%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP126-2.004 : TPTP v8.2.0. Released v1.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n018.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 : Mon Jun 24 06:38:52 EDT 2024 % Result : Unsatisfiable 58.57s 58.62s % Output : CNFRefutation 58.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GRP126-2.004 : TPTP v8.2.0. Released v1.2.0. % 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n018.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 : Thu Jun 20 10:32:53 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.55 start to proof:theBenchmark % 58.55/58.60 %------------------------------------------- % 58.55/58.60 % File :CSE---1.7 % 58.55/58.60 % Problem :theBenchmark % 58.55/58.60 % Transform :cnf % 58.55/58.60 % Format :tptp:raw % 58.55/58.60 % Command :java -jar mcs_scs.jar %d %s % 58.55/58.60 % 58.55/58.60 % Result :Theorem 58.000000s % 58.55/58.60 % Output :CNFRefutation 58.000000s % 58.55/58.60 %------------------------------------------- % 58.57/58.61 %-------------------------------------------------------------------------- % 58.57/58.61 % File : GRP126-2.004 : TPTP v8.2.0. Released v1.2.0. % 58.57/58.61 % Domain : Group Theory (Quasigroups) % 58.57/58.61 % Problem : (a.b).(b.a) = b % 58.57/58.61 % Version : [Sla93] axioms : Augmented. % 58.57/58.61 % English : Generate the multiplication table for the specified quasi- % 58.57/58.61 % group with 4 elements. % 58.57/58.61 % 58.57/58.61 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res % 58.57/58.61 % : [Sla93] Slaney (1993), Email to G. Sutcliffe % 58.57/58.62 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti % 58.57/58.62 % Source : [TPTP] % 58.57/58.62 % Names : % 58.57/58.62 % 58.57/58.62 % Status : Unsatisfiable % 58.57/58.62 % Rating : 0.00 v2.4.0, 0.00 v2.1.0 % 58.57/58.62 % Syntax : Number of clauses : 32 ( 26 unt; 1 nHn; 31 RR) % 58.57/58.62 % Number of literals : 47 ( 0 equ; 25 neg) % 58.57/58.62 % Maximal clause size : 6 ( 1 avg) % 58.57/58.62 % Maximal term depth : 1 ( 1 avg) % 58.57/58.62 % Number of predicates : 5 ( 5 usr; 0 prp; 1-3 aty) % 58.57/58.62 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty) % 58.57/58.62 % Number of variables : 22 ( 0 sgn) % 58.57/58.62 % SPC : CNF_UNS_EPR_NEQ_NHN % 58.57/58.62 % 58.57/58.62 % Comments : [SFS93]'s axiomatization has been modified for this. % 58.57/58.62 % : Substitution axioms are not needed, as any positive equality % 58.57/58.62 % literals should resolve on negative ones directly. % 58.57/58.62 % : Version 2 has simple isomorphism avoidance (as mentioned in % 58.57/58.62 % [FSB93]) % 58.57/58.62 % : tptp2X: -f tptp -s4 GRP126-2.g % 58.57/58.62 %-------------------------------------------------------------------------- % 58.57/58.62 cnf(e_1_then_e_2,axiom, % 58.57/58.62 next(e_1,e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(e_2_then_e_3,axiom, % 58.57/58.62 next(e_2,e_3) ). % 58.57/58.62 % 58.57/58.62 cnf(e_3_then_e_4,axiom, % 58.57/58.62 next(e_3,e_4) ). % 58.57/58.62 % 58.57/58.62 cnf(e_2_greater_e_1,axiom, % 58.57/58.62 greater(e_2,e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(e_3_greater_e_1,axiom, % 58.57/58.62 greater(e_3,e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(e_4_greater_e_1,axiom, % 58.57/58.62 greater(e_4,e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(e_3_greater_e_2,axiom, % 58.57/58.62 greater(e_3,e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(e_4_greater_e_2,axiom, % 58.57/58.62 greater(e_4,e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(e_4_greater_e_3,axiom, % 58.57/58.62 greater(e_4,e_3) ). % 58.57/58.62 % 58.57/58.62 cnf(no_redundancy,axiom, % 58.57/58.62 ( ~ product(X,e_1,Y) % 58.57/58.62 | ~ next(X,X1) % 58.57/58.62 | ~ greater(Y,X1) ) ). % 58.57/58.62 % 58.57/58.62 cnf(element_1,axiom, % 58.57/58.62 group_element(e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(element_2,axiom, % 58.57/58.62 group_element(e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(element_3,axiom, % 58.57/58.62 group_element(e_3) ). % 58.57/58.62 % 58.57/58.62 cnf(element_4,axiom, % 58.57/58.62 group_element(e_4) ). % 58.57/58.62 % 58.57/58.62 cnf(e_1_is_not_e_2,axiom, % 58.57/58.62 ~ equalish(e_1,e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(e_1_is_not_e_3,axiom, % 58.57/58.62 ~ equalish(e_1,e_3) ). % 58.57/58.62 % 58.57/58.62 cnf(e_1_is_not_e_4,axiom, % 58.57/58.62 ~ equalish(e_1,e_4) ). % 58.57/58.62 % 58.57/58.62 cnf(e_2_is_not_e_1,axiom, % 58.57/58.62 ~ equalish(e_2,e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(e_2_is_not_e_3,axiom, % 58.57/58.62 ~ equalish(e_2,e_3) ). % 58.57/58.62 % 58.57/58.62 cnf(e_2_is_not_e_4,axiom, % 58.57/58.62 ~ equalish(e_2,e_4) ). % 58.57/58.62 % 58.57/58.62 cnf(e_3_is_not_e_1,axiom, % 58.57/58.62 ~ equalish(e_3,e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(e_3_is_not_e_2,axiom, % 58.57/58.62 ~ equalish(e_3,e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(e_3_is_not_e_4,axiom, % 58.57/58.62 ~ equalish(e_3,e_4) ). % 58.57/58.62 % 58.57/58.62 cnf(e_4_is_not_e_1,axiom, % 58.57/58.62 ~ equalish(e_4,e_1) ). % 58.57/58.62 % 58.57/58.62 cnf(e_4_is_not_e_2,axiom, % 58.57/58.62 ~ equalish(e_4,e_2) ). % 58.57/58.62 % 58.57/58.62 cnf(e_4_is_not_e_3,axiom, % 58.57/58.62 ~ equalish(e_4,e_3) ). % 58.57/58.62 % 58.57/58.62 cnf(product_total_function1,axiom, % 58.57/58.62 ( ~ group_element(X) % 58.57/58.62 | ~ group_element(Y) % 58.57/58.62 | product(X,Y,e_1) % 58.57/58.62 | product(X,Y,e_2) % 58.57/58.62 | product(X,Y,e_3) % 58.57/58.62 | product(X,Y,e_4) ) ). % 58.57/58.62 % 58.57/58.62 cnf(product_total_function2,axiom, % 58.57/58.62 ( ~ product(X,Y,W) % 58.57/58.62 | ~ product(X,Y,Z) % 58.57/58.62 | equalish(W,Z) ) ). % 58.57/58.62 % 58.57/58.62 cnf(product_right_cancellation,axiom, % 58.57/58.62 ( ~ product(X,W,Y) % 58.57/58.62 | ~ product(X,Z,Y) % 58.57/58.62 | equalish(W,Z) ) ). % 58.57/58.62 % 58.57/58.62 cnf(product_left_cancellation,axiom, % 58.57/58.62 ( ~ product(W,Y,X) % 58.57/58.62 | ~ product(Z,Y,X) % 58.57/58.62 | equalish(W,Z) ) ). % 58.57/58.62 % 58.57/58.62 cnf(product_idempotence,axiom, % 58.57/58.62 product(X,X,X) ). % 58.57/58.62 % 58.57/58.62 cnf(qg4,negated_conjecture, % 58.57/58.62 ( ~ product(X,Y,Z1) % 58.57/58.62 | ~ product(Y,X,Z2) % 58.57/58.62 | product(Z1,Z2,Y) ) ). % 58.57/58.62 % 58.57/58.62 %-------------------------------------------------------------------------- % 58.57/58.62 %------------------------------------------- % 58.57/58.62 % Proof found % 58.57/58.62 % SZS status Theorem for theBenchmark % 58.57/58.62 % SZS output start Proof % 58.57/58.62 %ClaNum:32(EqnAxiom:0) % 58.57/58.62 %VarNum:52(SingletonVarNum:22) % 58.57/58.62 %MaxLitNum:6 % 58.57/58.62 %MaxfuncDepth:0 % 58.57/58.62 %SharedTerms:29 % 58.57/58.62 %goalClause: 31 % 58.57/58.62 [1]P1(a1) % 58.57/58.62 [2]P1(a2) % 58.57/58.62 [3]P1(a3) % 58.57/58.62 [4]P1(a4) % 58.57/58.62 [5]P4(a1,a2) % 58.57/58.62 [6]P4(a2,a3) % 58.57/58.62 [7]P4(a3,a4) % 58.57/58.62 [8]P2(a2,a1) % 58.57/58.63 [9]P2(a3,a1) % 58.57/58.63 [10]P2(a3,a2) % 58.57/58.63 [11]P2(a4,a1) % 58.57/58.63 [12]P2(a4,a2) % 58.57/58.63 [13]P2(a4,a3) % 58.57/58.63 [15]~P3(a1,a2) % 58.57/58.63 [16]~P3(a1,a3) % 58.57/58.63 [17]~P3(a1,a4) % 58.57/58.63 [18]~P3(a2,a1) % 58.57/58.63 [19]~P3(a2,a3) % 58.57/58.63 [20]~P3(a2,a4) % 58.57/58.63 [21]~P3(a3,a1) % 58.57/58.63 [22]~P3(a3,a2) % 58.57/58.63 [23]~P3(a3,a4) % 58.57/58.63 [24]~P3(a4,a1) % 58.57/58.63 [25]~P3(a4,a2) % 58.57/58.63 [26]~P3(a4,a3) % 58.57/58.63 [14]P5(x141,x141,x141) % 58.57/58.63 [27]~P4(x271,x272)+~P2(x273,x272)+~P5(x271,a1,x273) % 58.57/58.63 [28]~P5(x283,x284,x281)+P3(x281,x282)+~P5(x283,x284,x282) % 58.57/58.63 [29]~P5(x293,x291,x294)+P3(x291,x292)+~P5(x293,x292,x294) % 58.57/58.63 [30]~P5(x301,x303,x304)+P3(x301,x302)+~P5(x302,x303,x304) % 58.57/58.63 [31]~P5(x314,x313,x311)+P5(x311,x312,x313)+~P5(x313,x314,x312) % 58.57/58.63 [32]~P1(x322)+~P1(x321)+P5(x321,x322,a2)+P5(x321,x322,a3)+P5(x321,x322,a4)+P5(x321,x322,a1) % 58.57/58.63 %EqnAxiom % 58.57/58.63 % 58.57/58.63 %------------------------------------------- % 58.69/58.76 cnf(189,plain, % 58.69/58.76 (~P5(a4,x1891,a1)+~P5(x1891,a4,a2)+~P2(a4,a3)), % 58.69/58.76 inference(scs_inference,[],[6,13,27,31])). % 58.69/58.76 cnf(195,plain, % 58.69/58.76 (~P5(x1951,a4,a2)+~P5(a4,x1951,a1)), % 58.69/58.76 inference(scs_inference,[],[14,13,5,28,27,189])). % 58.69/58.76 cnf(1311,plain, % 58.69/58.76 (~P5(a4,x13111,a1)+~P5(x13111,a4,a1)), % 58.69/58.76 inference(scs_inference,[],[17,14,28,31])). % 58.69/58.76 cnf(2397,plain, % 58.69/58.76 (~P5(a3,x23971,a1)+~P5(x23971,a3,a1)), % 58.69/58.76 inference(scs_inference,[],[21,14,28,31])). % 58.69/58.76 cnf(2578,plain, % 58.69/58.76 (~P5(a3,x25781,a2)+~P5(x25781,a3,a2)), % 58.69/58.76 inference(scs_inference,[],[22,14,28,31])). % 58.69/58.76 cnf(3302,plain, % 58.69/58.76 (~P5(a3,x33021,a4)+~P5(x33021,a3,a4)), % 58.69/58.76 inference(scs_inference,[],[26,14,28,31])). % 58.69/58.76 cnf(3649,plain, % 58.69/58.76 (~P5(a4,a4,a1)), % 58.69/58.76 inference(scs_inference,[],[17,14,29,31])). % 58.69/58.76 cnf(3801,plain, % 58.69/58.76 (~P5(a3,a3,a2)), % 58.69/58.76 inference(scs_inference,[],[19,14,29,31])). % 58.69/58.76 cnf(4438,plain, % 58.69/58.76 (~P5(a4,a4,a3)), % 58.69/58.76 inference(scs_inference,[],[23,14,29,31])). % 58.69/58.76 cnf(4893,plain, % 58.69/58.76 (~P5(a3,a4,a3)+P5(a3,a3,a1)+P5(a3,a3,a4)), % 58.69/58.76 inference(scs_inference,[],[26,3801,3,29,32])). % 58.69/58.76 cnf(4984,plain, % 58.69/58.76 (P5(a3,a3,a4)+~P5(a3,a4,a3)), % 58.69/58.76 inference(scs_inference,[],[4893,2397])). % 58.69/58.76 cnf(5075,plain, % 58.69/58.76 (~P5(a3,a4,a3)), % 58.69/58.76 inference(scs_inference,[],[4984,3302])). % 58.69/58.76 cnf(5348,plain, % 58.69/58.76 (~P5(a3,a3,a1)), % 58.69/58.76 inference(scs_inference,[],[16,14,29,31])). % 58.69/58.76 cnf(5802,plain, % 58.69/58.76 (P5(a2,a1,a3)+P5(a2,a1,a1)+P5(a2,a1,a4)), % 58.69/58.76 inference(scs_inference,[],[18,14,1,2,29,32])). % 58.69/58.76 cnf(6165,plain, % 58.69/58.76 (~P5(a4,a4,a2)), % 58.69/58.76 inference(scs_inference,[],[20,14,29,31])). % 58.69/58.76 cnf(6528,plain, % 58.69/58.76 (~P5(a3,a2,a3)+P5(a3,a3,a4)), % 58.69/58.76 inference(scs_inference,[],[22,3801,5348,3,29,32])). % 58.69/58.76 cnf(6619,plain, % 58.69/58.76 (~P5(a3,a2,a3)), % 58.69/58.76 inference(scs_inference,[],[6528,3302])). % 58.69/58.76 cnf(6801,plain, % 58.69/58.76 (~P5(a4,a1,a4)), % 58.69/58.76 inference(scs_inference,[],[24,6165,3649,4438,4,29,32])). % 58.69/58.76 cnf(8253,plain, % 58.69/58.76 (P5(a4,a3,a2)+P5(a4,a3,a1)+P5(a4,a3,a3)), % 58.69/58.76 inference(scs_inference,[],[26,14,3,4,29,32])). % 58.69/58.76 cnf(8344,plain, % 58.69/58.76 (~P5(a3,a4,a2)+P5(a4,a3,a1)+P5(a4,a3,a3)), % 58.69/58.76 inference(scs_inference,[],[8253,2578])). % 58.69/58.76 cnf(8435,plain, % 58.69/58.76 (~P5(a3,a4,a2)+P5(a4,a3,a3)), % 58.69/58.76 inference(scs_inference,[],[8344,195])). % 58.69/58.76 cnf(10072,plain, % 58.69/58.76 (~P5(a3,a4,a2)), % 58.69/58.76 inference(scs_inference,[],[6619,8435,31])). % 58.69/58.76 cnf(10074,plain, % 58.69/58.76 (P5(x100741,x100741,x100741)), % 58.69/58.76 inference(rename_variables,[],[14])). % 58.69/58.76 cnf(10078,plain, % 58.69/58.76 (P5(a3,a4,a1)+P5(a3,a4,a4)), % 58.69/58.76 inference(scs_inference,[],[14,10074,10072,5075,3,5,4,27,30,32])). % 58.69/58.76 cnf(10984,plain, % 58.69/58.76 (P5(a3,a4,a1)+~P5(a4,a3,a1)), % 58.69/58.76 inference(scs_inference,[],[6801,10078,31])). % 58.69/58.76 cnf(11075,plain, % 58.69/58.76 (~P5(a4,a3,a1)), % 58.69/58.76 inference(scs_inference,[],[10984,1311])). % 58.69/58.76 cnf(251390,plain, % 58.69/58.76 (P5(x2513901,x2513901,x2513901)), % 58.69/58.76 inference(rename_variables,[],[14])). % 58.69/58.76 cnf(251395,plain, % 58.69/58.76 (P5(a2,a1,a3)), % 58.69/58.76 inference(scs_inference,[],[6,13,15,16,14,251390,27,30,29,5802])). % 58.69/58.76 cnf(251403,plain, % 58.69/58.76 (~P5(a4,a1,a1)), % 58.69/58.76 inference(scs_inference,[],[9,251395,17,22,14,27,28,30])). % 58.69/58.76 cnf(251414,plain, % 58.69/58.76 (~P5(a4,a3,a4)), % 58.69/58.76 inference(scs_inference,[],[20,26,251395,14,30,29])). % 58.69/58.76 cnf(251417,plain, % 58.69/58.76 (P5(a4,a1,a2)), % 58.69/58.76 inference(scs_inference,[],[1,251403,6801,20,26,251395,4,14,30,29,32])). % 58.69/58.76 cnf(251438,plain, % 58.69/58.76 ($false), % 58.69/58.76 inference(scs_inference,[],[251414,251417,11075,23,16,4,3,14,30,29,32]), % 58.69/58.76 ['proof']). % 58.79/58.85 % SZS output end Proof % 58.79/58.85 % Total time :58.000000s %------------------------------------------------------------------------------