%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP123-3.003 : 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 : n032.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 06:38:46 EDT 2024 % Result : Unsatisfiable 58.44s 58.52s % Output : CNFRefutation 58.87s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.08 % Problem : GRP123-3.003 : TPTP v8.2.0. Released v1.2.0. % 0.00/0.08 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.08/0.27 % Computer : n032.cluster.edu % 0.08/0.27 % Model : x86_64 x86_64 % 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.27 % Memory : 8042.1875MB % 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.27 % CPULimit : 300 % 0.08/0.27 % WCLimit : 300 % 0.08/0.27 % DateTime : Thu Jun 20 09:13:23 EDT 2024 % 0.08/0.27 % CPUTime : % 0.12/0.45 start to proof:theBenchmark % 58.42/58.50 %------------------------------------------- % 58.42/58.50 % File :CSE---1.7 % 58.42/58.50 % Problem :theBenchmark % 58.42/58.50 % Transform :cnf % 58.42/58.50 % Format :tptp:raw % 58.42/58.50 % Command :java -jar mcs_scs.jar %d %s % 58.42/58.50 % 58.42/58.50 % Result :Theorem 58.010000s % 58.42/58.50 % Output :CNFRefutation 58.010000s % 58.42/58.50 %------------------------------------------- % 58.42/58.51 %-------------------------------------------------------------------------- % 58.42/58.51 % File : GRP123-3.003 : TPTP v8.2.0. Released v1.2.0. % 58.42/58.51 % Domain : Group Theory (Quasigroups) % 58.42/58.51 % Problem : (3,2,1) conjugate orthogonality % 58.42/58.51 % Version : [Sla93] axioms : Augmented. % 58.42/58.51 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c. % 58.42/58.51 % Generate the multiplication table for the specified quasi- % 58.42/58.51 % group with 3 elements. % 58.42/58.51 % 58.42/58.51 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res % 58.42/58.51 % : [Sla93] Slaney (1993), Email to G. Sutcliffe % 58.42/58.51 % : [Zha94] Zhang (1994), Email to G. Sutcliffe % 58.42/58.51 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti % 58.42/58.51 % Source : [TPTP] % 58.42/58.51 % Names : % 58.42/58.51 % 58.42/58.51 % Status : Unsatisfiable % 58.42/58.51 % Rating : 0.00 v2.1.0 % 58.42/58.51 % Syntax : Number of clauses : 32 ( 20 unt; 2 nHn; 31 RR) % 58.44/58.51 % Number of literals : 71 ( 0 equ; 43 neg) % 58.44/58.51 % Maximal clause size : 6 ( 2 avg) % 58.44/58.51 % Maximal term depth : 1 ( 1 avg) % 58.44/58.51 % Number of predicates : 6 ( 6 usr; 0 prp; 1-3 aty) % 58.44/58.51 % Number of functors : 4 ( 4 usr; 4 con; 0-0 aty) % 58.44/58.51 % Number of variables : 47 ( 0 sgn) % 58.44/58.51 % SPC : CNF_UNS_EPR_NEQ_NHN % 58.44/58.51 % 58.44/58.51 % Comments : [SFS93]'s axiomatization has been modified for this. % 58.44/58.51 % : Substitution axioms are not needed, as any positive equality % 58.44/58.51 % literals should resolve on negative ones directly. % 58.44/58.51 % : [Zha94] has pointed out that either one of qg1_1 % 58.44/58.51 % or qg1_2 may be used, as each implies the other in this % 58.44/58.51 % scenario, with the help of cancellation. The dependence % 58.44/58.51 % cannot be proved, so both have been left in here. % 58.44/58.51 % : Version 3 has complex isomorphism avoidance (mentioned in % 58.44/58.52 % [SFS95] % 58.44/58.52 % : tptp2X: -f tptp -s3 GRP123-3.g % 58.44/58.52 %-------------------------------------------------------------------------- % 58.44/58.52 cnf(e_0_then_e_1,axiom, % 58.44/58.52 next(e_0,e_1) ). % 58.44/58.52 % 58.44/58.52 cnf(e_1_then_e_2,axiom, % 58.44/58.52 next(e_1,e_2) ). % 58.44/58.52 % 58.44/58.52 cnf(e_2_then_e_3,axiom, % 58.44/58.52 next(e_2,e_3) ). % 58.44/58.52 % 58.44/58.52 cnf(e_1_greater_e_0,axiom, % 58.44/58.52 greater(e_1,e_0) ). % 58.44/58.52 % 58.44/58.52 cnf(e_2_greater_e_0,axiom, % 58.44/58.52 greater(e_2,e_0) ). % 58.44/58.52 % 58.44/58.52 cnf(e_3_greater_e_0,axiom, % 58.44/58.52 greater(e_3,e_0) ). % 58.44/58.52 % 58.44/58.52 cnf(e_2_greater_e_1,axiom, % 58.44/58.52 greater(e_2,e_1) ). % 58.44/58.52 % 58.44/58.52 cnf(e_3_greater_e_1,axiom, % 58.44/58.52 greater(e_3,e_1) ). % 58.44/58.52 % 58.44/58.52 cnf(e_3_greater_e_2,axiom, % 58.44/58.52 greater(e_3,e_2) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle1,axiom, % 58.44/58.52 ( ~ cycle(X,Y) % 58.44/58.52 | ~ cycle(X,Z) % 58.44/58.52 | equalish(Y,Z) ) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle2,axiom, % 58.44/58.52 ( ~ group_element(X) % 58.44/58.52 | cycle(X,e_0) % 58.44/58.52 | cycle(X,e_1) % 58.44/58.52 | cycle(X,e_2) ) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle3,axiom, % 58.44/58.52 cycle(e_3,e_0) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle4,axiom, % 58.44/58.52 ( ~ cycle(X,Y) % 58.44/58.52 | ~ cycle(W,Z) % 58.44/58.52 | ~ next(X,W) % 58.44/58.52 | ~ greater(Y,e_0) % 58.44/58.52 | ~ next(Z,Z1) % 58.44/58.52 | equalish(Y,Z1) ) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle5,axiom, % 58.44/58.52 ( ~ cycle(X,Z1) % 58.44/58.52 | ~ cycle(Y,e_0) % 58.44/58.52 | ~ cycle(W,Z2) % 58.44/58.52 | ~ next(Y,W) % 58.44/58.52 | ~ greater(Y,X) % 58.44/58.52 | ~ greater(Z1,Z2) ) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle6,axiom, % 58.44/58.52 ( ~ cycle(X,e_0) % 58.44/58.52 | ~ product(X,e_1,Y) % 58.44/58.52 | ~ greater(Y,X) ) ). % 58.44/58.52 % 58.44/58.52 cnf(cycle7,axiom, % 58.44/58.52 ( ~ cycle(X,Y) % 58.44/58.52 | ~ product(X,e_1,Z) % 58.44/58.52 | ~ greater(Y,e_0) % 58.44/58.52 | ~ next(X,X1) % 58.44/58.52 | equalish(Z,X1) ) ). % 58.44/58.52 % 58.44/58.52 cnf(element_1,axiom, % 58.44/58.52 group_element(e_1) ). % 58.44/58.52 % 58.44/58.52 cnf(element_2,axiom, % 58.44/58.52 group_element(e_2) ). % 58.44/58.52 % 58.44/58.52 cnf(element_3,axiom, % 58.44/58.52 group_element(e_3) ). % 58.44/58.52 % 58.44/58.52 cnf(e_1_is_not_e_2,axiom, % 58.44/58.52 ~ equalish(e_1,e_2) ). % 58.44/58.52 % 58.44/58.52 cnf(e_1_is_not_e_3,axiom, % 58.44/58.52 ~ equalish(e_1,e_3) ). % 58.44/58.52 % 58.44/58.52 cnf(e_2_is_not_e_1,axiom, % 58.44/58.52 ~ equalish(e_2,e_1) ). % 58.44/58.52 % 58.44/58.52 cnf(e_2_is_not_e_3,axiom, % 58.44/58.52 ~ equalish(e_2,e_3) ). % 58.44/58.52 % 58.44/58.52 cnf(e_3_is_not_e_1,axiom, % 58.44/58.52 ~ equalish(e_3,e_1) ). % 58.44/58.52 % 58.44/58.52 cnf(e_3_is_not_e_2,axiom, % 58.44/58.52 ~ equalish(e_3,e_2) ). % 58.44/58.52 % 58.44/58.52 cnf(product_total_function1,axiom, % 58.44/58.52 ( ~ group_element(X) % 58.44/58.52 | ~ group_element(Y) % 58.44/58.52 | product(X,Y,e_1) % 58.44/58.52 | product(X,Y,e_2) % 58.44/58.52 | product(X,Y,e_3) ) ). % 58.44/58.52 % 58.44/58.52 cnf(product_total_function2,axiom, % 58.44/58.52 ( ~ product(X,Y,W) % 58.44/58.52 | ~ product(X,Y,Z) % 58.44/58.52 | equalish(W,Z) ) ). % 58.44/58.52 % 58.44/58.52 cnf(product_right_cancellation,axiom, % 58.44/58.52 ( ~ product(X,W,Y) % 58.44/58.52 | ~ product(X,Z,Y) % 58.44/58.52 | equalish(W,Z) ) ). % 58.44/58.52 % 58.44/58.52 cnf(product_left_cancellation,axiom, % 58.44/58.52 ( ~ product(W,Y,X) % 58.44/58.52 | ~ product(Z,Y,X) % 58.44/58.52 | equalish(W,Z) ) ). % 58.44/58.52 % 58.44/58.52 cnf(product_idempotence,axiom, % 58.44/58.52 product(X,X,X) ). % 58.44/58.52 % 58.44/58.52 cnf(qg1_1,negated_conjecture, % 58.44/58.52 ( ~ product(X1,Y1,Z1) % 58.44/58.52 | ~ product(X2,Y2,Z1) % 58.44/58.52 | ~ product(Z2,Y1,X1) % 58.44/58.52 | ~ product(Z2,Y2,X2) % 58.44/58.52 | equalish(X1,X2) ) ). % 58.44/58.52 % 58.44/58.52 cnf(qg1_2,negated_conjecture, % 58.44/58.52 ( ~ product(X1,Y1,Z1) % 58.44/58.52 | ~ product(X2,Y2,Z1) % 58.44/58.52 | ~ product(Z2,Y1,X1) % 58.44/58.52 | ~ product(Z2,Y2,X2) % 58.44/58.52 | equalish(Y1,Y2) ) ). % 58.44/58.52 % 58.44/58.52 %-------------------------------------------------------------------------- % 58.44/58.52 %------------------------------------------- % 58.44/58.52 % Proof found % 58.44/58.52 % SZS status Theorem for theBenchmark % 58.44/58.52 % SZS output start Proof % 58.44/58.53 %ClaNum:32(EqnAxiom:0) % 58.44/58.53 %VarNum:109(SingletonVarNum:47) % 58.44/58.53 %MaxLitNum:6 % 58.44/58.53 %MaxfuncDepth:0 % 58.44/58.53 %SharedTerms:23 % 58.44/58.53 %goalClause: 31 32 % 58.44/58.53 [1]P1(a1) % 58.44/58.53 [2]P1(a3) % 58.44/58.53 [3]P1(a4) % 58.44/58.53 [4]P5(a2,a1) % 58.44/58.53 [5]P5(a1,a3) % 58.44/58.53 [6]P5(a3,a4) % 58.44/58.53 [7]P2(a1,a2) % 58.44/58.53 [8]P2(a3,a2) % 58.44/58.53 [9]P2(a3,a1) % 58.44/58.53 [10]P2(a4,a2) % 58.44/58.53 [11]P2(a4,a1) % 58.44/58.53 [12]P2(a4,a3) % 58.44/58.53 [13]P3(a4,a2) % 58.44/58.53 [15]~P4(a1,a3) % 58.44/58.53 [16]~P4(a1,a4) % 58.44/58.53 [17]~P4(a3,a1) % 58.44/58.53 [18]~P4(a3,a4) % 58.44/58.53 [19]~P4(a4,a1) % 58.44/58.53 [20]~P4(a4,a3) % 58.44/58.53 [14]P6(x141,x141,x141) % 58.44/58.53 [24]~P2(x241,x242)+~P6(x242,a1,x241)+~P3(x242,a2) % 58.44/58.53 [22]~P3(x223,x221)+P4(x221,x222)+~P3(x223,x222) % 58.44/58.53 [28]~P6(x283,x284,x281)+P4(x281,x282)+~P6(x283,x284,x282) % 58.44/58.53 [29]~P6(x293,x291,x294)+P4(x291,x292)+~P6(x293,x292,x294) % 58.44/58.53 [30]~P6(x301,x303,x304)+P4(x301,x302)+~P6(x302,x303,x304) % 58.44/58.53 [21]~P1(x211)+P3(x211,a1)+P3(x211,a3)+P3(x211,a2) % 58.44/58.53 [27]~P1(x272)+~P1(x271)+P6(x271,x272,a3)+P6(x271,x272,a4)+P6(x271,x272,a1) % 58.44/58.53 [26]P4(x261,x262)+~P5(x263,x262)+~P3(x263,x264)+~P6(x263,a1,x261)+~P2(x264,a2) % 58.44/58.53 [31]~P6(x315,x311,x316)+P4(x311,x312)+~P6(x313,x312,x314)+~P6(x313,x311,x315)+~P6(x314,x312,x316) % 58.44/58.53 [32]~P6(x321,x325,x326)+P4(x321,x322)+~P6(x323,x324,x322)+~P6(x323,x325,x321)+~P6(x322,x324,x326) % 58.44/58.53 [23]~P3(x235,x233)+~P3(x234,x231)+P4(x231,x232)+~P5(x233,x232)+~P5(x234,x235)+~P2(x231,a2) % 58.44/58.53 [25]~P3(x252,x255)+~P3(x253,x254)+~P5(x251,x252)+~P2(x251,x253)+~P2(x254,x255)+~P3(x251,a2) % 58.44/58.53 %EqnAxiom % 58.44/58.53 % 58.44/58.53 %------------------------------------------- % 58.64/58.77 cnf(42,plain, % 58.64/58.77 (P3(a1,a3)+P3(a1,a2)), % 58.64/58.77 inference(scs_inference,[],[1,14,15,7,5,13,22,28,26,24,21])). % 58.64/58.77 cnf(58,plain, % 58.64/58.77 (P3(a1,a2)), % 58.64/58.78 inference(scs_inference,[],[14,15,8,5,30,26,42])). % 58.64/58.78 cnf(432170,plain, % 58.64/58.78 (~P6(a4,a3,a3)), % 58.64/58.78 inference(scs_inference,[],[18,14,30])). % 58.64/58.78 cnf(432171,plain, % 58.64/58.78 (P6(x4321711,x4321711,x4321711)), % 58.64/58.78 inference(rename_variables,[],[14])). % 58.64/58.78 cnf(432176,plain, % 58.64/58.78 (P6(x4321761,x4321761,x4321761)), % 58.64/58.78 inference(rename_variables,[],[14])). % 58.64/58.78 cnf(432178,plain, % 58.64/58.78 (~P6(a3,a4,a3)), % 58.64/58.78 inference(scs_inference,[],[18,13,14,432171,432176,30,22,28,29])). % 58.64/58.78 cnf(432215,plain, % 58.64/58.78 (P6(x4322151,x4322151,x4322151)), % 58.64/58.78 inference(rename_variables,[],[14])). % 58.64/58.78 cnf(432219,plain, % 58.64/58.78 (~P6(a3,a4,a4)), % 58.64/58.78 inference(scs_inference,[],[20,13,58,14,432215,22,24,31,30])). % 58.64/58.78 cnf(432220,plain, % 58.64/58.78 (P6(x4322201,x4322201,x4322201)), % 58.64/58.78 inference(rename_variables,[],[14])). % 58.64/58.78 cnf(432222,plain, % 58.64/58.78 (~P6(a4,a3,a4)), % 58.64/58.78 inference(scs_inference,[],[20,13,58,14,432215,432220,22,24,31,30,29])). % 58.64/58.78 cnf(432239,plain, % 58.64/58.78 (P6(a3,a4,a1)), % 58.64/58.78 inference(scs_inference,[],[432178,432219,2,3,58,11,14,24,32,27])). % 58.64/58.78 cnf(432245,plain, % 58.64/58.78 (~P6(a1,a4,a3)), % 58.64/58.78 inference(scs_inference,[],[432178,432219,18,2,3,58,11,14,24,32,27,22,30,31])). % 58.64/58.78 cnf(432249,plain, % 58.64/58.78 (~P6(a1,a4,a1)), % 58.64/58.78 inference(scs_inference,[],[432239,17,30])). % 58.64/58.78 cnf(432256,plain, % 58.64/58.78 (P6(a4,a3,a1)), % 58.64/58.78 inference(scs_inference,[],[432170,432222,432239,17,2,3,13,58,14,30,22,24,27])). % 58.64/58.78 cnf(432268,plain, % 58.64/58.78 (P6(x4322681,x4322681,x4322681)), % 58.64/58.78 inference(rename_variables,[],[14])). % 58.64/58.78 cnf(432271,plain, % 58.64/58.78 (P6(x4322711,x4322711,x4322711)), % 58.64/58.78 inference(rename_variables,[],[14])). % 58.64/58.78 cnf(432275,plain, % 58.64/58.78 ($false), % 58.64/58.78 inference(scs_inference,[],[1,432245,432249,432256,16,3,15,14,432268,432271,29,31,27,30]), % 58.64/58.78 ['proof']). % 58.87/58.94 % SZS output end Proof % 58.87/58.94 % Total time :58.010000s %------------------------------------------------------------------------------