TSTP Solution File: GRP123-1.003 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP123-1.003 : 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 : 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 : Thu Aug 31 00:10:57 EDT 2023
% Result : Unsatisfiable 0.54s 0.62s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP123-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 20:03:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.56 start to proof:theBenchmark
% 0.54/0.61 %-------------------------------------------
% 0.54/0.61 % File :CSE---1.6
% 0.54/0.61 % Problem :theBenchmark
% 0.54/0.61 % Transform :cnf
% 0.54/0.61 % Format :tptp:raw
% 0.54/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.61
% 0.54/0.61 % Result :Theorem 0.010000s
% 0.54/0.61 % Output :CNFRefutation 0.010000s
% 0.54/0.61 %-------------------------------------------
% 0.54/0.62 %--------------------------------------------------------------------------
% 0.54/0.62 % File : GRP123-1.003 : TPTP v8.1.2. Released v1.2.0.
% 0.54/0.62 % Domain : Group Theory (Quasigroups)
% 0.54/0.62 % Problem : (3,2,1) conjugate orthogonality
% 0.54/0.62 % Version : [Sla93] axioms.
% 0.54/0.62 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c.
% 0.54/0.62 % Generate the multiplication table for the specified quasi-
% 0.54/0.62 % group with 3 elements.
% 0.54/0.62
% 0.54/0.62 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.54/0.62 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.54/0.62 % : [Zha94] Zhang (1994), Email to G. Sutcliffe
% 0.54/0.62 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.54/0.62 % Source : [Sla93]
% 0.54/0.62 % Names : QG1 [Sla93]
% 0.54/0.62 % : QG1 [FSB93]
% 0.54/0.62 % : QG1 [SFS95]
% 0.54/0.62 % : Bennett QG1 [TPTP]
% 0.54/0.62
% 0.54/0.62 % Status : Unsatisfiable
% 0.54/0.62 % Rating : 0.00 v2.1.0
% 0.54/0.62 % Syntax : Number of clauses : 16 ( 10 unt; 1 nHn; 15 RR)
% 0.54/0.62 % Number of literals : 34 ( 0 equ; 22 neg)
% 0.54/0.62 % Maximal clause size : 5 ( 2 avg)
% 0.54/0.62 % Maximal term depth : 1 ( 1 avg)
% 0.54/0.62 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 0.54/0.62 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.54/0.62 % Number of variables : 27 ( 0 sgn)
% 0.54/0.62 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.54/0.62
% 0.54/0.62 % Comments : [Sla93]'s axiomatization has been modified for this.
% 0.54/0.62 % : Substitution axioms are not needed, as any positive equality
% 0.54/0.62 % literals should resolve on negative ones directly.
% 0.54/0.62 % : [Zha94] has pointed out that either one of qg1_1
% 0.54/0.62 % or qg1_2 may be used, as each implies the other in this
% 0.54/0.62 % scenario, with the help of cancellation. The dependence
% 0.54/0.62 % cannot be proved, so both have been left in here.
% 0.54/0.62 % : tptp2X: -f tptp -s3 GRP123-1.g
% 0.54/0.62 %--------------------------------------------------------------------------
% 0.54/0.62 cnf(element_1,axiom,
% 0.54/0.62 group_element(e_1) ).
% 0.54/0.62
% 0.54/0.62 cnf(element_2,axiom,
% 0.54/0.62 group_element(e_2) ).
% 0.54/0.62
% 0.54/0.62 cnf(element_3,axiom,
% 0.54/0.62 group_element(e_3) ).
% 0.54/0.62
% 0.54/0.62 cnf(e_1_is_not_e_2,axiom,
% 0.54/0.62 ~ equalish(e_1,e_2) ).
% 0.54/0.62
% 0.54/0.62 cnf(e_1_is_not_e_3,axiom,
% 0.54/0.62 ~ equalish(e_1,e_3) ).
% 0.54/0.62
% 0.54/0.62 cnf(e_2_is_not_e_1,axiom,
% 0.54/0.62 ~ equalish(e_2,e_1) ).
% 0.54/0.62
% 0.54/0.62 cnf(e_2_is_not_e_3,axiom,
% 0.54/0.62 ~ equalish(e_2,e_3) ).
% 0.54/0.62
% 0.54/0.62 cnf(e_3_is_not_e_1,axiom,
% 0.54/0.62 ~ equalish(e_3,e_1) ).
% 0.54/0.62
% 0.54/0.62 cnf(e_3_is_not_e_2,axiom,
% 0.54/0.62 ~ equalish(e_3,e_2) ).
% 0.54/0.62
% 0.54/0.62 cnf(product_total_function1,axiom,
% 0.54/0.62 ( ~ group_element(X)
% 0.54/0.62 | ~ group_element(Y)
% 0.54/0.62 | product(X,Y,e_1)
% 0.54/0.62 | product(X,Y,e_2)
% 0.54/0.62 | product(X,Y,e_3) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(product_total_function2,axiom,
% 0.54/0.62 ( ~ product(X,Y,W)
% 0.54/0.62 | ~ product(X,Y,Z)
% 0.54/0.62 | equalish(W,Z) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(product_right_cancellation,axiom,
% 0.54/0.62 ( ~ product(X,W,Y)
% 0.54/0.62 | ~ product(X,Z,Y)
% 0.54/0.62 | equalish(W,Z) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(product_left_cancellation,axiom,
% 0.54/0.62 ( ~ product(W,Y,X)
% 0.54/0.62 | ~ product(Z,Y,X)
% 0.54/0.62 | equalish(W,Z) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(product_idempotence,axiom,
% 0.54/0.62 product(X,X,X) ).
% 0.54/0.62
% 0.54/0.62 cnf(qg1_1,negated_conjecture,
% 0.54/0.62 ( ~ product(X1,Y1,Z1)
% 0.54/0.62 | ~ product(X2,Y2,Z1)
% 0.54/0.62 | ~ product(Z2,Y1,X1)
% 0.54/0.62 | ~ product(Z2,Y2,X2)
% 0.54/0.62 | equalish(X1,X2) ) ).
% 0.54/0.62
% 0.54/0.62 cnf(qg1_2,negated_conjecture,
% 0.54/0.62 ( ~ product(X1,Y1,Z1)
% 0.54/0.62 | ~ product(X2,Y2,Z1)
% 0.54/0.62 | ~ product(Z2,Y1,X1)
% 0.54/0.62 | ~ product(Z2,Y2,X2)
% 0.54/0.62 | equalish(Y1,Y2) ) ).
% 0.54/0.62
% 0.54/0.62 %--------------------------------------------------------------------------
% 0.54/0.62 %-------------------------------------------
% 0.54/0.62 % Proof found
% 0.54/0.62 % SZS status Theorem for theBenchmark
% 0.54/0.62 % SZS output start Proof
% 0.54/0.62 %ClaNum:16(EqnAxiom:0)
% 0.54/0.62 %VarNum:63(SingletonVarNum:27)
% 0.54/0.62 %MaxLitNum:5
% 0.54/0.62 %MaxfuncDepth:0
% 0.54/0.62 %SharedTerms:12
% 0.54/0.62 %goalClause: 15 16
% 0.54/0.62 [1]P1(a1)
% 0.54/0.62 [2]P1(a2)
% 0.54/0.62 [3]P1(a3)
% 0.54/0.62 [5]~P2(a1,a2)
% 0.54/0.62 [6]~P2(a1,a3)
% 0.54/0.62 [7]~P2(a2,a1)
% 0.54/0.62 [8]~P2(a2,a3)
% 0.54/0.62 [9]~P2(a3,a1)
% 0.54/0.62 [10]~P2(a3,a2)
% 0.54/0.62 [4]P3(x41,x41,x41)
% 0.54/0.62 [12]~P3(x123,x124,x121)+P2(x121,x122)+~P3(x123,x124,x122)
% 0.54/0.62 [13]~P3(x133,x131,x134)+P2(x131,x132)+~P3(x133,x132,x134)
% 0.54/0.62 [14]~P3(x141,x143,x144)+P2(x141,x142)+~P3(x142,x143,x144)
% 0.54/0.62 [11]~P1(x112)+~P1(x111)+P3(x111,x112,a2)+P3(x111,x112,a3)+P3(x111,x112,a1)
% 0.54/0.62 [15]~P3(x155,x151,x156)+P2(x151,x152)+~P3(x153,x152,x154)+~P3(x153,x151,x155)+~P3(x154,x152,x156)
% 0.54/0.62 [16]~P3(x161,x165,x166)+P2(x161,x162)+~P3(x163,x164,x162)+~P3(x163,x165,x161)+~P3(x162,x164,x166)
% 0.54/0.62 %EqnAxiom
% 0.54/0.62
% 0.54/0.62 %-------------------------------------------
% 0.54/0.62 cnf(60,plain,
% 0.54/0.62 (~P3(a2,a3,a2)),
% 0.54/0.62 inference(scs_inference,[],[8,4,14,13])).
% 0.54/0.62 cnf(70,plain,
% 0.54/0.62 (P3(x701,x701,x701)),
% 0.54/0.62 inference(rename_variables,[],[4])).
% 0.54/0.62 cnf(72,plain,
% 0.54/0.62 (~P3(a1,a3,a1)),
% 0.54/0.62 inference(scs_inference,[],[10,9,4,70,14,13])).
% 0.54/0.62 cnf(73,plain,
% 0.54/0.62 (P3(x731,x731,x731)),
% 0.54/0.62 inference(rename_variables,[],[4])).
% 0.54/0.62 cnf(79,plain,
% 0.54/0.62 (~P3(a1,a3,a2)),
% 0.54/0.62 inference(scs_inference,[],[3,10,9,8,4,70,73,60,2,14,13,12,11,15])).
% 0.54/0.62 cnf(86,plain,
% 0.54/0.62 (P3(x861,x861,x861)),
% 0.54/0.62 inference(rename_variables,[],[4])).
% 0.54/0.62 cnf(91,plain,
% 0.54/0.62 (P3(a1,a3,a3)),
% 0.54/0.62 inference(scs_inference,[],[3,10,4,86,79,72,1,16,14,12,11])).
% 0.54/0.62 cnf(96,plain,
% 0.54/0.62 (P3(x961,x961,x961)),
% 0.54/0.62 inference(rename_variables,[],[4])).
% 0.54/0.62 cnf(98,plain,
% 0.54/0.62 ($false),
% 0.54/0.62 inference(scs_inference,[],[4,96,9,91,13,12,14]),
% 0.54/0.63 ['proof']).
% 0.54/0.63 % SZS output end Proof
% 0.54/0.63 % Total time :0.010000s
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