%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GRP176-2 : 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 : n029.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 06:39:08 EDT 2024
% Result : Unsatisfiable 76.12s 76.15s
% Output : CNFRefutation 76.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : GRP176-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.04/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % 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 09:24:09 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.61/0.64 start to proof:theBenchmark
% 76.12/76.14 %-------------------------------------------
% 76.12/76.14 % File :CSE---1.7
% 76.12/76.14 % Problem :theBenchmark
% 76.12/76.14 % Transform :cnf
% 76.12/76.14 % Format :tptp:raw
% 76.12/76.14 % Command :java -jar mcs_scs.jar %d %s
% 76.12/76.14
% 76.12/76.14 % Result :Theorem 75.450000s
% 76.12/76.14 % Output :CNFRefutation 75.450000s
% 76.12/76.14 %-------------------------------------------
% 76.12/76.15 %--------------------------------------------------------------------------
% 76.12/76.15 % File : GRP176-2 : TPTP v8.2.0. Bugfixed v1.2.1.
% 76.12/76.15 % Domain : Group Theory (Lattice Ordered)
% 76.12/76.15 % Problem : General form of distributivity
% 76.12/76.15 % Version : [Fuc94] (equality) axioms : Augmented.
% 76.12/76.15 % English :
% 76.12/76.15
% 76.12/76.15 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 76.12/76.15 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 76.12/76.15 % Source : [Sch95]
% 76.12/76.15 % Names : p07 [Sch95]
% 76.12/76.15
% 76.12/76.15 % Status : Unsatisfiable
% 76.12/76.15 % Rating : 0.05 v8.2.0, 0.08 v8.1.0, 0.10 v7.5.0, 0.08 v7.4.0, 0.13 v7.3.0, 0.05 v7.1.0, 0.00 v7.0.0, 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, 0.00 v2.0.0
% 76.12/76.15 % Syntax : Number of clauses : 17 ( 17 unt; 0 nHn; 1 RR)
% 76.12/76.15 % Number of literals : 17 ( 17 equ; 1 neg)
% 76.12/76.15 % Maximal clause size : 1 ( 1 avg)
% 76.12/76.15 % Maximal term depth : 4 ( 2 avg)
% 76.12/76.15 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 76.12/76.15 % Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% 76.12/76.15 % Number of variables : 35 ( 2 sgn)
% 76.12/76.15 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 76.12/76.15
% 76.12/76.15 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 76.12/76.15 % least_upper_bound > identity > a > b > c > d
% 76.12/76.15 % : ORDERING LPO greatest_lower_bound > least_upper_bound >
% 76.12/76.15 % inverse > product > identity > a > b > c > d
% 76.12/76.15 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 76.12/76.15 %--------------------------------------------------------------------------
% 76.12/76.15 %----Include equality group theory axioms
% 76.12/76.15 include('Axioms/GRP004-0.ax').
% 76.12/76.15 %----Include Lattice ordered group (equality) axioms
% 76.12/76.15 include('Axioms/GRP004-2.ax').
% 76.12/76.15 %--------------------------------------------------------------------------
% 76.12/76.15 cnf(p07_1,hypothesis,
% 76.12/76.15 inverse(multiply(X,Y)) = multiply(inverse(Y),inverse(X)) ).
% 76.12/76.15
% 76.12/76.15 cnf(prove_p07,negated_conjecture,
% 76.12/76.15 multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ).
% 76.12/76.15
% 76.12/76.15 %--------------------------------------------------------------------------
% 76.12/76.15 %-------------------------------------------
% 76.12/76.15 % Proof found
% 76.12/76.15 % SZS status Theorem for theBenchmark
% 76.12/76.15 % SZS output start Proof
% 76.12/76.15 %ClaNum:27(EqnAxiom:10)
% 76.12/76.15 %VarNum:76(SingletonVarNum:35)
% 76.12/76.15 %MaxLitNum:1
% 76.12/76.15 %MaxfuncDepth:3
% 76.12/76.15 %SharedTerms:14
% 76.12/76.15 %goalClause: 27
% 76.12/76.15 %singleGoalClaCount:1
% 76.12/76.15 [27]~E(f8(f7(a3,f7(a4,a6)),f7(a3,f7(a5,a6))),f7(a3,f7(f8(a4,a5),a6)))
% 76.12/76.15 [11]E(f7(a1,x111),x111)
% 76.12/76.15 [12]E(f2(x121,x121),x121)
% 76.12/76.15 [13]E(f8(x131,x131),x131)
% 76.12/76.15 [14]E(f7(f9(x141),x141),a1)
% 76.12/76.15 [15]E(f2(x151,x152),f2(x152,x151))
% 76.12/76.15 [16]E(f8(x161,x162),f8(x162,x161))
% 76.12/76.15 [17]E(f2(x171,f8(x171,x172)),x171)
% 76.12/76.15 [18]E(f8(x181,f2(x181,x182)),x181)
% 76.12/76.15 [19]E(f9(f7(x191,x192)),f7(f9(x192),f9(x191)))
% 76.12/76.15 [20]E(f2(f2(x201,x202),x203),f2(x201,f2(x202,x203)))
% 76.12/76.15 [21]E(f8(f8(x211,x212),x213),f8(x211,f8(x212,x213)))
% 76.12/76.15 [22]E(f7(f7(x221,x222),x223),f7(x221,f7(x222,x223)))
% 76.12/76.15 [23]E(f2(f7(x231,x232),f7(x231,x233)),f7(x231,f2(x232,x233)))
% 76.12/76.15 [24]E(f8(f7(x241,x242),f7(x241,x243)),f7(x241,f8(x242,x243)))
% 76.12/76.15 [25]E(f2(f7(x251,x252),f7(x253,x252)),f7(f2(x251,x253),x252))
% 76.12/76.15 [26]E(f8(f7(x261,x262),f7(x263,x262)),f7(f8(x261,x263),x262))
% 76.12/76.15 %EqnAxiom
% 76.12/76.15 [1]E(x11,x11)
% 76.12/76.15 [2]E(x22,x21)+~E(x21,x22)
% 76.12/76.15 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 76.12/76.15 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 76.12/76.15 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 76.12/76.15 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 76.12/76.15 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 76.12/76.15 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83))
% 76.12/76.15 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92))
% 76.12/76.15 [10]~E(x101,x102)+E(f9(x101),f9(x102))
% 76.12/76.15
% 76.12/76.15 %-------------------------------------------
% 76.12/76.16 cnf(1861,plain,
% 76.12/76.16 (E(f7(f8(x18611,x18612),x18613),f7(f8(x18612,x18611),x18613))),
% 76.12/76.16 inference(scs_inference,[],[16,10,4])).
% 76.12/76.16 cnf(1862,plain,
% 76.12/76.16 (E(f7(x18621,f8(x18622,x18623)),f7(x18621,f8(x18623,x18622)))),
% 76.12/76.16 inference(scs_inference,[],[16,10,4,5])).
% 76.12/76.16 cnf(1867,plain,
% 76.12/76.16 (~E(f7(a3,f7(f8(a4,a5),a6)),f8(f7(a3,f7(a4,a6)),f7(a3,f7(a5,a6))))),
% 76.12/76.16 inference(scs_inference,[],[27,16,10,4,5,6,7,8,9,2])).
% 76.12/76.16 cnf(1912,plain,
% 76.12/76.16 (E(f7(x19121,f7(f8(x19122,x19123),x19124)),f7(x19121,f7(f8(x19123,x19122),x19124)))),
% 76.12/76.16 inference(scs_inference,[],[1861,4,5])).
% 76.12/76.16 cnf(1927,plain,
% 76.12/76.16 (~E(f8(f7(a3,f7(a4,a6)),f7(a3,f7(a5,a6))),f7(a3,f7(f8(a5,a4),a6)))),
% 76.12/76.16 inference(scs_inference,[],[1862,1912,1867,5,4,8,10,7,6,9,3,2])).
% 76.12/76.16 cnf(2661,plain,
% 76.12/76.16 (E(f9(f8(x26611,x26611)),f9(x26611))),
% 76.12/76.16 inference(scs_inference,[],[13,10])).
% 76.12/76.16 cnf(2670,plain,
% 76.12/76.16 (E(f2(x26701,f9(f8(x26702,x26702))),f2(x26701,f9(x26702)))),
% 76.12/76.16 inference(scs_inference,[],[2661,10,8,7])).
% 76.12/76.16 cnf(2927,plain,
% 76.12/76.16 (~E(f8(f7(a3,f7(a5,a6)),f7(a3,f7(a4,a6))),f7(a3,f7(f8(a5,a4),a6)))),
% 76.12/76.16 inference(scs_inference,[],[16,2670,1927,10,8,6,7,9,4,5,3])).
% 76.12/76.16 cnf(3290,plain,
% 76.12/76.16 ($false),
% 76.12/76.16 inference(scs_inference,[],[24,2927,26,3,2,5]),
% 76.12/76.16 ['proof']).
% 76.12/76.17 % SZS output end Proof
% 76.12/76.17 % Total time :75.450000s
%------------------------------------------------------------------------------