TSTP Solution File: GRP132-1.002 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP132-1.002 : TPTP v8.1.2. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 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 : Thu Aug 31 00:11:12 EDT 2023
% Result : Unsatisfiable 0.55s 0.78s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : GRP132-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.09/0.15 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.15/0.36 % Computer : n017.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon Aug 28 20:42:43 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.20/0.61 start to proof:theBenchmark
% 0.55/0.77 %-------------------------------------------
% 0.55/0.77 % File :CSE---1.6
% 0.55/0.77 % Problem :theBenchmark
% 0.55/0.77 % Transform :cnf
% 0.55/0.77 % Format :tptp:raw
% 0.55/0.77 % Command :java -jar mcs_scs.jar %d %s
% 0.55/0.77
% 0.55/0.77 % Result :Theorem 0.120000s
% 0.55/0.77 % Output :CNFRefutation 0.120000s
% 0.55/0.77 %-------------------------------------------
% 0.55/0.77 %--------------------------------------------------------------------------
% 0.55/0.77 % File : GRP132-1.002 : TPTP v8.1.2. Released v1.2.0.
% 0.55/0.77 % Domain : Group Theory (Quasigroups)
% 0.55/0.77 % Problem : (3,1,2) conjugate orthogonality, no idempotence
% 0.55/0.77 % Version : [Sla93] axioms.
% 0.55/0.77 % English : Generate the multiplication table for the specified quasi-
% 0.55/0.77 % group with 2 elements.
% 0.55/0.77
% 0.55/0.77 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.55/0.77 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.55/0.77 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.55/0.77 % Source : [Sla93]
% 0.55/0.77 % Names : QG2-ni [Sla93]
% 0.55/0.77
% 0.55/0.77 % Status : Unsatisfiable
% 0.55/0.77 % Rating : 0.00 v2.1.0
% 0.55/0.77 % Syntax : Number of clauses : 10 ( 4 unt; 1 nHn; 10 RR)
% 0.55/0.77 % Number of literals : 27 ( 0 equ; 18 neg)
% 0.55/0.77 % Maximal clause size : 5 ( 2 avg)
% 0.55/0.77 % Maximal term depth : 1 ( 1 avg)
% 0.55/0.77 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 0.55/0.77 % Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.55/0.77 % Number of variables : 26 ( 0 sgn)
% 0.55/0.77 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.55/0.77
% 0.55/0.77 % Comments : Slaney's [1993] axiomatization has been modified for this.
% 0.55/0.77 % : Substitution axioms are not needed, as any positive equality
% 0.55/0.77 % literals should resolve on negative ones directly.
% 0.55/0.77 % : As in GRP130-1, either one of qg2_1 or qg2_2 may be used, as
% 0.55/0.77 % each implies the other in this scenario, with the help of
% 0.55/0.77 % cancellation. The dependence cannot be proved, so both have
% 0.55/0.77 % been left in here.
% 0.55/0.77 % : tptp2X: -f tptp -s2 GRP132-1.g
% 0.55/0.77 %--------------------------------------------------------------------------
% 0.55/0.77 cnf(element_1,axiom,
% 0.55/0.77 group_element(e_1) ).
% 0.55/0.78
% 0.55/0.78 cnf(element_2,axiom,
% 0.55/0.78 group_element(e_2) ).
% 0.55/0.78
% 0.55/0.78 cnf(e_1_is_not_e_2,axiom,
% 0.55/0.78 ~ equalish(e_1,e_2) ).
% 0.55/0.78
% 0.55/0.78 cnf(e_2_is_not_e_1,axiom,
% 0.55/0.78 ~ equalish(e_2,e_1) ).
% 0.55/0.78
% 0.55/0.78 cnf(product_total_function1,axiom,
% 0.55/0.78 ( ~ group_element(X)
% 0.55/0.78 | ~ group_element(Y)
% 0.55/0.78 | product(X,Y,e_1)
% 0.55/0.78 | product(X,Y,e_2) ) ).
% 0.55/0.78
% 0.55/0.78 cnf(product_total_function2,axiom,
% 0.55/0.78 ( ~ product(X,Y,W)
% 0.55/0.78 | ~ product(X,Y,Z)
% 0.55/0.78 | equalish(W,Z) ) ).
% 0.55/0.78
% 0.55/0.78 cnf(product_right_cancellation,axiom,
% 0.55/0.78 ( ~ product(X,W,Y)
% 0.55/0.78 | ~ product(X,Z,Y)
% 0.55/0.78 | equalish(W,Z) ) ).
% 0.55/0.78
% 0.55/0.78 cnf(product_left_cancellation,axiom,
% 0.55/0.78 ( ~ product(W,Y,X)
% 0.55/0.78 | ~ product(Z,Y,X)
% 0.55/0.78 | equalish(W,Z) ) ).
% 0.55/0.78
% 0.55/0.78 cnf(qg2_1,negated_conjecture,
% 0.55/0.78 ( ~ product(X1,Y1,Z1)
% 0.55/0.78 | ~ product(X2,Y2,Z1)
% 0.55/0.78 | ~ product(Z2,X1,Y1)
% 0.55/0.78 | ~ product(Z2,X2,Y2)
% 0.55/0.78 | equalish(X1,X2) ) ).
% 0.55/0.78
% 0.55/0.78 cnf(qg2_2,negated_conjecture,
% 0.55/0.78 ( ~ product(X1,Y1,Z1)
% 0.55/0.78 | ~ product(X2,Y2,Z1)
% 0.55/0.78 | ~ product(Z2,X1,Y1)
% 0.55/0.78 | ~ product(Z2,X2,Y2)
% 0.55/0.78 | equalish(Y1,Y2) ) ).
% 0.55/0.78
% 0.55/0.78 %--------------------------------------------------------------------------
% 0.55/0.78 %-------------------------------------------
% 0.55/0.78 % Proof found
% 0.55/0.78 % SZS status Theorem for theBenchmark
% 0.55/0.78 % SZS output start Proof
% 0.55/0.78 %ClaNum:10(EqnAxiom:0)
% 0.55/0.78 %VarNum:58(SingletonVarNum:26)
% 0.55/0.78 %MaxLitNum:5
% 0.55/0.78 %MaxfuncDepth:0
% 0.55/0.78 %SharedTerms:6
% 0.55/0.78 %goalClause: 9 10
% 0.55/0.78 [1]P1(a1)
% 0.55/0.78 [2]P1(a2)
% 0.55/0.78 [3]~P2(a1,a2)
% 0.55/0.78 [4]~P2(a2,a1)
% 0.55/0.78 [6]~P3(x63,x64,x61)+P2(x61,x62)+~P3(x63,x64,x62)
% 0.55/0.78 [7]~P3(x73,x71,x74)+P2(x71,x72)+~P3(x73,x72,x74)
% 0.55/0.78 [8]~P3(x81,x83,x84)+P2(x81,x82)+~P3(x82,x83,x84)
% 0.55/0.78 [5]~P1(x52)+~P1(x51)+P3(x51,x52,a2)+P3(x51,x52,a1)
% 0.55/0.78 [9]~P3(x95,x91,x96)+P2(x91,x92)+~P3(x93,x94,x92)+~P3(x93,x95,x91)+~P3(x94,x92,x96)
% 0.55/0.78 [10]~P3(x101,x105,x106)+P2(x101,x102)+~P3(x103,x102,x104)+~P3(x103,x101,x105)+~P3(x102,x104,x106)
% 0.55/0.78 %EqnAxiom
% 0.55/0.78
% 0.55/0.78 %-------------------------------------------
% 0.55/0.78 cnf(11,plain,
% 0.55/0.78 (~P3(a2,x111,x112)+~P3(a1,x111,x112)),
% 0.55/0.78 inference(scs_inference,[],[3,8])).
% 0.55/0.78 cnf(12,plain,
% 0.55/0.78 (~P3(x121,a2,x122)+~P3(x121,a1,x122)),
% 0.55/0.78 inference(scs_inference,[],[3,8,7])).
% 0.55/0.78 cnf(13,plain,
% 0.55/0.78 (~P3(x131,x132,a2)+~P3(x131,x132,a1)),
% 0.55/0.78 inference(scs_inference,[],[3,8,7,6])).
% 0.55/0.78 cnf(17,plain,
% 0.55/0.78 (~P3(a2,x171,a1)+~P3(a1,a1,a1)+~P3(a1,a2,x171)),
% 0.55/0.78 inference(scs_inference,[],[1,3,8,7,6,5,10])).
% 0.55/0.78 cnf(19,plain,
% 0.55/0.78 (~P3(x191,a2,a1)+~P3(a1,a1,a1)+~P3(a1,x191,a2)),
% 0.55/0.78 inference(scs_inference,[],[1,3,8,7,6,5,10,9])).
% 0.55/0.78 cnf(22,plain,
% 0.55/0.78 (~P3(x221,x222,a2)+~P3(x223,a1,x224)+~P3(x222,a2,x224)+~P3(x221,x223,a1)),
% 0.55/0.78 inference(scs_inference,[],[4,10,9])).
% 0.55/0.78 cnf(23,plain,
% 0.55/0.78 (P3(a1,a2,a1)+~P3(a2,a2,a2)),
% 0.55/0.78 inference(scs_inference,[],[1,2,11,5])).
% 0.55/0.78 cnf(24,plain,
% 0.55/0.78 (P3(a2,a2,a1)+P3(a2,a2,a2)),
% 0.55/0.78 inference(scs_inference,[],[2,5])).
% 0.55/0.78 cnf(35,plain,
% 0.55/0.78 (P3(a1,a1,a2)+~P3(a1,a2,x351)+~P3(a2,x351,a1)),
% 0.55/0.78 inference(scs_inference,[],[3,1,5,6,11,19,17])).
% 0.55/0.78 cnf(36,plain,
% 0.55/0.78 (~P3(a1,a2,a1)+P3(a1,a1,a2)),
% 0.55/0.78 inference(scs_inference,[],[3,1,5,6,11,19,17,7])).
% 0.55/0.78 cnf(44,plain,
% 0.55/0.78 (~P3(a1,a2,a1)+~P3(a2,a1,a2)),
% 0.55/0.78 inference(scs_inference,[],[36,11])).
% 0.55/0.78 cnf(51,plain,
% 0.55/0.78 (~P3(a1,a2,a2)+~P3(a2,x511,a1)+~P3(a1,a2,x511)),
% 0.55/0.78 inference(scs_inference,[],[35,12])).
% 0.55/0.78 cnf(53,plain,
% 0.55/0.78 (P3(a1,a2,a1)+~P3(a2,a2,a1)),
% 0.55/0.78 inference(scs_inference,[],[1,2,51,5])).
% 0.55/0.78 cnf(54,plain,
% 0.55/0.78 (~P3(a2,a2,a1)+~P3(a1,a2,a2)),
% 0.55/0.78 inference(scs_inference,[],[53,13])).
% 0.55/0.78 cnf(55,plain,
% 0.55/0.78 (P3(a2,a2,a2)+~P3(a1,a2,a2)),
% 0.55/0.78 inference(scs_inference,[],[54,24])).
% 0.55/0.78 cnf(56,plain,
% 0.55/0.78 (~P3(a1,a2,a2)+P3(a1,a2,a1)),
% 0.55/0.78 inference(scs_inference,[],[55,23])).
% 0.55/0.78 cnf(57,plain,
% 0.55/0.78 (P3(a1,a2,a1)),
% 0.55/0.78 inference(scs_inference,[],[2,1,56,5])).
% 0.55/0.79 cnf(58,plain,
% 0.55/0.79 (P3(a1,a1,a2)),
% 0.55/0.79 inference(scs_inference,[],[57,36])).
% 0.55/0.79 cnf(59,plain,
% 0.55/0.79 (~P3(a2,a1,a2)),
% 0.55/0.79 inference(scs_inference,[],[57,44])).
% 0.55/0.79 cnf(70,plain,
% 0.55/0.79 (~P3(a2,x701,a1)+~P3(x701,a1,a2)),
% 0.55/0.79 inference(scs_inference,[],[4,57,2,13,8,11,7,5,22])).
% 0.55/0.79 cnf(79,plain,
% 0.55/0.79 (~P3(a2,a1,a1)),
% 0.55/0.79 inference(scs_inference,[],[57,70,35])).
% 0.55/0.79 cnf(84,plain,
% 0.55/0.79 ($false),
% 0.55/0.79 inference(scs_inference,[],[58,59,57,79,2,1,9,7,5]),
% 0.55/0.79 ['proof']).
% 0.55/0.79 % SZS output end Proof
% 0.55/0.79 % Total time :0.120000s
%------------------------------------------------------------------------------