2172)))),
% 7.58/7.73 inference(scs_inference,[],[31,32,57,3,2])).
% 7.58/7.73 cnf(277,plain,
% 7.58/7.73 (~E(a1,f5(f5(a3,a1),f5(a3,a1)))),
% 7.58/7.73 inference(scs_inference,[],[56,46,212,3,2])).
% 7.58/7.73 cnf(411,plain,
% 7.58/7.73 (~E(f4(f6(x4111),x4111),f5(f5(a3,a1),f5(a3,a1)))),
% 7.58/7.73 inference(scs_inference,[],[69,277,3])).
% 7.58/7.73 cnf(426,plain,
% 7.58/7.73 (~E(f5(f5(a3,a1),f5(a3,a1)),f4(f6(x4261),x4261))),
% 7.58/7.73 inference(scs_inference,[],[61,217,411,3,2])).
% 7.58/7.73 cnf(432,plain,
% 7.58/7.73 (E(f4(x4321,x4322),f4(f2(f2(x4321,x4321),f2(x4321,x4321)),x4322))),
% 7.58/7.73 inference(scs_inference,[],[61,217,411,3,2,10,9,5,8,6,4])).
% 7.58/7.73 cnf(500,plain,
% 7.58/7.73 (~E(f5(f5(a3,a1),f5(a1,a3)),f4(f6(x5001),x5001))),
% 7.58/7.73 inference(scs_inference,[],[90,426,3])).
% 7.58/7.73 cnf(508,plain,
% 7.58/7.73 (~E(f4(f6(x5081),x5081),f5(f5(a3,a1),f5(a1,a3)))),
% 7.58/7.73 inference(scs_inference,[],[79,77,500,3,2])).
% 7.58/7.73 cnf(527,plain,
% 7.58/7.73 (~E(f4(f6(x5271),x5271),f5(f5(a1,a3),f5(a1,a3)))),
% 7.58/7.73 inference(scs_inference,[],[91,508,3])).
% 7.58/7.73 cnf(534,plain,
% 7.58/7.73 (E(f4(x5341,f5(x5342,x5343)),f4(f2(f2(x5341,x5341),f2(x5341,x5341)),f5(x5343,x5342)))),
% 7.58/7.73 inference(scs_inference,[],[92,432,527,2,3])).
% 7.58/7.73 cnf(544,plain,
% 7.58/7.73 ($false),
% 7.58/7.73 inference(scs_inference,[],[95,101,534,38,2,3]),
% 7.58/7.73 ['proof']).
% 7.58/7.73 % SZS output end Proof
% 7.58/7.73 % Total time :7.190000s
%------------------------------------------------------------------------------