%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP137-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 06:39:00 EDT 2024
% Result : Unsatisfiable 0.59s 0.77s
% Output : CNFRefutation 0.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15 % Problem : GRP137-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.09/0.15 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n021.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 20 09:50:38 EDT 2024
% 0.14/0.37 % CPUTime :
% 0.53/0.63 start to proof:theBenchmark
% 0.59/0.76 %-------------------------------------------
% 0.59/0.76 % File :CSE---1.7
% 0.59/0.76 % Problem :theBenchmark
% 0.59/0.76 % Transform :cnf
% 0.59/0.76 % Format :tptp:raw
% 0.59/0.76 % Command :java -jar mcs_scs.jar %d %s
% 0.59/0.76
% 0.59/0.76 % Result :Theorem 0.090000s
% 0.59/0.76 % Output :CNFRefutation 0.090000s
% 0.59/0.76 %-------------------------------------------
% 0.59/0.77 %--------------------------------------------------------------------------
% 0.59/0.77 % File : GRP137-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.59/0.77 % Domain : Group Theory (Lattice Ordered)
% 0.59/0.77 % Problem : Prove anti-symmetry axiom using the GLB transformation
% 0.59/0.77 % Version : [Fuc94] (equality) axioms.
% 0.59/0.77 % English : This problem proves the original anti-symmetry axiom from the
% 0.59/0.77 % equational axiomatization.
% 0.59/0.77
% 0.59/0.77 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.59/0.77 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.59/0.77 % Source : [Sch95]
% 0.59/0.77 % Names : ax_antisymb [Sch95]
% 0.59/0.77
% 0.59/0.77 % Status : Unsatisfiable
% 0.59/0.77 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 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 v2.0.0
% 0.59/0.77 % Syntax : Number of clauses : 18 ( 18 unt; 0 nHn; 3 RR)
% 0.59/0.77 % Number of literals : 18 ( 18 equ; 1 neg)
% 0.59/0.77 % Maximal clause size : 1 ( 1 avg)
% 0.59/0.77 % Maximal term depth : 3 ( 1 avg)
% 0.59/0.77 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.59/0.77 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.59/0.77 % Number of variables : 33 ( 2 sgn)
% 0.59/0.77 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.59/0.77
% 0.59/0.77 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.59/0.77 % least_upper_bound > identity > a > b
% 0.59/0.77 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.59/0.77 %--------------------------------------------------------------------------
% 0.59/0.77 %----Include equality group theory axioms
% 0.59/0.77 include('Axioms/GRP004-0.ax').
% 0.59/0.77 %----Include Lattice ordered group (equality) axioms
% 0.59/0.77 include('Axioms/GRP004-2.ax').
% 0.59/0.77 %--------------------------------------------------------------------------
% 0.59/0.77 cnf(ax_antisymb_1,hypothesis,
% 0.59/0.77 greatest_lower_bound(a,b) = a ).
% 0.59/0.77
% 0.59/0.77 cnf(ax_antisymb_2,hypothesis,
% 0.59/0.77 greatest_lower_bound(a,b) = b ).
% 0.59/0.77
% 0.59/0.77 cnf(prove_ax_antisymb,negated_conjecture,
% 0.59/0.77 a != b ).
% 0.59/0.77
% 0.59/0.77 %--------------------------------------------------------------------------
% 0.59/0.77 %-------------------------------------------
% 0.59/0.77 % Proof found
% 0.59/0.77 % SZS status Theorem for theBenchmark
% 0.59/0.77 % SZS output start Proof
% 0.59/0.77 %ClaNum:28(EqnAxiom:10)
% 0.59/0.77 %VarNum:72(SingletonVarNum:33)
% 0.59/0.77 %MaxLitNum:1
% 0.59/0.77 %MaxfuncDepth:2
% 0.59/0.77 %SharedTerms:7
% 0.59/0.77 %goalClause: 28
% 0.59/0.77 %singleGoalClaCount:1
% 0.59/0.77 [28]~E(a2,a1)
% 0.59/0.77 [11]E(f3(a1,a2),a1)
% 0.59/0.77 [12]E(f3(a1,a2),a2)
% 0.59/0.77 [13]E(f5(a4,x131),x131)
% 0.59/0.77 [14]E(f3(x141,x141),x141)
% 0.59/0.77 [15]E(f6(x151,x151),x151)
% 0.59/0.77 [16]E(f5(f7(x161),x161),a4)
% 0.59/0.77 [17]E(f3(x171,x172),f3(x172,x171))
% 0.59/0.77 [18]E(f6(x181,x182),f6(x182,x181))
% 0.59/0.77 [19]E(f3(x191,f6(x191,x192)),x191)
% 0.59/0.77 [20]E(f6(x201,f3(x201,x202)),x201)
% 0.59/0.77 [21]E(f3(f3(x211,x212),x213),f3(x211,f3(x212,x213)))
% 0.59/0.77 [22]E(f6(f6(x221,x222),x223),f6(x221,f6(x222,x223)))
% 0.59/0.77 [23]E(f5(f5(x231,x232),x233),f5(x231,f5(x232,x233)))
% 0.59/0.77 [24]E(f3(f5(x241,x242),f5(x241,x243)),f5(x241,f3(x242,x243)))
% 0.59/0.77 [25]E(f6(f5(x251,x252),f5(x251,x253)),f5(x251,f6(x252,x253)))
% 0.59/0.77 [26]E(f3(f5(x261,x262),f5(x263,x262)),f5(f3(x261,x263),x262))
% 0.59/0.77 [27]E(f6(f5(x271,x272),f5(x273,x272)),f5(f6(x271,x273),x272))
% 0.59/0.77 %EqnAxiom
% 0.59/0.77 [1]E(x11,x11)
% 0.59/0.77 [2]E(x22,x21)+~E(x21,x22)
% 0.59/0.77 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.59/0.77 [4]~E(x41,x42)+E(f3(x41,x43),f3(x42,x43))
% 0.59/0.77 [5]~E(x51,x52)+E(f3(x53,x51),f3(x53,x52))
% 0.59/0.77 [6]~E(x61,x62)+E(f5(x61,x63),f5(x62,x63))
% 0.59/0.77 [7]~E(x71,x72)+E(f5(x73,x71),f5(x73,x72))
% 0.59/0.77 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.59/0.77 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.59/0.77 [10]~E(x101,x102)+E(f7(x101),f7(x102))
% 0.59/0.77
% 0.59/0.77 %-------------------------------------------
% 0.59/0.78 cnf(29,plain,
% 0.59/0.78 (E(x291,f3(x291,x291))),
% 0.59/0.78 inference(scs_inference,[],[14,2])).
% 0.59/0.78 cnf(32,plain,
% 0.59/0.78 (E(x321,f6(x321,x321))),
% 0.59/0.78 inference(scs_inference,[],[15,2])).
% 0.59/0.78 cnf(39,plain,
% 0.59/0.78 (E(f5(x391,x392),f5(x391,f3(x392,x392)))),
% 0.59/0.78 inference(scs_inference,[],[29,24,2,3])).
% 0.59/0.78 cnf(42,plain,
% 0.59/0.78 (E(f5(x421,f3(x422,x422)),f5(x421,x422))),
% 0.59/0.78 inference(scs_inference,[],[39,2])).
% 0.59/0.78 cnf(55,plain,
% 0.59/0.78 (E(f5(f6(x551,x552),x553),f6(f5(x551,x553),f5(x552,x553)))),
% 0.59/0.78 inference(scs_inference,[],[27,2])).
% 0.59/0.78 cnf(62,plain,
% 0.59/0.78 (E(x621,f3(x621,f6(x621,x622)))),
% 0.59/0.78 inference(scs_inference,[],[19,2])).
% 0.59/0.78 cnf(63,plain,
% 0.59/0.78 (E(f5(f6(x631,x632),f3(x633,x633)),f6(f5(x631,x633),f5(x632,x633)))),
% 0.59/0.78 inference(scs_inference,[],[55,42,19,2,3])).
% 0.59/0.78 cnf(67,plain,
% 0.59/0.78 (E(x671,f3(f6(x671,x671),f6(f6(x671,x671),x672)))),
% 0.59/0.78 inference(scs_inference,[],[32,62,63,2,3])).
% 0.59/0.78 cnf(69,plain,
% 0.59/0.78 (E(f3(f6(x691,x691),f6(f6(x691,x691),x692)),x691)),
% 0.59/0.78 inference(scs_inference,[],[67,2])).
% 0.59/0.78 cnf(73,plain,
% 0.59/0.78 (~E(a2,f3(f6(a1,a1),f6(f6(a1,a1),x731)))),
% 0.59/0.78 inference(scs_inference,[],[28,69,20,2,3])).
% 0.59/0.78 cnf(96,plain,
% 0.59/0.78 (E(a2,f3(a1,a2))),
% 0.59/0.78 inference(scs_inference,[],[12,2])).
% 0.59/0.78 cnf(99,plain,
% 0.59/0.78 (E(a1,f3(a1,a2))),
% 0.59/0.78 inference(scs_inference,[],[11,2])).
% 0.59/0.78 cnf(100,plain,
% 0.59/0.78 (E(f3(f6(a2,a2),f6(f6(a2,a2),x1001)),f3(a1,a2))),
% 0.59/0.78 inference(scs_inference,[],[96,69,11,2,3])).
% 0.59/0.78 cnf(103,plain,
% 0.59/0.78 (E(f3(f6(a1,a1),f6(f6(a1,a1),x1031)),f3(a1,a2))),
% 0.59/0.78 inference(scs_inference,[],[99,69,100,2,3])).
% 0.59/0.78 cnf(105,plain,
% 0.59/0.78 (E(f3(a1,a2),f3(f6(a1,a1),f6(f6(a1,a1),x1051)))),
% 0.59/0.78 inference(scs_inference,[],[103,2])).
% 0.59/0.78 cnf(111,plain,
% 0.59/0.78 ($false),
% 0.59/0.78 inference(scs_inference,[],[105,96,73,3]),
% 0.59/0.78 ['proof']).
% 0.59/0.78 % SZS output end Proof
% 0.59/0.78 % Total time :0.090000s
%------------------------------------------------------------------------------