%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : GRP123-1.003 : TPTP v8.2.0. Released v1.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n027.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 58.55s 58.72s % Output : CNFRefutation 58.96s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : GRP123-1.003 : TPTP v8.2.0. Released v1.2.0. % 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.14/0.36 % Computer : n027.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Thu Jun 20 06:59:39 EDT 2024 % 0.14/0.36 % CPUTime : % 0.44/0.59 start to proof:theBenchmark % 58.55/58.70 %------------------------------------------- % 58.55/58.70 % File :CSE---1.7 % 58.55/58.70 % Problem :theBenchmark % 58.55/58.70 % Transform :cnf % 58.55/58.70 % Format :tptp:raw % 58.55/58.70 % Command :java -jar mcs_scs.jar %d %s % 58.55/58.70 % 58.55/58.70 % Result :Theorem 58.010000s % 58.55/58.70 % Output :CNFRefutation 58.010000s % 58.55/58.70 %------------------------------------------- % 58.55/58.72 %-------------------------------------------------------------------------- % 58.55/58.72 % File : GRP123-1.003 : TPTP v8.2.0. Released v1.2.0. % 58.55/58.72 % Domain : Group Theory (Quasigroups) % 58.55/58.72 % Problem : (3,2,1) conjugate orthogonality % 58.55/58.72 % Version : [Sla93] axioms. % 58.55/58.72 % English : If ab=xy and a*b = x*y then a=x and b=y, where c*b=a iff ab=c. % 58.55/58.72 % Generate the multiplication table for the specified quasi- % 58.55/58.72 % group with 3 elements. % 58.55/58.72 % 58.55/58.72 % Refs : [FSB93] Fujita et al. (1993), Automatic Generation of Some Res % 58.55/58.72 % : [Sla93] Slaney (1993), Email to G. Sutcliffe % 58.55/58.72 % : [Zha94] Zhang (1994), Email to G. Sutcliffe % 58.55/58.72 % : [SFS95] Slaney et al. (1995), Automated Reasoning and Exhausti % 58.55/58.72 % Source : [Sla93] % 58.55/58.72 % Names : QG1 [Sla93] % 58.55/58.72 % : QG1 [FSB93] % 58.55/58.72 % : QG1 [SFS95] % 58.55/58.72 % : Bennett QG1 [TPTP] % 58.55/58.72 % 58.55/58.72 % Status : Unsatisfiable % 58.55/58.72 % Rating : 0.00 v2.1.0 % 58.55/58.72 % Syntax : Number of clauses : 16 ( 10 unt; 1 nHn; 15 RR) % 58.55/58.72 % Number of literals : 34 ( 0 equ; 22 neg) % 58.55/58.72 % Maximal clause size : 5 ( 2 avg) % 58.55/58.72 % Maximal term depth : 1 ( 1 avg) % 58.55/58.72 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty) % 58.55/58.72 % Number of functors : 3 ( 3 usr; 3 con; 0-0 aty) % 58.55/58.72 % Number of variables : 27 ( 0 sgn) % 58.55/58.72 % SPC : CNF_UNS_EPR_NEQ_NHN % 58.55/58.72 % 58.55/58.72 % Comments : [Sla93]'s axiomatization has been modified for this. % 58.55/58.72 % : Substitution axioms are not needed, as any positive equality % 58.55/58.72 % literals should resolve on negative ones directly. % 58.55/58.72 % : [Zha94] has pointed out that either one of qg1_1 % 58.55/58.72 % or qg1_2 may be used, as each implies the other in this % 58.55/58.72 % scenario, with the help of cancellation. The dependence % 58.55/58.72 % cannot be proved, so both have been left in here. % 58.55/58.72 % : tptp2X: -f tptp -s3 GRP123-1.g % 58.55/58.72 %-------------------------------------------------------------------------- % 58.55/58.72 cnf(element_1,axiom, % 58.55/58.72 group_element(e_1) ). % 58.55/58.72 % 58.55/58.72 cnf(element_2,axiom, % 58.55/58.72 group_element(e_2) ). % 58.55/58.72 % 58.55/58.72 cnf(element_3,axiom, % 58.55/58.72 group_element(e_3) ). % 58.55/58.72 % 58.55/58.72 cnf(e_1_is_not_e_2,axiom, % 58.55/58.72 ~ equalish(e_1,e_2) ). % 58.55/58.72 % 58.55/58.72 cnf(e_1_is_not_e_3,axiom, % 58.55/58.72 ~ equalish(e_1,e_3) ). % 58.55/58.72 % 58.55/58.72 cnf(e_2_is_not_e_1,axiom, % 58.55/58.72 ~ equalish(e_2,e_1) ). % 58.55/58.72 % 58.55/58.72 cnf(e_2_is_not_e_3,axiom, % 58.55/58.72 ~ equalish(e_2,e_3) ). % 58.55/58.72 % 58.55/58.72 cnf(e_3_is_not_e_1,axiom, % 58.55/58.72 ~ equalish(e_3,e_1) ). % 58.55/58.72 % 58.55/58.72 cnf(e_3_is_not_e_2,axiom, % 58.55/58.72 ~ equalish(e_3,e_2) ). % 58.55/58.72 % 58.55/58.72 cnf(product_total_function1,axiom, % 58.55/58.72 ( ~ group_element(X) % 58.55/58.72 | ~ group_element(Y) % 58.55/58.72 | product(X,Y,e_1) % 58.55/58.72 | product(X,Y,e_2) % 58.55/58.72 | product(X,Y,e_3) ) ). % 58.55/58.72 % 58.55/58.72 cnf(product_total_function2,axiom, % 58.55/58.72 ( ~ product(X,Y,W) % 58.55/58.72 | ~ product(X,Y,Z) % 58.55/58.72 | equalish(W,Z) ) ). % 58.55/58.72 % 58.55/58.72 cnf(product_right_cancellation,axiom, % 58.55/58.72 ( ~ product(X,W,Y) % 58.55/58.72 | ~ product(X,Z,Y) % 58.55/58.72 | equalish(W,Z) ) ). % 58.55/58.72 % 58.55/58.72 cnf(product_left_cancellation,axiom, % 58.55/58.72 ( ~ product(W,Y,X) % 58.55/58.72 | ~ product(Z,Y,X) % 58.55/58.72 | equalish(W,Z) ) ). % 58.55/58.72 % 58.55/58.72 cnf(product_idempotence,axiom, % 58.55/58.72 product(X,X,X) ). % 58.55/58.72 % 58.55/58.72 cnf(qg1_1,negated_conjecture, % 58.55/58.72 ( ~ product(X1,Y1,Z1) % 58.55/58.72 | ~ product(X2,Y2,Z1) % 58.55/58.72 | ~ product(Z2,Y1,X1) % 58.55/58.72 | ~ product(Z2,Y2,X2) % 58.55/58.72 | equalish(X1,X2) ) ). % 58.55/58.72 % 58.55/58.72 cnf(qg1_2,negated_conjecture, % 58.55/58.72 ( ~ product(X1,Y1,Z1) % 58.55/58.72 | ~ product(X2,Y2,Z1) % 58.55/58.72 | ~ product(Z2,Y1,X1) % 58.55/58.72 | ~ product(Z2,Y2,X2) % 58.55/58.72 | equalish(Y1,Y2) ) ). % 58.55/58.72 % 58.55/58.72 %-------------------------------------------------------------------------- % 58.55/58.72 %------------------------------------------- % 58.55/58.72 % Proof found % 58.55/58.72 % SZS status Theorem for theBenchmark % 58.55/58.72 % SZS output start Proof % 58.67/58.73 %ClaNum:16(EqnAxiom:0) % 58.67/58.73 %VarNum:63(SingletonVarNum:27) % 58.67/58.73 %MaxLitNum:5 % 58.67/58.73 %MaxfuncDepth:0 % 58.67/58.73 %SharedTerms:12 % 58.67/58.73 %goalClause: 15 16 % 58.67/58.73 [1]P1(a1) % 58.67/58.73 [2]P1(a2) % 58.67/58.73 [3]P1(a3) % 58.67/58.73 [5]~P2(a1,a2) % 58.67/58.73 [6]~P2(a1,a3) % 58.67/58.73 [7]~P2(a2,a1) % 58.67/58.73 [8]~P2(a2,a3) % 58.67/58.73 [9]~P2(a3,a1) % 58.67/58.73 [10]~P2(a3,a2) % 58.67/58.73 [4]P3(x41,x41,x41) % 58.67/58.73 [12]~P3(x123,x124,x121)+P2(x121,x122)+~P3(x123,x124,x122) % 58.67/58.73 [13]~P3(x133,x131,x134)+P2(x131,x132)+~P3(x133,x132,x134) % 58.67/58.73 [14]~P3(x141,x143,x144)+P2(x141,x142)+~P3(x142,x143,x144) % 58.67/58.73 [11]~P1(x112)+~P1(x111)+P3(x111,x112,a2)+P3(x111,x112,a3)+P3(x111,x112,a1) % 58.67/58.73 [15]~P3(x155,x151,x156)+P2(x151,x152)+~P3(x153,x152,x154)+~P3(x153,x151,x155)+~P3(x154,x152,x156) % 58.67/58.73 [16]~P3(x161,x165,x166)+P2(x161,x162)+~P3(x163,x164,x162)+~P3(x163,x165,x161)+~P3(x162,x164,x166) % 58.67/58.73 %EqnAxiom % 58.67/58.73 % 58.67/58.73 %------------------------------------------- % 58.83/58.91 cnf(156720,plain, % 58.83/58.91 (P3(x1567201,x1567201,x1567201)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156723,plain, % 58.83/58.91 (P3(x1567231,x1567231,x1567231)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156726,plain, % 58.83/58.91 (P3(x1567261,x1567261,x1567261)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156730,plain, % 58.83/58.91 (P3(a1,a2,a3)+P3(a1,a2,a2)), % 58.83/58.91 inference(scs_inference,[],[1,2,5,4,156720,156723,156726,13,14,12,15,11])). % 58.83/58.91 cnf(156732,plain, % 58.83/58.91 (~P3(a2,x1567321,a1)+~P3(a1,x1567321,a2)), % 58.83/58.91 inference(scs_inference,[],[1,2,5,4,156720,156723,156726,13,14,12,15,11,16])). % 58.83/58.91 cnf(156736,plain, % 58.83/58.91 (~P3(a1,a3,a1)), % 58.83/58.91 inference(scs_inference,[],[6,4,13])). % 58.83/58.91 cnf(156754,plain, % 58.83/58.91 (P3(x1567541,x1567541,x1567541)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156757,plain, % 58.83/58.91 (P3(x1567571,x1567571,x1567571)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156760,plain, % 58.83/58.91 (P3(x1567601,x1567601,x1567601)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156766,plain, % 58.83/58.91 (P3(a1,a2,a3)), % 58.83/58.91 inference(scs_inference,[],[1,7,156736,3,4,156754,156757,156760,13,14,12,16,11,156730])). % 58.83/58.91 cnf(156771,plain, % 58.83/58.91 (P3(x1567711,x1567711,x1567711)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156774,plain, % 58.83/58.91 (P3(x1567741,x1567741,x1567741)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156776,plain, % 58.83/58.91 (P3(a1,a3,a2)), % 58.83/58.91 inference(scs_inference,[],[1,8,156766,156736,3,4,156771,13,14,12,11])). % 58.83/58.91 cnf(156782,plain, % 58.83/58.91 (~P3(a2,a3,a1)), % 58.83/58.91 inference(scs_inference,[],[1,8,156766,156736,3,4,156771,156774,13,14,12,11,15,156732])). % 58.83/58.91 cnf(156785,plain, % 58.83/58.91 (P3(x1567851,x1567851,x1567851)), % 58.83/58.91 inference(rename_variables,[],[4])). % 58.83/58.91 cnf(156792,plain, % 58.83/58.91 (P3(a2,a3,a3)), % 58.83/58.91 inference(scs_inference,[],[156776,156782,9,2,3,5,4,156785,13,14,12,11])). % 58.83/58.91 cnf(156798,plain, % 58.83/58.91 ($false), % 58.83/58.91 inference(scs_inference,[],[10,156792,9,4,13,14]), % 58.83/58.91 ['proof']). % 58.96/59.03 % SZS output end Proof % 58.96/59.03 % Total time :58.010000s %------------------------------------------------------------------------------