%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP152-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n028.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 : Mon Jun 24 06:39:02 EDT 2024
% Result : Unsatisfiable 185.19s 185.16s
% Output : CNFRefutation 185.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP152-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 20 07:58:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 185.19/185.14 %-------------------------------------------
% 185.19/185.14 % File :CSE---1.7
% 185.19/185.14 % Problem :theBenchmark
% 185.19/185.14 % Transform :cnf
% 185.19/185.14 % Format :tptp:raw
% 185.19/185.14 % Command :java -jar mcs_scs.jar %d %s
% 185.19/185.14
% 185.19/185.14 % Result :Theorem 184.550000s
% 185.19/185.14 % Output :CNFRefutation 184.550000s
% 185.19/185.14 %-------------------------------------------
% 185.19/185.15 %--------------------------------------------------------------------------
% 185.19/185.15 % File : GRP152-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 185.19/185.15 % Domain : Group Theory (Lattice Ordered)
% 185.19/185.15 % Problem : Prove least upper-bound axiom using the LUB transformation
% 185.19/185.15 % Version : [Fuc94] (equality) axioms.
% 185.19/185.15 % English : This problem proves the original least upper-bound axiom from
% 185.19/185.15 % the equational axiomatization.
% 185.19/185.16
% 185.19/185.16 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 185.19/185.16 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 185.19/185.16 % Source : [Sch95]
% 185.19/185.16 % Names : ax_lub3a [Sch95]
% 185.19/185.16
% 185.19/185.16 % Status : Unsatisfiable
% 185.19/185.16 % 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, 0.12 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
% 185.19/185.16 % Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 1 RR)
% 185.19/185.16 % Number of literals : 16 ( 16 equ; 1 neg)
% 185.19/185.16 % Maximal clause size : 1 ( 1 avg)
% 185.19/185.16 % Maximal term depth : 3 ( 2 avg)
% 185.19/185.16 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 185.19/185.16 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 185.19/185.16 % Number of variables : 33 ( 2 sgn)
% 185.19/185.16 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 185.19/185.16
% 185.19/185.16 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 185.19/185.16 % least_upper_bound > identity > a > b
% 185.19/185.16 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 185.19/185.16 %--------------------------------------------------------------------------
% 185.19/185.16 %----Include equality group theory axioms
% 185.19/185.16 include('Axioms/GRP004-0.ax').
% 185.19/185.16 %----Include Lattice ordered group (equality) axioms
% 185.19/185.16 include('Axioms/GRP004-2.ax').
% 185.19/185.16 %--------------------------------------------------------------------------
% 185.19/185.16 cnf(prove_ax_lub3a,negated_conjecture,
% 185.19/185.16 least_upper_bound(b,least_upper_bound(a,b)) != least_upper_bound(a,b) ).
% 185.19/185.16
% 185.19/185.16 %--------------------------------------------------------------------------
% 185.19/185.16 %-------------------------------------------
% 185.19/185.16 % Proof found
% 185.19/185.16 % SZS status Theorem for theBenchmark
% 185.19/185.16 % SZS output start Proof
% 185.19/185.16 %ClaNum:26(EqnAxiom:10)
% 185.19/185.16 %VarNum:72(SingletonVarNum:33)
% 185.19/185.16 %MaxLitNum:1
% 185.19/185.16 %MaxfuncDepth:2
% 185.19/185.16 %SharedTerms:6
% 185.19/185.16 %goalClause: 26
% 185.19/185.16 %singleGoalClaCount:1
% 185.19/185.16 [26]~E(f6(a3,f6(a4,a3)),f6(a4,a3))
% 185.19/185.16 [11]E(f5(a1,x111),x111)
% 185.19/185.16 [12]E(f2(x121,x121),x121)
% 185.19/185.16 [13]E(f6(x131,x131),x131)
% 185.19/185.16 [14]E(f5(f7(x141),x141),a1)
% 185.19/185.16 [15]E(f2(x151,x152),f2(x152,x151))
% 185.19/185.16 [16]E(f6(x161,x162),f6(x162,x161))
% 185.19/185.16 [17]E(f2(x171,f6(x171,x172)),x171)
% 185.19/185.16 [18]E(f6(x181,f2(x181,x182)),x181)
% 185.19/185.16 [19]E(f2(f2(x191,x192),x193),f2(x191,f2(x192,x193)))
% 185.19/185.16 [20]E(f6(f6(x201,x202),x203),f6(x201,f6(x202,x203)))
% 185.19/185.16 [21]E(f5(f5(x211,x212),x213),f5(x211,f5(x212,x213)))
% 185.19/185.16 [22]E(f2(f5(x221,x222),f5(x221,x223)),f5(x221,f2(x222,x223)))
% 185.19/185.16 [23]E(f6(f5(x231,x232),f5(x231,x233)),f5(x231,f6(x232,x233)))
% 185.19/185.16 [24]E(f2(f5(x241,x242),f5(x243,x242)),f5(f2(x241,x243),x242))
% 185.19/185.16 [25]E(f6(f5(x251,x252),f5(x253,x252)),f5(f6(x251,x253),x252))
% 185.19/185.16 %EqnAxiom
% 185.19/185.16 [1]E(x11,x11)
% 185.19/185.16 [2]E(x22,x21)+~E(x21,x22)
% 185.19/185.16 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 185.19/185.16 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 185.19/185.16 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 185.19/185.16 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 185.19/185.16 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 185.19/185.16 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 185.19/185.16 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 185.19/185.16 [10]~E(x101,x102)+E(f7(x101),f7(x102))
% 185.19/185.16
% 185.19/185.16 %-------------------------------------------
% 185.24/185.18 cnf(27,plain,
% 185.24/185.18 (E(x271,f2(x271,x271))),
% 185.24/185.18 inference(scs_inference,[],[12,2])).
% 185.24/185.18 cnf(28,plain,
% 185.24/185.18 (~E(f6(a3,f6(a4,a3)),f2(f6(a4,a3),f6(a4,a3)))),
% 185.24/185.18 inference(scs_inference,[],[26,12,2,3])).
% 185.24/185.18 cnf(30,plain,
% 185.24/185.18 (E(x301,f6(x301,x301))),
% 185.24/185.18 inference(scs_inference,[],[13,2])).
% 185.24/185.18 cnf(34,plain,
% 185.24/185.18 (E(x341,f5(a1,x341))),
% 185.24/185.18 inference(scs_inference,[],[11,2])).
% 185.24/185.18 cnf(38,plain,
% 185.24/185.18 (E(f5(x381,f2(x382,x383)),f2(f5(x381,x382),f5(x381,x383)))),
% 185.24/185.18 inference(scs_inference,[],[22,2])).
% 185.24/185.18 cnf(39,plain,
% 185.24/185.18 (E(x391,f5(a1,f2(x391,x391)))),
% 185.24/185.18 inference(scs_inference,[],[27,34,22,2,3])).
% 185.24/185.18 cnf(41,plain,
% 185.24/185.18 (E(f5(a1,f2(x411,x411)),x411)),
% 185.24/185.18 inference(scs_inference,[],[39,2])).
% 185.24/185.18 cnf(42,plain,
% 185.24/185.18 (E(f2(x421,x422),f2(f5(a1,x421),f5(a1,x422)))),
% 185.24/185.18 inference(scs_inference,[],[38,34,39,2,3])).
% 185.24/185.18 cnf(45,plain,
% 185.24/185.18 (E(f2(f5(a1,x451),f5(a1,x452)),f2(x451,x452))),
% 185.24/185.18 inference(scs_inference,[],[42,2])).
% 185.24/185.18 cnf(46,plain,
% 185.24/185.18 (E(x461,f5(a1,f6(x461,x461)))),
% 185.24/185.18 inference(scs_inference,[],[30,34,42,2,3])).
% 185.24/185.18 cnf(49,plain,
% 185.24/185.18 (E(f2(f5(a1,f2(x491,x492)),f5(a1,x493)),f2(x491,f2(x492,x493)))),
% 185.24/185.18 inference(scs_inference,[],[45,46,19,2,3])).
% 185.24/185.18 cnf(53,plain,
% 185.24/185.18 (E(f5(a1,f2(x531,x531)),f5(a1,x531))),
% 185.24/185.18 inference(scs_inference,[],[41,34,49,2,3])).
% 185.24/185.18 cnf(55,plain,
% 185.24/185.18 (E(f5(a1,x551),f5(a1,f2(x551,x551)))),
% 185.24/185.18 inference(scs_inference,[],[53,2])).
% 185.24/185.18 cnf(70,plain,
% 185.24/185.18 (E(x701,f2(x701,f6(x701,x702)))),
% 185.24/185.18 inference(scs_inference,[],[17,2])).
% 185.24/185.18 cnf(71,plain,
% 185.24/185.18 (E(x711,f6(x711,f2(x711,x712)))),
% 185.24/185.18 inference(scs_inference,[],[18,2])).
% 185.24/185.18 cnf(76,plain,
% 185.24/185.18 (E(f5(x761,f5(x762,x763)),f5(f5(x761,x762),x763))),
% 185.24/185.18 inference(scs_inference,[],[21,2])).
% 185.24/185.18 cnf(77,plain,
% 185.24/185.18 (E(a1,f5(f7(x771),x771))),
% 185.24/185.18 inference(scs_inference,[],[14,2])).
% 185.24/185.18 cnf(80,plain,
% 185.24/185.18 (E(f5(a1,x801),f6(x801,f2(x801,x802)))),
% 185.24/185.18 inference(scs_inference,[],[11,71,3])).
% 185.24/185.18 cnf(83,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,x831)),f5(a1,f2(x831,x831)))),
% 185.24/185.18 inference(scs_inference,[],[11,55,3])).
% 185.24/185.18 cnf(86,plain,
% 185.24/185.18 (E(f5(a1,a1),f5(f7(x861),x861))),
% 185.24/185.18 inference(scs_inference,[],[11,77,3])).
% 185.24/185.18 cnf(88,plain,
% 185.24/185.18 (E(f5(f7(x881),x881),f5(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[11,77,3,2])).
% 185.24/185.18 cnf(89,plain,
% 185.24/185.18 (E(f5(a1,f5(f7(x891),x891)),f5(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[11,88,3])).
% 185.24/185.18 cnf(92,plain,
% 185.24/185.18 (E(f5(a1,x921),f2(x921,f6(x921,x922)))),
% 185.24/185.18 inference(scs_inference,[],[11,70,3])).
% 185.24/185.18 cnf(95,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,a1)),f5(f7(x951),x951))),
% 185.24/185.18 inference(scs_inference,[],[11,86,3])).
% 185.24/185.18 cnf(98,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,x981)),f6(x981,f2(x981,x982)))),
% 185.24/185.18 inference(scs_inference,[],[11,80,3])).
% 185.24/185.18 cnf(100,plain,
% 185.24/185.18 (E(f6(x1001,f2(x1001,x1002)),f5(a1,f5(a1,x1001)))),
% 185.24/185.18 inference(scs_inference,[],[11,80,3,2])).
% 185.24/185.18 cnf(101,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,x1011)),f2(x1011,f6(x1011,x1012)))),
% 185.24/185.18 inference(scs_inference,[],[11,92,3])).
% 185.24/185.18 cnf(103,plain,
% 185.24/185.18 (E(f2(x1031,f6(x1031,x1032)),f5(a1,f5(a1,x1031)))),
% 185.24/185.18 inference(scs_inference,[],[11,92,3,2])).
% 185.24/185.18 cnf(107,plain,
% 185.24/185.18 (E(f5(a1,x1071),f5(a1,f6(x1071,x1071)))),
% 185.24/185.18 inference(scs_inference,[],[11,46,3])).
% 185.24/185.18 cnf(110,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,x1101)),f5(a1,f6(x1101,x1101)))),
% 185.24/185.18 inference(scs_inference,[],[11,107,3])).
% 185.24/185.18 cnf(113,plain,
% 185.24/185.18 (E(f5(a1,f5(f7(x1131),x1131)),a1)),
% 185.24/185.18 inference(scs_inference,[],[11,14,3])).
% 185.24/185.18 cnf(115,plain,
% 185.24/185.18 (E(a1,f5(a1,f5(f7(x1151),x1151)))),
% 185.24/185.18 inference(scs_inference,[],[11,14,3,2])).
% 185.24/185.18 cnf(118,plain,
% 185.24/185.18 (E(f5(a1,f5(f7(x1181),x1181)),f2(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[12,115,3,2])).
% 185.24/185.18 cnf(119,plain,
% 185.24/185.18 (E(f2(x1191,x1191),f6(x1191,f2(x1191,x1192)))),
% 185.24/185.18 inference(scs_inference,[],[12,71,3])).
% 185.24/185.18 cnf(130,plain,
% 185.24/185.18 (E(f6(x1301,f2(x1301,x1302)),f2(f2(x1301,x1301),f2(x1301,x1301)))),
% 185.24/185.18 inference(scs_inference,[],[12,119,3,2])).
% 185.24/185.18 cnf(151,plain,
% 185.24/185.18 (E(f2(f5(a1,x1511),f5(a1,x1512)),f2(f2(x1511,x1512),f2(x1511,x1512)))),
% 185.24/185.18 inference(scs_inference,[],[12,42,3,2])).
% 185.24/185.18 cnf(166,plain,
% 185.24/185.18 (E(f5(a1,f5(f7(x1661),x1661)),f6(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[13,115,3,2])).
% 185.24/185.18 cnf(325,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,x3251)),f2(f6(x3251,x3252),x3251))),
% 185.24/185.18 inference(scs_inference,[],[15,103,3,2])).
% 185.24/185.18 cnf(379,plain,
% 185.24/185.18 (E(f2(x3791,f2(x3792,x3793)),f2(x3793,f2(x3791,x3792)))),
% 185.24/185.18 inference(scs_inference,[],[15,19,3,2])).
% 185.24/185.18 cnf(397,plain,
% 185.24/185.18 (E(f5(a1,f5(a1,x3971)),f6(f2(x3971,x3972),x3971))),
% 185.24/185.18 inference(scs_inference,[],[16,100,3,2])).
% 185.24/185.18 cnf(404,plain,
% 185.24/185.18 (E(f2(f2(x4041,x4041),f2(x4041,x4041)),f6(f2(x4041,x4042),x4041))),
% 185.24/185.18 inference(scs_inference,[],[16,130,3,2])).
% 185.24/185.18 cnf(457,plain,
% 185.24/185.18 (E(f5(f5(a1,f7(x4571)),x4571),f2(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[21,118,3])).
% 185.24/185.18 cnf(461,plain,
% 185.24/185.18 (E(f5(f5(a1,f7(x4611)),x4611),f6(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[21,166,457,2,3])).
% 185.24/185.18 cnf(465,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x4651),f2(f6(x4651,x4652),x4651))),
% 185.24/185.18 inference(scs_inference,[],[21,325,461,2,3])).
% 185.24/185.18 cnf(469,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x4691),f6(f2(x4691,x4692),x4691))),
% 185.24/185.18 inference(scs_inference,[],[21,397,465,2,3])).
% 185.24/185.18 cnf(473,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),a1),f5(f7(x4731),x4731))),
% 185.24/185.18 inference(scs_inference,[],[21,469,95,2,3])).
% 185.24/185.18 cnf(476,plain,
% 185.24/185.18 (E(f5(f5(a1,f7(x4761)),x4761),f5(a1,a1))),
% 185.24/185.18 inference(scs_inference,[],[21,473,89,2,3])).
% 185.24/185.18 cnf(480,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x4801),f6(x4801,f2(x4801,x4802)))),
% 185.24/185.18 inference(scs_inference,[],[21,476,98,2,3])).
% 185.24/185.18 cnf(484,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x4841),f2(x4841,f6(x4841,x4842)))),
% 185.24/185.18 inference(scs_inference,[],[21,480,101,2,3])).
% 185.24/185.18 cnf(488,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x4881),f5(a1,f6(x4881,x4881)))),
% 185.24/185.18 inference(scs_inference,[],[21,484,110,2,3])).
% 185.24/185.18 cnf(492,plain,
% 185.24/185.18 (E(f5(f5(a1,f7(x4921)),x4921),a1)),
% 185.24/185.18 inference(scs_inference,[],[21,488,113,2,3])).
% 185.24/185.18 cnf(496,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x4961),f5(a1,f2(x4961,x4961)))),
% 185.24/185.18 inference(scs_inference,[],[21,492,83,2,3])).
% 185.24/185.18 cnf(499,plain,
% 185.24/185.18 (E(f5(a1,f2(x4991,x4991)),f5(f5(a1,a1),x4991))),
% 185.24/185.18 inference(scs_inference,[],[496,2])).
% 185.24/185.18 cnf(503,plain,
% 185.24/185.18 (E(f5(f5(a1,a1),x5031),f2(f5(a1,x5031),f5(a1,x5031)))),
% 185.24/185.18 inference(scs_inference,[],[22,499,3,2])).
% 185.24/185.18 cnf(538,plain,
% 185.24/185.18 (E(f6(f2(x5381,x5382),x5381),f2(x5381,x5381))),
% 185.24/185.18 inference(scs_inference,[],[27,404,3,2])).
% 185.24/185.18 cnf(541,plain,
% 185.24/185.18 (~E(a3,f2(f6(a4,a3),x5411))),
% 185.24/185.19 inference(scs_inference,[],[538,28,3,8])).
% 185.24/185.19 cnf(542,plain,
% 185.24/185.19 (~E(a3,f2(x5421,f2(x5422,f6(a4,a3))))),
% 185.24/185.19 inference(scs_inference,[],[379,541,3])).
% 185.24/185.19 cnf(568,plain,
% 185.24/185.19 (~E(a3,f2(x5681,f2(f6(a4,a3),x5682)))),
% 185.24/185.19 inference(scs_inference,[],[379,542,3])).
% 185.24/185.19 cnf(581,plain,
% 185.24/185.19 (~E(a3,f2(f5(a1,f6(a4,a3)),f5(a1,x5811)))),
% 185.24/185.19 inference(scs_inference,[],[151,568,3])).
% 185.24/185.19 cnf(592,plain,
% 185.24/185.19 (~E(a3,f5(f5(a1,a1),f6(a4,a3)))),
% 185.24/185.19 inference(scs_inference,[],[503,581,3])).
% 185.24/185.19 cnf(595,plain,
% 185.24/185.19 (~E(a3,f5(a1,f5(a1,f6(a4,a3))))),
% 185.24/185.19 inference(scs_inference,[],[76,592,3])).
% 185.24/185.19 cnf(1807,plain,
% 185.24/185.19 (E(f5(f2(x18071,x18071),x18072),f5(x18071,x18072))),
% 185.24/185.19 inference(scs_inference,[],[12,5,7,10,4])).
% 185.24/185.19 cnf(1830,plain,
% 185.24/185.19 (E(f6(x18301,f6(x18302,x18302)),f6(x18301,x18302))),
% 185.24/185.19 inference(scs_inference,[],[13,5,7,10,4,6,8,9])).
% 185.24/185.19 cnf(2408,plain,
% 185.24/185.19 (~E(f6(f6(a4,a3),a3),f6(a4,a3))),
% 185.24/185.19 inference(scs_inference,[],[26,16,595,2,3])).
% 185.24/185.19 cnf(2437,plain,
% 185.24/185.19 ($false),
% 185.24/185.19 inference(scs_inference,[],[20,1807,1830,2408,7,6,8,4,5,9,10,3]),
% 185.24/185.19 ['proof']).
% 185.24/185.19 % SZS output end Proof
% 185.24/185.19 % Total time :184.550000s
%------------------------------------------------------------------------------