TSTP Solution File: GRP123-2.003 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP123-2.003 : 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 : n006.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 0.66s
% Output : CNFRefutation 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRP123-2.003 : 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 20:04:51 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.57 start to proof:theBenchmark
% 0.54/0.65 %-------------------------------------------
% 0.54/0.65 % File :CSE---1.6
% 0.54/0.65 % Problem :theBenchmark
% 0.54/0.65 % Transform :cnf
% 0.54/0.65 % Format :tptp:raw
% 0.54/0.65 % Command :java -jar mcs_scs.jar %d %s
% 0.54/0.65
% 0.54/0.65 % Result :Theorem 0.030000s
% 0.54/0.65 % Output :CNFRefutation 0.030000s
% 0.54/0.65 %-------------------------------------------
% 0.54/0.65 %--------------------------------------------------------------------------
% 0.54/0.65 % File : GRP123-2.003 : TPTP v8.1.2. Released v1.2.0.
% 0.54/0.65 % Domain : Group Theory (Quasigroups)
% 0.54/0.65 % Problem : (3,2,1) conjugate orthogonality
% 0.54/0.65 % Version : [Sla93] axioms : Augmented.
% 0.54/0.65 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c.
% 0.54/0.65 % Generate the multiplication table for the specified quasi-
% 0.54/0.65 % group with 3 elements.
% 0.54/0.65
% 0.54/0.66 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.54/0.66 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.54/0.66 % : [Zha94] Zhang (1994), Email to G. Sutcliffe
% 0.54/0.66 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.54/0.66 % Source : [TPTP]
% 0.54/0.66 % Names :
% 0.54/0.66
% 0.54/0.66 % Status : Unsatisfiable
% 0.54/0.66 % Rating : 0.00 v2.1.0
% 0.54/0.66 % Syntax : Number of clauses : 22 ( 15 unt; 1 nHn; 21 RR)
% 0.54/0.66 % Number of literals : 42 ( 0 equ; 25 neg)
% 0.54/0.66 % Maximal clause size : 5 ( 1 avg)
% 0.54/0.66 % Maximal term depth : 1 ( 1 avg)
% 0.54/0.66 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.54/0.66 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% 0.54/0.66 % Number of variables : 30 ( 0 sgn)
% 0.54/0.66 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.54/0.66
% 0.54/0.66 % Comments : [SFS93]'s axiomatization has been modified for this.
% 0.54/0.66 % : Substitution axioms are not needed, as any positive equality
% 0.54/0.66 % literals should resolve on negative ones directly.
% 0.54/0.66 % : [Zha94] has pointed out that either one of qg1_1
% 0.54/0.66 % or qg1_2 may be used, as each implies the other in this
% 0.54/0.66 % scenario, with the help of cancellation. The dependence
% 0.54/0.66 % cannot be proved, so both have been left in here.
% 0.54/0.66 % : Version 2 has simple isomorphism avoidance (as mentioned in
% 0.54/0.66 % [FSB93])
% 0.54/0.66 % : tptp2X: -f tptp -s3 GRP123-2.g
% 0.54/0.66 %--------------------------------------------------------------------------
% 0.54/0.66 cnf(e_1_then_e_2,axiom,
% 0.54/0.66 next(e_1,e_2) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_2_then_e_3,axiom,
% 0.54/0.66 next(e_2,e_3) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_2_greater_e_1,axiom,
% 0.54/0.66 greater(e_2,e_1) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_3_greater_e_1,axiom,
% 0.54/0.66 greater(e_3,e_1) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_3_greater_e_2,axiom,
% 0.54/0.66 greater(e_3,e_2) ).
% 0.54/0.66
% 0.54/0.66 cnf(no_redundancy,axiom,
% 0.54/0.66 ( ~ product(X,e_1,Y)
% 0.54/0.66 | ~ next(X,X1)
% 0.54/0.66 | ~ greater(Y,X1) ) ).
% 0.54/0.66
% 0.54/0.66 cnf(element_1,axiom,
% 0.54/0.66 group_element(e_1) ).
% 0.54/0.66
% 0.54/0.66 cnf(element_2,axiom,
% 0.54/0.66 group_element(e_2) ).
% 0.54/0.66
% 0.54/0.66 cnf(element_3,axiom,
% 0.54/0.66 group_element(e_3) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_1_is_not_e_2,axiom,
% 0.54/0.66 ~ equalish(e_1,e_2) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_1_is_not_e_3,axiom,
% 0.54/0.66 ~ equalish(e_1,e_3) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_2_is_not_e_1,axiom,
% 0.54/0.66 ~ equalish(e_2,e_1) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_2_is_not_e_3,axiom,
% 0.54/0.66 ~ equalish(e_2,e_3) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_3_is_not_e_1,axiom,
% 0.54/0.66 ~ equalish(e_3,e_1) ).
% 0.54/0.66
% 0.54/0.66 cnf(e_3_is_not_e_2,axiom,
% 0.54/0.66 ~ equalish(e_3,e_2) ).
% 0.54/0.66
% 0.54/0.66 cnf(product_total_function1,axiom,
% 0.54/0.66 ( ~ group_element(X)
% 0.54/0.66 | ~ group_element(Y)
% 0.54/0.66 | product(X,Y,e_1)
% 0.54/0.66 | product(X,Y,e_2)
% 0.54/0.66 | product(X,Y,e_3) ) ).
% 0.54/0.66
% 0.54/0.66 cnf(product_total_function2,axiom,
% 0.54/0.66 ( ~ product(X,Y,W)
% 0.54/0.66 | ~ product(X,Y,Z)
% 0.54/0.66 | equalish(W,Z) ) ).
% 0.54/0.66
% 0.54/0.66 cnf(product_right_cancellation,axiom,
% 0.54/0.66 ( ~ product(X,W,Y)
% 0.54/0.66 | ~ product(X,Z,Y)
% 0.54/0.66 | equalish(W,Z) ) ).
% 0.54/0.66
% 0.54/0.66 cnf(product_left_cancellation,axiom,
% 0.54/0.66 ( ~ product(W,Y,X)
% 0.54/0.66 | ~ product(Z,Y,X)
% 0.54/0.66 | equalish(W,Z) ) ).
% 0.54/0.66
% 0.54/0.66 cnf(product_idempotence,axiom,
% 0.54/0.66 product(X,X,X) ).
% 0.54/0.66
% 0.54/0.66 cnf(qg1_1,negated_conjecture,
% 0.54/0.66 ( ~ product(X1,Y1,Z1)
% 0.54/0.66 | ~ product(X2,Y2,Z1)
% 0.54/0.66 | ~ product(Z2,Y1,X1)
% 0.54/0.66 | ~ product(Z2,Y2,X2)
% 0.54/0.66 | equalish(X1,X2) ) ).
% 0.54/0.66
% 0.54/0.66 cnf(qg1_2,negated_conjecture,
% 0.54/0.66 ( ~ product(X1,Y1,Z1)
% 0.54/0.66 | ~ product(X2,Y2,Z1)
% 0.54/0.66 | ~ product(Z2,Y1,X1)
% 0.54/0.66 | ~ product(Z2,Y2,X2)
% 0.54/0.66 | equalish(Y1,Y2) ) ).
% 0.54/0.66
% 0.54/0.66 %--------------------------------------------------------------------------
% 0.54/0.66 %-------------------------------------------
% 0.54/0.66 % Proof found
% 0.54/0.66 % SZS status Theorem for theBenchmark
% 0.54/0.66 % SZS output start Proof
% 0.54/0.66 %ClaNum:22(EqnAxiom:0)
% 0.54/0.66 %VarNum:69(SingletonVarNum:30)
% 0.54/0.66 %MaxLitNum:5
% 0.54/0.66 %MaxfuncDepth:0
% 0.54/0.66 %SharedTerms:17
% 0.54/0.66 %goalClause: 21 22
% 0.54/0.66 [1]P1(a1)
% 0.54/0.66 [2]P1(a2)
% 0.54/0.66 [3]P1(a3)
% 0.54/0.66 [4]P4(a1,a2)
% 0.54/0.66 [5]P4(a2,a3)
% 0.54/0.66 [6]P2(a2,a1)
% 0.54/0.66 [7]P2(a3,a1)
% 0.54/0.66 [8]P2(a3,a2)
% 0.54/0.66 [10]~P3(a1,a2)
% 0.54/0.66 [11]~P3(a1,a3)
% 0.54/0.66 [12]~P3(a2,a1)
% 0.54/0.66 [13]~P3(a2,a3)
% 0.54/0.66 [14]~P3(a3,a1)
% 0.54/0.66 [15]~P3(a3,a2)
% 0.54/0.66 [9]P5(x91,x91,x91)
% 0.54/0.66 [16]~P4(x161,x162)+~P2(x163,x162)+~P5(x161,a1,x163)
% 0.54/0.66 [18]~P5(x183,x184,x181)+P3(x181,x182)+~P5(x183,x184,x182)
% 0.54/0.66 [19]~P5(x193,x191,x194)+P3(x191,x192)+~P5(x193,x192,x194)
% 0.54/0.66 [20]~P5(x201,x203,x204)+P3(x201,x202)+~P5(x202,x203,x204)
% 0.54/0.66 [17]~P1(x172)+~P1(x171)+P5(x171,x172,a2)+P5(x171,x172,a3)+P5(x171,x172,a1)
% 0.54/0.66 [21]~P5(x215,x211,x216)+P3(x211,x212)+~P5(x213,x212,x214)+~P5(x213,x211,x215)+~P5(x214,x212,x216)
% 0.54/0.66 [22]~P5(x221,x225,x226)+P3(x221,x222)+~P5(x223,x224,x222)+~P5(x223,x225,x221)+~P5(x222,x224,x226)
% 0.54/0.66 %EqnAxiom
% 0.54/0.66
% 0.54/0.66 %-------------------------------------------
% 0.54/0.66 cnf(41,plain,
% 0.54/0.66 (P5(x411,x411,x411)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(46,plain,
% 0.54/0.66 (P5(x461,x461,x461)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(51,plain,
% 0.54/0.66 (P5(a3,a1,a2)),
% 0.54/0.66 inference(scs_inference,[],[1,3,8,11,4,9,41,46,20,16,19,18,17])).
% 0.54/0.66 cnf(55,plain,
% 0.54/0.66 (~P5(a2,a1,a1)),
% 0.54/0.66 inference(scs_inference,[],[12,9,20])).
% 0.54/0.66 cnf(56,plain,
% 0.54/0.66 (P5(x561,x561,x561)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(62,plain,
% 0.54/0.66 (~P5(a2,a1,a3)),
% 0.54/0.66 inference(scs_inference,[],[6,12,13,9,56,51,20,21,16,22])).
% 0.54/0.66 cnf(72,plain,
% 0.54/0.66 (P5(x721,x721,x721)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(74,plain,
% 0.54/0.66 (~P5(a1,a3,x741)+~P5(x741,a3,a1)),
% 0.54/0.66 inference(scs_inference,[],[14,4,9,72,20,16,21])).
% 0.54/0.66 cnf(78,plain,
% 0.54/0.66 (P5(a2,a1,a2)),
% 0.54/0.66 inference(scs_inference,[],[2,14,4,9,72,55,62,1,20,16,21,17])).
% 0.54/0.66 cnf(80,plain,
% 0.54/0.66 (~P5(a2,a3,a3)),
% 0.54/0.66 inference(scs_inference,[],[15,9,20])).
% 0.54/0.66 cnf(90,plain,
% 0.54/0.66 (P5(x901,x901,x901)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(99,plain,
% 0.54/0.66 (~P5(a1,a3,a2)),
% 0.54/0.66 inference(scs_inference,[],[3,6,13,15,9,90,80,78,2,18,20,19,17,16,74])).
% 0.54/0.66 cnf(104,plain,
% 0.54/0.66 (P5(x1041,x1041,x1041)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(109,plain,
% 0.54/0.66 (P5(x1091,x1091,x1091)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(112,plain,
% 0.54/0.66 (P5(x1121,x1121,x1121)),
% 0.54/0.66 inference(rename_variables,[],[9])).
% 0.54/0.66 cnf(114,plain,
% 0.54/0.66 ($false),
% 0.54/0.66 inference(scs_inference,[],[4,14,12,9,104,109,112,99,3,1,21,19,17,16,18,20]),
% 0.54/0.66 ['proof']).
% 0.54/0.67 % SZS output end Proof
% 0.54/0.67 % Total time :0.030000s
%------------------------------------------------------------------------------