%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP142-1 : 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 : n017.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 06:39:01 EDT 2024
% Result : Unsatisfiable 0.74s 0.83s
% Output : CNFRefutation 0.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP142-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33 % Computer : n017.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 20 09:12:54 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.74/0.83 %-------------------------------------------
% 0.74/0.83 % File :CSE---1.7
% 0.74/0.83 % Problem :theBenchmark
% 0.74/0.83 % Transform :cnf
% 0.74/0.83 % Format :tptp:raw
% 0.74/0.83 % Command :java -jar mcs_scs.jar %d %s
% 0.74/0.83
% 0.74/0.83 % Result :Theorem 0.240000s
% 0.74/0.83 % Output :CNFRefutation 0.240000s
% 0.74/0.83 %-------------------------------------------
% 0.74/0.83 %--------------------------------------------------------------------------
% 0.74/0.83 % File : GRP142-1 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.74/0.83 % Domain : Group Theory (Lattice Ordered)
% 0.74/0.83 % Problem : Prove greatest lower-bound axiom using the LUB transformation
% 0.74/0.83 % Version : [Fuc94] (equality) axioms.
% 0.74/0.83 % English : This problem proves the original greatest lower-bound axiom
% 0.74/0.83 % from the equational axiomatization.
% 0.74/0.83
% 0.74/0.83 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.74/0.83 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.74/0.83 % Source : [Sch95]
% 0.74/0.83 % Names : ax_glb2a [Sch95]
% 0.74/0.83
% 0.74/0.83 % Status : Unsatisfiable
% 0.74/0.83 % 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 v2.0.0
% 0.74/0.83 % Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 1 RR)
% 0.74/0.83 % Number of literals : 16 ( 16 equ; 1 neg)
% 0.74/0.83 % Maximal clause size : 1 ( 1 avg)
% 0.74/0.83 % Maximal term depth : 3 ( 2 avg)
% 0.74/0.83 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.74/0.83 % Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% 0.74/0.83 % Number of variables : 33 ( 2 sgn)
% 0.74/0.83 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.74/0.83
% 0.74/0.83 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.74/0.83 % least_upper_bound > identity > a > b
% 0.74/0.83 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.74/0.83 %--------------------------------------------------------------------------
% 0.74/0.83 %----Include equality group theory axioms
% 0.74/0.83 include('Axioms/GRP004-0.ax').
% 0.74/0.83 %----Include Lattice ordered group (equality) axioms
% 0.74/0.83 include('Axioms/GRP004-2.ax').
% 0.74/0.83 %--------------------------------------------------------------------------
% 0.74/0.83 cnf(prove_ax_glb2a,negated_conjecture,
% 0.74/0.83 least_upper_bound(greatest_lower_bound(a,b),a) != a ).
% 0.74/0.83
% 0.74/0.83 %--------------------------------------------------------------------------
% 0.74/0.83 %-------------------------------------------
% 0.74/0.83 % Proof found
% 0.74/0.83 % SZS status Theorem for theBenchmark
% 0.74/0.83 % SZS output start Proof
% 0.74/0.83 %ClaNum:26(EqnAxiom:10)
% 0.74/0.83 %VarNum:72(SingletonVarNum:33)
% 0.74/0.83 %MaxLitNum:1
% 0.74/0.83 %MaxfuncDepth:2
% 0.74/0.83 %SharedTerms:6
% 0.74/0.83 %goalClause: 26
% 0.74/0.83 %singleGoalClaCount:1
% 0.74/0.83 [26]~E(f6(f2(a3,a4),a3),a3)
% 0.74/0.83 [11]E(f5(a1,x111),x111)
% 0.74/0.83 [12]E(f2(x121,x121),x121)
% 0.74/0.83 [13]E(f6(x131,x131),x131)
% 0.74/0.83 [14]E(f5(f7(x141),x141),a1)
% 0.74/0.83 [15]E(f2(x151,x152),f2(x152,x151))
% 0.74/0.83 [16]E(f6(x161,x162),f6(x162,x161))
% 0.74/0.83 [17]E(f2(x171,f6(x171,x172)),x171)
% 0.74/0.83 [18]E(f6(x181,f2(x181,x182)),x181)
% 0.74/0.83 [19]E(f2(f2(x191,x192),x193),f2(x191,f2(x192,x193)))
% 0.74/0.83 [20]E(f6(f6(x201,x202),x203),f6(x201,f6(x202,x203)))
% 0.74/0.83 [21]E(f5(f5(x211,x212),x213),f5(x211,f5(x212,x213)))
% 0.74/0.83 [22]E(f2(f5(x221,x222),f5(x221,x223)),f5(x221,f2(x222,x223)))
% 0.74/0.83 [23]E(f6(f5(x231,x232),f5(x231,x233)),f5(x231,f6(x232,x233)))
% 0.74/0.83 [24]E(f2(f5(x241,x242),f5(x243,x242)),f5(f2(x241,x243),x242))
% 0.74/0.83 [25]E(f6(f5(x251,x252),f5(x253,x252)),f5(f6(x251,x253),x252))
% 0.74/0.83 %EqnAxiom
% 0.74/0.83 [1]E(x11,x11)
% 0.74/0.83 [2]E(x22,x21)+~E(x21,x22)
% 0.74/0.83 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.74/0.83 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43))
% 0.74/0.83 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52))
% 0.74/0.83 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 0.74/0.83 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 0.74/0.83 [8]~E(x81,x82)+E(f6(x81,x83),f6(x82,x83))
% 0.74/0.83 [9]~E(x91,x92)+E(f6(x93,x91),f6(x93,x92))
% 0.74/0.83 [10]~E(x101,x102)+E(f7(x101),f7(x102))
% 0.74/0.83
% 0.74/0.83 %-------------------------------------------
% 0.74/0.84 cnf(158,plain,
% 0.74/0.84 ($false),
% 0.74/0.84 inference(scs_inference,[],[26,16,18,3]),
% 0.74/0.84 ['proof']).
% 0.74/0.84 % SZS output end Proof
% 0.74/0.84 % Total time :0.240000s
%------------------------------------------------------------------------------