TSTP Solution File: GRP131-2.002 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GRP131-2.002 : 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 : n012.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 00:11:11 EDT 2023
% Result : Unsatisfiable 0.21s 0.73s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : GRP131-2.002 : TPTP v8.1.2. Released v1.2.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.13/0.35 % Computer : n012.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 21:05:39 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof:theBenchmark
% 0.21/0.72 %-------------------------------------------
% 0.21/0.72 % File :CSE---1.6
% 0.21/0.72 % Problem :theBenchmark
% 0.21/0.72 % Transform :cnf
% 0.21/0.72 % Format :tptp:raw
% 0.21/0.72 % Command :java -jar mcs_scs.jar %d %s
% 0.21/0.72
% 0.21/0.72 % Result :Theorem 0.100000s
% 0.21/0.72 % Output :CNFRefutation 0.100000s
% 0.21/0.72 %-------------------------------------------
% 0.21/0.73 %--------------------------------------------------------------------------
% 0.21/0.73 % File : GRP131-2.002 : TPTP v8.1.2. Released v1.2.0.
% 0.21/0.73 % Domain : Group Theory (Quasigroups)
% 0.21/0.73 % Problem : (3,2,1) conjugate orthogonality, no idempotence
% 0.21/0.73 % Version : [Sla93] axioms : Augmented.
% 0.21/0.73 % English : Generate the multiplication table for the specified quasi-
% 0.21/0.73 % group with 2 elements.
% 0.21/0.73
% 0.21/0.73 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res
% 0.21/0.73 % : [Sla93] Slaney (1993), Email to G. Sutcliffe
% 0.21/0.73 % : [Zha94] Zhang (1994), Email to G. Sutcliffe
% 0.21/0.73 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti
% 0.21/0.73 % Source : [TPTP]
% 0.21/0.73 % Names :
% 0.21/0.73
% 0.21/0.73 % Status : Unsatisfiable
% 0.21/0.73 % Rating : 0.00 v2.1.0
% 0.21/0.73 % Syntax : Number of clauses : 13 ( 6 unt; 1 nHn; 13 RR)
% 0.21/0.73 % Number of literals : 32 ( 0 equ; 21 neg)
% 0.21/0.73 % Maximal clause size : 5 ( 2 avg)
% 0.21/0.73 % Maximal term depth : 1 ( 1 avg)
% 0.21/0.73 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty)
% 0.21/0.73 % Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% 0.21/0.73 % Number of variables : 29 ( 0 sgn)
% 0.21/0.73 % SPC : CNF_UNS_EPR_NEQ_NHN
% 0.21/0.73
% 0.21/0.73 % Comments : Slaney's [1993] axiomatization has been modified for this.
% 0.21/0.73 % : Substitution axioms are not needed, as any positive equality
% 0.21/0.73 % literals should resolve on negative ones directly.
% 0.21/0.73 % : Zhang [Zha94] has pointed out that either one of qg1_1
% 0.21/0.73 % or qg1_2 may be used, as each implies the other in this
% 0.21/0.73 % scenario, with the help of cancellation. The dependence
% 0.21/0.73 % cannot be proved, so both have been left in here.
% 0.21/0.73 % : This version adds a simple isomorphism avoidance clause,
% 0.21/0.73 % mentioned in [FSB93].
% 0.21/0.73 % : tptp2X: -f tptp -s2 GRP131-2.g
% 0.21/0.73 %--------------------------------------------------------------------------
% 0.21/0.73 cnf(e_1_then_e_2,axiom,
% 0.21/0.73 next(e_1,e_2) ).
% 0.21/0.73
% 0.21/0.73 cnf(e_2_greater_e_1,axiom,
% 0.21/0.73 greater(e_2,e_1) ).
% 0.21/0.73
% 0.21/0.73 cnf(no_redundancy,axiom,
% 0.21/0.73 ( ~ product(X,e_1,Y)
% 0.21/0.73 | ~ next(X,X1)
% 0.21/0.73 | ~ greater(Y,X1) ) ).
% 0.21/0.73
% 0.21/0.73 cnf(element_1,axiom,
% 0.21/0.73 group_element(e_1) ).
% 0.21/0.73
% 0.21/0.73 cnf(element_2,axiom,
% 0.21/0.73 group_element(e_2) ).
% 0.21/0.73
% 0.21/0.73 cnf(e_1_is_not_e_2,axiom,
% 0.21/0.73 ~ equalish(e_1,e_2) ).
% 0.21/0.73
% 0.21/0.73 cnf(e_2_is_not_e_1,axiom,
% 0.21/0.73 ~ equalish(e_2,e_1) ).
% 0.21/0.73
% 0.21/0.73 cnf(product_total_function1,axiom,
% 0.21/0.73 ( ~ group_element(X)
% 0.21/0.73 | ~ group_element(Y)
% 0.21/0.73 | product(X,Y,e_1)
% 0.21/0.73 | product(X,Y,e_2) ) ).
% 0.21/0.73
% 0.21/0.73 cnf(product_total_function2,axiom,
% 0.21/0.73 ( ~ product(X,Y,W)
% 0.21/0.73 | ~ product(X,Y,Z)
% 0.21/0.73 | equalish(W,Z) ) ).
% 0.21/0.73
% 0.21/0.73 cnf(product_right_cancellation,axiom,
% 0.21/0.73 ( ~ product(X,W,Y)
% 0.21/0.73 | ~ product(X,Z,Y)
% 0.21/0.73 | equalish(W,Z) ) ).
% 0.21/0.73
% 0.21/0.73 cnf(product_left_cancellation,axiom,
% 0.21/0.73 ( ~ product(W,Y,X)
% 0.21/0.73 | ~ product(Z,Y,X)
% 0.21/0.73 | equalish(W,Z) ) ).
% 0.21/0.73
% 0.21/0.73 cnf(qg1_1,negated_conjecture,
% 0.21/0.73 ( ~ product(X1,Y1,Z1)
% 0.21/0.73 | ~ product(X2,Y2,Z1)
% 0.21/0.73 | ~ product(Z2,Y1,X1)
% 0.21/0.73 | ~ product(Z2,Y2,X2)
% 0.21/0.73 | equalish(X1,X2) ) ).
% 0.21/0.73
% 0.21/0.73 cnf(qg1_2,negated_conjecture,
% 0.21/0.73 ( ~ product(X1,Y1,Z1)
% 0.21/0.73 | ~ product(X2,Y2,Z1)
% 0.21/0.73 | ~ product(Z2,Y1,X1)
% 0.21/0.73 | ~ product(Z2,Y2,X2)
% 0.21/0.73 | equalish(Y1,Y2) ) ).
% 0.21/0.73
% 0.21/0.73 %--------------------------------------------------------------------------
% 0.21/0.73 %-------------------------------------------
% 0.21/0.73 % Proof found
% 0.21/0.73 % SZS status Theorem for theBenchmark
% 0.21/0.73 % SZS output start Proof
% 0.21/0.73 %ClaNum:13(EqnAxiom:0)
% 0.21/0.73 %VarNum:64(SingletonVarNum:29)
% 0.21/0.73 %MaxLitNum:5
% 0.21/0.73 %MaxfuncDepth:0
% 0.21/0.73 %SharedTerms:8
% 0.21/0.73 %goalClause: 12 13
% 0.21/0.73 [1]P1(a1)
% 0.21/0.73 [2]P1(a2)
% 0.21/0.73 [3]P4(a1,a2)
% 0.21/0.73 [4]P2(a2,a1)
% 0.21/0.73 [5]~P3(a1,a2)
% 0.21/0.73 [6]~P3(a2,a1)
% 0.21/0.73 [8]~P4(x81,x82)+~P2(x83,x82)+~P5(x81,a1,x83)
% 0.21/0.73 [9]~P5(x93,x94,x91)+P3(x91,x92)+~P5(x93,x94,x92)
% 0.21/0.73 [10]~P5(x103,x101,x104)+P3(x101,x102)+~P5(x103,x102,x104)
% 0.21/0.73 [11]~P5(x111,x113,x114)+P3(x111,x112)+~P5(x112,x113,x114)
% 0.21/0.73 [7]~P1(x72)+~P1(x71)+P5(x71,x72,a2)+P5(x71,x72,a1)
% 0.21/0.73 [12]~P5(x125,x121,x126)+P3(x121,x122)+~P5(x123,x122,x124)+~P5(x123,x121,x125)+~P5(x124,x122,x126)
% 0.21/0.73 [13]~P5(x131,x135,x136)+P3(x131,x132)+~P5(x133,x134,x132)+~P5(x133,x135,x131)+~P5(x132,x134,x136)
% 0.21/0.73 %EqnAxiom
% 0.21/0.73
% 0.21/0.73 %-------------------------------------------
% 0.21/0.74 cnf(15,plain,
% 0.21/0.74 (~P5(a2,x151,x152)+~P5(a1,x151,x152)),
% 0.21/0.74 inference(scs_inference,[],[3,5,8,11])).
% 0.21/0.74 cnf(16,plain,
% 0.21/0.74 (~P5(x161,a2,x162)+~P5(x161,a1,x162)),
% 0.21/0.74 inference(scs_inference,[],[3,5,8,11,10])).
% 0.21/0.74 cnf(22,plain,
% 0.21/0.74 (~P5(a2,x221,a1)+~P5(a1,a1,a1)+~P5(a1,x221,a2)),
% 0.21/0.74 inference(scs_inference,[],[1,3,5,8,11,10,9,7,13])).
% 0.21/0.74 cnf(24,plain,
% 0.21/0.74 (~P5(x241,a2,a1)+~P5(a1,a1,a1)+~P5(a1,a2,x241)),
% 0.21/0.74 inference(scs_inference,[],[1,3,5,8,11,10,9,7,13,12])).
% 0.21/0.74 cnf(28,plain,
% 0.21/0.74 (~P5(x281,x282,a2)+~P5(a1,x283,x284)+~P5(a2,x282,x284)+~P5(x281,x283,a1)),
% 0.21/0.74 inference(scs_inference,[],[6,12,13])).
% 0.21/0.74 cnf(30,plain,
% 0.21/0.74 (P5(a2,a2,a1)+P5(a2,a2,a2)),
% 0.21/0.74 inference(scs_inference,[],[2,7])).
% 0.21/0.74 cnf(36,plain,
% 0.21/0.74 (P5(a1,a1,a1)+~P5(a1,a2,a2)),
% 0.21/0.74 inference(scs_inference,[],[1,16,7])).
% 0.21/0.74 cnf(40,plain,
% 0.21/0.74 (~P5(a1,a2,a2)+~P5(a2,a1,a1)),
% 0.21/0.74 inference(scs_inference,[],[36,15])).
% 0.21/0.74 cnf(44,plain,
% 0.21/0.74 (P5(a1,a2,a1)+~P5(a2,a1,a1)),
% 0.21/0.74 inference(scs_inference,[],[2,1,40,7])).
% 0.21/0.74 cnf(45,plain,
% 0.21/0.74 (P5(a1,a1,a1)+P5(a1,a1,a2)),
% 0.21/0.74 inference(scs_inference,[],[1,7])).
% 0.21/0.74 cnf(53,plain,
% 0.21/0.74 (P5(a1,a2,a1)+P5(a2,a1,a2)),
% 0.21/0.74 inference(scs_inference,[],[2,1,44,7])).
% 0.21/0.74 cnf(67,plain,
% 0.21/0.74 (P5(a1,a1,a1)+~P5(a2,a1,a2)),
% 0.21/0.74 inference(scs_inference,[],[45,15])).
% 0.21/0.74 cnf(75,plain,
% 0.21/0.74 (~P5(a1,a2,a2)+~P5(a1,x751,a2)+~P5(a2,x751,a1)),
% 0.21/0.74 inference(scs_inference,[],[22,36])).
% 0.21/0.74 cnf(76,plain,
% 0.21/0.74 (P5(a1,a1,a2)+~P5(a1,a2,x761)+~P5(x761,a2,a1)),
% 0.21/0.74 inference(scs_inference,[],[24,45])).
% 0.21/0.74 cnf(79,plain,
% 0.21/0.74 (P5(a1,a2,a1)+~P5(a2,a2,a1)),
% 0.21/0.74 inference(scs_inference,[],[2,1,75,7])).
% 0.21/0.74 cnf(81,plain,
% 0.21/0.74 (P5(a2,a2,a2)+P5(a1,a2,a1)),
% 0.21/0.74 inference(scs_inference,[],[79,30])).
% 0.21/0.74 cnf(82,plain,
% 0.21/0.74 (P5(a1,a2,a1)+~P5(a2,a1,a2)),
% 0.21/0.74 inference(scs_inference,[],[81,16])).
% 0.21/0.74 cnf(83,plain,
% 0.21/0.74 (P5(a1,a2,a1)),
% 0.21/0.74 inference(scs_inference,[],[82,53])).
% 0.21/0.74 cnf(101,plain,
% 0.21/0.74 ($false),
% 0.21/0.74 inference(scs_inference,[],[3,83,1,2,76,24,10,11,8,36,28,15,7,67]),
% 0.21/0.74 ['proof']).
% 0.21/0.74 % SZS output end Proof
% 0.21/0.74 % Total time :0.100000s
%------------------------------------------------------------------------------