TSTP Solution File: GRP176-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP176-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n002.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 00:11:25 EDT 2023
% Result : Unsatisfiable 0.19s 0.64s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP176-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 23:22:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % File :CSE---1.6
% 0.19/0.64 % Problem :theBenchmark
% 0.19/0.64 % Transform :cnf
% 0.19/0.64 % Format :tptp:raw
% 0.19/0.64 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.64
% 0.19/0.64 % Result :Theorem 0.010000s
% 0.19/0.64 % Output :CNFRefutation 0.010000s
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 %--------------------------------------------------------------------------
% 0.19/0.64 % File : GRP176-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.19/0.64 % Domain : Group Theory (Lattice Ordered)
% 0.19/0.64 % Problem : General form of distributivity
% 0.19/0.64 % Version : [Fuc94] (equality) axioms.
% 0.19/0.64 % English :
% 0.19/0.64
% 0.19/0.64 % Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri
% 0.19/0.64 % : [Sch95] Schulz (1995), Explanation Based Learning for Distribu
% 0.19/0.64 % : [Dah95] Dahn (1995), Email to G. Sutcliffe
% 0.19/0.64 % Source : [TPTP]
% 0.19/0.64 % Names :
% 0.19/0.64
% 0.19/0.64 % Status : Unsatisfiable
% 0.19/0.64 % Rating : 0.04 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.00 v7.0.0, 0.11 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
% 0.19/0.64 % Syntax : Number of clauses : 16 ( 16 unt; 0 nHn; 1 RR)
% 0.19/0.64 % Number of literals : 16 ( 16 equ; 1 neg)
% 0.19/0.64 % Maximal clause size : 1 ( 1 avg)
% 0.19/0.64 % Maximal term depth : 4 ( 2 avg)
% 0.19/0.64 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.19/0.64 % Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% 0.19/0.64 % Number of variables : 33 ( 2 sgn)
% 0.19/0.64 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.19/0.64
% 0.19/0.64 % Comments : ORDERING LPO inverse > product > greatest_lower_bound >
% 0.19/0.64 % least_upper_bound > identity > a > b > c > d
% 0.19/0.64 % : ORDERING LPO greatest_lower_bound > least_upper_bound >
% 0.19/0.64 % inverse > product > identity > a > b > c > d
% 0.19/0.64 % : This is a standardized version of the problem that appears in
% 0.19/0.64 % [Sch95].
% 0.19/0.64 % : [Dah95] says "Easy from equational axioms, More difficult from
% 0.19/0.64 % monotonicity. The assumtion is a consequence of group theory."
% 0.19/0.64 % Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed.
% 0.19/0.64 %--------------------------------------------------------------------------
% 0.19/0.64 %----Include equality group theory axioms
% 0.19/0.64 include('Axioms/GRP004-0.ax').
% 0.19/0.64 %----Include Lattice ordered group (equality) axioms
% 0.19/0.64 include('Axioms/GRP004-2.ax').
% 0.19/0.64 %--------------------------------------------------------------------------
% 0.19/0.64 cnf(prove_p07,negated_conjecture,
% 0.19/0.64 multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))) ).
% 0.19/0.64
% 0.19/0.64 %--------------------------------------------------------------------------
% 0.19/0.64 %-------------------------------------------
% 0.19/0.64 % Proof found
% 0.19/0.64 % SZS status Theorem for theBenchmark
% 0.19/0.64 % SZS output start Proof
% 0.19/0.64 %ClaNum:26(EqnAxiom:10)
% 0.19/0.64 %VarNum:72(SingletonVarNum:33)
% 0.19/0.64 %MaxLitNum:1
% 0.19/0.64 %MaxfuncDepth:3
% 0.19/0.64 %SharedTerms:14
% 0.19/0.64 %goalClause: 26
% 0.19/0.64 %singleGoalClaCount:1
% 0.19/0.64 [26]~E(f8(f7(a3,f7(a4,a6)),f7(a3,f7(a5,a6))),f7(a3,f7(f8(a4,a5),a6)))
% 0.19/0.64 [11]E(f7(a1,x111),x111)
% 0.19/0.64 [12]E(f2(x121,x121),x121)
% 0.19/0.64 [13]E(f8(x131,x131),x131)
% 0.19/0.64 [14]E(f7(f9(x141),x141),a1)
% 0.19/0.64 [15]E(f2(x151,x152),f2(x152,x151))
% 0.19/0.64 [16]E(f8(x161,x162),f8(x162,x161))
% 0.19/0.64 [17]E(f2(x171,f8(x171,x172)),x171)
% 0.19/0.64 [18]E(f8(x181,f2(x181,x182)),x181)
% 0.19/0.64 [19]E(f2(f2(x191,x192),x193),f2(x191,f2(x192,x193)))
% 0.19/0.64 [20]E(f8(f8(x201,x202),x203),f8(x201,f8(x202,x203)))
% 0.19/0.64 [21]E(f7(f7(x211,x212),x213),f7(x211,f7(x212,x213)))
% 0.19/0.64 [22]E(f2(f7(x221,x222),f7(x221,x223)),f7(x221,f2(x222,x223)))
% 0.19/0.64 [23]E(f8(f7(x231,x232),f7(x231,x233)),f7(x231,f8(x232,x233)))
% 0.19/0.64 [24]E(f2(f7(x241,x242),f7(x243,x242)),f7(f2(x241,x243),x242))
% 0.19/0.64 [25]E(f8(f7(x251,x252),f7(x253,x252)),f7(f8(x251,x253),x252))
% 0.19/0.64 %EqnAxiom
% 0.19/0.64 [1]E(x11,x11)
% 0.19/0.64 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.64 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.64 [4]~E(x41,x42)+E(f7(x41,x43),f7(x42,x43))
% 0.19/0.64 [5]~E(x51,x52)+E(f7(x53,x51),f7(x53,x52))
% 0.19/0.64 [6]~E(x61,x62)+E(f2(x61,x63),f2(x62,x63))
% 0.19/0.64 [7]~E(x71,x72)+E(f2(x73,x71),f2(x73,x72))
% 0.19/0.64 [8]~E(x81,x82)+E(f8(x81,x83),f8(x82,x83))
% 0.19/0.64 [9]~E(x91,x92)+E(f8(x93,x91),f8(x93,x92))
% 0.19/0.64 [10]~E(x101,x102)+E(f9(x101),f9(x102))
% 0.19/0.64
% 0.19/0.64 %-------------------------------------------
% 0.19/0.65 cnf(28,plain,
% 0.19/0.65 (E(f2(f7(f9(x281),x281),f7(f9(x281),x281)),a1)),
% 0.19/0.65 inference(scs_inference,[],[12,14,2,3])).
% 0.19/0.65 cnf(38,plain,
% 0.19/0.65 (~E(f8(f7(a3,f7(a5,a6)),f7(a3,f7(a4,a6))),f7(a3,f7(f8(a4,a5),a6)))),
% 0.19/0.65 inference(scs_inference,[],[26,16,2,3])).
% 0.19/0.65 cnf(47,plain,
% 0.19/0.65 (~E(f7(a3,f8(f7(a5,a6),f7(a4,a6))),f7(a3,f7(f8(a4,a5),a6)))),
% 0.19/0.65 inference(scs_inference,[],[28,23,38,2,3])).
% 0.19/0.65 cnf(56,plain,
% 0.19/0.65 (~E(f8(f7(a5,a6),f7(a4,a6)),f7(f8(a4,a5),a6))),
% 0.19/0.65 inference(scs_inference,[],[47,5])).
% 0.19/0.65 cnf(59,plain,
% 0.19/0.65 (~E(f7(a3,f7(f8(a4,a5),a6)),f7(a3,f8(f7(a5,a6),f7(a4,a6))))),
% 0.19/0.65 inference(scs_inference,[],[12,13,47,5,3,2])).
% 0.19/0.65 cnf(68,plain,
% 0.19/0.65 ($false),
% 0.19/0.65 inference(scs_inference,[],[25,16,59,56,5,3,2,4]),
% 0.19/0.65 ['proof']).
% 0.19/0.65 % SZS output end Proof
% 0.19/0.65 % Total time :0.010000s
%------------------------------------------------------------------------------