TSTP Solution File: GRP135-1.002 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% 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 00:11:14 EDT 2023
% Result : Unsatisfiable 0.21s 0.67s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 23:13:19 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.21/0.56 start to proof:theBenchmark
% 0.21/0.66 %-------------------------------------------
% 0.21/0.66 % File :CSE---1.6
% 0.21/0.66 % Problem :theBenchmark
% 0.21/0.66 % Transform :cnf
% 0.21/0.66 % Format :tptp:raw
% 0.21/0.66 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.66
% 0.21/0.66 % Result :Theorem 0.050000s
% 0.21/0.66 % Output :CNFRefutation 0.050000s
% 0.21/0.66 %-------------------------------------------
% 0.21/0.67 %--------------------------------------------------------------------------
% 0.21/0.67 % File : GRP135-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.21/0.67 % Domain : Group Theory (Quasigroups)
% 0.21/0.67 % Problem : ((b.a).b).b) = a, no idempotence
% 0.21/0.67 % Version : [Sla93] axioms.
% 0.21/0.67 % English : Generate the multiplication table for the specified quasi-
% 0.21/0.67 % group with 2 elements.
% 0.21/0.67
% 0.21/0.67 % Refs : [Ben89] Bennett (1989), Quasigroup Identities and Mendelsohn D
% 0.21/0.67 % : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.21/0.67 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.21/0.67 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.21/0.67 % Source : [Sla93]
% 0.21/0.67 % Names : QG5-ni [Sla93]
% 0.21/0.67
% 0.21/0.67 % Status : Unsatisfiable
% 0.21/0.67 % Rating : 0.00 v2.1.0
% 0.21/0.67 % Syntax : Number of clauses : 9 ( 4 unt; 1 nHn; 9 RR)
% 0.21/0.67 % Number of literals : 20 ( 0 equ; 12 neg)
% 0.21/0.67 % Maximal clause size : 4 ( 2 avg)
% 0.21/0.67 % Maximal term depth : 1 ( 1 avg)
% 0.21/0.67 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 0.21/0.67 % Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.21/0.67 % Number of variables : 18 ( 0 sgn)
% 0.21/0.67 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.21/0.67
% 0.21/0.67 % Comments : Slaney's [1993] axiomatization has been modified for this.
% 0.21/0.67 % : Substitution axioms are not needed, as any positive equality
% 0.21/0.67 % literals should resolve on negative ones directly.
% 0.21/0.67 % : This problem is extensively investigated in [Ben89].
% 0.21/0.67 % : tptp2X: -f tptp -s2 GRP135-1.g
% 0.21/0.67 %--------------------------------------------------------------------------
% 0.21/0.67 cnf(element_1,axiom,
% 0.21/0.67 group_element(e_1) ).
% 0.21/0.67
% 0.21/0.67 cnf(element_2,axiom,
% 0.21/0.67 group_element(e_2) ).
% 0.21/0.67
% 0.21/0.67 cnf(e_1_is_not_e_2,axiom,
% 0.21/0.67 ~ equalish(e_1,e_2) ).
% 0.21/0.67
% 0.21/0.67 cnf(e_2_is_not_e_1,axiom,
% 0.21/0.67 ~ equalish(e_2,e_1) ).
% 0.21/0.67
% 0.21/0.67 cnf(product_total_function1,axiom,
% 0.21/0.67 ( ~ group_element(X)
% 0.21/0.67 | ~ group_element(Y)
% 0.21/0.67 | product(X,Y,e_1)
% 0.21/0.67 | product(X,Y,e_2) ) ).
% 0.21/0.67
% 0.21/0.67 cnf(product_total_function2,axiom,
% 0.21/0.67 ( ~ product(X,Y,W)
% 0.21/0.67 | ~ product(X,Y,Z)
% 0.21/0.67 | equalish(W,Z) ) ).
% 0.21/0.67
% 0.21/0.67 cnf(product_right_cancellation,axiom,
% 0.21/0.67 ( ~ product(X,W,Y)
% 0.21/0.67 | ~ product(X,Z,Y)
% 0.21/0.67 | equalish(W,Z) ) ).
% 0.21/0.67
% 0.21/0.67 cnf(product_left_cancellation,axiom,
% 0.21/0.67 ( ~ product(W,Y,X)
% 0.21/0.67 | ~ product(Z,Y,X)
% 0.21/0.67 | equalish(W,Z) ) ).
% 0.21/0.67
% 0.21/0.67 cnf(qg3,negated_conjecture,
% 0.21/0.67 ( ~ product(Y,X,Z1)
% 0.21/0.67 | ~ product(Z1,Y,Z2)
% 0.21/0.67 | product(Z2,Y,X) ) ).
% 0.21/0.67
% 0.21/0.67 %--------------------------------------------------------------------------
% 0.21/0.67 %-------------------------------------------
% 0.21/0.67 % Proof found
% 0.21/0.67 % SZS status Theorem for theBenchmark
% 0.21/0.67 % SZS output start Proof
% 0.21/0.67 %ClaNum:9(EqnAxiom:0)
% 0.21/0.67 %VarNum:39(SingletonVarNum:18)
% 0.21/0.67 %MaxLitNum:4
% 0.21/0.67 %MaxfuncDepth:0
% 0.21/0.67 %SharedTerms:6
% 0.21/0.67 %goalClause: 9
% 0.21/0.67 [1]P1(a1)
% 0.21/0.67 [2]P1(a2)
% 0.21/0.67 [3]~P2(a1,a2)
% 0.21/0.67 [4]~P2(a2,a1)
% 0.21/0.67 [6]~P3(x63,x64,x61)+P2(x61,x62)+~P3(x63,x64,x62)
% 0.21/0.67 [7]~P3(x73,x71,x74)+P2(x71,x72)+~P3(x73,x72,x74)
% 0.21/0.67 [8]~P3(x81,x83,x84)+P2(x81,x82)+~P3(x82,x83,x84)
% 0.21/0.67 [9]~P3(x92,x93,x94)+P3(x91,x92,x93)+~P3(x94,x92,x91)
% 0.21/0.67 [5]~P1(x52)+~P1(x51)+P3(x51,x52,a2)+P3(x51,x52,a1)
% 0.21/0.67 %EqnAxiom
% 0.21/0.67
% 0.21/0.67 %-------------------------------------------
% 0.21/0.67 cnf(10,plain,
% 0.21/0.67 (~P3(a2,x101,x102)+~P3(a1,x101,x102)),
% 0.21/0.67 inference(scs_inference,[],[3,8])).
% 0.21/0.67 cnf(11,plain,
% 0.21/0.67 (~P3(x111,a2,x112)+~P3(x111,a1,x112)),
% 0.21/0.67 inference(scs_inference,[],[3,8,7])).
% 0.21/0.67 cnf(12,plain,
% 0.21/0.67 (~P3(x121,x122,a2)+~P3(x121,x122,a1)),
% 0.21/0.67 inference(scs_inference,[],[3,8,7,6])).
% 0.21/0.67 cnf(16,plain,
% 0.21/0.67 (P3(a1,a2,a1)+~P3(a2,a2,a2)),
% 0.21/0.67 inference(scs_inference,[],[1,2,10,5])).
% 0.21/0.67 cnf(17,plain,
% 0.21/0.67 (P3(a2,a2,a1)+P3(a2,a2,a2)),
% 0.21/0.67 inference(scs_inference,[],[2,5])).
% 0.21/0.67 cnf(21,plain,
% 0.21/0.67 (P3(a1,a1,a1)+~P3(a1,a2,a2)),
% 0.21/0.67 inference(scs_inference,[],[1,11,5])).
% 0.21/0.67 cnf(23,plain,
% 0.21/0.67 (P3(a1,a2,a1)+P3(a2,a2,a1)),
% 0.21/0.67 inference(scs_inference,[],[16,17])).
% 0.21/0.67 cnf(24,plain,
% 0.21/0.67 (~P3(a1,a2,a2)+~P3(a2,a1,a1)),
% 0.21/0.67 inference(scs_inference,[],[21,10])).
% 0.21/0.68 cnf(25,plain,
% 0.21/0.68 (P3(a1,a1,a1)+P3(a1,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[1,5])).
% 0.21/0.68 cnf(26,plain,
% 0.21/0.68 (~P3(a1,a2,a1)+P3(a1,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[3,1,5,7])).
% 0.21/0.68 cnf(31,plain,
% 0.21/0.68 (~P3(x311,a2,a1)+~P3(a2,a1,x311)+P3(a1,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[3,1,5,7,6,10,9])).
% 0.21/0.68 cnf(34,plain,
% 0.21/0.68 (~P3(a1,a2,a2)+P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[2,1,24,5])).
% 0.21/0.68 cnf(36,plain,
% 0.21/0.68 (~P3(a1,a2,a1)+~P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[26,10])).
% 0.21/0.68 cnf(38,plain,
% 0.21/0.68 (P3(a1,a2,a1)+P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[1,2,34,5])).
% 0.21/0.68 cnf(40,plain,
% 0.21/0.68 (P3(a2,a2,a1)+~P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[36,23])).
% 0.21/0.68 cnf(41,plain,
% 0.21/0.68 (~P3(a2,a2,a1)+P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[38,10])).
% 0.21/0.68 cnf(43,plain,
% 0.21/0.68 (~P3(a2,a1,a2)+~P3(a2,a1,x431)+~P3(x431,a2,a1)),
% 0.21/0.68 inference(scs_inference,[],[31,10])).
% 0.21/0.68 cnf(44,plain,
% 0.21/0.68 (~P3(a1,a2,a2)+~P3(a2,a2,a1)),
% 0.21/0.68 inference(scs_inference,[],[43,34])).
% 0.21/0.68 cnf(45,plain,
% 0.21/0.68 (~P3(a2,a2,a1)+P3(a1,a2,a1)),
% 0.21/0.68 inference(scs_inference,[],[2,1,44,5])).
% 0.21/0.68 cnf(46,plain,
% 0.21/0.68 (~P3(a2,a2,a1)+~P3(a1,a1,a1)),
% 0.21/0.68 inference(scs_inference,[],[45,11])).
% 0.21/0.68 cnf(47,plain,
% 0.21/0.68 (P3(a1,a1,a2)+~P3(a2,a2,a1)),
% 0.21/0.68 inference(scs_inference,[],[46,25])).
% 0.21/0.68 cnf(48,plain,
% 0.21/0.68 (~P3(a2,a2,a1)+~P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[47,10])).
% 0.21/0.68 cnf(49,plain,
% 0.21/0.68 (~P3(a2,a2,a1)),
% 0.21/0.68 inference(scs_inference,[],[48,41])).
% 0.21/0.68 cnf(50,plain,
% 0.21/0.68 (P3(a2,a2,a2)),
% 0.21/0.68 inference(scs_inference,[],[49,17])).
% 0.21/0.68 cnf(51,plain,
% 0.21/0.68 (P3(a1,a2,a1)),
% 0.21/0.68 inference(scs_inference,[],[49,23])).
% 0.21/0.68 cnf(52,plain,
% 0.21/0.68 (~P3(a2,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[49,40])).
% 0.21/0.68 cnf(57,plain,
% 0.21/0.68 (P3(a1,a1,a2)),
% 0.21/0.68 inference(scs_inference,[],[51,26])).
% 0.21/0.68 cnf(70,plain,
% 0.21/0.68 ($false),
% 0.21/0.68 inference(scs_inference,[],[50,57,52,51,12,8,9]),
% 0.21/0.68 ['proof']).
% 0.21/0.68 % SZS output end Proof
% 0.21/0.68 % Total time :0.050000s
%------------------------------------------------------------------------------